Measurement of the Pseudoscalar Decay Constant fDs Using Charm-Tagged Events in e+e- Collis

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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.。

Masses and decay constants of B_q mesons in the QCD string approach

a rXiv:h ep-ph/61193v116Oct26Masses and decay constants of B q mesons in the QCD string approach A.M.Badalian ∗and Yu.A.Simonov †Institute of Theoretical and Experimental Physics,Moscow,Russia B.L.G.Bakker ‡Vrije Universiteit,Amsterdam,The Netherlands February 2,2008Abstract The relativistic string Hamiltonian is used to calculate the masses and decay constants of B q mesons:they appear to be expressed through onlythree fundamental values:the string tension σ,αs ,and the quark pole masses.The values f B =186MeV,f B s =222MeV are calculated while f B c depends on the c -quark pole mass used,namely f B c =440(424)MeV for m c =1.40(1.35)GeV.For the 1P states we predict the spin-averaged masses:¯M (B J )=5730MeV and ¯M (B sJ )=5830MeV which are in good agreement with the recent data of the D0and CDF Collaborations,at the same time owningto the string correction being by ∼50MeV smaller than in other calculations.1IntroductionThe decay constants of pseudoscalar (P)mesons f P can be directly mea-sured in P →µνdecays [1]and therefore they can be used as an importantcriterium to compare diﬀerent theoretical approaches and estimate their ac-curacy.Although during the last decade f P were calculated many times:in potential models[2,3,4],the QCD sum rule method[5],and in lattice QCD [6,7],here we again address the properties of the B,B s,B c mesons for several reasons.First,we use here the relativistic string Hamiltonian(RSH)[8],which is derived from the QCD Lagrangian with the use of theﬁeld correlator method (FCM)[9]and successfully applied to light mesons and heavy quarkonia [10,11].Here we show that the meson Green’s function and decay constants can also be derived with the use of FCM.Second,the remarkable feature of the RSH H R and also the correlator of the currents G(x)is that they are fully determined by a minimal number of fundamental parameters:the string tensionσ,ΛMS=250(5)MeV;(1) and the pole masses taken arem u(d)=0;m s=170(10)MeV;m c=1.40GeV;m b=4.84GeV.(2) Third,recently new data on the masses of B c and the P-wave mesons: B1,B2,and B s2have been reported by the D0and CDF Collaborations [12,13],which give additional information on the B q-meson spectra.Here we calculate the spin-averaged masses of the P-wave states B and B s.We would like to emphasize here that in our relativistic calculations no constituent masses are used.In the meson mass formula an overall(ﬁtting) constant,characteristic for potential models,is absent and the whole scheme appears to be rigid.Nevertheless,we take into account an important nonperturbative(NP) self-energy contribution to the quark mass,∆SE(q)(see below eq.(18)).For the heavy b quark∆SE(b)=0and for the c quark∆SE(c)≃−20MeV[10], which is also small.For any kind of mesons we use a universal static potential with pure scalarconﬁning term,V0(r)=σr−4r,(3)2where the couplingαB(r)possesses the asymptotic freedom property and saturates at large distances withαcrit(n f=4)=0.52[14].The coupling can be expressed throughαB(q)in momentum space,αB(r)=2qαB(q),(4)whereαB(q)=4πβ20ln t BΛ2B.Here the QCD constantΛB,is expressed as[15]ΛB(n f)=Λ2β0· 319n f (6)and M B(σ,ΛB)=(1.00±0.05)GeV is the so called background mass[14]. For heavy-light mesons withΛ2+m2i+p2In (8)m 1(m 2)is the pole (current)mass of a quark (antiquark).The variable ωi is deﬁned from extremum condition,which is taken either from(1)The exact condition:∂H 0p 2+m 2i .(10)ThenH 0ϕn = p 2+m 22+V 0(r ) ϕn =M n ϕn(11)reduces to the Salpeter equation,which just deﬁnes ωi (n )=∂˜ωi =0(the so-called einbein approxima-tion).As shown in [9]the diﬀerence between ωi and ˜ωi is <∼5%.For the RSH (7)the spin-averaged massM (nL )=ω12+m 212ωb +E n (µ)−2σηf p 2+m 2i nL ;µ=ω1ωbπωf ;(14)with ηf =0.9for a u (d )quark,ηf ∼=0.7for an s quark,ηf =0.4for a c quark,and ηb =0.Therefore,for a b quark ∆SE (b )=0.The mass formula(12)does not contain any overall constant C .Note that the presence of C violates linear behavior of Regge trajectories.The calculated masses of the low-lying states of B ,B s ,and B c mesons are given in Table 2,as well as their values taken from [2,3,6,7].It is of interest to notice that in our calculations the masses of the P -wave states appear to be by 30-70MeV lower than in [2]due to taking into account a string correction [11].4Table1:Masses of the low-lying B q mesons in the QCD String Approach B5280(5)a5279.0(5)5310252753B1(1P)¯M=5730a5721(8)D05734(5)CDFB s5369a5369.6(24)5390253623B s2¯M=58305839(3)D058802B∗c6330(5)a633826321(20)63Current CorrelatorThe FCM can be also used to deﬁne the correlator GΓ(x)of the currents jΓ(x),jΓ(x)=¯ψ1(x)Γψ2(x),(15) for S,P,V,and A channels(here the operatorΓ=t a⊗(1,γ5,γµ,iγµγ5)).The correlator,GΓ(x)≡ jΓ(x)jΓ(0) vac,(16) with the use of spectral decomposition of the currents jΓand the deﬁnition, vac|¯ψ1γ0γ5ψ2|P n(k=0) =f P n M n,(A,P)vac|¯ψ1γµψ2|V n(k,ε) =f V n M nεµ,(V)(17) can be presented as[3]GΓ(x)d x= n M n0|YΓe−H0T|0ω1ω2N c YΓ=p2 .(20)3Then from Eqs.(18)and(19)one obtains the following analytical expression for the decay constants(for a given state labelled n):f P(V)n 2=2N c M n|ϕn(0)|2.(21)This very transparent formula contains only well deﬁned factors:ω1andωb, the meson mass M n,andϕn the eigenvector ofˆH0.Then in the P channelf P n 2=6(m1m2+ω1ω2− p2 )Table2:Pseudoscalar constants of B q mesons(in MeV)f B189216(34)186(5)f B s218249(42)222(2)f B swhere the w.f.at the origin,ϕn(0),is a relativistic one.In the nonrelativistic limitωi→m i,ϕn(0)→ϕNR n(0)and one comes to the standard expression:f P n(0) 2→12•In our analytic approach with minimal input of fundamental parame-ters(σ,αs,m i)the calculated decay constants are f B=186MeV,f B s=222MeV,f B s/f B=1.19.•For B c the decay constant is very sensitive to m c(pole):f B c=440MeV(m c=1.40GeV)and f B c=425MeV(m c=1.35GeV)References[1]D.Silverman and H.Yao,Phys.Rev.D38,214(1988).[2]S.Godfrey and N.Isgur,Phys.Rev.D32,189(1985);S.Godfrey,Phys.Rev.D70,054017(2004).[3]D.Ebert,R.N.Faustov,and V.O.Galkin,hep-ph/0602110;Mod.Phys.Lett.A17,803(2002),and references therein.[4]G.Cvetic,C.S.Kim,G.L.Wang,and W.K.Namgung,Phys.Lett.B596,84(2004).[5]M.Jamin,nge,Phys.Rev.D65,056005(2002)and referencestherein.[6]A.Ali Khan et al.,Phys.Rev.D70,114501(2004),ibid.64,054504(2004);C.T.H.Davies et al.,Phys.Rev.Lett.92,022001(2004).[7]A.S.Kronfeld,hep-lat/0607011and references therein;I.F.Allison etal.,Phys Rev.Lett.94172001(2005);A.Gray et al.,Phys.Rev.Lett.95,212001(2005).[8]A.Yu.Dubin,A.B.Kaidalov,and Yu.A.Simonov,Phys.Lett.B323,41(1994);Phys.Atom Nucl.56,1745(1993);E.L.Gubankova and A.Yu.Dubin,Phys.Lett.B334,180(1994).[9]H.G.Dosch and Yu.A.Simonov,Phys.Lett.B205,339(1988);Yu.A.Simonov,Z.Phys.C53,419(1992);Yu.S.Kalashnikova,A.V.Nefediev,and Yu.A.Simonov,Phys.Rev.D64,014037(2001);Yu.A.Simonov,Phys.Atom.Nucl.67,553(2004).[10]A.M.Badalian,A.I.Veselov,and B.L.G.Bakker,Phys.Rev.D70,016007(2004);Phys.Atom.Nucl.67,1367(2004).8[11]A.M.Badalian and B.L.G.Bakker,Phys.Rev.D66,034025(2002);A.M.Badalian,B.L.G.Bakker,and Yu.A.Simonov,Phys.Rev.D66,034025(2002).[12]P.Catastini(for the D0and CDF Collab.),hep-ex/0605051;M.D.Cor-coran,hep-ex/0506061.[13]D.Acosta et al.(CDF Collab.),Phys.Rev.Lett.96,202001(2006);hep-ex/0508022.[14]A.M.Badalian and D.S.Kuzmenko,Phys.Rev.D65,016004(2002);A.M.Badalian and Yu.A.Simonov,Phys.Atom.Nucl.60,636(1997).[15]M.Peter,Phys.Rev.Lett.76,602(1997);Y.Schr¨o der,Phys.Lett.B447,321(1999).[16]Yu.A.Simonov,Phys.Lett.B515,137(2001).[17]Particle Data Group,S.Eidelman,et al.,Phys.Lett.B592,1(2004).[18]A.M.Badalian and Yu.A.Simonov(in preparation).9。

