Precise predictions for chargino and neutralino pair production in $e^+e^-$ annihilation

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A This is an updated version of chapter 8 of the L TE X A Companion reﬂecting changes in the AMS-L TEX distribution that made parts of this chapter obsolete. It is based in structure and content on the original documentation in the Companion with obsolete parts corrected but otherwise unchanged and should not be considered as part of a general revision of this book.
Chapter 8 of "The LaTeX Companion", updated for AMS-LaTeX version 1.2 (Sep. 1st 1997). Copyright © 1994-97 by Addison Wesley Longman, Inc. All rights reserved.
Chapter 8 of "The LaTeX Companion", updated for AMS-LaTeX version 1.2 (Sep. 1st 1997). Copyright © 1994-97 by Addison Wesley Longman, Inc. All rights reserved.
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215501265_肉苁蓉及其有效成分调节抗生素所致小鼠肠道菌群失调

肉苁蓉及其有效成分调节抗生素所致小鼠肠道菌群失调韩天雨，杨　栋，周树青，乔亚梅，尹　静，金　敏，李君文△（军事科学院军事医学研究院环境医学与作业医学研究所，天津３０００５０）【摘要】　目的：研究肉苁蓉及其有效成分肉苁蓉多糖和松果菊苷对抗生素相关性腹泻（ＡＡＤ）小鼠肠道菌群的影响。

方法：４８只Ｂａｌｂ／ｃ小鼠随机分为对照（ＣＯＮ）组、ＡＡＤ组、菊粉（ＩＮＵ）组、肉苁蓉（ＲＣＲ）组、肉苁蓉多糖（ＲＣＲＤＴ）组和松果菊苷（ＥＣＨ）组，每组８只，连续７ｄ灌胃盐酸林可霉（３ｇ／ｋｇ）造小鼠腹泻模型，随后灌胃ＩＮＵ（５ｇ／ｋｇ）、ＲＣＲ（５ｇ／ｋｇ）、ＲＣＲＤＴ（２００ｍｇ／ｋｇ）和ＥＣＨ（６０ｍｇ／ｋｇ）各０．２ｍｌ，１次／日，治疗７ｄ，ＣＯＮ组和ＡＡＤ组小鼠灌胃同体积的生理盐水。

通过观察小鼠一般体征、结肠ＨＥ染色、６ＳｒＤＮＡ高通量测序分析，综合评价肉苁蓉及其有效成分肉苁蓉多糖和松果菊苷对抗生素所致小鼠肠道菌群失调的作用。

结果：与ＣＯＮ组相比，ＡＡＤ组小鼠体重减轻，出现明显腹泻症状，结肠组织出现炎性改变，肠道菌群多样性降低（Ｐ＜０．０５），说明造模成功。

与ＡＡＤ组相比，ＩＮＵ组、ＲＣＲ组、ＲＣＲＤＴ组和ＥＣＨ组小鼠体重恢复，腹泻症状明显改善；ＥＣＨ组小鼠结肠病理恢复至正常水平；与ＡＡＤ组相比，ＲＣＲ组、ＲＣＲＤＴ组和ＥＣＨ组小鼠肠道厚壁菌门含量明显减少，Ｂｌａｕｔｉａ和Ｌａｃｈｎｏｃｌｏｓｔｒｉｄｉｕｍ含量增加，Ｃｌｏｓｔｒｉｄｉｕｍ＿ｓｅｎｓｕ＿ｓｔｒｉｃｔｏ＿１含量减少（Ｐ＜０．０５），此外，ＥＣＨ组小鼠肠道菌群丰度和多样性恢复至正常水平，肠道菌群结构得到良性调整，拟杆菌属、Ｆｌａｖｏｎｉｆｒａｃｔｏｒ、Ａｇａｔｈｏｂａｃｔｅｒ、Ｌａｃｈｎｏｃｌｏｓｔｒｉｄｉｕｍ、Ｐｒｅｖｏｔｅｌｌａ９等含量增加（Ｐ＜０．０１）。

结论：肉苁蓉及其有效成分肉苁蓉多糖和松果菊苷均可以调节抗生素所致肠道菌群失调，改善ＡＡＤ症状，其中松果菊苷的作用更明显。

西文生物医学期刊文献

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1.1 On The Promise of Bayesian Inference for

tatistics in Astronomical Investigation
3
admitting uncertainty in terms of a prior distribution for (bjI). Also, expecting low counts implies b will be rather small (see also the paper by John Nousek, this volume, in discussion of low count radiation from SN1987A). Using a prior p(sjbI) that is uniform over a `large' range (and does not depend on b), Loredo proceeds to summary inferences based on the posterior p(sjnbI) in his equation (5.13). Throughout the paper, such uniform priors are adopted as a routine on the basis of representing suitable forms of `ignorance' about the quantity concerned. If any area of Bayesian inference has received too much attention during the last couple of decades it is surely the search for unique and `objective' representation of ignorance { see 4] for a recent and partial review of the eld. The maximum entropy school has been in uential in physical sciences, as referenced by Loredo, and particularly predominant in expounding the view that a single prior may be found, in any given situation, to represent vagueness in the sense of maximum entropy subject to certain `plausible' assumptions that typically stand for little more than mathematical convenience in determining a unique solution in the resulting MaxEnt framework. There is nothing unique, objective or otherwise scienti cally persuasive about uniform priors for location parameters, or any of the plethora of vague, reference or indi erence priors that abound. In investigations which admit an `objective' (de ned simply as consensus of informed observers) data model as here (ie. p(njsI)), analysis should necessarily involve study of sensitivity to qualitative and quantitative aspects of the prior, including assessments of pre-data predictive validity of the fdata modelg:fpriorg combination, and post-data determination of the mapping from prior to posterior for ranges of scienti cally plausible priors. The issue of pre-data validity is addressed through the implied (prior) R predictive distribution for the data, here p(njbI) = p(njsI)p(sjbI)ds. When n is observed, the value of this density function provides the normalising constant in Bayes' theorem (C ?1 in Loredo's equation (5.6)). Prior to the data, however, this distribution describes the investigator's view of experimental outcome. A uniform prior over a very large range translates essentially into a similar (though discrete) uniform p(njbI), which most observers would be quite concerned about as a plausible and scienti cally valid representation of expectations. The issue is particularly acute in problems of low counts and source detection when s (when non-zero) will be tend to be small | reasonable priors for s, and thus predictions about n, should surely re ect this. Competing `reference' priors (and there are many { 4]), lead to posteriors that can di er markedly with low counts s, though all such priors claim some form of `vagueness' and `uniformity' (on some scale). Scienti c investigation must involve careful and thorough consideration of initial information, modes of incorporation of such information in summary inferences, and exploration of sensitivity to prior assumptions (which includes model and data assumptions and well as priors for model parameters { and sometimes the distinction is unclear and even irrelevant

QuEChERS

第42 卷第 11 期2023 年11 月Vol.42 No.111461~1468分析测试学报FENXI CESHI XUEBAO（Journal of Instrumental Analysis）QuEChERS/高效液相色谱-四极杆-飞行时间质谱法测定巧克力中的18种合成大麻素史洪飞*，徐伯芃，徐成鑫，周修齐，张吕悦，张玉曼，冶金，刘畅（南京警察学院刑事科学技术学院，江苏南京210023）摘要：建立了检测巧克力中18种合成大麻素的QuEChERS/高效液相色谱-四极杆-飞行时间质谱方法。

通过优化提取溶剂种类、提取条件和净化条件，确定200.0 mg巧克力采用1 mL甲醇超声提取10 min，取上层清液加入0.05 g C18和0.05 g PSA净化后，以乙腈和0.1%甲酸水溶液为流动相进行梯度洗脱，采用ZORBAXEclipse Plus C18（3.0 mm×100 mm，1.8 μm）色谱柱进行色谱分离，利用四极杆-飞行时间质谱检测。

18种合成大麻素在11 min内实现了分离，5F-EMB-PICA与5F-MDMB-PICA同分异构体通过色谱保留时间和二级质谱碎片实现分辨；5F-EMB-PINACA与5F-ADB同分异构体通过二级质谱碎片实现分辨。

18种合成大麻素在1~ 200 μg/L范围内呈良好线性关系，相关系数均不小于0.997 0，检出限为0.02~0.20 μg/L，定量下限为0.07~ 0.66 μg/L，在50、100、150 μg/kg加标水平下样品的回收率为86.2%~104%，仪器的相对标准偏差（RSD）为0.040%~2.0%，方法的日内RSD为0.32%~3.0%，日间RSD为1.3%~3.6%。

该方法灵敏度高、稳定性强、分析速度快，可为巧克力产品的安全监管和打击合成大麻素类毒品犯罪提供技术支持。

关键词：高效液相色谱-四极杆-飞行时间质谱法；QuEChERS；巧克力；合成大麻素中图分类号：O657.63；O657.7文献标识码：A 文章编号：1004-4957（2023）11-1461-08 Determination of 18 Synthetic Cannabinoids in Chocolate byQuEChERS/High Performance Liquid Chromatography-Quadru⁃pole-Time of Flight Mass SpectrometrySHI Hong-fei*，XU Bo-peng，XU Cheng-xin，ZHOU Xiu-qi，ZHANG Lü-yue，ZHANG Yu-man，YE Jin，LIU Chang（College of Criminal Science and Technology，Nanjing Police College，Nanjing　210023，China）Abstract：A method for the determination of 18 synthetic cannabinoids in chocolate based on QuEChERS/high performance liquid chromatography-quadrupole-time of flight mass spectrometry was established.By optimization the type of extraction solvent，sample extraction and purification conditions，it was determined that 200.0 mg of chocolate was extracted by ultrasonic extraction with1 mL of methanol for 10 min，and then the supernatant was purified by adding 0.05 g of C18 and 0.05g of PSA. The separation was achieved on ZORBAX Eclipse Plus C18（3.0 mm×100 mm，1.8 μm）column with gradient elution of acetonitrile and 0.1%formic acid aqueous solution as the mobile phase. Quadrupole-time of flight high resolution mass spectrometry was used for detection. Eighteen synthetic cannabinoids were separated and detected within 11 min. Two pairs of isomers：5F-EMB-PICA and 5F-MDMB-PICA were resolved by chromatographic retention time and secondary mass spectrum fragments；5F-EMB-PINACA and 5F-ADB are resolved by secondary mass spectrometry fragments. 18 synthetic cannabinoids obtained good linear relations in concentration ranges of 1-200 μg/L with correlation coefficients not less than 0.997 0. The limits of detection were between 0.02 μg/L and 0.20 μg/L，and the limits of quantitation were between 0.07 μg/L and 0.66 μg/L. The re⁃coveries of samples at spiked levels of 50，100 and 150 μg/kg were between 86.2% and 104%. The relative standard deviations（RSDs） of instrument was between 0.040% and 2.0%，the intra-day RS⁃Ds of method was between 0.32% and 3.0% and the inter-day RSDs of method was between 1.3% anddoi：10.19969/j.fxcsxb.23052202收稿日期：2023－05－22；修回日期：2023－07－18基金项目：云南省刑事科学技术重点实验室开放课题；2023年国家级大学生创新重点项目（202312213029Z）；中央高校基本科研业务费（LGYB201718 ）；江苏省“十四五”重点学科（公安技术）资助（苏教研函〔2022〕2号）；中央高校基本科研业务费（LGYB01611）∗通讯作者：史洪飞，高级实验师，研究方向：毒物毒品检验、食品药品环境检验检测技术与应用，E-mail：2657900976@1462分析测试学报第 42 卷3.6%. This method has the advantages of high sensitivity，strong stability and fast analysis speed，and provide technical support for the safety supervision of chocolate products and the fight against syn⁃thetic cannabinoid drug crimes.Key words：high performance liquid chromatography-quadrupole-time of flight mass spectrometry；QuEChERS；chocolate；synthetic cannabinoids合成大麻素是一类新精神活性物质，其与四氢大麻酚类天然大麻素的作用机理相似，通过与大麻素受体结合发挥作用，且精神活性作用更强［1］。

