Observation of the Decay B0-rho+rho- and Measurement of the Branching Fraction and Polariza
Study of B - rho pi decays at Belle
a r X i v :h e p -e x /0207007v 1 1 J u l 2002BELLEBelle Prerpint 2002-18KEK Preprint 2002-59Study of B →ρπdecays at BelleBelle Collaboration A.Gordon u ,Y.Chao z ,K.Abe h ,K.Abe aq ,N.Abe at ,R.Abe ac ,T.Abe ar ,Byoung Sup Ahn o ,H.Aihara as ,M.Akatsu v ,Y.Asano ay ,T.Aso aw ,V.Aulchenko b ,T.Aushev ℓ,A.M.Bakich an ,Y.Ban ag ,A.Bay r ,I.Bedny b ,P.K.Behera az ,jak m ,A.Bondar b ,A.Bozek aa ,M.Braˇc ko t ,m ,T.E.Browder g ,B.C.K.Casey g ,M.-C.Chang z ,P.Chang z ,B.G.Cheon am ,R.Chistov ℓ,Y.Choi am ,Y.K.Choi am ,M.Danilov ℓ,L.Y.Dong j ,J.Dragic u ,A.Drutskoy ℓ,S.Eidelman b ,V.Eiges ℓ,Y.Enari v ,C.W.Everton u ,F.Fang g ,H.Fujii h ,C.Fukunaga au ,N.Gabyshev h ,A.Garmash b ,h ,T.Gershon h ,B.Golob s ,m ,R.Guo x ,J.Haba h ,T.Hara ae ,Y.Harada ac ,N.C.Hastings u ,H.Hayashii w ,M.Hazumi h ,E.M.Heenan u ,I.Higuchi ar ,T.Higuchi as ,L.Hinz r ,T.Hokuue v ,Y.Hoshi aq ,S.R.Hou z ,W.-S.Hou z ,S.-C.Hsu z ,H.-C.Huang z ,T.Igaki v ,Y.Igarashi h ,T.Iijima v ,K.Inami v ,A.Ishikawa v ,H.Ishino at ,R.Itoh h ,H.Iwasaki h ,Y.Iwasaki h ,H.K.Jang a ℓ,J.H.Kang bc ,J.S.Kang o ,N.Katayama h ,Y.Kawakami v ,N.Kawamura a ,T.Kawasaki ac ,H.Kichimi h ,D.W.Kim am ,Heejong Kim bc ,H.J.Kim bc ,H.O.Kim am ,Hyunwoo Kim o ,S.K.Kim a ℓ,T.H.Kim bc ,K.Kinoshita e ,S.Korpar t ,m ,P.Krokovny b ,R.Kulasiri e ,S.Kumar af ,A.Kuzmin b ,Y.-J.Kwon bc ,nge f ,ai ,G.Leder k ,S.H.Lee a ℓ,J.Li ak ,A.Limosani u ,D.Liventsevℓ,R.-S.Lu z,J.MacNaughton k,G.Majumder ao, F.Mandl k,D.Marlow ah,S.Matsumoto d,T.Matsumoto au,W.Mitaroffk,K.Miyabayashi w,Y.Miyabayashi v,H.Miyake ae,H.Miyata ac,G.R.Moloney u,T.Mori d,T.Nagamine ar,Y.Nagasaka i,T.Nakadaira as,E.Nakano ad, M.Nakao h,J.W.Nam am,Z.Natkaniec aa,K.Neichi aq, S.Nishida p,O.Nitoh av,S.Noguchi w,T.Nozaki h,S.Ogawa ap, T.Ohshima v,T.Okabe v,S.Okuno n,S.L.Olsen g,Y.Onuki ac, W.Ostrowicz aa,H.Ozaki h,P.Pakhlovℓ,H.Palka aa,C.W.Park o,H.Park q,L.S.Peak an,J.-P.Perroud r, M.Peters g,L.E.Piilonen ba,J.L.Rodriguez g,F.J.Ronga r, N.Root b,M.Rozanska aa,K.Rybicki aa,H.Sagawa h,S.Saitoh h,Y.Sakai h,M.Satapathy az,A.Satpathy h,e,O.Schneider r,S.Schrenk e,C.Schwanda h,k,S.Semenovℓ,K.Senyo v,R.Seuster g,M.E.Sevior u,H.Shibuya ap,V.Sidorov b,J.B.Singh af,S.Staniˇc ay,1,M.Stariˇc m,A.Sugi v, A.Sugiyama v,K.Sumisawa h,T.Sumiyoshi au,K.Suzuki h,S.Suzuki bb,S.Y.Suzuki h,T.Takahashi ad,F.Takasaki h, K.Tamai h,N.Tamura ac,J.Tanaka as,M.Tanaka h,G.N.Taylor u,Y.Teramoto ad,S.Tokuda v,S.N.Tovey u,T.Tsuboyama h,T.Tsukamoto h,S.Uehara h,K.Ueno z, Y.Unno c,S.Uno h,hiroda h,G.Varner g,K.E.Varvell an,C.C.Wang z,C.H.Wang y,J.G.Wang ba,M.-Z.Wang z,Y.Watanabe at,E.Won o,B.D.Yabsley ba,Y.Yamada h, A.Yamaguchi ar,Y.Yamashita ab,M.Yamauchi h,H.Yanai ac,P.Yeh z,Y.Yuan j,Y.Yusa ar,J.Zhang ay,Z.P.Zhang ak,Y.Zheng g,and D.ˇZontar aya Aomori University,Aomori,Japanb Budker Institute of Nuclear Physics,Novosibirsk,Russiac Chiba University,Chiba,Japand Chuo University,Tokyo,Japane University of Cincinnati,Cincinnati,OH,USAf University of Frankfurt,Frankfurt,Germanyg University of Hawaii,Honolulu,HI,USAh High Energy Accelerator Research Organization(KEK),Tsukuba,Japani Hiroshima Institute of Technology,Hiroshima,Japanj Institute of High Energy Physics,Chinese Academy of Sciences,Beijing,PRChinak Institute of High Energy Physics,Vienna,Austria ℓInstitute for Theoretical and Experimental Physics,Moscow,Russiam J.Stefan Institute,Ljubljana,Slovenian Kanagawa University,Yokohama,Japano Korea University,Seoul,South Koreap Kyoto University,Kyoto,Japanq Kyungpook National University,Taegu,South Korear Institut de Physique des Hautes´Energies,Universit´e de Lausanne,Lausanne,Switzerlands University of Ljubljana,Ljubljana,Sloveniat University of Maribor,Maribor,Sloveniau University of Melbourne,Victoria,Australiav Nagoya University,Nagoya,Japanw Nara Women’s University,Nara,Japanx National Kaohsiung Normal University,Kaohsiung,Taiwany National Lien-Ho Institute of Technology,Miao Li,Taiwanz National Taiwan University,Taipei,Taiwanaa H.Niewodniczanski Institute of Nuclear Physics,Krakow,Polandab Nihon Dental College,Niigata,Japanac Niigata University,Niigata,Japanad Osaka City University,Osaka,Japanae Osaka University,Osaka,Japanaf Panjab University,Chandigarh,Indiaag Peking University,Beijing,PR Chinaah Princeton University,Princeton,NJ,USAai RIKEN BNL Research Center,Brookhaven,NY,USAaj Saga University,Saga,Japanak University of Science and Technology of China,Hefei,PR ChinaaℓSeoul National University,Seoul,South Koreaam Sungkyunkwan University,Suwon,South Koreaan University of Sydney,Sydney,NSW,Australiaao Tata Institute of Fundamental Research,Bombay,Indiaap Toho University,Funabashi,Japanaq Tohoku Gakuin University,Tagajo,Japanar Tohoku University,Sendai,Japanas University of Tokyo,Tokyo,Japanat Tokyo Institute of Technology,Tokyo,Japanau Tokyo Metropolitan University,Tokyo,Japanav Tokyo University of Agriculture and Technology,Tokyo,Japanaw Toyama National College of Maritime Technology,Toyama,Japanay University of Tsukuba,Tsukuba,Japanaz Utkal University,Bhubaneswer,Indiaba Virginia Polytechnic Institute and State University,Blacksburg,VA,USAbb Yokkaichi University,Yokkaichi,Japanbc Yonsei University,Seoul,South KoreaB events collected with the Belle detector at KEKB.Thebranching fractions B(B+→ρ0π+)=(8.0+2.3+0.7−2.0−0.7)×10−6and B(B0→ρ±π∓)=(20.8+6.0+2.8−6.3−3.1)×10−6are obtained.In addition,a90%confidence level upper limitof B(B0→ρ0π0)<5.3×10−6is reported.Key words:ρπ,branching fractionPACS:13.25.hw,14.40.Nd1on leave from Nova Gorica Polytechnic,Nova Gorica,Sloveniamodes are examined.Here and throughout the text,inclusion of charge con-jugate modes is implied and for the neutral decay,B0→ρ±π∓,the notation implies a sum over both the modes.The data sample used in this analysis was taken by the Belle detector[9]at KEKB[10],an asymmetric storage ring that collides8GeV electrons against3.5GeV positrons.This produces Υ(4S)mesons that decay into B0B pairs.The Belle detector is a general purpose spectrometer based on a1.5T su-perconducting solenoid magnet.Charged particle tracking is achieved with a three-layer double-sided silicon vertex detector(SVD)surrounded by a central drift chamber(CDC)that consists of50layers segmented into6axial and5 stereo super-layers.The CDC covers the polar angle range between17◦and 150◦in the laboratory frame,which corresponds to92%of the full centre of mass(CM)frame solid angle.Together with the SVD,a transverse momen-tum resolution of(σp t/p t)2=(0.0019p t)2+(0.0030)2is achieved,where p t is in GeV/c.Charged hadron identification is provided by a combination of three devices: a system of1188aerogelˇCerenkov counters(ACC)covering the momentum range1–3.5GeV/c,a time-of-flight scintillation counter system(TOF)for track momenta below1.5GeV/c,and dE/dx information from the CDC for particles with very low or high rmation from these three devices is combined to give the likelihood of a particle being a kaon,L K,or pion, Lπ.Kaon-pion separation is then accomplished based on the likelihood ratio Lπ/(Lπ+L K).Particles with a likelihood ratio greater than0.6are identified as pions.The pion identification efficiencies are measured using a high momentum D∗+data sample,where D∗+→D0π+and D0→K−π+.With this pion selection criterion,the typical efficiency for identifying pions in the momentum region0.5GeV/c<p<4GeV/c is(88.5±0.1)%.By comparing the D∗+data sample with a Monte Carlo(MC)sample,the systematic error in the particle identification(PID)is estimated to be1.4%for the mode with three charged tracks and0.9%for the modes with two.Surrounding the charged PID devices is an electromagnetic calorimeter(ECL) consisting of8736CsI(Tl)crystals with a typical cross-section of5.5×5.5cm2 at the front surface and16.2X0in depth.The ECL provides a photon energy resolution of(σE/E)2=0.0132+(0.0007/E)2+(0.008/E1/4)2,where E is in GeV.Electron identification is achieved by using a combination of dE/dx measure-ments in the CDC,the response of the ACC and the position and shape of the electromagnetic shower from the ECL.Further information is obtained from the ratio of the total energy registered in the calorimeter to the particle momentum,E/p lab.Charged tracks are required to come from the interaction point and have transverse momenta above100MeV/c.Tracks consistent with being an elec-tron are rejected and the remaining tracks must satisfy the pion identification requirement.The performance of the charged track reconstruction is studied using