Screening mass responses to the chemical potential at finite temperature

†
−5 0.00
0.01 ma
0.02
0.03
(4) .
ˆ 2 /dµ Figure 1. d2 M ˆ2 S for the pseudoscalar meson versus ma at T < Tc (β = 5.26, triangles) and T > Tc (β = 5.34, circles). Extrapolation to ma = 0 is also shown.
−
Lx 2
10
L2 + x 4 Lx x ˆ− 2 .
5
0
−Lx
ˆ tanh M
In this work, we consider the ﬂavor non-singlet mesons in QCD with two ﬂavors. The hadron correlator is then given by H (n)H (0)† = = G Tr P (ˆ µu )n0 ΓP (ˆ µd )0n Γ
3. Numerical Simulations and Results The simulations have been performed at ﬁnite temperature T /Tc ∈∼ [0.9, 1.1] on a 16 × 82 × 4 lattice with standard Wilson gauge action and with two dynamical ﬂavors of staggered quarks. We use the R-algorithm, with quark masses ma = 0.0125, 0.017 and 0.025. We also use a cornertype wall source after Coulomb gauge ﬁxing in each (y, z, t)-hyperplane. The ﬁrst derivative of the pseudoscalar meson correlator with respect to the isoscalar chemical potential is identically zero. For the isovector chemical potential, our simulation values for the ﬁrst derivative are very small in both phases. 3.1. Response of the pseudoscalar meson to the isoscalar chemical potential In the low temperature phase, the dependence of the mass on µ ˆ S is small. This behavior is to be expected, since, below the critical temperature and in the vicinity of zero µ ˆS , the pseudoscalar meson is still a Goldstone boson. In fact, the chiral extrapolation of the isoscalar response is