藏南泽当地区大反向逆冲断层变形研究———以磁组构与EBSD组构分析为例

１００００５６９／２０２１／０３７（１０）３１６７８４ＡｃｔａＰｅｔｒｏｌｏｇｉｃａＳｉｎｉｃａ　岩石学报ｄｏｉ：１０１８６５４／１００００５６９／２０２１１０１２藏南泽当地区大反向逆冲断层变形研究———以磁组构与ＥＢＳＤ组构分析为例曹新文１，２，３　孙知明１黄宝春２　曹勇１　裴军令１　叶小舟１　刘思琪２ＣＡＯＸｉｎＷｅｎ１，２，３，ＳＵＮＺｈｉｎｇＭｉｎｇ１，ＨＵＡＮＧＢａｏＣｈｕｎ２，ＣＡＯＹｏｎｇ１，ＰＥＩＪｕｎＬｉｎｇ１，ＹＥＸｉａｏＺｈｏｕ１ａｎｄＬＩＵＳｉＱｉ２１自然资源部古地磁与古构造重建重点实验室，中国地质科学院地质力学研究所，北京　１０００８１２北京大学地球与空间科学学院，教育部造山带与构造演化重点实验室，北京　１００８７１３自然资源部深地动力学实验室，中国地质科学院地质研究所，北京　１０００３７１ＭＮＲＫｅｙＬａｂｏｒａｔｏｒｙｏｆＰａｌｅｏｍａｇｎｅｔｉｓｍａｎｄＴｅｃｔｏｎｉｃＲｅｃｏｎｓｔｒｕｃｔｉｏｎ，ＩｎｓｔｉｔｕｔｅｏｆＧｅｏｍｅｃｈａｎｉｃｓ，ＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＧｅｏｌｏｇｉｃａｌＳｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ１０００８１，Ｃｈｉｎａ２ＭＯＥＫｅｙＬａｂｏｒａｔｏｒｙｏｆＯｒｏｇｅｎｉｃＢｅｌｔｓａｎｄＣｒｕｓｔａｌＥｖｏｌｕｔｉｏｎ，ＳｃｈｏｏｌｏｆＥａｒｔｈａｎｄＳｐａｃｅＳｃｉｅｎｃｅｓ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ１００８７１，Ｃｈｉｎａ３ＭＮＲＫｅｙＬａｂｏｒａｔｏｒｙｏｆＤｅｅｐＥａｒｔｈＤｙｎａｍｉｃｓ，ＩｎｓｔｉｔｕｔｅｏｆＧｅｏｌｏｇｙ，ＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＧｅｏｌｏｇｉｃａｌＳｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ１０００３７，Ｃｈｉｎａ２０２１０７３０收稿，２０２１０９２９改回ＣａｏＸＷ，ＳｕｎＺＭ，ＨｕａｎｇＢＣ，ＣａｏＹ，ＰｅｉＪＬ，ＹｅＸＺａｎｄＬｉｕＳＱ２０２１ＴｈｅｉｎｖｅｓｔｉｇａｔｉｏｎｓｏｆｔｈｅｄｅｆｏｒｍａｔｉｏｎｏｆｔｈｅＧｒｅａｔＣｏｕｎｔｅｒＴｈｒｕｓｔ（ＧＣＴ）ｉｎＺｅｄａｎｇａｒｅａ，ＳｏｕｔｈＴｉｂｅｔ：ＡｃａｓｅｓｔｕｄｙｏｆｍａｇｎｅｔｉｃｆａｂｒｉｃａｎｄＥＢＳＤａｎａｌｙｓｉｓＡｃｔａＰｅｔｒｏｌｏｇｉｃａＳｉｎｉｃａ，３７（１０）：３１６７－３１８４，ｄｏｉ：１０１８６５４／１００００５６９／２０２１１０１２ＡｂｓｔｒａｃｔＲｅｎｂｕＺｅｄａｎｇｔｈｒｕｓｔｆａｕｌｔｉｓｏｎｅｏｆｔｈｅｍｏｓｔｉｍｐｏｒｔａｎｔｐａｒｔｓｏｆｔｈｅＧｒｅａｔＣｏｕｎｔｅｒＴｈｒｕｓｔ（ＧＣＴ）ｉｎＳｏｕｔｈＴｉｂｅｔ，ａｓｗｅｌｌａｓｏｎｅｏｆｔｈｅｍｏｓｔａｃｔｉｖｅｆａｕｌｔｓｏｆｔｈｅＨｉｍａｌａｙａＯｒｏｇｅｎｙｉｎＣｅｎｏｚｏｉｃＴｈｅｉｎｖｅｓｔｉｇａｔｉｏｎｏｆｔｈｅｄｅｆｏｒｍｅｄｆａｂｒｉｃｈａｓｇｒｅａｔｉｍｐｏｒｔａｎｃｅｆｏｒｄｅｅｐｕｎｄｅｒｓｔａｎｄｉｎｇｏｆｔｈｅｏｒｏｇｅｎｅｖｏｌｕｔｉｏｎａｎｄｐｌａｔｅａｕｕｐｌｉｆｔＩｎｔｈｉｓｐａｐｅｒ，ｗｅｃｏｍｂｉｎｅｄｔｈｅｍｅｓｏｓｃｏｐｉｃａｎｄｍｉｃｒｏｓｔｒｕｃｔｕｒｅｓｏｆｔｈｅｆａｕｌｔｒｏｃｋｓ，ｅｓｐｅｃｉａｌｌｙ，ｔｈｅｃｏｍｐａｒｉｓｏｎａｎａｌｙｓｉｓｏｆｔｈｅＥｌｅｃｔｒｏｎＢａｃｋｓｃａｔｔｅｒｅｄＤｉｆｆｒａｃｔｉｏｎ（ＥＢＳＤ）ｆａｂｒｉｃｓｏｆｑｕａｒｔｚ，ｍｉｃａａｎｄｔｈｅａｎｉｓｏｔｒｏｐｙｏｆｍａｇｎｅｔｉｃｓｕｓｃｅｐｔｉｂｉｌｉｔｙ（ＡＭＳ）ｏｆｓａｍｐｌｅｓａｒｏｕｎｄｔｈｅｆａｕｌｔｚｏｎｅＴｈｅＡＭＳｒｅｓｕｌｔｓｓｕｇｇｅｓｔａｎｏｂｌａｔｅｍａｇｎｅｔｉｃｅｌｌｉｐｓｏｉｄｐｒｅｄｏｍｉｎａｎｔａｔｍｏｓｔｓａｍｐｌｅｓｉｔｅｓ，ａｎｄｍａｇｎｅｔｉｃｆｏｌｉａｔｉｏｎｓｎｅａｒｌｙｃｏｉｎｃｉｄｅｗｉｔｈｔｈｅｔｅｃｔｏｎｉｃｆｏｌｉａｔｉｏｎｓ（ｃｌｅａｖａｇｅｏｒｆａｕｌｔｐｌａｎｅ），ｂｏｔｈｏｆｗｈｉｃｈｓｕｇｇｅｓｔｓｔｒｏｎｇｔｅｃｔｏｎｉｃｆａｂｒｉｃｄｏｍｉｎａｎｔｏｆｔｈｅａｒｅａＳＮｄｉｒｅｃｔｅｄｍａｇｎｅｔｉｃｌｉｎｅａｔｉｏｎｉｎｌｉｎｅｗｉｔｈｔｈｅｆａｕｌｔｍｏｖｉｎｇｄｉｒｅｃｔｉｏｎｉｎｄｉｃａｔｅｄｔｈｅｃｏｎｔｉｎｕｉｎｇｔｈｒｕｓｔｉｎｇｈａｐｐｅｎｅｄｉｎｔｈｅｆａｕｌｔｚｏｎｅＱｕａｒｔｚｍｉｃｒｏｓｔｒｕｃｔｕｒｅｓｕｇｇｅｓｔｓｔｈａｔｔｈｉｓｆａｕｌｔｚｏｎｅａｔｌｅａｓｔｕｎｄｅｒｗｅｎｔｔｈｒｅｅｄｉｆｆｅｒｅｎｔｌｅｖｅｌｓｏｆｄｅｆｏｒｍａｔｉｏｎｍｅｃｈａｎｉｓｍ，ｎａｍｅｌｙ，ｔｈｅｄｉｓｓｏｌｕｔｉｏｎｃｒｅｅｐｓｔａｔｉｃｒｅｃｒｙｓｔａｌｌｉｚａｔｉｏｎ（ｑｕａｒｔｚｇｒａｉｎｓｓｈｏｗｓｐｏｌｙｇｏｎｓｅａｍｓ），ｔｈｅｂｕｌｇｉｎｇ（ＢＬＧ）ｒｅｃｒｙｓｔａｌｌｉｚａｔｉｏｎａｎｄｔｈｅｓｕｂｇｒａｉｎｒｏｔａｔｉｏｎ（ＳＧＲ）ｒｅｃｒｙｓｔａｌｌｉｚａｔｉｏｎ，ｒｅｓｐｅｃｔｉｖｅｌｙＬｏｗｄｅｆｏｒｍａｔｉｏｎｔｅｍｐｅｒａｔｕｒｅ（３００～４００℃）ｉｓｓｕｇｇｅｓｔｅｄｆｒｏｍｔｈｅｃａｘｅｓｏｆｑｕａｒｔｚＥＢＳＤｆａｂｒｉｃＴｈｅＣｒｙｓｔａｌｌｏｇｒａｐｈｉｃＰｒｅｆｅｒｒｅｄＯｒｉｅｎｔａｔｉｏｎ（ＣＰＯ）ｏｆｂｉｏｔｉｔｅｓｈｏｗｓｓｔｒｏｎｇｃｏｒｒｅｓｐｏｎｄｅｎｃｅｗｉｔｈｔｈｅｍａｇｎｅｔｉｃｆａｂｒｉｃｓｗｈｉｃｈｆｕｒｔｈｅｒｃｏｎｆｉｒｍｅｄｔｈｅｄｏｍｉｎａｎｃｅｏｆｐａｒａｍａｇｎｅｔｉｃｔｏｔｈｅＡＭＳＴｈｅｄｕｃｔｉｌｅｄｅｆｏｒｍａｔｉｏｎｏｆＧＣＴｉｎｔｈｅＺｅｄａｎｇａｒｅａｉｓｔｈｅｒｅｓｕｌｔｏｆｔｈｅｆａｕｌｔｉｎｄｕｃｔｉｌｅｚｏｎｅｏｆｔｈｅｍｉｄｄｌｅａｎｄｕｐｐｅｒｃｒｕｓｔｕｐｌｉｆｔｍｏｖｅｍｅｎｔｓｔａｇｅ，ａｌｓｏｒｅｐｒｅｓｅｎｔｔｈｅｐｌａｔｅａｕｕｐｌｉｆｔａｎｄｄｅｆｏｒｍａｔｉｏｎｏｆｔｈｅＴｅｔｈｙａｎＨｉｍａｌａｙａｎｓｉｎｃｅＣｅｎｏｚｏｉｃＫｅｙｗｏｒｄｓＧｒｅａｔＣｏｕｎｔｅｒＴｈｒｕｓｔ（ＧＣＴ）；Ｚｅｄａｎｇａｒｅａ，ＳｏｕｔｈＴｉｂｅｔ；Ａｎｉｓｏｔｒｏｐｙｏｆｍａｇｎｅｔｉｃｓｕｓｃｅｐｔｉｂｉｌｉｔｙ（ＡＭＳ）；ＥＢＳＤｆａｂｒｉｃ摘　要仁布泽当逆冲断层是喜马拉雅大反向逆冲断层（ＧＣＴ）在藏南地区的重要延伸部分，也是喜马拉雅造山带北部边界新生代最为活动的构造单元之一。