high momentumη→γγandη→π+π−π0decays.Based on the relative yields between data and MC,we assign a systematic error of2%to the single track reconstruction efficiency.Neutral pion candidates are detected with the ECL via their decayπ0→γγ. Theπ0mass resolution,which is asymmetric and varies slowly with theπ0 energy,averages toσ=4.9MeV/c2.The neutral pion candidates are selected fromγγpairs by requiring that their invariant mass to be within3σof the nominalπ0mass.To reduce combinatorial background,a selection criteria is applied to the pho-ton energies and theπ0momenta.Photons in the barrel region are required to have energies over50MeV,while a100MeV requirement is made for photons in the end-cap region.Theπ0candidates are required to have a momentum greater than200MeV/c in the laboratory frame.Forπ0s from BE2beam−p2B and the energy difference∆E=E B−E beam.Here, p B and E B are the momentum and energy of a B candidate in the CM frame and E beam is the CM beam energy.An incorrect mass hypothesis for a pion or kaon produces a shift of about46MeV in∆E,providing extra discrimination between these particles.The width of the M bc distributions is primarily due to the beam energy spread and is well modelled with a Gaussian of width 3.3MeV/c2for the modes with a neutral pion and2.7MeV/c2for the mode without.The∆E distribution is found to be asymmetric with a small tail on the lower side for the modes with aπ0.This is due toγinteractions withmaterial in front of the calorimeter and shower leakage out of the calorimeter. The∆E distribution can be well modelled with a Gaussian when no neutral particles are present.Events with5.2GeV/c2<M bc<5.3GeV/c2and|∆E|< 0.3GeV are selected for thefinal analysis.The dominant background comes from continuum e+e−→qB events and jet-like qi,j|p i||p j|P l(cosθij)i,k|p i||p k|,r l=),where L s and L qqD0π+ decays.By comparing the yields in data and MC after the likelihood ratiorequirement,the systematic errors are determined to be4%for the modes with aπ0and6%for the mode without.Thefinal variable used for continuum suppression is theρhelicity angle,θh, defined as the angle between the direction of the decay pion from theρin the ρrest frame and theρin the B rest frame.The requirement of|cosθh|>0.3 is made independently of the likelihood ratio as it is effective in suppressing the background from B decays as well as the qB events is used[14].The largest component of this background is found to come from decays of the type B→Dπ;when the D meson decays via D→π+π−,events can directly reach the signal region while the decay D→K−π+can reach the signal region with the kaon misidentified as a pion.Decays with J/ψandψ(2S) mesons can also populate the signal region if both the daughter leptons are misidentified as pions.These events are excluded by making requirements on the invariant mass of the intermediate particles:|M(π+π−)−M D0|>0.14 GeV/c2,|M(π+π0)−M D+|>0.05GeV/c2,|M(π+π−)−M J/ψ|>0.07GeV/c2 and|M(π+π−)−Mψ(2S)|>0.05GeV/c2.The widest cut is made around the D0mass to account for the mass shift due to misidentifying the kaons in D0 decays as pions.Fig.1shows the∆E and M bc distributions for the three modes analysed after all the selection criteria have been applied.The∆E and M bc plots are shown for events that lie within3σof the nominal M bc and∆E values,respectively. The signal yields are obtained by performing maximum likelihoodfits,each using a single signal function and one or more background functions.The signal functions are obtained from the MC and adjusted based on comparisons of B+→B0are assumed to be equal.The M bc distribution for all modes isfitted with a single Gaussian and an ARGUS background function[15].The normalization of the ARGUS function is left tofloat and shape of the function isfixed from the∆E sideband:−0.25 GeV<∆E<−0.08GeV and5.2GeV/c2<M bc<5.3GeV/c2.For the mode with only charged pions in thefinal state,the∆E distribution isfitted with a single Gaussian for the signal and a linear function withfixed shape for the continuum background.The normalization of the linear function is left to float and the slope isfixed from the M bc sideband,5.2GeV/c2<M bc<5.26GeV/c2,|∆E|<0.3GeV.There are also other rare B decays that are expected to contaminate the∆E distribution.For the mode without aπ0,these modes are of the type B0→h+h−(where h denotes aπor K),B→ρρ(including all combinations of charged and neutralρmesons,where the polarizations of theρmesons are assumed to be longitudinal)and B→Kππ(including the decays B+→ρ0K+,B+→K∗0π+,B+→K∗0(1430)0π+,B+→f0(980)K+ and B+→f0(1370)K+)[16].These background modes are accounted for by using smoothed histograms whose shapes have been determined by combining MC distributions.The three B→ρρmodes are combined into one histogram. The normalization of this component is allowed tofloat in thefit due to the uncertainty in the branching fractions of the B→ρρmodes.Likewise,the B→hh and all the B→Kππmodes are combined to form one hh and one Kππcomponent.The normalizations of these components arefixed to their expected yields,which are calculated using efficiencies determined by MC and branching fractions measured by previous Belle analyses[16,17].The∆Efits for the modes with aπ0in thefinal state have the signal compo-nent modelled by a Crystal Ball function[18]to account for the asymmetry in the∆E distribution.As for the B+→ρ0π+mode,the continuum background is modelled by a linear function withfixed slope.Unlike the B+→ρ0π+mode, a component is included for the background from the b→c transition.The pa-rameterization for rare B decays includes one component for the B→Kππ0 modes(B0→ρ+K−and B0→K∗+π−)[19]and one for all the B→ρρmodes.The normalization of the B→ρρcomponent is left tofloat while the other components from B decays arefixed to their expected yields.Table1summarizes the results of the∆Efits,showing the number of events, signal yields,reconstruction efficiencies,statistical significance and branching fractions or upper limits for eachfit.The statistical significance is defined assystematic error in thefitted signal yield is estimated by independently varying eachfixed parameter in thefit by1σ.Thefinal results are B(B+→ρ0π+)=(8.0+2.3+0.7−2.0−0.7)×10−6and B(B0→ρ±π∓)=(20.8+6.0+2.8−6.3−3.1)×10−6where thefirst error is statistical and the second is systematic.For theρ0π0mode,one standard deviation of the systematic error is added to the statistical limit to obtain a conservative upper limit at90%confidence of5.3×10−6.The possibility of a nonresonant B→πππbackground is also examined.To check for this type of background,the M bc and∆E yields are determined for differentππinvariant mass bins.Byfitting the M bc distribution inππinvariant mass bins with B→ρπand B→πππMC distributions,the nonresonant contribution is found to be below4%.To account for this possible background, errors3.7%and3.2%are added in quadrature to the systematic errors of the ρ+π−andρ0π+modes,respectively.Theππinvariant mass distributions are shown in Fig.2.Two plots are shown for theρ+π−andρ0π+modes,one with events from the M bc sideband superimposed over the events from the signal region(upper)and one with events from signal MC superimposed over events from the signal region with the sideband subtracted(lower).Fig.3 shows the distribution of the helicity variable,cosθh,for the two modes with all selection criteria applied except the helicity condition.Events fromρπdecays are expected to follow a cos2θdistribution while nonresonant and other background decays have an approximately uniform distribution.The helicity plots are obtained byfitting the M bc distribution in eight helicity bins ranging from−1to1.The M bc yield is then plotted against the helicity bin for each mode and the expected MC signal distributions are superimposed.Both the ππmass spectrum and the helicity distributions provide evidence that the signal events are consistent with being fromρπdecays.The results obtained here can be used to calculate the ratio of branching frac-tions R=B(B0→ρ±π∓)/B(B+→ρ0π+),which gives R=2.6±1.0±0.4, where thefirst error is statistical and second is systematic.This is consistent with values obtained by CLEO[20]and BaBar[21,22]as shown in Table2. Theoretical calculations done at tree level assuming the factorization approx-imation for the hadronic matrix elements give R∼6[3].Calculations that include penguin contributions,off-shell B∗excited states or additionalππres-onances[4–8]might yield better agreement with the the measured value of R.In conclusion,statistically significant signals have been observed in the B→ρπmodes using a31.9×106BWe wish to thank the KEKB accelerator group for the excellent operation of the KEKB accelerator.We acknowledge support from the Ministry of Ed-ucation,Culture,Sports,Science,and Technology of Japan and the Japan Society for the Promotion of Science;the Australian Research Council and the Australian Department of Industry,Science and Resources;the National Science Foundation of China under contract No.10175071;the Department of Science and Technology of India;the BK21program of the Ministry of Education of Korea and the CHEP SRC program of the Korea Science and Engineering Foundation;the Polish State Committee for Scientific Research under contract No.2P03B17017;the Ministry of Science and Technology of the Russian Federation;the Ministry of Education,Science and Sport of the Republic of Slovenia;the National Science Council and the Ministry of Education of Taiwan;and the U.S.Department of Energy.References[1] A.E.Snyder and H.R.Quinn,Phys.Rev.D48,2139(1993).