中国物理学会年秋季会议资料.ppt

Early theories: 0.9-1.3 Measurements: smaller Recent theories:0.5-0.7
experiment and theoretical prediction
Motivation
(3770) is thought to decay almost entirely to pure DDbar, but there is large
|Vcs | [|Vcd|]
f
K
(0)
[
f
(0)]
s [d] K [ ]
(d ) (K0)
(D0 Kll ) / (D Kll ) 1
PDG04 BF
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)/
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)
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0.2
The called “Longstanding puzzle” in Charm decay!
BF[
(3770)
D0
0
D
,
D
D
,
DD]
and BLeabharlann [ (3770) non DD]Motivation
Search for some exclusive non-DDbar decays
BES observed 12 signal events for the decay (3770) non D D measured the branching fraction to be
BF ( (3770) J / ) (0.34 0.14 0.09)%
CLEO confirmed BES observation of the decay, and measured the branching fractions to be

The decay $rho^{0}to pi^{+}+pi^{-}+gamma$ and the coupling constant g$_{rhosigmagamma}$

$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。

Pi and PiPi Decays of Excited D Mesons

a r X i v :h e p -p h /0112223v 1 17 D e c 2001πand ππDecays of Excited D MesonsT.A.L¨a hde a and D.O.Riska aa HelsinkiInstitute of Physics,University of Helsinki,PL 64Helsinki,Finland(Received:February 1,2008)The πand ππdecay widths of the excited charm mesons are calculated using a Hamiltonian model within the framework of the covariant Blankenbecler-Sugar equation.The pion-light constituent quark coupling is described by the chiral pseudovector Lagrangian.1IntroductionThe pionic decay widths of the excited charm mesons (D mesons)are interesting observables,since they depend straightforwardly on the coupling of pions to light constituent quarks.The D mesons consist of one light (u,d )quark and a heavy charm (c )antiquark,of which it is only the light constituent quark that couples to pions.The coupling of light constituent quarks to pions may be described by the chiral model [1],which includes the pseudovector Lagrangian and,for ππdecay,also a Weinberg-Tomozawa term.In order to predict the decay widths of the excited D meson states,a model for the radial wavefunctions is needed.Here the interaction between the quarks is modeled as the sum of a screened one-gluon exchange (OGE)and a scalar linear conﬁning interaction.The wavefunctions are obtained as solutions of the covariant Blankenbecler-Sugar equation [2].These are then used together with the chiral Lagrangian to obtain predictions for the π[3]and ππ[4]decays of the excited D mesons.1800200022002400260028003000320034001S 03S 1 1P 1 3P 0 3P 1 3P 2 1D 2 3D 1 3D 2 3D 3Empirical and calculated D meson spectra (State energies in MeV)DD *D ** ?D 1D 2*Experimental CalculatedFigure 1:Empirical and calculated spec-tra of the D meson from ref.[3].The D ∗is an S -wave spin-triplet state which lies almost exactly at threshold for decay to Dπ.The decay widths for πdecay of the D ∗are predicted here along with those of the four L =1states,which can de-cay to both D ∗πand Dπ.These states can also decay to D ∗ππand Dππ.Note that empirical data is only available for the spin triplet states with L =1and total angular momentum J =1and J =2.2Single pion decayThe chiralLagrangian describingthecoupling between pions and light constituent quarks may be written as [3]L =ig q A2f π4EE ′1−P 2−k 2/42f π2m ¯q +E +E ′4EE ′(E +m ¯q )(E ′+m ¯q )ωπ σq ·p ′+ p g qA =0.8729keV 64keV 41keV4f 2π¯ψq γµ τ· φπ×∂µ φπψq .(4)Together,the Lagrangians(1,4)give rise to amplitudes forππdecay,which are usually expressed in the form T=δab T++12fπ 24m q,(5)A−=0,(6) B+=− g q A s−m2q−12fπ2 2+4m2q 1u−m2q +1πwidth Total15.718.813.614.927.727.813.221.8。

磁共振中一些常用简化附缩写用语

COSY
( Homonuclear chemical shift ) COrrelation SpectroscopY
CP
Cross Polarization
CPD
Composite-Pulse Decoupling
CP/MAS
Cross Polarization/Magic Angle Spinning
BBDR
Broad Band Double Resonance
BIRD
Bilinear Rotation Decoupling
BOLD
Blood Oxygenation Level Dependent
BR-24
Burum & Rhim (pulse sequence)
CAMELSPIN
Cross-relaxation Appropriate for Minimolecules Emulated by Locked SPNs
GRASS
Gradient-Recalled Acquisition in the Steady State
GRASP
Gradient-Accelerated Spectroscopy
GROPE
Generalized compensation for Resonance Offset and Pulse length errors
MQ(C)
Multiple-Quantum ( Coherence )
MQF
Multiple-Quantum Filter
MQMAS
Multiple-Quantum Magic-Angle Spinning
MQS
Multi Quantum Spectroscopy