propane

Quasiclassical trajectory calculations of collisional energy transfer in propane systemsApichart Linhananta and Kieran F.Lim*¤Centre for Chiral and Molecular T echnologies,School of Biological and Chemical Sciences,Deakin University,Geelong,V ictoria3217,Australia.E-mail:lim=.auRecei v ed6th December1999,Accepted27th January2000Published on the Web9th March2000Quasiclassical trajectory calculations of collisional energy transfer(CET)and rotational energy transfer from highly vibrationally excited propane to rare bath gases are reported.The calculations employed atomÈatom pairwise-additive Lennard-Jones,Buckingham exponential and hard-sphere intermolecular potentials to examine the dependence of CET on the intermolecular potential and to establish a protocol for future work on larger alkane systems.The role of the torsional(internal)and molecular(external)rotors in the energy-transfer mechanism were parison of the results with our earlier work on ethane]neon systems(A. Linhananta and K.F.Lim,Phys.Chem.Chem.Phys.,1999,1,3467)suggests that the internal and external rotors play a signiÐcant role in the deactivation mechanism for highly vibrationally excited alkanes.I.IntroductionGas-phase chemical reaction rates are strongly dependent on intermolecular collisional energy transfer(CET).CET is a vital component in any combustion-model and atmospheric-model systems.The only experimental CET quantities for hydrocarbon fuel molecules have been inferred““indirectlyÏÏfrom measurements of pressure-dependent reaction rates.1h3 Despite this,there have been no systematic theoretical dynamics studies of CET of hydrocarbon and halogenated hydrocarbons.In fact,most theoretical studies have been on small molecules.3h14The exceptions are the quasiclassical tra-jectory(QCT)calculations of azulene,toluene,benzene and hexaÑuorobenzene systems.15h23We have recently reported QCT calculations for highly vibrationally excited ethane in neon bath gas.24This and the recent work by Svedung et al. are,to our knowledge,theÐrst theoretical CET studies of an alkane with internal rotors.24,25Comparisons of theoretical and experimental studies of CET show that many of the dominant energy transfer mecha-nisms in small molecules are also present in large mol-ecules.3h6However,there are several di†erences between large-substrate and small-substrate behaviours.A notable example is that in the CET from a““smallÏÏsubstrate to a rare gas collider the trend He[Ne[Ar is observed,26h28 whereas the opposite trend of He\Ne\Ar is observed for ““largeÏÏsubstrates.29h39Theoretical studies of CET on small molecules employing various techniquesÈquantum,semi-classical and classical dynamicsÈall have correctly predicted the small-substrate behaviour.40,41This is not the case for large-substrate systems where QCT simulations incorrectly found the same smallsubstrate trend.15h18The discrepancy may be due to the lack of reliable data on the intermolecular potential surface involving large molecules and is most likely to be manifested in systems with the small collider helium bath gas.42,43¤Lim Pak Kwan.The aforementioned QCT calculations of large-substrate molecules have been on aromatic hydrocarbons because they have been most amenable to experimental studies using spec-troscopic probes.There have been fewer studies28,44h47on alkanes and branched-alkanes,which are the main com-ponents of common combustion fuels,and their halogenated analogues,which are important in ozone and““greenhouseÏÏchemistry.TheÐrst most obvious di†erences between alkanes and aromatics are their shapes,which are expected to a†ect the rotational energy transfer(RET).Since rotation to trans-lation(R]T)energy transfer and vibration to rotation (V]R)energy transfer are often more efficient than vibration to translation(V]T)energy transfer,this can have a strong inÑuence on the overall CET.Another crucial aspect is theÑexibility of alkanes.QCT simulations of alkanes would require the development of an efficient algorithm for sampling conformer space.Related to theÑexibility,as well as to RET,is the role of internal rotors in the CET mechanism.QCT calculations of highly vibra-tionally excited ethane in neon bath gas show that there is an interrelationship between the internal methyl rotors and the external rotation giving rise to V]torsion,R energyÑow in theÐrst collision,resulting in an““enhancedÏÏCET in sub-sequent collisions.24The same e†ect is also observed in experiments on the deactivation of highly vibrationally excited benzene and toluene,where toluene has much larger CET values than benzene.37This e†ect suggests that the torsional rotors in alkanes are important.Since the use of intramolecular torsional potential terms (nine such terms for each additional methylene unit)24plus a sampling of the conformational space may prove to be cost-prohibitive for large(r)alkane systems,there is a need to establish an e†ective protocol for QCT alkane simulations. Use of a hard-sphere potential will reduce a substrateÈcollider collision into a sequence of““sudden-impactÏÏatomÈatom encounters.Furthermore,there is no need to calculate molec-ular interactions at medium-to-large atomic separations.This paper““benchmarksÏÏCET using a hard-sphere potential against the more-commonly used Lennard-Jones andDOI:10.1039/a909614k Phys.Chem.Chem.Phys.,2000,2,1385È13921385This journal is The Owner Societies2000(Buckingham-type exponential-6models,by performing QCT calculations on the propane ]monatomic collider systems.The role of the torsional (internal)and molecular (external)rotors in the energy-transfer mechanism are reported.II.Quasiclassical trajectory calculationsA.Intermolecular potentialThe lack of knowledge of the detailed form of intermolecular potentials has always been a hindrance to quasiclassical mod-elling of CET.This is especially true for large-substrate systems,where there is a paucity of reliable theoretical and experimental data.Previous trajectory calculations of large molecules usually modelled the intermolecular potential by pairwise-additive atom Èatom potentials:7h 24,48h 50the inter-action parameters were usually obtained by semiempirical methods.Collins and coworkers have ““builtÏÏintermolecular potentials by interpolation of ab initio data:51h 53thus far they have only applied their method to relatively small polyato-mics whereas we wish to use a protocol that can be consistent-ly and easily ““scaled upÏÏfor larger alkane systems.Hence in this work three pairwise-additive atom Èatom intermolecular potentials were employed.The Ðrst intermolecular potential was the pairwise-additive Lennard-Jones (LJ)potential with atom Èatom terms given by V ij \4e ijCA p ij r ij B 12[A p ij r ijB 6D,(1)(i \C,H;j \rare gas),where is the atom Èatom centre-of-r ijmass separation,and and are the Lennard-Jones radiusp ij e ijand well depth,respectively.The LJ parameters were chosen by the method of Lim to match empirical values.16,29,54The second intermolecular potential was the pairwise-additive Buckingham exponential (exp-6)potential with atom Èatom terms given byV ij \A ij exp([c ij r ij )[C ij r ij~6,(2)where the parameter determines the repulsive steepness ofc ijthe potential.55The parameters and were chosen toA ij C ijmatch empirical values.16,29,54The last intermolecular potential was a pairwise-additive hard-sphere (HS)potentialV ij \GO ,0,r ij O r ij vdW ,r ij [r ijvdW ,(3)where is the van der Waals radius 56between atoms i andr ijvdW j .This potential is in the spirit of the e†ective mass theory.57The HS potential is tested here to determine if it can be used to derive useful qualitative information:if so then it would be a useful model for simulations of larger alkanes.The intermolecular parameters for propane ]Rg (Rg \rare gases He,Ne and Ar)potentials are given in Table 1.B.Intramolecular potentialA simple harmonic valence force Ðeld,consisting of harmonic stretches,bends and torsions,was used to describe the propane substrate:V intra\;i V stretch,i ];i V bend,i ];iV torsion,i .(4)The Ðrst two terms have been deÐned previously.15,58,59The harmonic stretching and bending force constants were obtained by the empirical prescription of Lindner:60k str,CC\4.705]102J m ~2,J m ~2,k str,CH \4.702]102k bend,CCH\6.67]10~17J rad ~2,and J rad ~2.k bend,HCH\5.61]10~17The Ðnal term in eqn.(4)is a 3-fold methyl torsional potential,which was assumed to be:V torsion,i \V 0n ;j /1n cos 2A 3qij 2B.(5)The torsional angles are the nine H ÈC ÈC ÈH or H ÈC ÈC ÈCq ijdihedral angles for each of the i th C ÈC bonds.Each carbon centre was assumed to have perfect tetrahedral geometry with C ÈC and C ÈH bond lengths of 0.1543nm and 0.1093nm,respectively.To study the e†ect of the torsion,the torsional barrier parameter was taken to be 0(free rotors)and 13.8V 0kJ mol ~1(experimental barriers).61The direction of the bond vectors was deÐned so that the staggered conformer has the lowest-energy geometry.The free-rotor model has apparent harmonic torsional ““vibrationalÏÏfrequencies of 9.2and 9.3cm ~1while the hindered-rotor model has apparent harmonic torsional ““vibrationalÏÏfrequencies of 167.4and 186.3cm ~1.These fre-quencies arise from the numerical normal mode analysis and are used in the selection of initial conditions.58,59,62The other 25vibrational frequencies compare favourably with experi-mental group frequencies of putational detailsTrajectory calculations were performed using program MARINER 58which is a customised version of VENUS96.59The LJ and exp-6potential models,selection of initial condi-tions,and general methodology are standard options in program MARINER/VENUS96.58,59,62The initial impact energy was chosen from a 300K thermal distribution.InE transthe majority of cases,the initial rotational angular momentum of propane was chosen from a thermal distribution at 300K.The rotational temperature was varied from 100to 1500K to investigate the RET of propane ]argon by the HS model.The initial vibrational phases and displacements were chosen from microcanonical ensembles at E @\41000,30000or 15000cm ~1,where E @is the rovibrational energy above the zero-point energy.These initial conditions are appropriate for comparison with the Ðrst few collisions in time-resolved infra-red Ñuorescence and ultraviolet absorption experi-ments.3h 6,29h 38,64Note that experiments measure the CET values of a cascade of collisions.The rovibrational energy dis-tribution of subsequent collisions will not be microcanonical,Table 1Intermolecular potential parametersLJ model exp-6model HS model p (e /k B )Aij Cij c ij r vdW /nm/K /kJ mol ~1/10~6kJ mol ~1nm 6/nm 1/nm H ÉÉÉHe 0.28258.0882294712479.945.50.325C ÉÉÉHe 0.291517.6931859254179745.60.345H ÉÉÉNe 0.293817.00103476168.5345.70.305C ÉÉÉNe 0.302034.156********.6945.90.325H ÉÉÉAr 0.306628.87140033519.240.80.335C ÉÉÉAr0.321658.025809650187641.00.3551386Phys .Chem .Chem .Phys .,2000,2,1385È1392but the CET behaviour of these subsequent collisions can be inferred 18,65,66from the microcanonical values.For the models employing the LJ and exp-6intermolecular potentials,trajectories were initialised with a centre-of-mass separation of 1.2nm and the classical equations of motion were integrated by the Adams ÈMoulton algorithm 58,59,62until the distance between the monatomic collider and the closest hydrogen exceeded a critical value of 1.0nm,at which point the trajectory was terminated.The initial impact param-eter b was chosen with importance sampling 16,17,58,59,62for values between 0nm and nm (He and Ne)or 0.9nmb m\0.8(Ar).These initial and Ðnal conditions were chosen by per-forming preliminary runs which showed that an insigniÐcant amount of energy was transferred at larger distances.For the HS interaction model,there is no intermolecular interaction until the point of impact,when the propane sub-strate is still described by a (near)microcanonical putationally,this is achieved by initialising trajectories as above,but translating the colliders to the point of initial contact without altering the rovibrational phases and orienta-tion.The translation was performed using an algorithm devel-oped by Alder and Wainwright 67,68to model hard-sphere Ñuid systems.After this initial point of contact,the trajectory was propagated normally.At each time step,the interatomic distances between the rare gas collider and every propane atom were checked for overlap.If an atom Èatom encounter occurred,the trajectory was projected back to the point of impact and the impulsive momentum transfer was calcu-lated.68The process was repeated until another encounter occurred or until the distance between the monatomic collider and the closest hydrogen exceeded a critical value,at which point the trajectory was terminated.Program MARINER 58was altered to implement the HS potential and trajectory-propagation algorithms.The short-ranged HS interaction per-mitted critical values as low as 0.4nm.Since the equations of motion are integrated for a comparatively short period,the HS model required much less computing time than the LJ and exp-6models.For E @\15000and 30000cm ~1,the integration time step was chosen to be 0.085fs,which is sufficient to conserve total energy to within 0.5cm ~1.This is approximately four times larger than the time step used in our previous ethane trajec-tory calculations.24Propane has less excitation per vibra-tional mode and hence energy can be conserved by larger time steps.For E @\41000cm ~1,it was necessary to employ a time step of 0.075fs to conserve energy.The numerical insta-bilities associated with the inversion of the methyl group(s)previously observed in simulations of ethane 24and toluene 16,17were not observed here.The calculations were performed on a DEC Alpha 3000/300LX workstation and an SGI Power Challenge Super-computer.In calculations that employed the LJ or exp-6intermolecular potentials,batches of 3000trajectories required approximately 60CPU hours for He collider and 100CPU hours for Ar on the workstation.The HS model decreased the required CPU time by a factor of 10:this reduction will be very signiÐcant in the study of larger alkanes.CPU time was reduced by a factor of about 4on the supercomputer.D.Rotation energy and torsional angular momentum It is well documented that rotational energy transfer is an effi-cient pathway for CET.3,24,65,66,69However,while angular momenta are well-deÐned,rovibrational coupling gives rise to an ambiguity in the deÐnition of rotational energy.Previous quasiclassical simulations employed several di†erent methods to decouple the rotational and vibrational energies.One method 11deÐnes the rotational energy asE rot \1(JI ~1J ),(6)where I and J are,respectively,the instantaneous moment of inertia and angular momentum.In a second method isE rotapproximated by the instantaneous angular momentum,but the moment of inertia is taken to be the equilibrium geometry value.11Both deÐnitions give rotational energies that oscillate with time.There is an alternative deÐnition that is valid for symmetrical top rotors:65E rot \1B effJ 2,(7)where J is the magnitude of the rotational angular momentum and is an e†ective rotational constant.This deÐnitionB effdecoupled the rovibrational energy so that the rotational energy includes only the ““adiabatic partÏÏ,whereas the ““activeÏÏpart is included with the vibrational energyE V \E [E rot,(8)where and E are,respectively,the vibrational and totalE Vinternal energies.Eqn.