[2]I.Bediaga,R.E.Blanco,C.G¨o bel,and R.M´e ndez-Galain,Phys.Rev.Lett.81,4067(1998).[3]M.Bauer,B.Stech,and M.Wirbel,Z.Phys.C34,103(1987).[4] A.Deandrea et al.,Phys.Rev.D62,036001(2000).[5]Y.H.Chen,H.Y.Cheng,B.Tseng and K.C.Yang,Phys.Rev.D60,094014(1999).[6] C.D.Lu and M.Z.Yang,Eur.Phys.J C23,275(2002).[7]J.Tandean and S.Gardner,SLAC-PUB-9199;hep-ph/0204147.[8]S.Gardner and Ulf-G.Meißner,Phys.Rev.D65,094004(2002).[9]Belle Collaboration,A.Abashian et al.,Nucl.Instr.and Meth.A479,117(2002).[10]E.Kikutani ed.,KEK Preprint2001-157(2001),to appear in Nucl.Instr.andMeth.A.[11]G.C.Fox and S.Wolfram,Phys.Rev.Lett.41,1581(1978).[12]This modification of the Fox-Wolfram moments wasfirst proposed in a seriesof lectures on continuum suppression at KEK by Dr.R.Enomoto in May and June of1999.For a more detailed description see Belle Collaboration,K.Abe et al.,Phys.Lett.B511,151(2001).[13]CLEO Collaboration,D.M.Asner et al.,Phys.Rev.D53,1039(1996).[14]These MC events are generated with the CLEO group’s QQ program,see/public/CLEO/soft/QQ.The detector response is simulated using GEANT,R.Brun et al.,GEANT 3.21,CERN Report DD/EE/84-1,1984.[15]The ARGUS Collaboration,H.Albrecht et al.,Phys.Lett.B241,278(1990).[16]Belle Collaboration,A.Garmash et al.,Phys.Rev.D65,092005(2002).[17]Belle Collaboration,K.Abe et al.,Phys.Rev.Lett.87,101801(2001).[18]J.E.Gaiser et al.,Phys.Rev.D34,711(1986).[19]Belle Collaboration,K.Abe et al.,BELLE-CONF-0115,submitted as acontribution paper to the2001International Europhysics Conference on High Energy Physics(EPS-HEP2001).[20]CLEO Collaboration,C.P.Jessop et al.,Phys.Rev.Lett.85,2881(2000).[21]Babar Collaboration,B.Aubert et al.,submitted as a contribution paper tothe20th International Symposium on Lepton and Photon Interactions at High Energy(LP01);hep-ex/0107058.[22]BaBar Collaboration,B.Aubert et al.,submitted as a contribution paper tothe XXXth International Conference on High Energy Physics(ICHEP2000);hep-ex/0008058.Table1∆Efit results.Shown for each mode are the number of events in thefit,the signal yield,the reconstruction efficiency,the branching fraction(B)or90%confidence level upper limit(UL)and the statistical significance of thefit.Thefirst error in the branching fraction is statistical,the second is systematic.ρ0π+15424.3+6.9−6.29.68.0+2.3+0.7−2.0−0.74.4σρ+π−30144.6+12.8−13.46.820.8+6.0+2.8−6.3−3.13.7σρ0π0116−4.4±8.58.5<5.3-Experiment B(B0→ρ±π∓)×10−6B(B+→ρ0π+)×10−6RE v e n t s /16 M e VE v e n t s /3 M e V /c2(b) ρ0π+Signal backgrd02.557.51012.51517.52022.55.25.225 5.25 5.2755.3E v e n t s /18 M e VE v e n t s /2 M e V /c2(d) ρ+π-Signal backgrd051015202530355.25.225 5.25 5.2755.3∆E(GeV)E v e n t s /18 M e V(e) ρ0π024681012-0.2-0.10.10.2(GeV/c 2)E v e n t s /2 M e V /c2M bc (f) ρ0πSignal backgrd02468101214165.25.225 5.25 5.2755.3Fig.1.The ∆E (left)and M bc (right)fits to the three B →ρπmodes:ρ0π+,ρ+π−and ρ0π0.The histograms show the data,the solid lines show the total fit and the dashed lines show the continuum component.In (a)the contribution from the B →ρρand B →hh modes is shown by the cross hatched component.In (c)the cross hatched component shows the contribution from the b →c transition and B →ρρmodes.102030405060+0(GeV/c 2)E v e n t s /0.1 G e V /c2M(π+π0)(GeV/c 2)E v e n t s /0.1 G e V /c2(GeV/c 2)E v e n t s /0.1 G e V /c2+-(GeV/c 2)E v e n t s /0.1 G e V /c2M(π+ π-)510152025Fig.2.The M (ππ)distributions for B 0→ρ±π∓(left)and B +→ρ0π+(right)events in the signal region.Plots (a)and (b)show sideband events superimposed;plots (c)and (d)show the sideband subtracted plots with signal MC superimposed.-1-0.500.51M b c y i e l d (E v e n t s )cos θh-1-0.500.51M b c y i e l d (E v e n t s )cos θhFig.3.The ρmeson helicity distributions for B 0→ρ±π∓(a)and B +→ρ0π+(b).Signal MC distributions are shown superimposed.。
24个希腊字母
24个希腊字母24个希腊字母αal·pha [ ‘əelfə ] n. ①阿尔法〔希腊语字母表首字母α，相当于英语的a〕. ②. 最初. ③【天】α星，主星. alpha and omega首尾，始终；全体. alpha plus最高级的，最好的. alpha decay 【原】α衰变. alpha rays 【物】α射线. alpharhythm [wave]脑中每秒钟约十下的波动. alphascope 计算机屏幕显示器.βbeta [ ‘ bi:tə，beitɔ ] n. ①希腊字母第二字〔Β，β〕.②第二位的东西. ③【天】β星〔星座中第二等最亮的星〕. beta decay 【原】β衰变. beta minus 仅次于第二等. beta particle 【物】β粒子，β质子. beta plus 略高于第二等. beta ray 【化】β射线. beta test 【心】不用文字及口答的一种智力测验.γgam·ma [ ‘ gəemə ] n. ①希腊语的第三个字母〔Γ，γ=〔英〕G，g〕；第三位的东西；【虫】γ纹蛾；【天】（亮度居于第三位的）γ星. ②〔pl.〕γ量，微克（=100万分之一克）. ③【物】伽马（磁场强度单位，=10-5奥斯特）. ④【摄】灰度（非线性）系数. gamma decay 【物】γ衰变. gamma globulin γ球蛋白. gamma minus 仅次于第三等. gamma plus 稍高于第三等. gamma ray 【物】①光（量）子.②γ射线. gamma ray astronomy γ射线天文学. gammasonde γ探空仪.δdel·ta [ ‘deltə ] n. ①希腊语字母表第四字母〔Δ，δ〕.②（河流的）三角洲；三角形物. ③〔D-〕通讯中用以代替d的词. delta metalδ齐[（旧读jì）指合金，也指调味品]，δ合金. the delta of the Nile 尼罗河三角洲【生】三角波〔显示熟睡状态的脑电波〕.εep·si·lon [ ep’sailən ] n. ①希腊语字母表第五字母〔Ε，ε=〔英〕短音e〕. ②【数】小的正数.ζze·ta [ zi:tə ] n. 希腊语第六个字母[Ζ，ζ].ηe·ta [‘i:tə ] n. 希腊语字母表第七字母〔Η，η.，相当英语的长音e〕.θthe·ta [ ‘θi:tə] n. 希腊字母表的第八字母〔Θ，θ，相当于英语的th〕.ιi·o·ta [ ai ‘əutə ] n. ①希腊语的第九个字母〔即Ι，ι=i〕.②微小，一点. have not an iota of没有一点儿…. not change by an iota丝毫不变.κ kap·pa [ ‘ kəepə ] n. ①希腊语的第十个字母“Κ，κ”.②（遗传学上的）卡巴粒.λlamb·da [‘ləemdə] n. ①希腊语第十一个字母〔Λ，λ与英语字母L相当〕. ②微升〔百万分之一升〕. ③λ粒子〔=lambda particle〕. lambda hyperon λ超子.μmu [ mju: ] n. 希腊语的第十二字母〔Μ，μ〕；百万分之一；千分之一毫米.νnu [ nju: ] n. 希腊语的第十三字母〔Ν，ν；相当于英语的n〕.ξxi [ sai，zai Gr. ksi: ] n. 希腊字母表第十四个字母〔Ξ，ξ〕.οo·mi·cron [ əu‘ maikrən ] n. 希腊字母表第十五字母〔Ο，ο〕.πpi [ pai ] n. ①希腊字母表的第十六字母〔Ππ，和英语的p相当〕.②【数】圆周率.ρrho [ rəu ] n. ①希腊语第十七个字母〔Ρ，ρ相当于英语的r〕. ②【原】ρ介子（= rho meson）.σsig·ma [ ‘sigmə] 希腊字母表的第十八字母〔Σ，σ，相当于英语的s〕【动、植】S[Σ]形；【心】千分之一秒.τtau [ tɔ:，tau ] n. ①希腊字母第十九字〔Τ，τ相当于拉丁字母的t〕.②T字形. ③T字形物. tau cross T字形十字架.υup·si·lon [ ju:p ‘ sailən ] n. 希腊语字母表第二十字〔Υ，υ相当于英语的u〕.φphi [ fai ] n. 希腊字母表的第二十一字母〔Φ，φ和英语ph相当〕；=500. Phi Beta Kappa〔美〕①ΦΒΚ联谊会〔美国大学优秀生的荣誉组织〕.②ΦΒΚ联谊会会员. Phi Bete [ beit ] =Phi Beta Kappa. Phi Bete house 〔美俚〕大学图书馆.χchi [kai，ki: ] n. 希腊语字母表第22字母（Χ，χ）〔相当于英语的ch〕. a chi2（=χ2）square test【生】卡方测验.ψpsi [ p sai ] n. 希腊语的第二十三字母〔Ψ、ψ，相当于英语的ps〕.ωo·me·ga [ ‘əumigə] n. 希腊字母末字[Ω，ω]；终，末尾；结论，死；【数】自然数有序序列的序数（常用ω表示）. alpha and omega始与终，首尾，始末，全部.。
dai观察方法
dai观察方法Observation is a crucial aspect of the scientific method. It involves using the five senses to gather information about the world around us and can be conducted in various ways.观察是科学方法的一个关键方面。
它涉及使用五种感官来收集有关我们周围世界的信息，可以通过各种方式进行。
One method of observation is through controlled experiments. This involves setting up a controlled environment and manipulating variables to observe the effects. For example, in a biology lab, researchers might set up an experiment to observe the growth of plants under different light conditions.观察的一种方法是通过控制性实验。
这涉及建立一个受控环境，并操纵变量以观察效果。
例如，在生物实验室中，研究人员可能会设置一个实验以观察不同光照条件下植物的生长情况。
Another method of observation is through naturalistic observation. This involves watching and recording the behavior of subjects in theirnatural environment. For example, a researcher might observe the behavior of chimpanzees in the wild to better understand their social dynamics.观察的另一种方法是通过自然观察。
湿地生态恢复技术研究现状与展望
湿地原油污染通过生物炭和鼠李糖脂表面活性剂修复，湿地
Ｆｉｇ．１ Ｔｗｏ ｒｅｓｔｏｒａｔｉｏｎ ｍｏｄｅｌｓ ｏｆ ｄａｍａｇｅｄ ｗｅｔｌａｎｄｓ
土壤水分通过调控水文周期修复［１７］ 。美国Ｊａｍａｉｃａ 湾滨海
表 １ 湿地类型及其恢复策略
Ｔａｂｌｅ １ Ｗｅｔｌａｎｄ ｔｙｐｅｓ ａｎｄ ｒｅｓｔｏｒａｔｉｏｎ ｍｅａｓｕｒｅｓ
选择策略的不同，具体湿地类型与其选择的恢复策略见表 １。
动恢复是目前最佳的恢复模式。 其优势在于成本控制较低
３．２ 湿地恢复技术 湿地恢复技术主要目的是使用对环境
以及恢复后的湿地与周围景观的一致性相对较高。
友好的生态技术以及工程措施对严重退化的湿地进行修复
改造的科学过程，包括生境修复、生物修复和生态功能修复，
安徽农业科学，Ｊ．Ａｎｈｕｉ Ａｇｒｉｃ．Ｓｃｉ． ２０２３，５１（２２） ：２０－２５
湿地生态恢复技术研究现状与展望
于 寒１，２ ，周茜冉１ ，邹元春２ ，田 雪２ ，孙明阳３ ，王婧瑜４ ，曹 蕊１ ，张鉴昊１ ，姜 明２∗（１．吉林农业大学，吉林长春 １３０１１８；
２．中国科学院东北地理与农业生态研究，吉林长春 １３０１０２；３．吉林建筑大学，吉林长春 １３０１１９；４．吉林省农业科学院，吉林长春 １３０１１８）
１ 湿地恢复理论
护湿地生态系统自有功能；③提高生态系统抵御外界干扰的
湿地恢复理论是指应用生态技术或生态工程手段修复
能力，防止外来物种的入侵及生物的死亡；④要遵循生态工
正在退化或重建消失的湿地，恢复湿地受干扰前的结构、功