Parity-even and Parity-odd Mesons in Covariant Light-front Approach

0
–
–
fsu¯ (160)
22 (210) −186
11
–
–
fcu¯ (200)
86 (220) −127
45
130
−36
fcs¯ (230)
71 (230) −121
38
122
−38
fbu¯ (180) 112 (180) −123
68
140
−15
From Table 1 we see that the decay constants of light scalar resonances are sup-
for form factors in B → D, D∗, D∗∗ (D∗∗ denoting generic p-wave charmed mesons) transitions agree with those in the ISGW2 model.4 Relativistic eﬀects are mild in
B → D transition, but they could be more prominent in heavy-to-light transitions,
especially at maximum recoil (q2 = 0). For example, we obtain V0Ba1 ay constants and form factors
Consider the decay constants for mesons with the quark content q1q¯2 in the 2S+1LJ = 1S0, 3P0, 3S1, 3P1, 1P1 conﬁgurations. In the SU(N)-ﬂavor limit (m1 = m2) the decay constants fS(3P0) and f1P1 should vanish.6 In the heavy quark limit (m1 → ∞), it is more convenient to use the LjJ = P23/2, P13/2, P11/2 and P01/2 basis as the heavy quark spin sQ and the total angular momentum of the light

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a r X i v :h e p -e x /0607094v 1 28 J u l 2006B A B A R -PUB-06/010SLAC-PUB-11968Measurement of the Pseudoscalar Decay Constant f D s Using Charm-Tagged Events in e +e −Collisions at√R.Kroeger,49J.Reidy,49D.A.Sanders,49D.J.Summers,49H.W.Zhao,49S.Brunet,50D.Cˆo t´e,50M.Simard,50 P.Taras,50F.B.Viaud,50H.Nicholson,51N.Cavallo,52,‡G.De Nardo,52D.del Re,52F.Fabozzi,52,‡C.Gatto,52 L.Lista,52D.Monorchio,52P.Paolucci,52D.Piccolo,52C.Sciacca,52M.Baak,53H.Bulten,53G.Raven,53 H.L.Snoek,53C.P.Jessop,54J.M.LoSecco,54T.Allmendinger,55G.Benelli,55K.K.Gan,55K.Honscheid,55D.Hufnagel,55P.D.Jackson,55H.Kagan,55R.Kass,55T.Pulliam,55A.M.Rahimi,55R.Ter-Antonyan,55Q.K.Wong,55N.L.Blount,56J.Brau,56R.Frey,56O.Igonkina,56M.Lu,56R.Rahmat,56N.B.Sinev,56D.Strom,56J.Strube,56E.Torrence,56F.Galeazzi,57A.Gaz,57M.Margoni,57M.Morandin,57A.Pompili,57 M.Posocco,57M.Rotondo,57F.Simonetto,57R.Stroili,57C.Voci,57M.Benayoun,58J.Chauveau,58P.David,58 L.Del Buono,58Ch.de la Vaissi`e re,58O.Hamon,58B.L.Hartﬁel,58M.J.J.John,58Ph.Leruste,58J.Malcl`e s,58 J.Ocariz,58L.Roos,58G.Therin,58P.K.Behera,59L.Gladney,59J.Panetta,59M.Biasini,60R.Covarelli,60 M.Pioppi,60C.Angelini,61G.Batignani,61S.Bettarini,61F.Bucci,61G.Calderini,61M.Carpinelli,61R.Cenci,61F.Forti,61M.A.Giorgi,61A.Lusiani,61G.Marchiori,61M.A.Mazur,61M.Morganti,61N.Neri,61E.Paoloni,61G.Rizzo,61J.Walsh,61M.Haire,62D.Judd,62D.E.Wagoner,62J.Biesiada,63N.Danielson,63P.Elmer,63u,63C.Lu,63J.Olsen,63A.J.S.Smith,63A.V.Telnov,63F.Bellini,64G.Cavoto,64A.D’Orazio,64E.Di Marco,64R.Faccini,64F.Ferrarotto,64F.Ferroni,64M.Gaspero,64L.Li Gioi,64M.A.Mazzoni,64S.Morganti,64G.Piredda,64F.Polci,64F.Safai Tehrani,64C.Voena,64M.Ebert,65H.Schr¨o der,65R.Waldi,65 T.Adye,66N.De Groot,66B.Franek,66E.O.Olaiya,66F.F.Wilson,66R.Aleksan,67S.Emery,67A.Gaidot,67 S.F.Ganzhur,67G.Hamel de Monchenault,67W.Kozanecki,67M.Legendre,67B.Mayer,67G.Vasseur,67 Ch.Y`e che,67M.Zito,67W.Park,68M.V.Purohit,68A.W.Weidemann,68J.R.Wilson,68M.T.Allen,69D.Aston,69R.Bartoldus,69P.Bechtle,69N.Berger,69A.M.Boyarski,69R.Claus,69J.P.Coleman,69M.R.Convery,69M.Cristinziani,69J.C.Dingfelder,69D.Dong,69J.Dorfan,69G.P.Dubois-Felsmann,69D.Dujmic,69W.Dunwoodie,69R.C.Field,69T.Glanzman,69S.J.Gowdy,69M.T.Graham,69V.Halyo,69C.Hast,69T.Hryn’ova,69W.R.Innes,69M.H.Kelsey,69P.Kim,69M.L.Kocian,69D.W.G.S.Leith,69S.Li,69J.Libby,69S.Luitz,69V.Luth,69H.L.Lynch,69D.B.MacFarlane,69H.Marsiske,69R.Messner,69D.R.Muller,69C.P.O’Grady,69V.E.Ozcan,69A.Perazzo,69M.Perl,69B.N.Ratcliﬀ,69A.Roodman,69A.A.Salnikov,69R.H.Schindler,69J.Schwiening,69A.Snyder,69J.Stelzer,69D.Su,69M.K.Sullivan,69K.Suzuki,69S.K.Swain,69J.M.Thompson,69J.Va’vra,69N.van Bakel,69M.Weaver,69A.J.R.Weinstein,69 W.J.Wisniewski,69M.Wittgen,69D.H.Wright,69A.K.Yarritu,69K.Yi,69C.C.Young,69P.R.Burchat,70 A.J.Edwards,70S.A.Majewski,70B.A.Petersen,70C.Roat,70L.Wilden,70S.Ahmed,71M.S.Alam,71R.Bula,71 J.A.Ernst,71V.Jain,71B.Pan,71M.A.Saeed,71F.R.Wappler,71S.B.Zain,71W.Bugg,72M.Krishnamurthy,72 S.M.Spanier,72R.Eckmann,73J.L.Ritchie,73A.Satpathy,73C.J.Schilling,73R.F.Schwitters,73J.M.Izen,74I.Kitayama,74X.C.Lou,74S.Ye,74F.Bianchi,75F.Gallo,75D.Gamba,75M.Bomben,76L.Bosisio,76C.Cartaro,76F.Cossutti,76G.Della Ricca,76S.Dittongo,76S.Grancagnolo,nceri,76L.Vitale,76V.Azzolini,77F.Martinez-Vidal,77Sw.Banerjee,78B.Bhuyan,78C.M.Brown,78D.Fortin,78K.Hamano,78 