(7)is a valid approximation for sym-metrical top molecules.70The main advantage of this deÐni-tion is that,classically,it is a conserved quantity.The equilibrium Cartesian principal moments of inertia of propane are kg m 2,kgI xx \1.11]10~45I yy\9.7]10~46m 2and kg m 2.Hence,propane is a goodI zz\2.97]10~46approximation of a symmetrical top and it is possible to deÐne the rotational energy by eqn.(7),with the approx-imationB eff \12hc (I xx I yy I zz)~1@3.(9)It was shown in our previous work on ethane 24that the coupling between external and internal rotors enhances the overall CET.Hence the torsional angular momentum of propane was also monitored in this work.Whereas ethane has only one torsional rotor which lies along its molecular axis,propane has two distinct and unparallel torsional rotors.The deÐnition of the torsional angular momentum introduced for ethane is generalised by calculating the rotational angular momentum of the methyl group and the associated ethyl groupJ methyl \;i /H,H,Hr i ]p iJ ethyl\;i /C,H,Hr i ]p i,(10)where is the angular momentum of the methyl groupJ methyland is the angular momentum of the associated ethylJ ethylrotor.Note that for consistency with eqn.(5),only the six atoms directly bonded to each torsional C ÈC bond have been included in the summation in eqn.(10).The torsional angular momentum is then deÐned asJ tor \o (J methyl [J ethyl)Éa o ,(11)where is a unit vector parallel to the CC torsional axis.The a CET to/from the torsional rotors was monitored by calcu-lating the average torsional angular momentum change*J tor \J tor (Ðnal)[J tor(initial).(12)E.Data analysisTrajectory data were analysed by a bootstrap algorithm 71,72in program PEERAN.16,73Some 3000È5000trajectories were performed for each potential model.This was sufficient to obtain average energy-transfer quantities with statistical uncertainties of about 10%.However,the uncertainties for the average rotational energy transfer were about 20%,due to the initial rotational-energy Boltzmann distribution (rather than an initial microcanonical distribution).Trajectory averagesPhys .Chem .Chem .Phys .,2000,2,1385È13921387deÐned by (for both overall CET and RET)S*E n TtrajS*E n T traj \1N ;i /1N bi bm(*E i )n(13)are related to experimentally obtained quantities S*E n T by ratio of collision cross-sectionsS*E n T \p b m 2p p LJ2X (2,2)RS*E n T traj (14)where is the LJ collision cross-section and is thep LJ 2X (2,2)R b mmaximum impact parameter in the trajectory simulation.This normalisation removes the ambiguity related to the elastic scattering at high impact parameter.74The input LJ param-eters were obtained from ref.29.At 300K,the LJ collision cross-section values of nm 2,0.4834nm 2p LJ2X (2,2)R \0.3976and 0.6945nm 2for propane ]He,propane ]Ne and propane ]Ar,respectively,were obtained using the program COLRATE.75This corresponds to the LJ collision frequencies of m 3s ~1,328.58]10~18m 3s ~1Z LJ,coll\523.29]10~18and 382.37]10~18m 3s ~1,respectively.In this paper,we have reported both the Ðrst and second moments of the trajectory data since the Ðrst moment is usually more useful for comparison with experiment,but the QCT second moment is statistically more reliable.74Some experiments can determine both the Ðrst and second moments of the CET probability.3,5III.Results and discussionA.The e†ect of the torsional barrierFigs.1and 2show the CET values,[S*E T and S*E 2T 1@2,and the RET values,as functions of energy E @aboveS*E RT ,zero-point energy for propane ]neon.One set of results areFig.1Dependence of energy-transfer quantities on torsional barrier for deactivation of vibrationally excited propane by neon bath gas:)Hindered-rotor (LJ);Free-rotor (LJ);Hindered-rotor (exp-6);L +…Free-rotor (exp-6).Fig.2Dependence of rotational energy transfer on torsional barrier for deactivation of vibrationally excited propane by neon bath gas:)Hindered-rotor (LJ);Free-rotor (LJ);Hindered-rotor (exp-6);L +…Free-rotor (exp-6).for the free-rotor model the other for the hindered-(V 0\0),rotor model kJ mol ~1).These results are for the LJ(V 0\13.8and exp-6intermolecular potentials.The overall deactivation,[S*E T and S*E 2T 1@2,is larger for the hindered-rotor model,similar to results for ethane ]neon.24The torsional angular momentum transfer is shownS*J torT in Fig.3.Note that for the hindered-rotor modelsS*J torT with both LJ and exp-6intermolecular potentials are virtually identical:the reason for this is unclear.Overall,S*J torTdecreases,but remains positive,with the presence of a barrier In contrast,for ethane ]neon changes from posi-V 0.S*J torT tive to negative over a similar range of values.24This di†er-V 0ence is probably due to the higher torsional moment of inertia for propane torsion compared to ethane(CH 3ÈCCH 2)This means that propane torsion has higher(CH 3ÈCH 3).density of states and can more readily gain torsional excita-tion than ethane torsion,explaining why is positiveS*J torT for propane,but negative for ethane.In ethane,the torsion acts like a vibration providing an efficient torsion ]T pathway.24The increase in [S*E T and S*E 2T 1@2(Fig.1)for the hindered-rotor model suggests that propane torsions play the same role in the CET mechanism.The RET is smaller for the propane free-rotor modelS*E RT than the hindered-rotor model (Fig.2),contrary to the ethane results.24For ethane,the torsion is aligned along the molecu-lar axis,hence any increase in methyl-rotor angular momen-tum contributes to both (internal)torsional excitation S*J torTand (external)rotational excitation The propane free-S*E RT .rotor model has Ðve (three external and two internal)indepen-Fig.3Dependence of torsional angular momentum change on tor-sional barrier for deactivation of vibrationally excited propane by neon bath gas:Hindered-rotor (LJ);Free-rotor (LJ);)L +Hindered-rotor (exp-6);Free-rotor (exp-6).Note that the two sets …of hindered-rotor results are almost identical.1388Phys .Chem .Chem .Phys .,2000,2,1385È1392dent rotors,none of which have coincident axes.The extra rotors mean that there is less energy available to the external rotors in any V ]torsion,R energy redistribution.Noteworthy is the fact that the di†erences between the free-rotor and hindered-rotor models persist up to E @\41000cm ~1.For ethane ]neon,there is an onset of near-free-rotor behaviour at E @\30000cm ~1:at E @\41000cm ~1there is no signiÐcant di†erence between the free-and hindered-rotor models.However,the larger number of vibrational modes in propane,which decreases the excitation per torsional mode,ensures that the di†erences remain even at very high excita-tion.Hence correct theoretical treatments of internal rotors become even more essential for larger molecules.B.Trajectory results for LJ and exp-6modelsThe CET results for the deactivation of highly excited propane by helium,neon and argon are shown in Fig.4,where the intermolecular interactions have been modelled by the LJ and exp-6potentials.Three important features are:(1)Energy transfer increases with increasing E @and is in accord with theoretical and experimental studies on the deac-tivation of highly vibrationally excited molecules.(2)The LJ potential results in larger CET values than the exp-6model,since the LJ potential has a much harder repul-sive part than the exp-6potential.There are numerous works which concluded that CET depends mainly on the repulsive part of the intermolecular potential and that,in general,a harder repulsive part results in larger energy transfers.9,16,17(3)The deactivator efficiency shows the trend He [Ne [Ar which,unfortunately,is in discord with experi-mental trends for Ñuorinated alkane systems.28To our knowledge,there has been no experimental study of CET in propane ]rare gas systems.““IndirectÏÏstudies of related systems include 2-bromopropane ]Ne ([S*E T \130cm ~1for E @\17000È21000cm ~1)76andFig.4Energy-transfer quantities for deactivation of vibrationally excited propane by rare gases:Helium (LJ);Neon (LJ);)K |Argon (LJ);Helium (exp-6);Neon (exp-6);Argon (exp-6).+=>isotopically-substituted cyclopropane ]He (S*E 2T 1@2\200È400cm ~1for E @D 22000cm ~1).2These CET quantities were not directly measured,but were inferred from pressure-dependent thermal reaction rates at elevated temperatures.Some more recent studies using time-resolved optoacoustic spectroscopy include ([S*E T \114cm ~1atC 3F 8]Ar E @\15000cm ~1and [S*E T \300cm ~1at E @\40000cm ~1).46These studies reveal no information about RET nor the role of torsional modes.These experimental CET quan-tities correlate well with our present calculations (Fig.4)but also indicate a need for fresh experimental studies.The decreasing trend with collider He [Ne [Ar has been observed in many other QCT studies.9,15,18,77Although the lack of qualitative agreement with experiment is disappoint-ing,these studies and the present work have used very crude intermolecular potential models.Given the lack of detailed information about polyatomic intermolecular potential sur-faces,the intention in the present and other studies has been to use a set of consistent and transferable potentials,16much in the spirit of molecular mechanics force Ðelds.Experience with simulations on other systems would suggest that the exp-6model potentials predict ““betterÏÏCET values than the LJ potentials.17Fig.5plots the RET of propane ]rare gas systems.For Ne and Ar,monotonically increases with E @,whereas forS*E RT He,it initially increases but decreases at higher excitation energy.In all cases,RET is larger for the LJ model which is in accord with the CET behaviour.Clary and Kroes 78and others 16,17,40have observed that RET is larger for heavier colliders because the collision duration is closer to the rota-tional period of the molecular substrate.Fig.6plots the torsional angular momentum transfer as a function of E @.is largest for He and smal-S*J tor T S*J torT lest for Ar,which is the same trend as for CET.This implies that,in addition to the external rotor gateway,the torsional rotor is a gateway for facile CET via V,torsion ]torsion,T.24An interesting feature of Fig.6is that seems to beS*J torT Fig.5Rotational energy transfer for deactivation of vibrationally excited propane by rare gases:Helium (LJ);Neon (LJ);)K |Argon (LJ);Helium (exp-6);Neon (exp-6);Argon (exp-6).+=>Phys .Chem .Chem .Phys .,2000,2,1385È13921389Fig.6Torsional angular momentum change for deactivation ofvibrationally excited propane by rare gases:Helium(LJ);Neon)K(LJ);Argon(LJ);Helium(exp-6);Neon(exp-6);Argon|+=>(exp-6).insensitive to the intermolecular potential.However,the factthat it depends on the type of bath gas indicates a dependenceon the mass of the deactivator.This suggests that isS*JtorTinsensitive to theÐne details of the intermolecular potentialand can be modelled by either LJ or exp-6potentials.C.Trajectory results for hard-sphere modelLJ and exp-6potentials have long-range attractive terms andare computationally expensive.Since HS is a short-rangepotential,it is computationally cheaper in terms of computertime than other potential models by an order of magnitude.Inthis section we compare the results of the short-range HS withthe longer-range potentials.Fig.7shows S*E T and S*E2T1@2for the HS model.Fig.8shows the RET for the HS model.The qualitative behavioursare the same as for the LJ and exp-6models but the energy-transfer values are several times larger than for the LJ andexp-6model.This is not surprising in view of the““hardnessÏÏof the HS potential.9,16,17Another important feature is thatS*E T and S*E2T1@2for He are several times larger than forNe and Ar.This is also true for the LJ model(Fig.3)whichindicates that the HS and LJ models tend to give CET valuesthat are much too high for helium colliders.Table2lists the average number of encounters per collision,for He,Ne and Ar colliders.This average includes onlyNC,trajectories in which collisions have occurred.As expected NCTable2Average number of atomÈatom encounters NcE@/cm~1150003000041000Propane]He 1.967 1.884 1.847Propane]Ne 3.145 2.952 2.852Propane]Ar 3.753 3.501 3.400Fig.7Energy-transfer quantities for deactivation of vibrationallyexcited propane by rare gases for the HS model:Helium;Neon;+=Argon.>is largest for Ar and smallest for He due to their reducedmasses.also decreases with increasing E@which suggestsNCthat a more highly excited substrate imparts more energy perencounter to the deactivator,reducing the collision duration.Fig.9shows S*E T,and for propane]argonS*EVT S*ERTsystems at rotational temperatures300,1000andTROT\100,1500K.In these simulations,initial excitation wasÐxed atE@\15000cm~1and the initial translational temperaturewas K.It can also be seen that RETTtrans\300S*ERTdecreases with increasing the magnitude of the vibra-TROT;tional energy transfer also decreases with increasingS*EVTThis implies that rotationally cold systems exhibitTROT.V]R,T energy transfer,whereas rotationally hot systemsexhibit V,R]R,T.It can be seen that the overall[S*E T islarger for larger which agrees with the hypothesis thatTROTthe external rotation is a facile CET path.This behaviour hasFig.8Rotational energy transfer for deactivation of vibrationallyexcited propane by rare gases for the HS model.Helium;Neon;+=Argon.>1390Phys.Chem.Chem.Phys.,2000,2,1385È1392。