程学的原理及要求，模拟生态系统的现状及景观分布格局；
能以及其生物、物理和化学特性，恢复原有湿地应有属性
FRM（18）
FRM（18） GREEK LETTERS原⽂地址: /archives/12484The Greeks are vital tools in risk management. Each Greek measures the sensitivity of the value of a portfolio to a small change in a given underlying parameter, so that component risks may be treated in isolation, and the portfolio rebalanced accordingly to achieve a desired exposure; see for example delta hedging.The Greeks in the Black-Scholes model are relatively easy to calculate, a desirable property of financialmodels, and are very useful for derivatives traders, especially those who seek to hedge their portfolios from adverse changes in market conditions. For this reason, those Greeks which are particularly useful for hedging delta, gamma and vega are well-defined for measuring changes in Price, Time and Volatility. Although rho is a primary input into the Black-Scholes model, the overall impact on the value of an option corresponding to changes in the risk-free interest rate is generally insignificant and therefore higher-order derivatives involving the risk-free interest rate are not common.The most common of the Greeks are the first order derivatives: Delta, Theta, Vega and Rho as well as Gamma, a second-order derivative of the value function. The remaining sensitivities in this list are common enough that they have common names, but this list is by no means exhaustive.Volatility Time to Risk-FreeSpotPrice (S)Gamma (ΓVega (νCharmCharm or delta decay, measures the instantaneous rate of change of delta over the passage of time. Charm has also been called DdeltaDtime. Charm can be an important greek to measure/monitor when delta-hedging a position over a weekend. Charm is a second order derivative of the option value, once to price and once to time. It is also then the (minus) derivative of theta with respect to the underlying’s price.delta对时间的。
Unit 3 Diverse Cultures Discovering Useful 课件
Discovering Useful Structures
Grammar
Understanding the use of ellipsis in English
Activity 1 Read the following sentences and find the words that have been
Activity 3
Understanding the use of ellipsis in English
Read the conversation. Find out which words have been left out . Justin：Yes，I have（heard of the Chinese novel Journey to the West） . Why （do you ask if I） （have heard of the Chinese novel Journey to the West） ? Linlin： In the back of the （Huangguoshu） Waterfall，you will find a cave，which is the home of the Monkey King （from Journey to the West）. Justin：（That’s） really （true）? （It’s） cool! I’ll definitely check it out. Linlin： And I strongly recommend the ethnic minority villages （on your trip to Guizhou） . You’ll find Chinese culture is much more diverse than you thought （it was）. Justin：（This all） sounds great. Thanks!
Higgs bosons decay into bottom-strange in two Higgs Doublets Models
a r X i v :h e p -p h /0409218v 2 9 M a r 2005LPHEP-04-03September 2004Higgs bosons decay into bottom-strangein two Higgs Doublets ModelsAbdesslam ArhribD´e partement de Math´e matiques,Facult´e des Sciences et TechniquesB.P 416Tanger,Morocco.andLPHEA,D´e partement de Physique,Facult´e des Sciences-Semlalia,B.P.2390Marrakech,Morocco.AbstractWe analyze the decays {h 0,H 0,A 0}→¯s b within two Higgs Doublet Models with Natural Flavor Conservation (2HDM)type I and II.It is found that the Higgs bosons decay into bottom-strange can lead to a branching ratio in the range 10−5→10−3for small tan β≈0.1→0.5and rather light charged Higgs in the 2HDM type I.Whentan β>∼1,one can easily reach a branching ratio of the order 10−5.In 2HDM typeII,without imposing b →sγconstraint,the situation is the same as in 2HDM type I.If b →sγconstraint on charged Higgs mass (M H ±≥350GeV)is imposed,we obtain Br (h 0→¯s b )in the range 10−5–10−6.A comparison between the rates of h 0→¯s b and h 0→γγis made.It is found that in the fermiophobic scenario,h 0→γγis still the dominant decay mode.1IntroductionOne of the goals of the next generation of high energy colliders,such as the large hadroncollider LHC[1]or the linear collider LC[2]or muon colliders,is to probe top Flavor-Changing Neutral Couplings‘top FCNC’as well as the Higgs Flavor-Changing NeutralCouplings‘Higgs FCNC’.FCNC of heavy quarks have been intensively studied both from the theoretical and experimental point of view.Such processes are being well established inthe Standard Model(SM)and are excellent probes for the presence of new physics effectssuch as Supersymmetry,extended Higgs sector and extra fermions families.Within the SM,with one Higgs doublet,the FCNC Z¯t c vanishes at tree-level by theGIM mechanism,while theγ¯t c and g¯t c couplings are zero as a consequence of the unbrokenSU(3)c×U(1)em gauge symmetry.The Higgs FCNC H¯t c and H¯s b couplings also vanish due to the existence of only one Higgs doublet.Both top FCNC and Higgs FCNC aregenerated at one loop level by charged current exchange,but they are very suppressed by the GIM mechanism.The calculation of the branching ratios for top decays yields the SM predictions[3],[4]:Br(t→Zc)=1.3×10−13,Br(t→γc)=4.3×10−13,Br(t→gc)=3.8×10−11,Br(t→Hc)=5.6→3.2×10−14for M H=115→130GeV.(1) While for Higgs FCNC,calculation within SM leads to:Br(H→¯s b)≈10−7(resp10−9)m H=100(resp200)GeVBr(H→¯t c)≈1.5×10−16(resp3×10−13)m H=200(resp500)GeV(2) Many SM extensions predict that these top and Higgs FCNC can be orders of magnitude larger than their SM values(see[5]for an overview).For the Higgs FCNC,an important class of models where Higgs FCNC appear at tree level are the so called Two Higgs Doublet Model without Natural Flavor Conservation(NFC)2HDM-III[6,7,8,9].In this class of models,the branching ratio of h→¯t c can be larger than10%in some cases[7].In the framework of2HDM with NFC type I and II,top and Higgs FCNC have been studied in [10,11].It was shown that in2HDM-II the Br(Φ→¯t c),Φ=h0or H0,may reach10−5 for CP-even states[11].This rate is almost eight orders of magnitude larger than the SM one.Top and Higgs FCNC couplings have been addressed also in supersymmetry[12,13,14,15,16].In those studies it has been shown that Br(h0→¯s b)can be in the range of10−4-10−3. This rate originates mainly from theflavor violation interactions mediated by the gluino [12,14].In case of MSSM with R parity conservation,the top FCNC coupling t→ch0, can reach10−4branching ratio[15]in case offlavour violation induced by gluino.Hence,Higgs and top FCNC offer a good place to search for new physics,which maymanifest itself if those couplings are observed in future experiments such as LHC or LC [1,2].Therefore,models which can enhance those FCNC couplings are welcome.The aim of this paper is to study Higgs FCNC couplings such asΦ→¯s b,Φ=h0,H0,A0,in the framework of NFC two Higgs Doublet Models type I and II.It is found that the branching ratios of Br(Φ→¯s b),Φ=h0,H0,A0,can be greater than>∼10−5in quite asubstantial region of the2HDM parameters space.Br(Φ→¯t c)requires large tanβand light charged Higgs[11]while Br(Φ→¯s b)requires rather small tanβtogether with light charged Higgs and large soft breaking termλ5.We would like to mention here that due to the isolated top quark signature,Higgs FCNC Φ→¯t c event may be easy to search for experimentally.However,it is very difficult to isolate Higgs FCNCΦ→¯s b events from the background.The paper is organized as follows.In the next section,the2HDM is introduced.Rel-evant couplings are given,theoretical and experimental constraints on2HDM parameters are discussed.In the third section,we will study the effects of2HDM on Br(Φ→¯s b) which are evaluated in2HDM-I and2HDM-II.A comparison between Br(h0→¯s b)and Br(h0→γγ)is also discussed.Our conclusion is given in section4.2The2HDMTwo Higgs Doublet Models(2HDM)are formed by adding an extra complex SU(2)L⊗U(1)Y scalar doublet to the SM Lagrangian.Motivations for such a structure include CP–violation in the Higgs sector and the fact that some models of dynamical electroweak symmetry breaking yield the2HDM as their low-energy effective theory[17].The most general2HDM scalar potential which is both SU(2)L⊗U(1)Y and CP in-variant is given by[18]:V(Φ1,Φ2)=λ1(|Φ1|2−v21)2+λ2(|Φ2|2−v22)2+λ3((|Φ1|2−v21)+(|Φ2|2−v22))2+λ4(|Φ1|2|Φ2|2−|Φ+1Φ2|2)+λ5(ℜ(Φ+1Φ2)−v1v2)2+λ6[ℑ(Φ+1Φ2)]2(3) whereΦ1andΦ2have weak hypercharge Y=1,v1and v2are respectively the vacuum expectation values ofΦ1andΦ2and theλi are real–valued parameters.Note that this potential violates the discrete symmetryΦi→−Φi softly by the dimension two term λ5ℜ(Φ+1Φ2).The above scalar potential has8independent parameters(λi)i=1,...,6,v1andv2.After electroweak symmetry breaking,the combination v21+v22is thusfixed by the√electroweak scale through v21+v22=(2H0H+H−=−ig2M Wsin(β−α)(M2H0−M2H±)(5) h0H+H−=−ig2M Wcos(β−α)(M2h0−M2H±)(7) A0H+G−=−g g2(8)We need also the couplings of scalar boson to a pair of fermions both in2HDM-I and 2HDM-II.In those couplings,the relevant terms are as follows:h0¯t t∝M t cosαsinβ,A0¯t t∝M tsinβ,H0¯bb∝M bsinαtanβ2HDM−I(10)h0¯bb∝M b sinαcosβ,A0¯bb∝M b tanβ2HDM−II(11)(H−¯bt)L∝M b tanβ2HDM−I(12) (H−¯bt)L∝M b tanβ,(H−¯bt)R∝M t1718 Figure1:Generic contribution toΦ→f1f2in SM d1→d10,in2HDM d11→d18iv)Unitarity and perturbativity constraints on scalar parameters:It is well known that the unitarity bounds coming from a tree-level analysis[25,26]put severe constraints on all scalar trilinear and quartic couplings.The tree level unitarity bounds are derived with the help of the equivalence theorem,which itself is a high-energy approximation where it is assumed that the energy scale is much larger than the Z0and W±gauge-boson masses.We will use,instead of unitarity constraints,the perturbativity constraints by assuming that allλi satisfy:|λi|≤4π.