R.Kowalewski,78I.M.Nugent,78J.M.Roney,78R.J.Sobie,78J.J.Back,79P.F.Harrison,tham,79G.B.Mohanty,79H.R.Band,80X.Chen,80B.Cheng,80S.Dasu,80M.Datta,80A.M.Eichenbaum,80K.T.Flood,80J.J.Hollar,80J.R.Johnson,80P.E.Kutter,80H.Li,80R.Liu,80B.Mellado,80A.Mihalyi,80A.K.Mohapatra,80Y.Pan,80M.Pierini,80R.Prepost,80P.Tan,80S.L.Wu,80Z.Yu,80and H.Neal81(The B A B A R Collaboration)1Laboratoire de Physique des Particules,F-74941Annecy-le-Vieux,France2Universitat de Barcelona,Facultat de Fisica Dept.ECM,E-08028Barcelona,Spain3Universit`a di Bari,Dipartimento di Fisica and INFN,I-70126Bari,Italy4Institute of High Energy Physics,Beijing100039,China5University of Bergen,Institute of Physics,N-5007Bergen,Norway6Lawrence Berkeley National Laboratory and University of California,Berkeley,California94720,USA7University of Birmingham,Birmingham,B152TT,United Kingdom8Ruhr Universit¨a t Bochum,Institut f¨u r Experimentalphysik1,D-44780Bochum,Germany9University of Bristol,Bristol BS81TL,United Kingdom10University of British Columbia,Vancouver,British Columbia,Canada V6T1Z111Brunel University,Uxbridge,Middlesex UB83PH,United Kingdom12Budker Institute of Nuclear Physics,Novosibirsk630090,Russia13University of California at Irvine,Irvine,California92697,USA14University of California at Los Angeles,Los Angeles,California90024,USA15University of California at Riverside,Riverside,California92521,USA16University of California at San Diego,La Jolla,California92093,USA17University of California at Santa Barbara,Santa Barbara,California93106,USA 18University of California at Santa Cruz,Institute for Particle Physics,Santa Cruz,California95064,USA 19California Institute of Technology,Pasadena,California91125,USA20University of Cincinnati,Cincinnati,Ohio45221,USA21University of Colorado,Boulder,Colorado80309,USA22Colorado State University,Fort Collins,Colorado80523,USA23Universit¨a t Dortmund,Institut f¨u r Physik,D-44221Dortmund,Germany24Technische Universit¨a t Dresden,Institut f¨u r Kern-und Teilchenphysik,D-01062Dresden,Germany25Ecole Polytechnique,LLR,F-91128Palaiseau,France26University of Edinburgh,Edinburgh EH93JZ,United Kingdom27Universit`a di Ferrara,Dipartimento di Fisica and INFN,I-44100Ferrara,Italy28Laboratori Nazionali di Frascati dell’INFN,I-00044Frascati,Italy29Universit`a di Genova,Dipartimento di Fisica and INFN,I-16146Genova,Italy30Harvard University,Cambridge,Massachusetts02138,USA31Universit¨a t Heidelberg,Physikalisches Institut,Philosophenweg12,D-69120Heidelberg,Germany32Imperial College London,London,SW72AZ,United Kingdom33University of Iowa,Iowa City,Iowa52242,USA34Iowa State University,Ames,Iowa50011-3160,USA35Johns Hopkins University,Baltimore,Maryland21218,USA36Universit¨a t Karlsruhe,Institut f¨u r Experimentelle Kernphysik,D-76021Karlsruhe,Germany37Laboratoire de l’Acc´e l´e rateur Lin´e aire,IN2P3-CNRS et Universit´e Paris-Sud11,Centre Scientiﬁque d’Orsay,B.P.34,F-91898ORSAY Cedex,France38Lawrence Livermore National Laboratory,Livermore,California94550,USA39University of Liverpool,Liverpool L697ZE,United Kingdom40Queen Mary,University of London,E14NS,United Kingdom41University of London,Royal Holloway and Bedford New College,Egham,Surrey TW200EX,United Kingdom42University of Louisville,Louisville,Kentucky40292,USA43University of Manchester,Manchester M139PL,United Kingdom44University of Maryland,College Park,Maryland20742,USA45University of Massachusetts,Amherst,Massachusetts01003,USA 46Massachusetts Institute of Technology,Laboratory for Nuclear Science,Cambridge,Massachusetts02139,USA47McGill University,Montr´e al,Qu´e bec,Canada H3A2T848Universit`a di Milano,Dipartimento di Fisica and INFN,I-20133Milano,Italy49University of Mississippi,University,Mississippi38677,USA50Universit´e de Montr´e al,Physique des Particules,Montr´e al,Qu´e bec,Canada H3C3J751Mount Holyoke College,South Hadley,Massachusetts01075,USA52Universit`a di Napoli Federico II,Dipartimento di Scienze Fisiche and INFN,I-80126,Napoli,Italy53NIKHEF,National Institute for Nuclear Physics and High Energy Physics,NL-1009DB Amsterdam,The Netherlands 54University of Notre Dame,Notre Dame,Indiana46556,USA55Ohio State University,Columbus,Ohio43210,USA56University of Oregon,Eugene,Oregon97403,USA57Universit`a di Padova,Dipartimento di Fisica and INFN,I-35131Padova,Italy 58Universit´e s Paris VI et VII,Laboratoire de Physique Nucl´e aire et de Hautes Energies,F-75252Paris,France 59University of Pennsylvania,Philadelphia,Pennsylvania19104,USA60Universit`a