Neutralino decay of MSSM neutral Higgs bosons

a r X i v :0803.4134v 1 [h e p -p h ] 28 M a r 2008Neutralino decay of MSSM neutral Higgs bosonsTarek IbrahimDepartment of Physics,Faculty of Science,Alexandria University,Egypt andDepartment of Physics,Northeastern University,Boston,MA 02115-5000,USA1AbstractWe compute the one loop corrected eﬀective Lagrangian for the neutralino-neutralino-neutral Higgs interactions χ0ℓχ0k H 0m .The analysis completes the previous analyseswhere similar corrections were computed for the ¯ffH0mcouplings,where f stands for Standard Model quarks and leptons and for the chargino-chargino-neutral Higgscouplings χ+l χ−k H 0m within the minimal supersymmetric standard model MSSM.The eﬀective one loop Lagrangian is then applied to the computation of the neu-tral Higgs decays.The sizes of the supersymmetric loop corrections of the neutralHiggs decay widths into χ0ℓχ0k (ℓ=1,2,3,4;k =1,2,3,4)are investigated and the supersymmetric loop correction is found to be in the range of ∼10%in sig-niﬁcant regions of the parameter space.By including the loop corrections of theother decay channels ¯bb ,¯t t ,¯ττ,¯c c ,and χ−i χ+j (i =1,2;j =1,2),the correc-tions to branching ratios for H 0m →χ0ℓχ0k can reach as high as 50%.The eﬀectsof CP phases on the branching ratio are also investigated.A discussion of theimplications of the analysis for colliders is given.1INTRODUCTIONThe Higgs couplings to matter and gaugeﬁelds are of current interest as they aﬀect diﬀerent phenomena which could be tested in low energy processes[1].Recently calculations of the supersymmetric one loop corrections to the Higgs boson cou-plings were given and their implications for the neutral Higgs boson decays into ¯bb,¯t t,¯ττ,¯c c andχ−χ+j were analyzed[2].These decays are of great importanceias they diﬀer from the Higgs decay predictions in the Higgs sector of the standard model.In this work we extend the analysis to include the loop corrections of the χ0ℓχ0k H0m couplings and the neutral Higgs decay into pairs of neutralinos.The com-plete analysis of the one loop corrected partial widths of the above channels allows one to investigate also the eﬀects of these corrections on the branching ratios of diﬀerent modes.In this paper we include the eﬀect of CP phases arising from the soft supersym-metric breaking parameters.It is well known that large CP phases would induce electric dipole moments of the fermions in the theory.However these large CP phases can be made compatible[3,4,5]with the severe experimental constraints that exist on the electric dipole moments of the electron[6],of the neutron[7], and of the Hg199[8].It is well known that if the phases are large they aﬀect a variety of low energy phenomena[9].Some works in this direction have included the eﬀects of CP phases on the neutral Higgs boson system.These phases induce mixings between the neutral CP even and the CP odd Higgs and can aﬀect the decay of the neutral and charged Higgs into diﬀerent modes[10].The current analysis of∆Lχ0χ0H0and neutral Higgs decay into neutralinos is based on the eﬀective Lagrangian method where the couplings of the electroweak eigen states H11and H22with neutralinos are radiatively corrected using the zero external momentum approximation.The same technique has been used in calcu-lating the eﬀective Lagrangian and decays of H0m into quarks and leptons[1,11,12] and into chargino pairs[2].It has been used also in the analysis of the eﬀective Lagrangian of charged Higgs with quarks[1,13]and their decays into¯t b andνττ[14]and into chargino+neutralino[15].The neutral Higgs decays into neutralinos have been investigated before in the CP conserving case[16,17].However,the analysis for the neutral Higgs decays into neutralinos,with one loop corrections, in the CP violating case where the neutral Higgs sector is modiﬁed in couplings, spectrum and mixings,does not exist.We evaluate the radiative corrections to the Higgs boson masses and mixngs by using the eﬀective potential approximation.We include the corrections from the top and bottom quarks and squarks[18],from the chargino,the W and the charged Higgs sector[19]and from the neutralino,Z boson,and the neutral Higgs bosons[20].It is important to notice that the corrections to the Higgs eﬀective potential from the diﬀerent sectors mentioned above are all one-loop corrections.The corrections of the interaction∆Lχ0χ0H0to be considered in this work are all one-loop level ones.So the analysis presented here is a consistent one loop study.The outline of the rest of the paper is as follows:In Sec.2we compute theeﬀective Lagrangian for theχ0ℓχ0k H0m interaction.In Sec.3we give an analysis of the decay widths of the neutral Higgs bosons into neutralinos using the eﬀective Lagrangian.In Sec.4we give a numerical analysis of the size of the loop eﬀects on the partial decay widths and on the branching ratios.In Sec.5we discuss the implications of the corrections considered here,in the environment of the Large Hadron Collider LHC.Conclusions are given in Sec.6.2LOOP CORRECTIONS TO NEUTRAL HIGGS COUPLINGSThe tree-level Lagrangian forχ0ℓχ0k H0interaction isL=θkℓχ0k P Rχ0ℓH22+H.c.,(1) where H11and H22are the neutral states of the two Higgs isodoublets in the minimal supersymmetric standard model(MSSM),i.e.,(H1)= H11H21 ,(H2)= H12H22 (2) andθkℓ=−gQ∗′kℓandτkℓ=gS′ℓk whereQ′ij=12[X∗3i(X∗2j−tanθW X∗1j)](3)S′ij=12[X∗4j(X∗2i−tanθW X∗1i)](4)The matrix elements X are deﬁned asX T Mχ0X=diag(mχ01,mχ02,mχ03,mχ04)(5)where Mχ0is the4×4neutralino mass matrix.The loop corrections produce shifts in the couplings of Eq.(1)and the eﬀective Lagrangian with loop corrected couplings is given byL eff=(θkℓ+δθkℓ)χ0k P Lχ0ℓH22+(τkℓ+δτkℓ)χ0k P Rχ0ℓH1∗1+H.c.(6)In this work we calculate the loop correctionsδθkℓ,∆τkℓ,∆θkℓandδτkℓusing the zero external momentum approximation.2.1Loop analysis ofδθkℓand∆τkℓContributions toδθkℓand∆τkℓarise from the fourteen loop diagram of Fig. 1. We discuss now in detail the contribution of each of these diagrams.The basic integral that enters in the loop analysis isJ= d4ℓ(ℓ2−m21+iǫ)(ℓ2−m22+iǫ)(ℓ2−m23+iǫ)(7) where m1,m2and m3are the masses of the particles running inside the loops. This integral givesJ=i(m21−m23)1(m21−m22)×[m22m23ln(m22m21)+m21m22ln(m21(4π)21m21)+m21−m23](10)We begin with the loop diagram of Fig.1(i),part(a),which contributes the following toδθkℓand∆τkℓ:δθ(1)kℓ=−2i=12j=1m t8π2F∗ji(βtℓD t1j+α∗tℓD t2j)×(α∗tk D∗t1i−γ∗tk D∗t2i)f(m2t,m2˜t i,m2˜t j)(11)where F ji is given byF ji=−gM Z2cosθW((13sin2θW)D∗t1j D t1i+2√2m W sinββtk=eQ t X′∗1k+gcosθWX′2k(13)where X′’s are given byX′1k=X1k cosθW+X2k sinθWX′2k=−X1k sinθW+X2k cosθW(14) The matrix elements D q are diagonalizing the squark mass2matrix as followsD+q M2˜q D q=diag(m2˜q1,m2˜q2)(15)Next for the loop Fig.1(i),part(b),weﬁndδθ(2)kℓ=−2i=12j=1m b8π2H∗ij(βbℓD b1j+α∗bℓD b2j)×(α∗bk D∗b1i−γ∗bk D∗b2i)f(m2b,m2˜b i,m2˜b j)(16) and H ij is given byH ij=−gM Z2cosθW((−13sin2θW)D∗b1i D b1j−1√√For the loop of Fig.1(ii),part(b),weﬁndδθ(4)kℓ=0∆τ(4)kℓ=2j=1h b m2b√2π2cos2θWQ′∗ij R′′′kj L′′′iℓ×mχ0i mχ0j f(m2χ0i,m2χ0j,m2Z)∆τ(5)kℓ=0(21)where the couplings L′′′ij and R′′′ij are given byL′′′ij=−R′′′∗ij=−12X∗4i X4j(22)For loop of Fig.1(ii),part(d),weﬁndδθ(6)kℓ=4i=14j=13n=1g34√−2(Y m2−iY m3cosβ)(Y n2+iY n3cosβ)}mχ0i 4√16π2f(m2χ0i,m2H0m,m2H0n)(24)For loop of Fig.1(i),part(d),weﬁndδθ(8)kℓ=−2g3m Z cosβ2cos3θW4i=1R′′′ki L′′′iℓmχ0i√16π2f(m2χ0i,m2Z,m2Z)(25)For loop of Fig.1(ii),part(e),weﬁndδθ(9)kℓ=−2i=12j=1ǫkjǫ′∗ℓiφ∗ij cosβsinβmχ+i mχ+j√√√√2√16π2f(m2χ+i,m2H−,m2H−)∆τ(10)kℓ=gm W22i=1ǫ′kiǫ∗ℓi cos2βsinβ(1+2sin2β−cos2βtan2θW)×mχ+iFor loop of Fig.1(i),part(f),weﬁndδθ(11)kℓ=−2i=1g32m W cosβR ki L∗ℓimχ+i√4π2f(m2χ+i,m2W−,m2W−)(30)where L and R are deﬁned asL ij=−12X∗4i V∗j2+X∗2i V∗j1R ij=12X3i U j2+X2i U j1(31)For loop of Fig.1(ii),part(f),weﬁndδθ(12)kℓ=0∆τ(12)kℓ=2i=12j=1g2φ∗ij L kj R∗ℓimχ+imχ+j8π2(βτℓDτ1i+α∗τℓDτ2i)×(α∗τk D∗τ1i−γ∗τk D∗τ2i)f(m2˜τi,m2τ,m2τ)(33)wherehτ=gmτ2m W cosβ(34)For loop of Fig.1(i),part(g),weﬁndδθ(14)kℓ=−2i=12j=1mτ8π2H∗τji(βτℓDτ1i+α∗τℓDτ2i)×(α∗τk D∗τ1j−γ∗τk D∗τ2j)f(m2τ,m2˜τi,m2˜τj)(35)and Hτij is given byHτij=−gM Z2cosθW((−1√√The loop corrections forδθkℓand∆τkℓare given byδθkℓ=14 n=1δθ(n)kℓ∆τkℓ=14n=1∆τ(n)kℓ(37)2.2Loop analysis of∆θkℓandδτkℓWe do the same analysis of Figure2as for Figure1.We write down here theﬁnal results for both corrections from the fourteen loops together.The corrections are written in the same order of the loops in Figure2.∆θkℓ=−2i=12j=1m t8π2G ji(αbℓD b1j−γbℓD b2j)(β∗bk D∗b1i+αbk D∗b2i)f(m2b,m2˜b i,m2˜b j)+2j=1m2t h t4√16π2f(m2χ0i,m2H0m,m2H0n)−2g3m Z sinβ2cos3θW4i=1R′′′ki L′′′iℓmχ0i2√16π2f(m2χ+i,m2H−,m2H−)−2 i=1g32m W sinβR ki L∗ℓi mχ+i4π2f(m2χ+i,m2χ+j,m2W−)+0−2 i=12 j=1mτThe correctionsδτkℓare given byδτkℓ=−2i=12j=1m t8π2G ji(βbℓD b1j+α∗bℓD b2j)(α∗bk D∗b1i−γ∗bk D∗b2i)f(m2b,m2˜b i,m2˜b j)+0+0 +4i=14j=1g34π2S′ij{Q′ℓi(Y n1+iY n3sinβ)−S′ℓi(Y n2+iY n3cosβ)}{Q′jk(Y n1+iY n3sinβ)−S′jk(Y n2+iY n3cosβ)}mχ0i mχ0j f(m2χ0i,m2χ0j,m2H0n)+g3m Z cosβ2cosθW4i=13n=13m=1{Q′ℓi(Y n1+iY n3sinβ)−S′ℓi(Y n2+iY n3cosβ)}{Q′ik(Y m1+iY m3sinβ)−S′ik(Y m2+iY m3cosβ)}{tanβ(Y n2−iY n3cosβ)(3Y m2+iY m3cosβ)−4Y n1(Y m2−iY m3cosβ)−2tanβ(Y m1−iY m3sinβ)(Y n1+iY n3sinβ)}mχ0i√16π2f(m2χ0i,m2Z,m2Z)−2 i=12 j=1ǫ′kjǫ∗ℓiψij cosβsinβmχ+i mχ+j2√16π2f(m2χ+i,m2H−,m2H−)−2 i=1g32m W sinβR∗ℓi L ki mχ+i8π2Gτij(βτℓDτ1i+α∗τℓDτ2i)(α∗τk D∗τ1j−γ∗τk D∗τ2j)f(m2τ,m2˜τi,m2˜τj)(39) where G ij,E ij,h t,ψij and Gτij are given byG ij=gM Z2cosθW((−13sin2θW)D∗b1i D b1j−1√√2−23sin2θW D∗t2i D t2j)sinβ−gm2t2m W sinβ(D∗t1i D t1j+D∗t2i D t2j)−gm t A t2m W sinβD∗t2i D t2jh t=gm t2m W sinβ,ψjk=−gU k1V j2(40)Gτij=gM Z2cosθW((−1√χ0k(αmS kℓ+γ5αmP kℓ)χ0ℓ+H.c(42)whereαmS kℓ=12{(Y m1−iY m3sinβ)(θkℓ+δθkℓ+∆τkℓ)+(Y m2+iY m3cosβ)(τkℓ+∆θkℓ+δτkℓ)}(43)and whereαmP kℓ=12{(Y m2+iY m3cosβ)(τkℓ+δτkℓ−∆θkℓ)+(Y m1−iY m3sinβ)(−θkℓ+∆τkℓ−δθkℓ)}(44)Next we discuss the implications of the above result for the decay of the neutral Higgs.The partial width of the decay H0m→χ0kχ0ℓis given byΓmkℓ(H0m→χ0kχ0ℓ)=1[(m2χ0ℓ+m2χ0k−M2H0m)2−4m2χ0k m2χ0ℓ] {12(|αmS kℓ|2−|αmP kℓ|2)(2mχ0k mχ0ℓ)}(45)The neutral Higgs bosons can decay into diﬀerent modes.However,there are important channels for this decay to occur,¯bb,¯t t,¯s s,¯c c,¯ττ,χ+iχ−j andχ0iχ0j. The other channels of neutral Higgs decay are the decaying modes into the other fermions of the SM,squarks,sleptons,other Higgs bosons,W and Z boson pairs, one Higgs and a vector boson,γγpairs andﬁnally into the gluonic decay i.e, H0m→gg.The lightest SM fermions channels could be ignored for the smallness of their couplings.We choose the region in the parameter space where we canignore the other channels which either are not allowed kinematically or suppressedby their couplings.Thus in this work,squarks and sleptons are too heavy to be relevant in neutral Higgs decay.The neutral Higgs decays into non-supersymmetric ﬁnal states that involve gauge bosons and/or other Higgs bosons are ignored as well.In the region of large tanβ,these decays are very small and can be neglected asﬁnal states[21].We calculate the radiative corrected partial decay widths of the important channels mentioned above.In the case of CP violating case under investigation we use the analysis of[2],for the radiatively correctedΓof neutral Higgs into quarks,leptons and chargino pairs.For the radiatively corrected decay width into neutralino we use the current analysis.We deﬁneΓ(H0m→χ0kχ0ℓ)−Γ0(H0m→χ0kχ0ℓ)∆Γmkℓ=Br0(H0m→χ0kχ0ℓ)(47) where theﬁrst term in the numerator is the branching ratio including the full loop corrections and the second term is the branching ratio evaluated at the tree level. The analysis of this section is utilized in Sec.