(14) Those perturbative constraints on theλi allow us to investigate a larger parameter space than the one allowed by unitarity constraints.We would like to mention also that when performing the scan over the2HDM parameters space,we realize that for some points the widthsΓΦof the scalar particles become bigger than their corresponding masses:ΓΦ≥MΦ(Φ=h0,H0,A0,H±).This happens both when we impose tree level unitarity constraints and/or perturbativity constraints.Thewidth becomes large specially when the pure scalar decays like H0→h0h0,H0→H+H−, h0→H+H−,H0→A0A0and h0→A0A0are open.Wefind it is natural to add to the above constraints the requirement that the width of the scalar particles remains smaller than the mass of the corresponding particles:ΓΦ<MΦ(15) From the experimental point of view,the combined null–searches from all four CERN LEP collaborations derive the lower limit M H±≥78.6GeV(95%CL),a limit which applies to all models in which Br(H±→τντ)+Br(H±→c¯s)=1.For the neutral Higgs bosons, OPAL collaboration has put a limit on h0and A0masses of the2HDM.They conclude1e-171e-161e-15 1e-14 1e-13 1e-12 1e-11 1e-10 1e-09M H (GeV)2 Γ(H-->tc)(GeV)2 x Br(H-->tc)1e-101e-091e-08 1e-07 1e-06 1e-05 0.0001 0.001M H (GeV)2 Γ(H-->sb)(GeV)2 Br(H-->sb)Br(H-->µ µ)Figure 2:SM width and Branching ratio for H →¯t c (left)and H →¯s b (right)as a functionof Higgs mass.that the regions 1<∼M h <∼44GeV and 12<∼M A <∼56GeV are excluded at 95%CL independent of αand tan β[27].For simplicity we will assume that all scalar particles masses are >∼90GeV.3Higgs FCNC in 2HDM3.1Higgs FCNC in SMBefore presenting our results in 2HDM,we would like to give the Branching ratio of H →¯t c and H →¯s b in the SM.To our best knowledge,the first calculation for Br (H →¯s b )has been carried out in [28].However,in [28],numerical results have been given only for a very light Higgs boson M H =9GeV.Recently a new estimation,using dimensional analysisand power counting,has appeared both for Br (H →¯s b )[14]and Br (H →¯tc )[11].We refer the reader to [11,14]for more details on those estimations.Here we present exactresult based on diagrammatic calculations both for Br (H →¯s b )and Br (H →¯tc ).We give numerical results for the width as well as for the branching ratio.The Feynman diagrams contributing to those process in SM are depicted in Fig .(1)d 1→d 10.In the case of H →¯t c ,in Fig.(1)(f 1,f 2)=(t,c )and f ′i =d,s,b ,while for H →¯s b(f 1,f 2)is (b,s )and f ′i =u,c,t .The full loop calculation presented here is done with the help of FormCalc [29].FF and LoopTools packages [30]are used in numerical analysis.The numerical results shown in eqs.(1,2)is derived by FormCalc [29].In the SM,as expected,the branching ratio of H →¯t c and H →¯s b are very suppresseddue to GIM mechanism.The branching ratio is very small in both cases for higher Higgs mass M H ≥2M Z where H →W +W −and H →Z 0Z 0are open.Both in SM and 2HDM,the decay widths ΓSM Φand Γ2HDMΦof scalar particles:Φ=H SM ,h0,H0,A0and H±are computed at tree level as follows:ΓSMΦ=fΓ(Φ→f¯f)+Γ(Φ→V V)Γ2HDMΦ=fΓ(Φ→f¯f)+Γ(Φ→V V)+Γ(Φ→V H i)+Γ(Φ→H i H j)(16)QCD corrections toΦ→f¯f andΦ→{gg,γγ,γZ,V∗V∗,V V∗,V∗H i}decays are not included in the widths.The decay widths of the Higgs bosons are taken from[31]. For a Higgs mass heavier than250GeV,we get branching ratio of the order10−14→10−12(resp10−10→10−9)for H→¯t c(resp H→¯s b).In the case of H→¯s b,the branching ratio is enhanced for Higgs boson mass of the order M H≈100→120GeV where the width of the Higgs is very narrow.We have plotted in Fig.(2)both the decay width and the branching ratios of H→¯t c(left plot)and H→¯s b (right plot)as well as the branching ratio of H→µ+µ−.As it can be seen from the right plot Br(H→¯s b)is two orders of magnitude smaller than Br(H→µ+µ−).Since the decay width of H→¯t c is very suppressed,the threshold for t¯t production is absent in Fig.2(left).The situation is slightly different for H→¯s b where the decay width of H→¯s b is about6order of magnitude larger than decay width of H→¯t c.From the right plot of Fig.(2)one can see that the Br of H→¯s b is smaller once the t¯t threshold has been passed.3.2h0→¯s bTurning now to the2HDM Higgs bosons FCNC couplingsΦ→¯s b,Φ=h0,H0,A0.The Feynman diagrams are depicted in Fig.(1).The amplitude is sensitive to theΦH+H−and ΦH±G∓couplings through diagrams d12,13,14as well as to theΦt¯t and(H−¯bt)L,R couplings through diagrams d11,12,13,14.In2HDM,it is expected that the dominant contribution to the amplitude ofΦ0→¯s b comes from diagram d12.The amplitude of d12is proportional to the trilinear Higgs couplingΦ0H+H−and is given by(Φ=h0,H0):M d12=Φ0H+H−αV tstan2βM b2u(M b)(17)where we have neglected the strange quark mass.In the conventions of[29],the arguments of the Passarino-Veltman functions C i are{M2b,M2s,M2Φ,M2H±,M2t,M2H±}.The Yukawa coupling Y b of the bottom is model dependant and is given by Y b=−1/tanβ(resp Y b= tanβ)for2HDM-I(resp2HDM-II).In2HDM-I,1+tanβY b=0,the amplitude of d12is enhanced by M2tλ5−5−6H +M (GeV)H +M (GeV)λ5Figure 3:Contours for 2×Br (h 0→¯s b )in 2HDM-II tan β=0.3(left),tan β=1.5(right)in the (M H ±,λ5)plane with M h =110GeV,M H =180GeV,sin α=0.1and M A 0=M H ±We also give other numerical results for specific 2HDM parameters where Br (h 0→¯s b )and Br (H 0→¯s b )get their maximum values without violating δρand perturbativity constraints.We show in Fig.(3)contour plots for Br (h 0→¯s b )in 2HDM-II tan β=0.3(left)and tan β=1.5GeV (right)in the (M H ±,λ5)plane.λ5is varied in the perturbative range |λ5|<4π.The other inputs are M h =110GeV,M H =180GeV,sin α=0.1and M A 0=M H ±.The width Γh 0is computed at tree level according to eq.(16).Since the mass of h 0is taken at 110GeV,only light fermions contribute to Γh 0and so the width is very narrow and is of the order 57×10−4(resp 83×10−5GeV)at tan β=0.3(resp tan β=1.5).Such narrow width could enhance the branching ratio Br (h 0→¯s b ).We would like to mention first that for this set of parameters,the perturbativity of scalar quartic couplings λi is violated around λ5>∼5.5.We get |λ1|>4πfor tan β=0.3,while for tan β=1.5there is no such bound.Large branching ratios can be obtained for light charged Higgs mass.This can be seen in the left panel black and blue areas of Fig.(3)which correspond to small tan β=0.3and large |λ5|.In those areas the coupling h 0H +H −gets its largest value (see also Fig.