di Perugia,Dipartimento di Fisica and INFN,I-06100Perugia,Italy 61Universit`a di Pisa,Dipartimento di Fisica,Scuola Normale Superiore and INFN,I-56127Pisa,Italy62Prairie View A&M University,Prairie View,Texas77446,USA63Princeton University,Princeton,New Jersey08544,USA64Universit`a di Roma La Sapienza,Dipartimento di Fisica and INFN,I-00185Roma,Italy65Universit¨a t Rostock,D-18051Rostock,Germany66Rutherford Appleton Laboratory,Chilton,Didcot,Oxon,OX110QX,United Kingdom67DSM/Dapnia,CEA/Saclay,F-91191Gif-sur-Yvette,France68University of South Carolina,Columbia,South Carolina29208,USA69Stanford Linear Accelerator Center,Stanford,California94309,USA70Stanford University,Stanford,California94305-4060,USA71State University of New York,Albany,New York12222,USA72University of Tennessee,Knoxville,Tennessee37996,USA73University of Texas at Austin,Austin,Texas78712,USA74University of Texas at Dallas,Richardson,Texas75083,USA75Universit`a di Torino,Dipartimento di Fisica Sperimentale and INFN,I-10125Torino,Italy76Universit`a di Trieste,Dipartimento di Fisica and INFN,I-34127Trieste,Italy77IFIC,Universitat de Valencia-CSIC,E-46071Valencia,Spain78University of Victoria,Victoria,British Columbia,Canada V8W3P679Department of Physics,University of Warwick,Coventry CV47AL,United Kingdom80University of Wisconsin,Madison,Wisconsin53706,USA81Yale University,New Haven,Connecticut06511,USA(Dated:February7,2008)Using230.2fb−1of e+e−annihilation data collected with the B A B A R detector at and near the peakof theΥ(4S)resonance,489±55events containing the pure leptonic decay D+s→µ+νµhave beenisolated in charm-tagged events.The ratio of partial widthsΓ(D+s→µ+νµ)/Γ(D+s→φπ+)ismeasured to be0.143±0.018±0.006allowing a determination of the pseudoscalar decay constantf D s=(283±17±7±14)MeV.The errors are statistical,systematic,and from the D+s→φπ+branching ratio,respectively.PACS numbers:13.20.He,14.40.Nd,14.60.FgMeasurements of pure leptonic decays of charmed pseu-doscalar mesons are of particular theoretical importance.They provide an unambiguous determination of the over-lap of the wavefunctions of the heavy and light quarkswithin the meson,represented by a single decay constant(f M)for each meson species(M).The partial width fora D+s meson to decay to a single leptonﬂavor(l)and itsaccompanying neutrino(νl),is given byΓ(D+s→l+νl)=G2F|V cs|2m2D s 2,(1)where m Ds and m l are the D+s and lepton masses,re-spectively,G F is the Fermi constant,and V cs is theCKM matrix element giving the coupling of the weakcharged current to the c and s quarks[1].The partialwidth is governed by two opposing terms in m2l.Theﬁrst term reﬂects helicity suppression in the decay of thespin-0meson,requiring the charged lepton to be in itsunfavored helicity state.The second term is a phase-space factor.As a result,the ratio ofτ:µ:e de-cays is approximately10:1:ttice calcula-tions have resulted in f Ds=(249±17)MeV and a ratiof Ds/f D=1.24±0.07[2].CLEO-c has recently measureda value for f D=(223±17)MeV[3].We present herein the most precise measurement todate of the ratioΓ(D+s→µ+νµ)/Γ(D+s→φπ+)andthe decay constant f Ds.The data(230.2fb−1)were col-lected with the B A B A R detector at the asymmetric-energye+e−storage ring PEP-II at and below theΥ(4S)reso-nance.The B A B A R detector is described in detail else-where[4].Brieﬂy,the components used in this analysisare the tracking system composed of aﬁve-layer siliconvertex detector and a40-layer drift chamber(DCH),theCherenkov detector(DIRC)for chargedπ–K discrim-ination,the CsI(Tl)calorimeter(EMC)for photon andelectron identiﬁcation,and the18-layerﬂux return(IFR)located outside the1.5T solenoid coil and instrumentedwith resistive plate chambers for muon identiﬁcation andhadron rejection.The analysis proceeds as follows.In order to measureD+s→µ+νµ,the decay chain D∗+s→γD+s,D+s→µ+νµis reconstructed from D∗+s mesons produced in the hardfragmentation of continuum c5FIG.1:Tag mass distribution,showing the signal and side-band regions,in events with a recoil muon.All tag modes are combined,scaling their mass and width to that of the D0→K−π+mode.Muons used in this analysis are identiﬁed with an average eﬃciency of≈70%,while the pion misidentiﬁcation rateis≈2.5%.Clusters of energy in the EMC not associated with charged tracks are identiﬁed as photon candidates.The photon CM energy must exceed0.115GeV.The CM missing energy(E∗miss)and