(4)where we give a numerical analysis of the size of the loop eﬀects and discuss the eﬀect of the loop corrections on the branching ratios.4NUMERICAL ANALYSISIn this section we investigate the size of the loop corrections on the partial decay widths and the branching ratios of the neutral Higgs bosons decay into neutralinos. The analysis of Sec.2and Sec.3is quite general and valid for the minimal supersymmetric standard model.For the sake of numerical analysis we will limit the parameter space by working within the framework of the SUGRA model[22]. Speciﬁcally we will work within the framework of the the extended nonuniversal mSUGRA model including CP phases.We take as our parameter space at the grand uniﬁcation scale to be the following:the universal scalar mass m0,the universal gaugino mass m1/2,the universal trilinear coupling|A0|,the ratio ofthe Higgs vacuum expectation values tanβ=<H2>/<H1>where H2gives mass to the up quarks and H1gives mass to the down quarks and the leptons.In addition,we take for CP phases the following:the phaseθµof the Higgs mixing parameterµ,the phaseαAof the trilinear coupling A0and the phasesξi(i= 1,2,3)of the SU(3)C,SU(2)L and U(1)Y gaugino masses.In this analysis the electroweak symmetry is broken by radiative eﬀects which allows one to determine the magnitude ofµbyﬁxing M Z.In the analysis we use one loop renormalization group(RGEs)equations for the evolution of the soft SUSY breaking parameters and for the parameterµ,and two loop RGEs for the gauge and Yukawa couplings. In the numerical analysis we compute the loop corrections and also analyze their dependence on the phases.The masses of particles involved in the analysis areordered as follows:for neutralinos mχ01<mχ02<mχ03<mχ04and for the neutralHiggs(m H1,m H2,m H3)→(m H,m h,m A)in the limit of no CP mixing where m His the heavy CP even Higgs,m h is the light CP even Higgs,and m A is the CP odd Higgs.Weﬁrst discuss the size of the loop corrections of the partial decay width deﬁned in Eq.(46).As was mentioned before,the loop corrected partial widths of the neutral Higgs decay into neutralinos have been investigated in the absence of CP violating phases[16,17].The magnitude of the corrections in these analyses is of the order of∼10%of the tree level value.The current analysis supports this result.In Fig.(3),we give a plot of∆Γ113as functions of tanβfor the speciﬁc set of inputs given in theﬁgure caption.We notice that the partial decay width gets a change of2∼12%of its tree level value.The role played by tanβin this analysis is complicated and is coming from diﬀerent regions in the analysis.First of all,it aﬀects the spectrum and couplings of neutral Higgs with neutralinos at tree level through the diagonalizing matrices of both neutral Higgs bosons and neutralino. We alsoﬁnd that tanβis playing a crucial rule at the one loop level analysis.The neutral Higgs mass2matrix receives corrections from the stop,sbottom,chargino and neutralino sectors and these corrections are sensitive to the value of tanβ.We also see the explicit and implicit eﬀects of tanβin the loop corrected couplings of neutralinos with neutral Higgs presented in Eq.(43)and Eq.(44)forαmS kℓand αmP kℓrespectively.We also notice that the CP violating phaseθµcan aﬀect the value of this change.This eﬀect has not been discussed in the previous analyses because these analyses have been carried out for the CP conservation case.We can also trace down the role played by the phaseθµin the analysis.We can seethat,θµaﬀects the tree level of analysis through its presence in the neutralinomass matrix and at loop level where it can produce mixing in the neutral Higgssector and also aﬀects the radiative corrected couplings between the neutralinosand neutral Higgs bosons.In the limit where CP violating phases are set to zeroand by using the same inputs of[16],we were able to have a fair agreement withwith their Figs.2-4,6.In the work of[17]only8out of28diagrams of the currentanalysis are calculated.By including these diagrams only in the comparison,ouranalysis is in fair agreement with their Figs.2,3,5,7and9for their inputs.Now we compute the loop correction eﬀects of the branching ratios of theneutral Higgs decays into neutralinos.The branching ratio of a decay mode is theratio between the partial decay rate of this mode and the total decay rate for allpossible channels.In the parameter space we are investigating,these channels aredecays into charginos,heavy quarks,taus,and neutralinos.In Figs.(4)and(5)wegive a plot of∆Br1→χ02χ02and∆Br3→χ01χ03as functions of m1/2for the speciﬁc set of inputs given in the captions of theseﬁgures.Weﬁrst notice that the loopcorrection of the branching ratios can reach as high as35%of the tree level value forthe case of H1boson and as high as55%for the case of H3boson.We also can seethe eﬀect of the CP violating phaseθµin these twoﬁgures.In the branching ratiostudy,this CP violating phase can aﬀect many decay modes of neutral Higgs intodiﬀerent quarks and leptons via radiative corrections of these modes.It can aﬀectboth tree and loop level of the analysis in the cases of decays into charginos andneutralinos due to the presence of the parameterµin the chargino,neutralino andsfermion mass matrices.The role played by the parameter m1/2is mainly throughthe chargino and neutralino mass matrices since the gaugino masses˜m1and˜m2are originating from m1/2at GUT scale.The parameter m1/2is also aﬀecting theevolution of the other soft supersymmetry breaking parameters like the trilinearcouplings A f from GUT scale down to the electroweak scale.In Figs.(6)and(7)we give a plot of∆Br1→χ01χ02and∆Br3→χ02χ02as functions ofθµfor the speciﬁc set of inputs given in the captions of theseﬁgures. We notice in these twoﬁgures that the loop corrections of the branching ratios for these modes can reach as high as35%of the tree level value.We see here again the eﬀect of the CP violating phaseθµon the corrections of branching ratio for these decay modes.In the case of H3decay,one can see thatθµaﬀects not only the magnitude of∆Br3→χ02χ02but also its sign depending onθµ.The analysis of these twoﬁgures also shows the importance of the parameter tanβin the loopcorrections for these the branching ratios.This parameter is important at tree level through neutral Higgs couplings with diﬀerent quarks and leptons and through the diagonalization of the neutral Higgs,chargino and neutralino mass matrices.At one loop level,it aﬀects both neutral Higgs spectrum and couplings with diﬀerent ﬁelds.In Figs.(8)and(9)we give a plot of∆Br1→χ01χ03and∆Br3→χ01χ02as functions ofα0for the speciﬁc set of inputs given in the captions of theseﬁgures. We notice in these twoﬁgures that the loop correction of the branching ratios for these modes can reach as high as40%of the tree level.The eﬀects of the magnitude of|A0|and its CP violating phase are clear in both modes and could be understood form the eﬀect of the trilinear couplings on the squark and slepton mass2matrices in the stop case through A t,in the sbottom case through A b,in the stau case through the parameter Aτ.In Figs.(10)and(11)we give a plot of∆Br1→χ01χ03and∆Br3→χ01χ02as functions ofξ2for the speciﬁc set of inputs given in the captions of theseﬁgures. Here weﬁnd thatξ2phase has a smaller eﬀect on the loop corrections.The reason for this could be understood qualitatively from the fact that the chargino and neutralino loops that carry the eﬀect of this phase are correcting the tree level of the analysis less than that of the other loops in this region of the parameter space. 5RELEV ANCE OF RESULTS AT LHCThe production of the MSSM Higgs particles at the Large Hadron Collider LHC √(the lightest neutralinoχ01,assumed to be the lightest supersymmetric particle(the LSP)and carries missing energy.The two fermions will most often be quarks, leading to two jets and missing E T in theﬁnal state.To obtain a clean signature, one should only focus on the case where the two SM fermions are leptons.Thus the process under consideration isH1,H3→χ02χ02→4ℓ±+E miss T(ℓ=e,µ)(48) The above process provides a clear signature containing two pairs of leptons with opposite sign and sameﬂavor,in addition to a substantial amount of missing energy due to the escaping lightest neutralino.In their analysis,the authors of [25]show that one can distinguish this signal from the(mainly SUSY)background for values of tanβ=5−40.Their analysis for the decay of Heavy Higgs bosons into neutralinos is based on the HDECAY package[26].This analysis does not take into account the loop corrections of the neutral Higgs vertices with neutralinos and is carried out in the CP conserving scenario.They also study the decay of neutralinos into leptons in the limit of vanishing CP phases.In the case(2)of theﬁrst paper of[25],the author used the inputs M2=180,M1=100,µ=500, m˜=250and M˜q,˜g=1000GeV.It is shown in Fig.(6)of[25],for integrated ℓluminosity of100fb−1,that the expectation to discover the Higgs bosons with a clear and visible signature over the background occurs for m A=380GeV and tanβ=10.Now by putting these parameters by hand in our analysis with setting all the CP phases to zero,we get for∆Br322,deﬁned by Eq.(47),the value of ∼−25%.So the tree value of the branching ratio that was used in the analysis of [25]would have been suppressed by radiative corrections of the above percentage and that would of course change the output of the analysis.In the analysis of[27],the authors investigate the same four-lepton signal with missing energy at LHC.In their top Fig.3,they use for their inputs,tanβ=20, M1=5the branching ratios of neutral Higgs into the neutralino and thus the inclusion of these corrections in their analysis would enhance the event number at LHC.We note further,that the couplings of the Higgs bosons to the SM particles and their supersymmetric partners are modiﬁed by the CP violation phases.The Higgs boson masses and their CP properties are modiﬁed as well from those predicted in the CP conserving case.Thus the cross sections for MSSM Higgs particles production and their decay signatures could also be much more complicated than in the CP preserving scenario.So an analysis that considers the Higgs bosons production and their detection in the environment of LHC with CP violating phases would be much more involved and is beyond the scope of this paper.6CONCLUSIONIn this paper we have worked out the loop corrections toχ0kχ0ℓH0m couplings within MSSM.This analysis extends previous analysis of supersymmetric loop corrections to the couplings of neutral Higgs bosons with charginos and with standard model fermions within minimal supersymmetric standard models including the full set of allowed CP phases.The result of the analysis is then applied to the computation of the decay of the neutral Higgs bosons to neutralino pairs.In the absence of loop corrections,the lightest Higgs boson mass is less than M Z and including these corrections can lift the lightest Higgs mass above M Z.In the CP invariance scenario the spectrum of the neutral Higgs sector consists of two CP even Higgs bosons and one CP odd Higgs boson.With the inclusion of CP phases,the Higgs boson mass eigenstates are no longer CP even and CP odd states 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[arXiv:hep-ph/0111245].J.Ellis,J.S.Lee and A.Pilaftsis,arXiv:hep-ph/0404167,E.Chrisova,H.Eberl,W.Majerotto,and S.Kraml,J.High Energy Phys.12(2002)021;E.Christova,H.Eberl,W.Majerotto,and S.Kraml,Nucl.Phys.B639,263(2002);647,359(E)(2002)T.Ibrahim,P.Nath,Phys and A.Psinas.Rev.D70,035006(2004).D.A.Demir,Phys.Rev.D60,055006(1999);T.Ibrahim and P.Nath,Phys.Rev.D63,035009 (2001);Phys.Rev.D66,015005(2002).[11]K.S.Babu and C.F.Kolda,Phys.Lett.B451,77,1999.[12]T.Ibrahim,P.Nath,Phys.Rev.D68,015008(2003).[13]D.A.Demir and K.A.Olive,Phs.Rev.D65,034007(2002);G.Degrassi,P.Gambino,and G.F.Giudice,J.High Energy Phys.12,009(2000);G.Be-langer,F.Boudjema,A.Pukhov,and A.Semenov,mun.149,103(2002).[14]T.Ibrahim,P.Nath,Phys.Rev.D69,075001(2004)[15]T.Ibrahim,P.Nath and A.Psinas,Phys.Rev.D70,035006(2004).[16]H.Eberl,M.Kncel,W.Majerotto,Y.Yamada,Nucl.Phys.B625(2002)372;H.Eberl,hep-ph/0410209.[17]Z.Ren-You,M.Wen-Gan,ng-Hui and 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美国EPA标准—8325