(4)).In this case one can obtain branching ratio in the range:10−4<Br (h 0→¯s b )<6×10−4for M H ±<200GeV ,λ5<∼−1.2and λ5>∼3.For charged Higgs mass greater than 200GeV,there is also a region where the branching ratio can be in the range 10−5→10−4.This can be achieved by taking large and negative λ5<∼−1.In the case of positive λ5andM H ±>∼250GeV,the branching ratio decreases to a value <∼10−5.When tan β=1.5,the coupling h 0t ¯tis reduced,and we are left only with a small region where the branching ratio Br (h 0→¯s b )is of the order 10−5→10−4for M H ±<∼250GeV and large |λ5|>∼5.In both plots (left and right),the coupling h 0H +H −reaches itsM h M H M H±M Aλ52×Γ¯s b2×Γγγ−.98.210−37×10−46×10−36×10−35×10−35×10−3140 34011010064×10−62×10−610−410−4−.98.4610−32×10−47×10−32×10−32×10−37×10−3115 2501101905×10−45×10−510−410−4.18.19×10−410−32×10−43×10−3.525×10−2Table1:Maximum Branching ratios of h0→¯s b in2HDM-I and II and corresponding 2HDM parameters,all masses and decay width are in GeV.In Br and widthsΓcolumns, the upper row is for2HDM-I and the down row is for2HDM-IIminimal value in the region whereλ5≈0→2,which explains why the branching ratio is so small in this region.Now we turn to the case where M H±=M A,δρ=0.We have performed a system-atic scan over the full2HDM parameters space taking into accountδρand perturbativity constraints.The maximum branching ratios found for h0→¯s b in2HDM-I and II are displayed in table1.We show not only width and Br of h0→¯s b but also the width and Br of h0→γγfor comparison.The total width of the HiggsΓh0is also given.WhenΓh0 becomes comparable to the width of h0→¯s b and/or h0→γγ,those decays widths have to be included in the total widthΓh0in order to compute the Br¯s b and Brγγ.Thefirst three columns of table1are for2HDM parameters.From4th to8th columns we give Br and widths.In those columns,the upper row is for2HDM-I and the down row is for2HDM-II.In2HDM-I,Br(h0→¯s b)of the order10−3can be reached in the limit sinα→−0.98 (α→−π/2)and small tanβ≤0.5.In fact,this limit(α→−π/2)is very close to fermiophobic scenarioα=±π/2.In the fermiophobic limit,all couplings of h0to down quarks and leptons are suppressed eq.(10).In this limit,h0¯t t is also suppressed eq.(9).The width of light Higgs h0(M h<160GeV)is then very tiny in the limit sinα→−0.98.This tiny width together with large h0H+H−are the sources of enhancement of the Br(h0→¯s b) to10−3level.This can be seen in thefirst,second and third lines of table1In2HDM-II,the couplings of h0to down quarks and leptons are suppressed for sinα≈0.1 eq.(11).Hence,the width of light Higgs(M h<160GeV)is very tiny in the limit sinα≈0.1.Moreover,in this limit,the coupling h0¯t t is enhanced in both models2HDM-I and II.The decay widthΓ(h0→¯s b)which was≈10−6for sinα=−0.98is of the order ≈10−5for sinα=0.1.Consequently,the Br(h0→¯s b)reaches10−3.1e-081e-071e-06 1e-05 0.0001 0.001 0.01 0.1B r λ5h 0-->sb: 2HDMI h 0-->sb: 2HDMII h 0-->γγ: 2HDMI h 0-->γγ: 2HDMII1e-111e-10 1e-09 1e-08 1e-07 1e-06 1e-05 0.0001 0.001 0.01B rλ5h 0-->sb: 2HDMI h 0-->sb: 2HDMIIh 0-->γγ: 2HDMIh 0-->γγ: 2HDMII Figure 4:2×Br (h 0→γγ)and 2×Br (h 0→¯s b )in 2HDM-I and II,m H ±=100GeV,tan β=0.3(left)and tan β=5(right).All the other parameters are the same as in Fig.(3).In this scenario,as one can see from table 1,the Br(h 0→γγ)in 2HDM-I is 2×10−4which is smaller than Br(h 0→¯s b )=9×10−4.This is mainly due to the fact that the trilinear coupling h 0H +H −is very suppressed in this scenario (see more details in next section).As one can see from the last line of the table 1,there exist also values of sin α=0.18,far from fermiophobic scenario but with small λ5=0,where Br(h 0→¯s b )can be of the order 10−3.3.3Can h 0→¯s b compete with h 0→γγ?It is well known that the decay h 0→γγis loop induced and so is suppressed.In the SM,the branching ratio Br (H SM →γγ)is about ≈10−3for Higgs mass in the range M H =100→160GeV.Hence,with maximum branching ratio for h 0→¯s b of the order 1×10−4→6×10−4in 2HDM-I or II,it is legitimate to compare h 0→γγand h 0→¯s b in 2HDM-I or II.Of course,even if h 0→¯s b and h 0→γγhas a competitive branching ratio,we should keep in mind that h 0→γγdecay has a clear signature while the FCNC decay h 0→¯s b has not.We illustrate in Fig.(4)the branching ratio for h 0→¯s b and h 0→γγboth in 2HDM-I and II.The charged Higgs mass is fixed to 100GeV.It is clear that in the case tan β=0.3h 0→γγis about one order of magnitude bigger than h 0→¯s b .While,in the case of tan β=5h 0→γγis more than four orders of magnitude bigger than h 0→¯s b .This is because at tan β=0.3(resp tan β=5)the W loop are suppressed by a factor h 0W +W −∝sin(β−α)≈0.2(resp enhanced by h 0W +W −∝sin(β−α)≈0.96).All the dips observed in the plots correspond to the minimum of the coupling h 0H −H +.Those dips are not located at the same λ5,this is due to a destructive interference with others diagrams.H +M (GeV)λ5H +M (GeV)Figure 5:Contours for 2×Br (H 0→¯s b )in 2HDM-II in the plan (M H ±,λ5)M H =140GeV (left),(M H ±,M H )λ5=5(right)with tan β=0.3,M h =110GeV,sin α=0.95and M A 0=M H ±When h 0H −H +coupling is very suppressed,it may be possible that the Br(h 0→¯s b )could be higher than Br(h 0→γγ)as it can be seen both in the left plot of Fig.(4)for λ5=2.5and in table 1for sin α=0.1in 2HDM-II.However,even if Br(h 0→γγ)and Br(h 0→¯s b )become comparable,we should keep in mind that h 0→γγhas a very clear signature while h 0→¯s b does not.An interesting feature of the 2HDM-I,is its fermiophobic scenario.The light CP-even Higgs h 0of the 2HDM-I is fermiophobic in the limit α→π/2,all h 0couplings to fermions vanishes for α=π/2[32,18].If h 0,with a mass in the range 100→160GeV,is fermiophobic the dominant decay mode is h 0→γγ.It has been shown in Ref.[33]that in the fermiophobic limit,the branching ratio of the one loop induced decay h 0→¯bb ∗is below 10%→30%.As the decay h 0→¯s b is concerned,we have checked by systematic scan that in the fermiophobic limit,the decay width of h 0→γγis more than one order of magnitude bigger than the width of h 0→¯s b .3.4H 0→¯s bWe now discuss the heavy CP-even decay H 0→¯s b .Our numerical results are shown inFig.(5).To maximize the coupling H 0¯tt ,we choose of course small tan β≈0.3and large sin α≈0.95.In the right plot of Fig.(5),we show contour plots for Br (H 0→¯s b )in the plane (M H ±,λ5)for M H =140GeV.For CP-even Higgs mass 140GeV,H 0→W +W −,H 0→ZZ ,H 0→¯tt ,H 0→A 0Z and H 0→H i H j are not yet open,and so the width is narrow.In particular,for the set of parameters fixed here:M h =110GeV,sin α=0.95M h M H M H±M Aλ52×Γ¯s b2×Γγγ.1.510−34×10−53×10−210−34×10−48×10−3100 155115103-610−66×10−72×10−52×10−5.08.452×10−38×10−5.733×10−23×10−48×10−3100 1251151035×10−46×10−52×10−42×10−4.9.110−310−32×10−42×10−3.515×10−2100 1451151032×10−43×10−52×10−43×10−41e-121e-11 1e-10 1e-09 1e-08 1e-07 1e-06 1e-050.00010.001B r (A 0-->s b )M Atan β=0.2tan β=0.3tan β=1.5tan β=60 0.0010.010.1 1 10 100 1000ΓA 0 (G e V )M Atan β=0.2tan β=0.3tan β=1.5tan β=60Figure 6:2×Br (A 0→¯s b )(left)and CP-odd A 0width ΓA 0(right)as function of M A for several values of tan βto down quarks and leptons are suppressed for sin α≈0.1(resp |sin α|≈0.9).In those cases the total Higgs width is very tiny and so the branching ratio of H 0→¯s b is enhanced.Of course,Br(H 0→¯s b )reach 10−3only for light charged Higgs,which is strongly disfavored by b →sγconstraint [24]in 2HDM-II.From table 2,one can see also that in 2HDM-II and for sin α≈{0.9,−0.98}the Br(H 0→¯s b )and Br(H 0→γγ)are of comparable size.This is again mainly due to the suppression of the coupling H 0H +H −in those limits.As in the case of light CP-even Higgs h 0,there exist values of sin α=−0.58far from fermiophobic limit with small λ5=0where Br(H 0→¯s b )can reach 10−3.3.5A 0→¯s bLet us now look at 2HDM contribution to A 0→¯s b .Since A 0is CP-odd,it does not couple to a pair of charged Higgs.The only pure trilinear scalar coupling which contributes to A 0→¯s b is A 0H ±G ∓eq.(8).Unlike the couplings H 0H +H −and h 0H +H −eqs (4,6),which depend both on Higgs masses,tan βas well as the soft breaking term λ5,the couplingA 0H ±G ∓depends only on the splitting M 2H ±−M 2A .As mentioned above,such splitting should not be too large,otherwise the δρconstraint is not satisfied.As one can readfrom eqs.(9,13),the couplings A 0¯t t and (H −¯bt )R are proportional to M t /tan β.Henceenhancement is expected at small tan β.As we stressed before,our 2HDM parameters in this case are:tan β,M A and M H ±.For simplification,we use the MSSM sum-rules to fix charged Higgs mass and αby using tan β,CP-odd mass M A and a SUSY scale which we take at 1TeV.CP-odd mass will be varied from 100GeV to 600GeV without worrying about perturbativity.tan βis taken to be >∼0.1.We present our numerical results for A 0→¯s b in 2HDM-II in Fig.