momentum( p∗miss) are calculated from the four-momenta of the incominge+e−,the tag four-momentum,and the four-momenta of all remaining tracks and photons in the event.The energy of the charged particles that do not belong tothe tag is calculated from the track momentum under a pion mass hypothesis.Assigning a mass according to the most likely particle hypothesis has negligible eﬀecton the missing energy resolution.Since the neutrino in the signal decay leads to a large missing energy in theevent,the requirement E∗miss>0.38GeV is made. The neutrino CM four-momentum(p∗ν=(| p∗ν|, p∗ν)) is estimated from the muon CM four-momentum(p∗µ) and p∗miss,using a technique adopted from Ref.[5].Thediﬀerence| p∗miss− p∗ν|is minimized,while the invariant mass of the neutrino-muon pair is required to be the known mass of the D+s[6].Studies of simulated decays of signal and background cc events it peaks at a negative value signiﬁcantly separated from the signal.A requirement p corr>−0.06GeV/c is imposed.To reduce contributions from background events where particles are lost along the beam pipe in the forward direction,a requirement on the neutrino CM polar angleθ∗ν>38◦is made.The muon CM four-momentum(p∗µ)is combined with p∗νto form the D+s candidate.Unlike the signal D+s,a large num-ber of random D+s combinations have the muon candi-date aligned with the D+sﬂight direction.A requirement cos(αµ,Ds)<0.90is made on the angle between the muondirection in the D+s frame and the D+sﬂight direction in the CM frame.The D+s candidate is then combined with a photon candidate to form the D∗+s.The CM momen-tum of correctly reconstructed D∗+s is typically higher than that of random combinations;signal candidates are required to have| p∗D∗+s|>3.55GeV/c.The resulting sig-nal detection eﬃciency in tagged events isǫSig=8.13%.The selection requirements on E∗miss,αµ,Ds,p corr,θ∗ν, and| p∗D∗+s|are optimized using simulation to maximize the signiﬁcance s/√c where the tag is incorrectly reconstructed. Although these events potentially contain the signal de-cay,they are also subtracted using the tag sidebands. These two sources amount to≈42%of the background. The second class of background events(≈26%)are correctly tagged cc fragmentation or indecays of D∗+(s),excluding the signal decay chain.If the photon used in the reconstruction originates from aπ0ofa D∗+(s)decay,the∆M distribution peaks sharply around 70MeV/c2;otherwise it isﬂat.A small background (≈1%)arises from decays D∗+s→γD+s→γτ+ντwith τ+→π+(π0)ντand the charged pion being misidentiﬁed as a muon.Its∆M distribution peaks close to that of the signal.Other backgrounds(≈10%)include signal events with an incorrectly chosen photon candidate,and hadronic c6FIG.2:∆M distribution of charm-tagged events passing thesignal selection.The tag can be from the tag signal region(solid lines)or the sidebands(dashed lines).In the bottomplot the signal muon is replaced with an electron to estimatethe semileptonic charm andτdecay background.usually aπ+or a K+,being misidentiﬁed as a muon.These backgrounds have aﬂat∆M distribution.Events that pass the signal selection are grouped intofour sets,depending on whether the tag lies in the sig-nal region or the sideband regions,and on whether thelepton is a muon or an electron(Fig.2).For each leptontype the sideband∆M distribution is subtracted.Theelectron distribution,scaled by the relative phase-spacefactor(0.97)appropriate to semileptonic charm mesondecays and leptonicτdecays is then subtracted fromthe muon distribution.The resulting∆M distributionisﬁtted with a function(N Sig f Sig+N Bkgd f Bkgd)(∆M),where f Sig and f Bkgd describe the simulated signal andbackground∆M distributions.The function f Sig is adouble Gaussian distribution.The function f Bkgd con-sists of a double and a single Gaussian distribution de-scribing the two peaking background components,anda function[7]describing theﬂat background component.The relative sizes of the background components,alongwith all parameters except N Sig and N Bkgd areﬁxed tothe values estimated from simulation.Theχ2ﬁt yieldsN Sig=489±55(stat)signal events and has aﬁt proba-bility of8.9%(Fig.3).The branching fraction of D+s→µ+νµcannot be de-termined directly,since the production rate of D(∗)+smesons in c7FIG.4:∆M distribution of selected D∗+s→γD+s→γφπ+ events after the tag sideband is subtracted.The solid line is theﬁtted signal and background distribution(Nφπfφπ+ NφπBkgd fφπBkgd),the dashed line is the background distribu-tion(NφπBkgd fφπBkgd)alone.pion to be at least0.8GeV/c.The eﬃciency-correctedD∗+s momentum distribution in data is compared to that of D∗+s in simulated D∗+s→γD+s→γφπ+events.A harder momentum spectrum is observed in data.The de-tection eﬃciencies for signal and D∗+s→γD+s→γφπ+ events are re-evaluated after weighting simulated events to match the D∗+s momentum distribution measured in data.The correction to the eﬃciency ratio is+1.5%. With both corrections applied,the partial width ra-tio is determined to beΓµν/Γφπ=(N/ǫ)Sig/(N/ǫ)φπ×B(φ→K+K−)=0.143±0.018(stat),with B(φ→K+K−)=49.1%[6].The combined systematic uncertainty due to the cor-rections applied,taken as half the size of each correction, is1.0%.The systematic error in the signal eﬃciency due to selection criteria insensitive to the D∗+s momentum is evaluated using reconstructed D∗0→γD0→γK−π+ events.The conditions present in the signal are emulated by removing the charged pion,taken to represent the neu-trino,from these events.The signal reconstruction and selection steps are repeated,and the selection eﬃciencies compared between simulated and data events.The as-signed systematic uncertainty is1.4%.For the D+s→φπ+selection,requirements on the D+s andφvertexﬁt probability contribute a systematic uncertainty of0.7%, estimated from comparisons of D+s→φπ+events in sim-ulation and data.Control samples of e+e−→µ+µ−γand D∗+→π+D0→π+K−π+events are used to mea-sure the particle identiﬁcation eﬃciencies of muons and charged kaons and pions in data,and to correct the sim-ulated signal and D∗+s→γD+s→γφπ+eﬃciencies.An uncertainty of0.7%is associated with these corrections, mainly due to the limited statistics of the control sam-ples.The systematic uncertainties in the track recon-struction eﬃciency cancel partially in the D+s→µ+νµto D+s→φπ+ratio and contribute1.2%.An additional uncertainty of1.1%is due to the statistical limitations of the simulated signal and D+s→φπ+event samples.Simulation studies are used to evaluate the systematic uncertainties arising from a possible inadequate param-eterization of the signal(0.9%)and background(2.3%) shapes.Simulations are also used to determine the sys-tematic uncertainty associated with the subtraction of the electron sample(0.4%).The error on the branching ratio B(φ→K+K−)is1.2%,the uncertainty on the D+s→f0(980)π+background is1.1%.The total sys-tematic uncertainty onΓ(D+s→µ+νµ)/Γ(D+s→φπ+) is3.9%.Using the B A B A R average for the branching ratio B(D+s→φπ+)=(4.71±0.46)%[8][9],we obtain the branching fraction B(D+s→µ+νµ)=(6.74±0.83±0.26±0.66)×10−3and the decay constant f Ds=(283±17±7±14)MeV.Theﬁrst and second errors are statistical and systematic,respectively;the third is the uncertainty from B(D+s→φπ+).The ratio of our value for f D s to f D from the CLEO-c measurement,f Ds/f D=1.27±0.14, is consistent with lattice QCD.Using B(D+s→φπ+)PDG=(3.6±0.9)%[6],the branching fraction is B(D+s→µ+νµ)=(5.15±0.63±0.20±1.29)×10−3and the decay constant f Ds=(248±15±6±31)MeV.We are grateful for the excellent luminosity and ma-chine conditions provided by our PEP-II colleagues,and for the substantial dedicated eﬀort from the computing organizations that support B A B A R.The collaborating institutions wish to thank SLAC for its support and kind hospitality.This work is supported by DOE and NSF(USA),NSERC(Canada),IHEP(China),CEA and CNRS-IN2P3(France),BMBF and DFG(Germany), INFN(Italy),FOM(The Netherlands),NFR(Norway), MIST(Russia),and PPARC(United Kingdom).Indi-viduals have received support from the Marie Curie EIF (European Union)and the A.P.Sloan Foundation.∗Also at Laboratoire de Physique Corpusculaire,Clermont-Ferrand,France†Also with Universit`a di Perugia,Dipartimento di Fisica, Perugia,Italy‡Also with Universit`a della Basilicata,Potenza,Italy[1]Charge conjugation is implied throughout this Letter.[2]C.Aubin et al.,Phys.Rev.Lett.95,122002(2005).[3]CLEO Collaboration,M.Artuso et al.,Phys.Rev.Lett.95,251801(2005).[4]B A B A R Collaboration,B.Aubert et al.,Nucl.Instrum.Methods Phys.Res.,Sect.A479,1(2002).[5]CLEO Collaboration,M.Chadha et al.,Phys.Rev.D58,032002(1998).[6]Particle Data Group,S.Eidelman et al.,Phys.Lett.B592,1(2004).[7]¯A(∆M|∆M0,a,b,c)= 1−exp −∆M−∆M0∆M0 a+b ∆M8to appear in Phys.Rev.D-Rapid Communications.091104(2005).[9]B A B A R Collaboration,B.Aubert et al.,hep-ex/0605036,。