CD-ROM 8325 - 1Revision 0December 1996METHOD 8325SOLVENT EXTRACTABLE NONVOLATILE COMPOUNDS BY HIGH PERFORMANCE LIQUID CHROMATOGRAPHY/PARTICLE BEAM/MASS SPECTROMETRY (HPLC/PB/MS)1.0SCOPE AND APPLICATION1.1This method describes the use of high performance liquid chromatography (HPLC),coupled with particle beam (PB) mass spectrometry (MS), for the determination of benzidines and nitrogen-containing pesticides in water and wastewater. The following compounds can be determined by this method:Compound CAS No.aBenzidine 92-87-5Benzoylprop ethyl 33878-50-1Carbaryl 63-25-2o-Chlorophenyl thiourea 5344-82-13,3'-Dichlorobenzidine 91-94-13,3'-Dimethoxybenzidine 119-90-43,3'-Dimethylbenzidine 612-82-8Diuron 330-54-1Linuron (Lorox)330-55-2Monuron 150-68-5Rotenone 83-79-4Siduron1982-49-6Chemical Abstract Service Registry Numbera 1.2The method also may be appropriate for the analysis of benzidines and nitrogen-containing pesticides in non-aqueous matrices. The method may be applicable to other compounds that can be extracted from a sample with methylene chloride and are amenable to separation on a reverse phase liquid chromatography column and transferable to the mass spectrometer with a particle beam interface.1.3Preliminary investigation indicates that the following compounds also may be amenable to this method: Aldicarb sulfone, Carbofuran, Methiocarb, Methomyl (Lannate), Mexacarbate (Zectran), and N-(1-Naphthyl)thiourea. Ethylene thiourea and o-Chlorophenyl thiourea have been successfully analyzed by HPLC/PB/MS, but have not been successfully extracted from a water matrix.1.4Tables 4 - 6 present method detection limits (MDLs) for the target compounds, ranging from 2 to 25 µg/L. The MDLs are compound- and matrix-dependent.1.5This method is restricted to use by, or under the supervision of, analysts experienced in the use of HPLC and skilled in the interpretation of particle beam mass spectrometry. Each analyst must demonstrate the ability to generate acceptable results with this method.2.0SUMMARY OF METHOD2.1The target compounds for this method must be extracted from the sample matrix prior to analysis.2.1.1Benzidines and nitrogen-containing pesticides are extracted from aqueousmatrices at a neutral pH with methylene chloride, using a separatory funnel (Method 3510), a continuous liquid-liquid extractor (Method 3520), or other suitable technique.2.1.2Solid samples are extracted using Methods 3540 (Soxhlet), 3541 (AutomatedSoxhlet), 3550 (Ultrasonic extraction), or other suitable technique.2.2An aliquot of the sample extract is introduced into the HPLC instrument and a gradient elution program is used to chromatographically separate the target analytes, using reverse-phase liquid chromatography.2.3Once separated, the analytes are transferred to the mass spectrometer via a particle beam HPLC/MS interface. Quantitation is performed using an external standard approach.2.4An optional internal standard quantitation procedure is included for samples which contain coeluting compounds or where matrix interferences preclude the use of the external standard procedure.2.5The use of ultraviolet/visible (UV/VIS) detection is an appropriate option for the analysis of routine samples, whose general composition has been previously determined.3.0INTERFERENCES3.1Refer to Methods 3500 and 8000 for general discussions of interferences with the sample extraction and chromatographic separation procedures.3.2Although this method relies on mass spectrometric detection, which can distinguish between chromatographically co-eluting compounds on the basis of their masses, co-elution of two or more compounds will adversely affect method performance. When two compounds coelute, the transport efficiency of both compounds through the particle beam interface generally improves, and the ion abundances observed in the mass spectrometer increase. The degree of signal enhancement by coelution is compound-dependent.3.2.1This coelution effect invalidates the calibration curve and, if not recognized, willresult in incorrect quantitative measurements. Procedures are given in this method to check for co-eluting compounds, and must be followed to preclude inaccurate measurements.3.2.2An optional internal standard calibration procedure has been included for use ininstances of severe co-elution or matrix interferences.3.3 A major source of potential contamination is HPLC columns which may contain silicon compounds and other contaminants that could prevent the determination of method analytes. Generally, contaminants will be leached from the columns into mobile phase and produce a variable background. Figure 1 shows unacceptable background contamination from a column with stationary phase bleed.CD-ROM8325 - 2Revision 0December 1996CD-ROM 8325 - 3Revision 0December 19963.4Contamination may occur when a sample containing low analyte concentrations is analyzed immediately after a sample containing relatively high analyte concentrations. After analysis of a sample containing high analyte concentrations, one or more method blanks should be analyzed.Normally, with HPLC, this is not a problem unless the sample concentrations are at the percent level.4.0APPARATUS AND MATERIALS4.1High performance liquid chromatograph (HPLC) - An analytical system with programmable solvent delivery system and all necessary accessories including 5 µL injection loop,analytical columns, purging gases, etc. The solvent delivery system must be capable, at a minimum,of handling a binary solvent system, and must be able to accurately deliver flow rates between 0.20- 0.40 mL/min. Pulse dampening is recommended, but not required. The chromatographic system must be able to be interfaced with a mass spectrometer (MS). An autoinjector is recommended and should be capable of accurately delivering 1 - 10 µL injections without affecting the chromatography.4.1.1HPLC Columns - An analytical column is needed, and a guard column is highlyrecommended.4.1.1.1Analytical Column - Reverse phase column, C chemically bonded to184-10 µm silica particles, 150 - 200 mm x 2 mm, (Waters C-18 Novapak or equivalent).Residual acidic sites should be blocked (endcapped) with methyl or other non-polargroups and the stationary phase must be bonded to the solid support to minimize columnbleed. Select a column that exhibits minimal bleeding. New columns must beconditioned overnight before use by pumping a 75 - 100% v/v acetonitrile:water solutionthrough the column at a rate of about 0.05 mL/min. Other packings and column sizesmay be used if appropriate performance can be achieved.4.1.1.2Guard Column - Packing similar to that used in analytical column.4.1.2HPLC/MS interface - The particle beam HPLC/MS interface must reduce the ionsource pressure to a level compatible with the generation of classical electron ionization (EI)mass spectra, i.e., about 1 x 10 - 1 x 10Torr, while delivering sufficient quantities of analytes -4 -6to the conventional EI source to meet sensitivity, accuracy, and precision requirements. The concentrations of background components with masses greater than 62 Daltons should be reduced to levels that do not produce ions greater than a relative abundance of 10% in the mass spectra of the analytes.4.2Mass spectrometer system - The mass spectrometer must be capable of electron ionization at a nominal electron energy of 70 eV. The spectrometer should be capable of scanning from 45 to 500 amu in 1.5 seconds or less (including scan overhead). The spectrometer should produce a mass spectrum that meets the criteria in Table 1 when 500 ng or less of DFTPPO are introduced into the HPLC.4.3Data system - A computer system must be interfaced to the mass spectrometer, and must be capable of the continuous acquisition and storage on machine-readable media of all mass spectra obtained throughout the duration of the chromatographic program. The computer software must be capable of searching any HPLC/MS data file for ions of a specified mass and plotting such abundance data versus time or scan number.4.4Volumetric flasks - Class A, in various sizes, for preparation of standards.CD-ROM 8325 - 4Revision 0December 19964.5Vials - 10-mL amber glass vials with polytetrafluororethylene (PTFE)-lined screw caps or crimp tops.4.6 Analytical balance - capable of weighing 0.0001 g.4.7Extract filtration apparatus4.7.1Syringe - 10-mL, with Luer-Lok fitting.4.7.2Syringe filter assembly, disposable - 0.45 µm pore size PTFE filter in filterassembly with Luer-Lok fitting (Gelman Acrodisc, or equivalent).5.0REAGENTS5.1Reagent grade chemicals shall be used in all tests. Unless otherwise indicated, it is intended that all reagents shall conform to the specifications of the Committee on Analytical Reagents of the American Chemical Society, where such specifications are available. Other grades may be used, provided it is first ascertained that the reagent is of sufficiently high purity to permit its use without lessening the accuracy of the determination.5.2Organic-free reagent water - All references to water in this method refer to organic-free reagent water, as defined in Chapter One.5.3Solvents - All solvents must be HPLC-grade or equivalent.5.3.1Acetonitrile, CH CN 35.3.2Methanol, CH OH 35.3.3Ammonium acetate, NH OOCCH , (0.01M in water).435.4Mobile phase - Two mobile phase solutions are needed, and are designated Solvent A and Solvent B. Degas both solvents in an ultrasonic bath under reduced pressure and maintain by purging with a low flow of helium.5.4.1Solvent A is a water:acetonitrile solution (75/25, v/v) containing ammoniumacetate at a concentration of 0.01M.5.4.2Solvent B is 100 % acetonitrile.5.5Stock standard solutions - Stock solutions may be prepared from pure standard materials or purchased as certified solutions. Commercially-prepared stock standards may be used at any concentration if they are certified by the manufacturer.5.5.1Prepare stock standard solutions by accurately weighing 0.0100 g of pure materialin a volumetric flask. Dilute to known volume in a volumetric flask. If compound purity is certified at 96% or greater, the weight may be used without correction to calculate the concentration of the stock standard. Commercially-prepared stock standards may be used at any concentration if they are certified by the manufacturer or by an independent source.CD-ROM 8325 - 5Revision 0December 19965.5.1.1Dissolve benzidines and nitrogen-containing pesticides in methanol,acetonitrile, or organic-free reagent water.5.5.1.2Certain analytes, such as 3,3'-dimethoxybenzidine, may require dilutionin 50% (v/v) acetonitrile:water or methanol:water solution.5.5.1.3Benzidines may be used for calibration purposes in the free base or acidchlorides forms. However, the concentration of the standard should be calculated as thefree base.5.5.2Transfer the stock standard solutions into amber bottles with PTFE-linedscrew-caps or crimp tops. Store at -10E C or less and protect from light. Stock standard solutions should be checked frequently for signs of degradation or evaporation, especially just prior to preparing calibration standards from them.5.6Surrogate spiking solution - The recommended surrogates are benzidine-D ,8caffeine-N , 3,3'-dichlorobenzidine-D , and bis(perfluorophenyl)-phenylphosphine oxide. Prepare 152 6a solution of the surrogates in methanol or acetonitrile at a concentration of 5 mg/mL of each. Other surrogates may be included in this solution as needed. (A 10-µL aliquot of this solution added to 1L of water gives a concentration of 50 µg/L of each surrogate). Store the surrogate spiking solution in an amber vial in a freezer at -10E C or less.5.7MS performance check solution - Prepare a 100 ng/µL solution of DFTPPO in acetonitrile.Store this solution in an amber vial in a freezer at -10E C or less.5.8Calibration solutionsThis method describes two types of calibration procedures that may be applied to the target compounds: external standard calibration, and internal standard calibration. Each procedure requires separate calibration standards. In addition, the performance characteristics of the HPLC/PB/MS system indicate that it may be necessary to employ a second order regression for calibration purposes, unless a very narrow calibration range is chosen. See Method 8000 for additional information on non-linear calibration techniques.5.8.1For external standard calibration, prepare calibration standards for all targetcompounds and surrogates in acetonitrile. DFTPPO may be added to one or more calibration solutions to verify MS tune (see Sec. 7.3). Store these solutions in amber vials at -10E C or less. Check these solutions at least quarterly for signs of deterioration.5.8.2Internal standard calibration requires the use of suitable internal standards (seeMethod 8000). Ideally, stable, isotopically-labeled, analogs of the target compounds should be used. These labeled compounds are included in the calibration standards and must also be added to each sample extract immediately prior to analysis. Prepare the calibration standards in a fashion similar to that for external standard calibration, but include each internal standard in each of the calibration standards.The concentration of the internal standards should be 50 - 100 times the lowestconcentration of the unlabeled target compounds. In addition, the concentration of the internal standards does not vary with the concentrations of the target compounds, but is held constant.Store these solutions in amber vials at -10E C or less. Check these solutions at least quarterly for signs of deterioration.5.9Internal standard spiking solution - This solution is required when internal standard quantitation is used. Prepare a solution containing each of the internal standards that will be used for quantitation of target compounds (see Sec. 5.8.2) in methanol. The concentration of this solution must be such that a 1-µL volume of the spiking solution added to a 1-mL final extract will result in a concentration of each internal standard that is equal to the concentration of the internal standard in the calibration standards in Sec. 5.8.2. Store this solution in an amber vial at -10E C or less. Check this solution at least quarterly for signs of deterioration. This solution is not necessary if only external standard calibration will be used.5.10Sodium chloride, NaCl - granular, used during sample extraction.6.0SAMPLE COLLECTION, PRESERVATION, AND HANDLING6.1See the introductory material to this chapter, Organic Analytes, Sec. 4.1.6.2Samples should be extracted within 7 days and analyzed within 30 days of extraction. Extracts should be stored in amber vials at -10E C or less.7.0PROCEDURE7.1Samples may be extracted by Method 3510 (separatory funnel), Method 3520 (continuous extractor), Method 3535 (solid-phrase extraction), or other appropriate technique. Prior to extraction, add a 10-µL aliquot of the surrogate spiking solution and 100 g of sodium chloride to the sample, and adjust the pH of the sample to 7.0. Samples of other matrices should be extracted by an appropriate sample preparation technique. The concentration of surrogates in the sample should be 20-50 times the method detection limit. Concentrate the extract to 1 mL, and exchange the solvent to methanol, following the procedures in the extraction method.7.2Establish chromatographic, particle beam interface, and mass spectrometer conditions, using the following conditions as guidance.Mobile phase purge:Helium at 30 mL/min, continuousMobile phase flow rate:0.25 - 0.3 mL/min through the columnGradient elution:Hold for 1 min at 25% acetonitrile (Solvent A), thenprogram linearly to about 70% acetonitrile (60%Solvent B) in 29 min. Start data acquisitionimmediately.Desolvation chamber temperature:45 - 80E CIon source temperature:250 - 290E CElectron energy:70 eVScan range:62 to 465 amu, at #1.5 sec/scan NOTE:Post-column addition is an option that improves system precision and, thereby, may improve sensitivity. Post-column flow rates depend on the requirements ofthe interface and may range from 0.1 to 0.7 mL/min of acetonitrile. Maintain aminimum of 30% acetonitrile in the interface.Analyte-specific chromatographic conditions are also shown in Table 2. (The particle beam interface conditions will depend on the type of nebulizer).CD-ROM8325 - 6Revision 0December 19967.2.1The analyst should follow the manufacturer's recommended conditions for theirinterface's optimum performance. The interface is usually optimized during initial installation by flow injection with caffeine or benzidine, and should utilize a mobile phase of acetonitrile/water (50/50, v/v). Major maintenance may require re-optimization.7.2.2Fine tune the interface by making a series of injections into the HPLC column ofa medium concentration calibration standard and adjusting the operating conditions (Sec. 7.2)until optimum sensitivity and precision are obtained for the maximum number of target compounds.7.3Initial calibration7.3.1Once the operating conditions have been established, calibrate the MS mass andabundance scales using DFTPPO to meet the recommended criteria in Table 1.7.3.2Inject a medium concentration standard containing DFTPPO, or separately injectinto the HPLC a 5-µL aliquot of the 100 ng/µL DFTPPO solution and acquire a mass spectrum.Use HPLC conditions that produce a narrow (at least ten scans per peak) symmetrical peak.If the spectrum does not meet the criteria (Table 1), the MS ion source must be retuned and adjusted to meet all criteria before proceeding with calibration. An average spectrum across the HPLC peak may be used to evaluate the performance of the system.Manual (not automated) ion source tuning procedures specified by the manufacturer should be employed during tuning. Mass calibration should be accomplished while an acetonitrile/water (50/50, v/v) mixture is pumped through the HPLC column and the optimized particle beam interface. For optimum long-term stability and precision, interface and ion source parameters should be set near the center of a broad signal plateau rather than at the peak of a sharp maximum (sharp maxima exhibit short-term variations with particle beam interfaces and gradient elution conditions).7.3.3System performance criteria for the medium concentration standard - Evaluatethe stored HPLC/MS data with the data system software and verify that the HPLC/PB/MS system meets the following performance criteria.7.3.3.1HPLC performance - 3,3'-dimethylbenzidine and3,3'-dimethoxybenzidine should be separated by a valley whose height is less than 25%of the average peak height of these two compounds. If the valley between them exceeds25%, modify the gradient. If this fails, the HPLC column requires maintenance. SeeSec. 7.4.6.7.3.3.2Peak tailing - Examine a total ion chromatogram and examine thedegree of peak tailing. Severe tailing indicates a major problem and systemmaintenance is required to correct the problem. See Sec. 7.4.67.3.3.3MS sensitivity - The signal-to-noise ratio for any compound's spectrumshould be at least 3:1.7.3.3.4Column bleed - Figure 1 shows an unacceptable chromatogram withcolumn bleed. Figure 2 shows an acceptable ion chromatogram. Figure 3 is the massspectrum of dimethyloctadecyl-silanol, a common stationary phase bleed product. Ifunacceptable column bleed is present, the column must be changed or conditioned toproduce an acceptable background.CD-ROM8325 - 7Revision 0December 19967.3.3.5Coeluting compounds - Compounds which coelute cannot be measuredaccurately because of carrier effects in the particle beam interface. Peaks must beexamined carefully for coeluting substances and if coeluting compounds are present atgreater than 10% of the concentration of the target compound, either conditions must beadjusted to resolve the components, or internal standard calibration must be used.7.3.4Once optimized, the same instrument operating conditions must be used for theanalysis of all calibration standards, samples, blanks, etc.7.3.5Once all the performance criteria are met, inject a 5-µL aliquot of each of theother calibration standards using the same HPLC/MS conditions.7.3.5.1The general method of calibration is a second order regression ofintegrated ion abundances of the quantitation ions (Table 3) as a function of amountinjected. For second order regression, a sufficient number of calibration points must beobtained to accurately determine the equation of the curve. (See Method 8000 for theappropriate number of standards to be employed for a non-linear calibration). Non-linearcalibration models can be applied to either the external standard or the internal standardcalibration approaches described here.7.3.5.2For some analytes the instrument response may be linear over a narrowconcentration range. In these instances, an average calibration factor (externalstandard) or average response factor (internal standard) may be employed for samplequantitation (see Method 8000).7.3.6If a linear calibration model is used, calculate the mean calibration factor orresponse factor for each analyte, including the surrogates, as described in Method 8000.Calculate the standard deviation (SD) and the relative standard deviation (RSD) as well. The RSD of an analyte or surrogate must be less than or equal to 20%, if the linear model is to be applied. Otherwise, proceed as described in Method 8000.7.4Calibration verificationPrior to sample analysis, verify the MS tune and initial calibration at the beginning of each 8-hour analysis shift using the following procedure:7.4.1Inject a 5-µL aliquot of the DFTPPO solution or a mid-level calibration standardcontaining 500 ng of DFTPPO, and acquire a mass spectrum that includes data for m/z 62-465. If the spectrum does not meet the criteria in Table 1, the MS must be retuned to meet the criteria before proceeding with the continuing calibration check.7.4.2Inject a 5-µL aliquot of a medium concentration calibration solution and analyzewith the same conditions used during the initial calibration.7.4.3Demonstrate acceptable performance for the criteria shown in Sec. 7.3.3.7.4.4Using the initial calibration (either linear or non-linear, external standard or internalstandard), calculate the concentrations in the medium concentration calibration solution and compare the results to the known values in the calibration solution. If calculated concentrations deviate by more than 20% from known values, adjust the instrument and inject the standard again. If the calibration cannot be verified with the second injection, then a new CD-ROM8325 - 8Revision 0December 1996initial calibration must be performed after taking corrective actions such as those described in Sec. 7.9.7.5Sample Analysis7.5.1The column should be conditioned overnight before each use by pumping aacetonitrile:water (70% v/v) solution through it at a rate of about 0.05 mL/min.7.5.2Filter the extract through a 0.45 µm filter. If internal standard calibration isemployed, add 10 µL of the internal standard spiking solution to the 1-mL final extract immediately before injection.7.5.3Analyze a 5-µL aliquot of the extract, using the operating conditions establishedin Secs. 7.2 and 7.3.7.6Qualitative identificationThe qualitative identification of compounds determined by this method is based on retention time and on comparison of the sample mass spectrum, after background correction, with characteristic ions in a reference mass spectrum. The reference mass spectrum must be generated by the laboratory using the conditions of this method. The characteristic ions from the reference mass spectrum are defined as the three ions of greatest relative intensity, or any ions over 30% relative intensity, if less than three such ions occur in the reference spectrum. Compounds are identified when the following criteria are met.7.6.1The intensities of the characteristic ions of a compound must maximize in thesame scan or within one scan of each other. Selection of a peak by a data system target compound search routine where the search is based on the presence of a target chromatographic peak containing ions specific for the target compound at a compound-specific retention time will be accepted as meeting this criterion.7.6.2The retention time of the sample component is within ± 10% of the retention timeof the standard.7.6.3The relative intensities of the characteristic ions agree within 20% of the relativeintensities of these ions in the reference spectrum. (Example: For an ion with an abundance of 50% in the reference spectrum, the corresponding abundance in a sample spectrum can range between 30% and 70%.)7.6.4Structural isomers that produce very similar mass spectra should be identified asindividual isomers if they have sufficiently different HPLC retention times. Sufficient GC resolution is achieved if the height of the valley between two isomer peaks is less than 25% of the sum of the two peak heights. Otherwise, structural isomers are identified as isomeric pairs.7.6.5Identification is hampered when sample components are not resolvedchromatographically and produce mass spectra containing ions contributed by more than one analyte. When HPLC peaks obviously represent more than one sample component (i.e., a broadened peak with shoulder(s) or a valley between two or more maxima), appropriate selection of analyte spectra and background spectra is important.CD-ROM8325 - 9Revision 0December 19967.6.6Examination of extracted ion current profiles of appropriate ions can aid in theselection of spectra, and in qualitative identification of compounds. When analytes coelute(i.e., only one chromatographic peak is apparent), the identification criteria may be met, buteach analyte spectrum will contain extraneous ions contributed by the coeluting compound.7.7Quantitative Analysis7.7.1Complete chromatographic resolution is necessary for accurate and precisemeasurements of analyte concentrations. Compounds which coelute cannot be measured accurately because of carrier effects in the particle beam interface. Peaks must be examined carefully for coeluting substances and if coeluting compounds are present at greater than 10% of the concentration of the target compound, either conditions must be adjusted to resolve the components, or the results for the target compound must be flagged as potentially positively biased.7.7.2Calculate the concentration of each analyte, using either the external standardor internal standard calibration. See Method 8000 for the specific equations to be employed for either the non-linear or linear calibration models.7.7.3If the response for any quantitation ion exceeds the initial calibration range of theHPLC/PB/MS system, the sample extract must be diluted and reanalyzed. When internal standard calibration is employed, additional internal standard must be added to the diluted extract to maintain the same concentration as in the calibration standards.7.8HPLC-UV/VIS Detection (optional)7.8.1Prepare calibration solutions as outlined in Sec. 5.8.7.8.2Inject 5 µL of each calibration solution onto the HPLC, using the chromatographicconditions outlined in Secs. 7.2.1 and 7.2.2. Integrate the area under the full chromatographic peak at the optimum wavelength (or at 230 nm if that option is not available) for each target compound at each concentration.7.8.3The retention time of the chromatographic peak is an important criterion foranalyte identification. Therefore, the ratio of the retention time of the sample analyte to the standard analyte should be 1.0 ± 0.1.7.8.4Calculate calibration factors or response factors as described in Method 8000,for either external standard or internal standard calibration, and evaluate the calibration linearity as described in Method 8000.7.8.5Verify the calibration at the beginning of each 8-hour analytical shift, as describedabove.7.8.6Once the calibration has been verified, inject a 5-µL aliquot of the sample extract,start the HPLC gradient elution, load and inject the sample aliquot, and begin data acquisition.Refer to Method 8000 for guidance on calculation of concentration.7.9Corrective ActionsWhen the initial calibration cannot be verified, one or more of the following corrective actions may be necessary.CD-ROM8325 - 10Revision 0December 1996。