(6).As can be seenfrom the left plot,the Branching ratio Br(A0→¯s b)is greater than10−5only for small tanβ≈0.1→0.35and light M A and M H±.For light M A<∼200GeV and low tanβ<∼1, the width of A0is still small and so the branching ratio is enhanced.For M A>∼200GeV, the decay A0→h0Z is open and the decay widthΓA0increases.Therefore,the branching ratio is reduced.Note that for tanβ=0.2,we cut offthe curve at M A≈400GeV where the widthΓA0starts to be greater than M A.At large tanβ,due to the bottom Yukawa coupling,both the partial widthΓ(A0→¯s b)and total widthΓA0are enhanced,and the branching ratio is saturated in the range[10−6,10−5].The situation is almost the same in2HDM-I.4ConclusionsIn the framework of the2HDM with naturalflavor conservation,we have studied various Higgs FCNCΦ→¯s b.The study has been carried out taking into account the experimental constraint on theρparameter and also perturbativity constraints on all the scalar quartic couplingsλi.Numerical results for the branching ratios have been discussed.We empha-sized the effect coming from both top and bottom Yukawa couplings and pure trilinear scalar couplings such as h0H+H−and H0H+H−.We have shown that,in2HDM-I and2HDM-II,the branching ratios of Higgs FCNC {h0,H0,A0}→¯s b are enhanced to the range of10−4→7×10−4for small tanβ,rather light charged Higgs boson and large soft breaking termλ5.The branching ratio of Br({h0,H0}→¯s b)can be pushed to10−3level when sinαis close to fermiophobic limit(sinα≈−0.98) or sinα≈0.1and even for sinαfar from those limits but with smallλ5=0. Charged Higgs mass of2HDM-I is not constrained by b→sγ,Br({h0,H0}→¯s b)can be of the order10−4→10−3for light charged Higgs which is comparable to size of SUSY pre-dictions[12,14].Those branching ratios rates,could still leads to large number of events at LHC[11].In2HDM-II with b→sγconstraint,branching ratios of{h0,H0}→¯s b are smaller than 10−5(resp10−4)for tanβ>1(resp tanβ<1).In the case of light CP-even m h0≈100→160GeV,we have also shown that the branching ratio of Br(h0→¯s b)is well below Br(h0→γγ)in most of the case.This is also the case in the fermiophobic scenario of2HDM-I.One interesting scenario is that both Br(h0→γγ)and Br(h0→¯s b)develop a dips for someλ5(see Fig.4).Those dips are not located at the sameλ5due to the presence of diagrams which contribute to h0→¯s b but not to h0→γγ.The dip for Br(h0→¯s b)is located forλ5=1while for Br(h0→γγ)it is located forλ5≈2.5.Forλ5≈2.5,we are already away from Br(h0→¯s b)dip,the Br(h0→¯s b)is slightly higher than Br(h0→γγ).Acknowledgments This work was done within the framework of the Associate Scheme of ICTP.Thanks to Thomas Hahn for his help.We also want to thank Andrew Akeroyd for discussions and for reading the manuscript.References[1]M.Beneke,I.Efthymipopulos,M.L.Mangano,J.Womersley(conveners)et al.,reportin the Workshop on Standard Model Physics(and more)at the LHC,Geneva,hep-ph/0003033[2]J.A.Aguilar-Saavedra et al.[ECFA/DESY LC Physics Working Group Collabora-tion],arXiv:hep-ph/0106315.[3]G.Eilam,J.L.Hewett and A.Soni,Phys.Rev.D44(1991)1473[Erratum-ibid.D59(1999)039901].[4]B.Mele,S.Petrarca and A.Soddu,Phys.Lett.B435,401(1998)[5]J.A.Aguilar-Saavedra,Acta Phys.Polon.B35(2004)2695[arXiv:hep-ph/0409342].E.W.N.Glover et al.,Acta Phys.Polon.B35(2004)2671[arXiv:hep-ph/0410110].0409342,0410110[6]T.P.Cheng and M.Sher,Phys.Rev.D35,3484(1987).[7]W.S.Hou,Phys.Lett.B296,179(1992).[8]D.Atwood,L.Reina and A.Soni,Phys.Rev.D55,3156(1997)[9]D.Atwood,L.Reina and A.Soni,Phys.Rev.D53,1199(1996)[arXiv:hep-ph/9506243].W.S.Hou,G.L.Lin and C.Y.Ma,Phys.Rev.D56,7434(1997). 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The decay $rho^{0}to pi^{+}+pi^{-}+gamma$ and the coupling constant g$_{rhosigmagamma}$
a rXiv:n ucl-t h /441v28Ma y2The decay ρ0→π++π−+γand the coupling constant g ρσγA.Gokalp ∗and O.Yilmaz †Physics Department,Middle East Technical University,06531Ankara,Turkey(February 8,2008)Abstract The experimental branching ratio for the radiative decay ρ0→π++π−+γis used to estimate the coupling constant g ρσγfor a set of values of σ-meson parameters M σand Γσ.Our results are quite different than the values of this constant used in the literature.PACS numbers:12.20.Ds,13.40.HqTypeset using REVT E XThe radiative decay processρ0→π++π−+γhas been studied employing different approaches[1,5].There are two mechanisms that can contribute to this radiative decay: thefirst one is the internal bremsstrahlung where one of the charged pions from the decay ρ0→π++π−emits a photon,and the second one is the structural radiation which is caused by the internal transformation of theρ-meson quark structure.Since the bremsstrahlung is well described by quantum electrodynamics,different methods have been used to estimate the contribution of the structural radiation.Singer[1]calculated the amplitude for this decay by considering only the bremsstrahlung mechanism since the decayρ0→π++π−is the main decay mode ofρ0-meson.He also used the universality of the coupling of theρ-meson to pions and nucleons to determine the coupling constant gρππfrom the knowledge of the coupling constant gρter,Renard [3]studied this decay among other vector meson decays into2π+γfinal states in a gauge invariant way with current algebra,hard-pion and Ward-identities techniques.He,moreover, established the correspondence between these current algebra results and the structure of the amplitude calculated in the single particle approximation for the intermediate states.In corresponding Feynman diagrams the structural radiation proceeds through the intermediate states asρ0→S+γwhere the meson S subsequently decays into aπ+π−pair.He concluded that the leading term is the pion bremsstrahlung and that the largest contribution to the structural radiation amplitude results from the scalarσ-meson intermediate state.He used the rough estimate gρσγ≃1for the coupling constant gρσγwhich was obtained with the spin independence assumption in the quark model.The coupling constant gρππwas determined using the then available experimental decay rate ofρ-meson and also current algebra results as3.2≤gρππ≤4.9.On the other hand,the coupling constant gσππwas deduced from the assumed decay rateΓ≃100MeV for theσ-meson as gσππ=3.4with Mσ=400MeV. Furthermore,he observed that theσ-contribution modifies the shape of the photon spectrum for high momenta differently depending on the mass of theσ-meson.We like to note, however,that the nature of theσ-meson as a¯q q state in the naive quark model and therefore the estimation of the coupling constant gρσγin the quark model have been a subject ofcontroversy.Indeed,Jaffe[6,7]lately argued within the framework of lattice QCD calculation of pseudoscalar meson scattering amplitudes that the light scalar mesons are¯q2q2states rather than¯q q states.Recently,on the other hand,the coupling constant gρσγhas become an important input for the studies ofρ0-meson photoproduction on nucleons.The presently available data[8] on the photoproduction ofρ0-meson on proton targets near threshold can be described at low momentum transfers by a simple one-meson exchange model[9].Friman and Soyeur [9]showed that in this picture theρ0-meson photoproduction cross section on protons is given mainly byσ-exchange.They calculated theγσρ-vertex assuming Vector Dominance of the electromagnetic current,and their result when derived using an effective Lagrangian for theγσρ-vertex gives the value gρσγ≃2.71for this coupling ter,Titov et al.[10]in their study of the structure of theφ-meson photoproduction amplitude based on one-meson exchange and Pomeron-exchange mechanisms used the coupling constant gφσγwhich they calculated from the above value of gρσγinvoking unitary symmetry arguments as gφσγ≃0.047.They concluded that the data at low energies near threshold can accommodate either the second Pomeron or the scalar mesons exchange,and the differences between these competing mechanisms have profound effects on the cross sections and the polarization observables.It,therefore,appears of much interest to study the coupling constant gρσγthat plays an important role in scalar meson exchange mechanism from a different perspective other than Vector Meson Dominance as well.For this purpose we calculate the branching ratio for the radiative decayρ0→π++π−+γ,and using the experimental value0.0099±0.0016for this branching ratio[11],we estimate the coupling constant gρσγ.Our calculation is based on the Feynman diagrams shown in Fig.1.Thefirst two terms in thisfigure are not gauge invariant and they are supplemented by the direct term shown in Fig.1(c)to establish gauge invariance.Guided by Renard’s[3]current algebra results,we assume that the structural radiation amplitude is dominated byσ-meson intermediate state which is depicted in Fig. 1(d).We describe theρσγ-vertex by the effective LagrangianL int.ρσγ=e4πMρMρ)2 3/2.(3)The experimental value of the widthΓ=151MeV[11]then yields the value g2ρππ2gσππMσ π· πσ.(4) The decay width of theσ-meson that follows from this effective Lagrangian is given asΓσ≡Γ(σ→ππ)=g2σππ8 1−(2Mπ2iΓσ,whereΓσisgiven by Eq.(5).Since the experimental candidate forσ-meson f0(400-1200)has a width (600-1000)MeV[11],we obtain a set of values for the coupling constant gρσγby considering the ranges Mσ=400-1200MeV,Γσ=600-1000MeV for the parameters of theσ-meson.In terms of the invariant amplitude M(Eγ,E1),the differential decay probability for an unpolarizedρ0-meson at rest is given bydΓ(2π)31Γ= Eγ,max.Eγ,min.dEγ E1,max.E1,min.dE1dΓ[−2E2γMρ+3EγM2ρ−M3ρ2(2EγMρ−M2ρ)±Eγfunction ofβin Fig.5.This ratio is defined byΓβRβ=,Γtot.