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Created: 9/15/2006 13:44
Citation: W.-M. Yao et al. (Particle Data G (URL: )
Additional Z Bosons Z SM with standard couplings Mass m > 825 GeV, CL = 95% (p p direct search) Mass m > 1500 GeV, CL = 95% (electroweak ﬁt) ZLR of SU(2)L ×SU(2)R ×U(1) (with gL = gR ) Mass m > 630 GeV, CL = 95% (p p direct search) Mass m > 860 GeV, CL = 95% (electroweak ﬁt) Zχ of SO(10) → SU(5)×U(1)χ (with gχ =e /cosθW ) Mass m > 690 GeV, CL = 95% (p p direct search) Mass m > 781 GeV, CL = 95% (electroweak ﬁt) Zψ of E6 → SO(10)×U(1)ψ (with gψ =e /cosθW ) Mass m > 675 GeV, CL = 95% (p p direct search) Mass m > 366 GeV, CL = 95% (electroweak ﬁt) Zη of E6 → SU(3)×SU(2)×U(1)×U(1)η (with gη =e /cosθW ) Mass m > 720 GeV, CL = 95% (p p direct search) Mass m > 619 GeV, CL = 95% (electroweak ﬁt) Scalar Leptoquarks Mass m > 256 GeV, CL = 95% (1st generation, pair prod.) Mass m > 298 GeV, CL = 95% (1st gener., single prod.) Mass m > 202 GeV, CL = 95% (2nd gener., pair prod.) Mass m > 73 GeV, CL = 95% (2nd gener., single prod.) Mass m > 148 GeV, CL = 95% (3rd gener., pair prod.) (See the Particle Listings for assumptions on leptoquark quantum numbers and branching fractions.)

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