= Eγ,max.50dEγdΓdEγ≃constant.(10)ΓσM3σFurthermore,the values of the coupling constant gρσγresulting from our estimation are in general quite different than the values of this constant usually adopted for the one-meson exchange mechanism calculations existing in the literature.For example,Titov et al.[10] uses the value gρσγ=2.71which they obtain from Friman and Soyeur’s[9]analysis ofρ-meson photoproduction using Vector Meson Dominance.It is interesting to note that in their study of pion dynamics in Quantum Hadrodynamics II,which is a renormalizable model constructed using local gauge invariance based on SU(2)group,that has the sameLagrangian densities for the vertices we use,Serot and Walecka[14]come to the conclusion that in order to be consistent with the experimental result that s-waveπN-scattering length is anomalously small,in their tree-level calculation they have to choose gσππ=12.Since they use Mσ=520MeV this impliesΓσ≃1700MeV.If we use these values in our analysis,we then obtain gρσγ=11.91.Soyeur[12],on the other hand,uses quite arbitrarly the values Mσ=500 MeV,Γσ=250MeV,which in our calculation results in the coupling constant gρσγ=6.08.We like to note,however,that these values forσ-meson parameters are not consistent with the experimental data onσ-meson[11].Our analysis and estimation of the coupling constant gρσγusing the experimental value of the branching ratio of the radiative decayρ0→π++π−+γgive quite different values for this coupling constant than used in the literature.Furthermore,since we obtain this coupling constant as a function ofσ-meson parameters,it will be of interest to study the dependence of the observables of the reactions,such as for example the photoproduction of vector mesons on nucleonsγ+N→N+V where V is the neutral vector meson, analyzed using one-meson exchange mechanism on these parameters.AcknowledgmentsWe thank Prof.Dr.M.P.Rekalo for suggesting this problem to us and for his guidance during the course of our work.We also wish to thank Prof.Dr.T.M.Aliev for helpful discussions.REFERENCES[1]P.Singer,Phys.Rev.130(1963)2441;161(1967)1694.[2]V.N.Baier and V.A.Khoze,Sov.Phys.JETP21(1965)1145.[3]S.M.Renard,Nuovo Cim.62A(1969)475.[4]K.Huber and H.Neufeld,Phys.Lett.B357(1995)221.[5]E.Marko,S.Hirenzaki,E.Oset and H.Toki,Phys.Lett.B470(1999)20.[6]R.L.Jaffe,hep-ph/0001123.[7]M.Alford and R.L.Jaffe,hep-lat/0001023.[8]Aachen-Berlin-Bonn-Hamburg-Heidelberg-Munchen Collaboration,Phys.Rev.175(1968)1669.[9]B.Friman and M.Soyeur,Nucl.Phys.A600(1996)477.[10]A.I.Titov,T.-S.H.Lee,H.Toki and O.Streltrova,Phys.Rev.C60(1999)035205.[11]Review of Particle Physics,Eur.Phys.J.C3(1998)1.[12]M.Soyeur,nucl-th/0003047.[13]S.I.Dolinsky,et al,Phys.Rep.202(1991)99.[14]B.D.Serot and J.D.Walecka,in Advances in Nuclear Physics,edited by J.W.Negeleand E.Vogt,Vol.16(1986).TABLESTABLE I.The calculated coupling constant gρσγfor differentσ-meson parametersΓσ(MeV)gρσγ500 6.97-6.00±1.58 8008.45±1.77600 6.16-6.68±1.85 80010.49±2.07800 5.18-9.11±2.64 90015.29±2.84900 4.85-10.65±3.14 90017.78±3.23Figure Captions:Figure1:Diagrams for the decayρ0→π++π−+γFigure2:The photon spectra for the decay width ofρ0→π++π−+γ.The contributions of different terms are indicated.Figure3:The pion energy spectra for the decay width ofρ0→π++π−+γ.The contri-butions of different terms are indicated.Figure4:The decay width ofρ0→π++π−+γas a function of minimum detected photon energy.Figure5:The ratio Rβ=Γβ。
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The BABAR Collaboration, B. Aubert, R. Barate, D. Boutigny, J.-M. Gaillard, A. Hicheur, Y. Karyotakis, J. P. Lees, P. Robbe, V. Tisserand, A. Zghiche Laboratoire de Physique des Particules, F-74941 Annecy-le-Vieux, France A. Palano, A. Pompili Universit` a di Bari, Dipartimento di Fisica and INFN, I-70126 Bari, Italy J. C. Chen, N. D. Qi, G. Rong, P. Wang, Y. S. Zhu Institute of High Energy Physics, Beijing 100039, China G. Eigen, I. Ofte, B. Stugu University of Bergen, Inst. of Physics, N-5007 Bergen, Norway G. S. Abrams, A. W. Borgland, A. B. Breon, D. N. Brown, J. Button-Shafer, R. N. Cahn, E. Charles, C. T. Day, M. S. Gill, A. V. Gritsan, Y. Groysman, R. G. Jacobsen, R. W. Kadel, J. Kadyk, L. T. Kerth, Yu. G. Kolomensky, J. F. Kral, G. Kukartsev, C. LeClerc, M. E. Levi, G. Lynch, L. M. Mir, P. J. Oddone, T. J. Orimoto, M. Pripstein, N. A. Roe, A. Romosan, M. T. Ronan, V. G. Shelkov, A. V. Telnov, W. A. Wenzel Lawrence Berkeley National Laboratory and University of California, Berkeley, CA 94720, USA K. Ford, T. J. Harrison, C. M. Hawkes, D. J. Knowles, S. E. Morgan, R. C. Penny, A. T. Watson, N. K. Watson University of Birmingham, Birmingham, B15 2TT, United Kingdom T. Held, K. Goetzen, H. Koch, B. Lewandowski, M. Pelizaeus, K. Peters, H. Schmuecker, M. Steinke Ruhr Universit¨ at Bochum, Institut f¨ ur Experimentalphysik 1, D-44780 Bochum, Germany N. R. Barlow, J. T. Boyd, N. Chevalier, W. N. Cottingham, M. P. Kelly, T. E. Latham, C. Mackay, F. F. Wilson University of Bristol, Bristol BS8 1TL, United Kingdom K. Abe, T. Cuhadar-Donszelmann, C. Hearty, T. S. Mattison, J. A. McKenna, D. Thiessen University of British Columbia, Vancouver, BC, Canada V6T 1Z1 P. Kyberd, A. K. McKemey Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom V. E. Blinov, A. D. Bukin, V. B. Golubev, V. N. Ivanchenko, E. A. Kravchenko, A. P. Onuchin, S. I. Serednyakov, Yu. I. Skovpen, E. P. Solodov, A. N. Yushkov Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia D. Best, M. Bruinsma, M. Chao, D. Kirkby, A. J. Lankford, M. Mandelkern, R. K. Mommsen, W. Roethel, D. P. Stoker University of California at Irvine, Irvine, CA 92697, USA C. Buchanan, B. L. Hartfiel University of California at Los Angeles, Los Angeles, CA 90024, USA
Contational Symposium on Lepton and Photon Interactions at High Energies, 8/11 — 8/16/2003, Fermilab, Illinois USA
Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309 Work supported in part by Department of Energy contract DE-AC03-76SF00515.
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B. C. Shen University of California at Riverside, Riverside, CA 92521, USA D. del Re, H. K. Hadavand, E. J. Hill, D. B. MacFarlane, H. P. Paar, Sh. Rahatlou, V. Sharma University of California at San Diego, La Jolla, CA 92093, USA J. W. Berryhill, C. Campagnari, B. Dahmes, N. Kuznetsova, S. L. Levy, O. Long, A. Lu, M. A. Mazur, J. D. Richman, W. Verkerke University of California at Santa Barbara, Santa Barbara, CA 93106, USA T. W. Beck, J. Beringer, A. M. Eisner, C. A. Heusch, W. S. Lockman, T. Schalk, R. E. Schmitz, B. A. Schumm, A. Seiden, M. Turri, W. Walkowiak, D. C. Williams, M. G. Wilson University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, CA 95064, USA J. Albert, E. Chen, G. P. Dubois-Felsmann, A. Dvoretskii, D. G. Hitlin, I. Narsky, F. C. Porter, A. Ryd, A. Samuel, S. Yang California Institute of Technology, Pasadena, CA 91125, USA S. Jayatilleke, G. Mancinelli, B. T. Meadows, M. D. Sokoloff University of Cincinnati, Cincinnati, OH 45221, USA T. Abe, F. Blanc, P. Bloom, S. Chen, P. J. Clark, W. T. Ford, U. Nauenberg, A. Olivas, P. Rankin, J. Roy, J. G. Smith, W. C. van Hoek, L. Zhang University of Colorado, Boulder, CO 80309, USA J. L. Harton, T. Hu, A. Soffer, W. H. Toki, R. J. Wilson, J. Zhang Colorado State University, Fort Collins, CO 80523, USA D. Altenburg, T. Brandt, J. Brose, T. Colberg, M. Dickopp, R. S. Dubitzky, A. Hauke, H. M. Lacker, E. Maly, R. M¨ uller-Pfefferkorn, R. Nogowski, S. Otto, J. Schubert, K. R. Schubert, R. Schwierz, B. Spaan, L. Wilden Technische Universit¨ at Dresden, Institut f¨ ur Kern- und Teilchenphysik, D-01062 Dresden, Germany D. Bernard, G. R. Bonneaud, F. Brochard, J. Cohen-Tanugi, P. Grenier, Ch. Thiebaux, G. Vasileiadis, M. Verderi Ecole Polytechnique, LLR, F-91128 Palaiseau, France A. Khan, D. Lavin, F. Muheim, S. Playfer, J. E. Swain University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom M. Andreotti, V. Azzolini, D. Bettoni, C. Bozzi, R. Calabrese, G. Cibinetto, E. Luppi, M. Negrini, L. Piemontese, A. Sarti Universit` a di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy E. Treadwell Florida A&M University, Tallahassee, FL 32307, USA F. Anulli,1 R. Baldini-Ferroli, M. Biasini,1 A. Calcaterra, R. de Sangro, D. Falciai, G. Finocchiaro, P. Patteri, I. M. Peruzzi,1 M. Piccolo, M. Pioppi,1 A. Zallo Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy