Study of J/Psi decays into eta Kstar Kstar-bar
aa r X i v : . [ h e p - e x ] N ov Study of J /ψ decays into η K ∗ K ∗ M. Ablikim , J. Z. Bai , Y. Bai , Y. Ban , X. Cai , H. F. Chen , H. S. Chen , H. X. Chen , J. C. Chen ,Jin Chen , X. D. Chen , Y. B. Chen , Y. P. Chu , Y. S. Dai , Z. Y. Deng , S. X. Du a , J. Fang , C. D. Fu ,C. S. Gao , Y. N. Gao , S. D. Gu , Y. T. Gu , Y. N. Guo , Z. J. Guo b , F. A. Harris , K. L. He , M. He ,Y. K. Heng , H. M. Hu , T. Hu , G. S. Huang c , X. T. Huang , Y. P. Huang , X. B. Ji , X. S. Jiang ,J. B. Jiao , D. P. Jin , S. Jin , G. Li , H. B. Li , J. Li , L. Li , R. Y. Li , W. D. Li , W. G. Li , X. L. Li ,X. N. Li , X. Q. Li , Y. F. Liang , B. J. Liu d , C. X. Liu , Fang Liu , Feng Liu , H. M. Liu , J. P. Liu ,H. B. Liu e , J. Liu , Q. Liu , R. G. Liu , S. Liu , Z. A. Liu , F. Lu , G. R. Lu , J. G. Lu , C. L. Luo ,F. C. Ma , H. L. Ma , Q. M. Ma , M. Q. A. Malik , Z. P. Mao , X. H. Mo , J. Nie , S. L. Olsen , R. G. Ping ,N. D. Qi , J. F. Qiu , G. Rong , X. D. Ruan , L. Y. Shan , L. Shang , C. P. Shen , X. Y. Shen ,H. Y. Sheng , H. S. Sun , S. S. Sun , Y. Z. Sun , Z. J. Sun , X. Tang , J. P. Tian , G. L. Tong ,G. S. Varner , X. Wan , L. Wang , L. L. Wang , L. S. Wang , P. Wang , P. L. Wang , Y. F. Wang , Z. Wang ,Z. Y. Wang , C. L. Wei , D. H. Wei , N. Wu , X. M. Xia , G. F. Xu , X. P. Xu , Y. Xu , M. L. Yan ,H. X. Yang , M. Yang , Y. X. Yang , M. H. Ye , Y. X. Ye , C. X. Yu , C. Z. Yuan , Y. Yuan , Y. Zeng ,B. X. Zhang , B. Y. Zhang , C. C. Zhang , D. H. Zhang , H. Q. Zhang , H. Y. Zhang , J. W. Zhang ,J. Y. Zhang , X. Y. Zhang , Y. Y. Zhang , Z. X. Zhang , Z. P. Zhang , D. X. Zhao , J. W. Zhao ,M. G. Zhao , P. P. Zhao , Z. G. Zhao , B. Zheng , H. Q. Zheng , J. P. Zheng , Z. P. Zheng , B. Zhong L. Zhou , K. J. Zhu , Q. M. Zhu , X. W. Zhu , Y. S. Zhu , Z. A. Zhu , Z. L. Zhu , B. A. Zhuang , B. S. Zou (BES Collaboration) Institute of High Energy Physics, Beijing 100049, People’s Republic of China China Center for Advanced Science and Technology(CCAST), Beijing 100080, People’s Republic of China Guangxi Normal University, Guilin 541004, People’s Republic of China Guangxi University, Nanning 530004, People’s Republic of China Henan Normal University, Xinxiang 453002, People’s Republic of China Huazhong Normal University, Wuhan 430079, People’s Republic of China Hunan University, Changsha 410082, People’s Republic of China Liaoning University, Shenyang 110036, People’s Republic of China Nanjing Normal University, Nanjing 210097, People’s Republic of China Nankai University, Tianjin 300071, People’s Republic of China Peking University, Beijing 100871, People’s Republic of China Shandong University, Jinan 250100, People’s Republic of China Sichuan University, Chengdu 610064, People’s Republic of China Tsinghua University, Beijing 100084, People’s Republic of China University of Hawaii, Honolulu, HI 96822, USA University of Science and Technology of China, Hefei 230026, People’s Republic of China Wuhan University, Wuhan 430072, People’s Republic of China Zhejiang University, Hangzhou 310028, People’s Republic of China a Current address: Zhengzhou University, Zhengzhou 450001, People’s Republic of China b Current address: Johns Hopkins University, Baltimore, MD 21218, USA c Current address: University of Oklahoma, Norman, Oklahoma 73019, USA d Current address: University of Hong Kong, Pok Fu Lam Road, Hong Kong e Current address: Graduate University of Chinese Academy of Sciences, Beijing 100049, People’s Republic ofChina
We report the first observation of J /ψ → η K ∗ K ∗ decay in a J /ψ sample of 58 million events collected withthe BESII detector. The branching fraction is determined to be (1 . ± . ± . × − . The selected signalevent sample is further used to search for the Y (2175) resonance through J /ψ → ηY (2175) , Y (2175) → K ∗ K ∗ .No evidence of a signal is seen. An upper limit of Br( J /ψ → ηY (2175)) · Br( Y (2175) → K ∗ K ∗ ) < . × − is set at the 90% confidence level. . Introduction Following the observation of Y (2175) by theBaBar Collaboration in e + e − → γ ISR φf (980)via initial-state radiation [1], the resonance wasobserved by the BES Collaboration in J/ψ → ηφf (980) [2] and more recently by the Belle Col-laboration in e + e − → γ ISR φπ + π − [3]. Since boththe Y (2175) and Y (4260) [4] are observed in e + e − annihilation via initial-state radiation andthese two resonances have similar decay modes, itwas speculated that Y (2175) may be an s -quarkversion of Y (4260) [1]. There have been a num-ber of different interpretations proposed for the Y (4260), that include a gc ¯ c hybrid [5] [6] [7], a4 S c ¯ c state [8], a [ cs ] S [¯ c ¯ s ] S tetraquark state[9], or a baryonium [10]. Likewise Y (2175) hasbeen correspondingly interpreted as: a gs ¯ s hybrid[11], a 2 D s ¯ s state [12], or a s ¯ ss ¯ s tetraquarkstate [13]. None of these interpretations has ei-ther been established or ruled out by experimen-tal observations.According to Ref. [12], a hybrid state mayhave very different decay patterns compared to aquarkonium state. Measuring the branching frac-tions of some decay modes may shed light on un-derstanding the nature of Y (2175). Among thosepromising decay modes, Y (2175) → K ∗ K ∗ is ofspecial importance. This decay mode is forbiddenif Y (2175) is a hybrid state but allowed if it is aquarkonium state.On the other hand, there are still lots ofunknown decay modes of J /ψ and investigat-ing more of them is useful to understand themechanism of J /ψ decays. Based on a sam-ple of 58M J /ψ events collected by the BESIIdetector at the Beijing Electron-Positron Col-lider (BEPC), a search for the process J /ψ → ηY (2175) , Y (2175) → K ∗ K ∗ is performed. Inaddition, the first measurement of the branchingfraction Br( J /ψ → η K ∗ K ∗ ) is obtained.
2. Detector and data samples
The upgraded Beijing Spectrometer detector(BESII) was located at the Beijing Electron-Positron Collider (BEPC). BESII was a largesolid-angle magnetic spectrometer which is de- scribed in detail in Ref. [14]. The momentumof charged particles is determined by a 40-layercylindrical main drift chamber (MDC) which hasa momentum resolution of σ p /p=1 . p p ( p in GeV/c). Particle identification is accom-plished using specific ionization ( dE/dx ) mea-surements in the drift chamber and time-of-flight(TOF) information in a barrel-like array of 48scintillation counters. The dE/dx resolution is σ dE/dx ≃ . σ T OF = 180 ps. Radially outside ofthe time-of-flight counters is a 12-radiation-lengthbarrel shower counter (BSC) comprised of gastubes interleaved with lead sheets. The BSC mea-sures the energy and direction of photons withresolutions of σ E /E ≃ / √ E ( E in GeV), σ φ = 7 . σ z = 2 .
3. Analysis
The decay channel under investigation, J /ψ → η K ∗ K ∗ , η → γγ, K ∗ → K + π − , K ∗ → K − π + ,has two charged kaons, two charged pions, andtwo photons in its final state. A candidate eventis therefore required to have four good chargedtracks reconstructed in the MDC with net chargezero and at least two isolated photons in the BSC.A good charged track is required to (1) be wellfitted to a three dimensional helix in order to en-sure a correct error matrix in the kinematic fit;(2) originate from the interaction region, i.e. thepoint of closest approach of the track to the beamaxis is within 2 cm of the beam axis and within 20cm from the center of the interaction region alongthe beam line; (3) have a polar angle θ , within therange | cos θ | < .
8; and (4) have a transverse mo-mentum greater than 70 MeV/ c . The TOF andd E/ d x information is combined to form a particle2identification confidence level for the π , K , and p hypotheses, and the particle type with the high-est confidence level is assigned to each track. Thefour charged tracks selected are further requiredto be consistent with an unambiguously identi-fied K + π + K − π − combination. An isolated neu-tral cluster is considered as a good photon when(1) the energy deposited in the BSC is greaterthan 60 MeV, (2) the angle between the near-est charged track and the cluster is greater than15 ◦ , (3) the angle between the cluster develop-ment direction in the BSC and the photon emis-sion direction is less than 30 ◦ , and (4) at least twolayers have deposits in the BSC and the first hitis in the beginning six layers. A four-constraint(4-C) kinematic fit is performed to the hypothe-sis J/ψ → γγK + K − π + π − , and if there are morethan two good photons, the combination with thesmallest χ γγK + K − π + π − value is selected. We fur-ther require that χ γγK + K − π + π − <
20. Becausewe are not interest in the events of which thetwo photons come from π , we require the invari-ant mass of two photons to be greater than 0 . c . J /ψ → η K ∗ K ∗ After applying the above event selection cri-teria, Fig. 1(a) shows the scatter plot of M K + π − versus M K − π + . One can see K ∗ K ∗ , K ∗ K − π + , K ∗ K + π − , and K + π − K − π + events scatteredin different regions of the plot. The signal re-gion in this analysis is defined by | M K ± π ∓ − m K ∗ ( m K ∗ ) | < .
05 GeV/ c , which is shown asthe middle box in Fig. 1(a). Other boxes shownare side-band regions, and events in these regionsare used to estimate the background in the sig-nal region. The K ± π ∓ invariant mass spectra areshown in Fig. 1(b), where the solid histogram is K + π − and the dashed histogram is K − π + . Fig-ure 2(a) shows the γγ invariant mass spectrum forevents in the signal region, where an η is seen. InFig. 2(a), the shaded histogram is the spectrumobtained requiring two good photons, while thedashed histogram is the spectrum for more thantwo photons. When there are more than two pho-tons, the ratio of signal over background is muchlower. In order to remove potential backgroundsas much as possible, we also require the number of good photons to be two.Figure 2(b) shows the γγ invariant mass spec-trum of events surviving the above selection,while the shaded histogram is the normalizedbackground estimated using the side-band regionsshown in Fig. 1(a). The number of J /ψ → η K ∗ K ∗ events is determined by fitting the spec-tra in Fig. 2(b). The J /ψ → η K ∗ K ∗ branchingfraction is determined using Br ( J /ψ → η K ∗ K ∗ ) = N sig − N sb N J/ψ · ǫ · Br ( K ∗ → K + π − ) · Br ( K ∗ → K − π + ) · Br ( η → γγ ) , where N sig = 347 is the number of events in thesignal region, obtained by fitting the spectrumin Fig. 2(b) (the blank histogram); N sb = 138 isthe number of background events estimated fromside-band regions, obtained by fitting the spec-trum in Fig. 2(b) (the shaded histogram); N J /ψ isthe total number of J /ψ events [17]; ǫ = 1 .
79% isthe detection efficiency obtained from MC simula-tion of J /ψ → η K ∗ K ∗ ; and Br ( K ∗ → K + π − ), Br ( K ∗ → K − π + ) and Br ( η → γγ ) are the cor-responding branching fractions. Figures 3(a) and3(b) show respectively the fitting results of thesignal and side-band events, where the shape ofthe γγ invariant mass spectrum obtained fromthe MC sample J /ψ → η K ∗ K ∗ is used as thesignal shape and a third order Chebyshev poly-nomial is used as the background shape. The J /ψ → η K ∗ K ∗ branching fraction is deter-mined to be Br ( J /ψ → η K ∗ K ∗ ) = (1 . ± . × − , where the error is statistical only. It is the firstmeasurement for this decay mode of J /ψ and itis shown that this mode is a typical three bod-ies decay. The branching fraction is compatiblewith the result of Br ( J /ψ → ηK + K − π + π − ) =(1 . ± . × − given by BaBar Collaboration[16]. It is worth mention of that this branchingfraction is several times smaller than the radia-tive decay mode J /ψ → γ K ∗ K ∗ which is verydifferent from the situation of p ¯ p that the branch-ing fraction of J /ψ → ηp ¯ p is much bigger than J /ψ → γp ¯ p . M(K + p - ) (GeV/c ) M ( K - p + ) ( G e V / c ) p ) (GeV/c ) E v en t s / ( M e V / c ) Figure 1. (a) Scatter plot of M K + π − versus M K − π + invariant mass, where the middle box is the signalregion and the other boxes are the side-band regions. (b) The invariant mass spectra of K ± π ∓ ; the solidhistogram is K + π − and the dashed is K − π + . J /ψ → η Y (2175) → η K ∗ K ∗ Next, we search for a possible resonance re-coiling against η . So in addition to the aboverequirements, we require that the γγ invariantmass satisfies | M γγ − m η | < .
04 GeV/ c anddefine the side-band region to be 0.1 GeV/ c < | M γγ − m η | < .
14 GeV/ c . The K ∗ K ∗ invariant mass spectrum recoiling against η for J /ψ → η K ∗ K ∗ is shown in Fig. 4, where thedashed histogram is the contribution from phasespace for J /ψ → η K ∗ K ∗ and the shaded his-togram is the contribution from the normalizedside-band events in the η , K ∗ and K ∗ side-bandregions. There is no obvious enhancement in theregion around 2.175 GeV/ c .The backgrounds in the selected event sampleare studied with MC simulations. For the decay J /ψ → η K ∗ K ∗ , the possible main backgroundchannels are: J /ψ → η K ∗ K ∗ → (3 π ) K ∗ K ∗ ; J /ψ → a +0 K − K ∗ → ( ηπ + ) K − K ∗ + c.c. ; J /ψ → ρ + K ∗− K ∗ → ( π + π )( K − π ) K ∗ + c.c. ; J /ψ → γπ K ∗ K ∗ ; J /ψ → φη ′ → K + K − ηπ + π − ; for each channel a sizable MC sample is simulated.There is no peak around 2.175 GeV/ c in the K ∗ K ∗ invariant mass distribution in any back-ground channel.We fit the mass distribution to determine apossible signal, where three parts are included inthe total probability distribution function (p.d.f):(1) for the signal p.d.f, we use the shape of the K ∗ K ∗ invariant mass spectrum obtained fromMC simulation of J /ψ → ηY (2175) → η K ∗ K ∗ produced with the mass and width of Y (2175)fixed to BaBar’s results; (2) for the normalizedphase space contribution p.d.f., we use the shapeof the K ∗ K ∗ invariant mass distribution ob-tained in the J /ψ → η K ∗ K ∗ MC simulation,normalized with the branching ratio obtained inthe previous section; (3) for the other possiblebackgrounds, we use a third order Chebyshevpolynomial.The product branching ratio is determined us-ing Br ( J /ψ → ηY (2175)) · Br ( Y (2175) → K ∗ K ∗ ) = N obs N J /ψ · ǫ · Br ( K ∗ → K + π − ) · Br ( K ∗ → K − π + ) · Br ( η → γγ ) =(0 . ± . × − , where N obs = 11 ±
12 is the number of sig-nal events, N J /ψ is the total number of J /ψ events [17], ǫ = 1 .
57% is the detection effi-ciency obtained from MC simulation of J /ψ → ηY (2175) → η K ∗ K ∗ , where the first step de-cay used an angular distribution 1 + cos θ , θ is the polar angle of the η momentum in thecenter of mass frame, Br ( K ∗ → K + π − ) and Br ( K ∗ → K − π + ) and Br ( η → γγ ) are thecorresponding branching fractions. The error isonly the statistical error. The signal significanceis only 0 . σ .The upper limit of Br ( J /ψ → ηY (2175)) · Br ( Y (2175) → K ∗ K ∗ ) at the 90% confidencelevel is obtained using a Bayesian approach [18].We obtain the upper limit: Br ( J /ψ → ηY (2175)) · Br ( Y (2175) → K ∗ K ∗ ) < N obsup N J /ψ · ǫ · Br ( K ∗ → K + π − ) · Br ( K ∗ → K − π + ) · Br ( η → γγ ) · (1 − σ sys ) =2 . × − , where N obsup = 31 is upper limit at the 90% con-fidence level, σ sys is the systematic error dis-cussed below, and the other symbols are definedas above.
4. Systematic Errors
In this analysis, the systematic errors on thebranching fraction and upper limit mainly comefrom the following sources:
The systematic errors from MDC tracking andkinematic fitting are estimated by using simula-tions with different MDC wire resolutions [15].In this analysis, the systematic errors from thissource are 12.8% for J /ψ → η K ∗ K ∗ and 12.0%for J /ψ → ηY (2175) → η K ∗ K ∗ . The photon detection efficiency is studied inreference [15]. The results indicate that the sys-tematic error is less than 1% for each photon.Two good photons are required in this analysis, so 2% is taken as the systematic error for the pho-ton detection efficiency.
In references [15] and [19], the efficiencies ofpion and kaon identification are analyzed. Thesystematic error from PID is about 1% for eachcharged track. In this analysis, four chargedtracks are required, so 4% is taken as the sys-tematic error from PID.
The branching fraction uncertainties for η → γγ and K ∗ ( K ∗ ) → K + π − ( K − π + ) from PDG08[18] are taken as systematic errors. J /ψ events The number of J /ψ events is (57 . ± . × ,determined from the number of inclusive 4-pronghadrons [17]. The uncertainty 4.72% is taken asa systematic error. J /ψ → η K ∗ K ∗ branching fraction When fitting the γγ invariant mass spectrum,as described in section III.A, the η signal shapeobtained from MC is fixed, and different orderpolynomials are used for the background shape.The difference is taken as the systematic error forthe background uncertainty. We also use differ-ent regions in fitting the invariant mass spectrum.The total systematic error from fitting is 6.7%. Br( J /ψ → η Y (2175) ) · Br( Y (2175) → K ∗ K ∗ ) upper limit When fitting the invariant mass spectrum of K ∗ K ∗ , as described in section III.B, there arethree sources of systematic error: for the firstp.d.f, we used the different resonance parametersmeasured by BaBar and BES, and take the differ-ence as the systematic error from the uncertaintyof signal parameters; for the second, the system-atic error comes from the error of the branchingfraction of J /ψ → η K ∗ K ∗ measured in sectionIII.A; for the third, we used the difference be-tween fitting with a third order Chebyshev poly-nomial and fitting with the invariant mass shapefrom K ∗ K ∗ side-band events as the systematicerror for the background uncertainty. Combin- M( gg ) (GeV/c ) E v en t s / ( M e V / c ) gg ) (GeV/c ) E v en t s / ( M e V / c ) (a) (b) Figure 2. (a) The γγ invariant mass spectrum for data; the dashed histogram is from the N γ > N γ = 2 events, and the blank histogram is from all events. (b) The γγ invariant mass spectrum for N γ = 2, where the blank histogram is from signal region events, and theshaded one is from the side-band regions events. ) ) (GeV/c gg M(0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 ) E v en t s / ( . G e V / c ) (GeV/c gg M(0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 ) E v en t s / ( . G e V / c (a) ) ) (GeV/c gg M(0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 ) E v en t s / ( . G e V / c ) (GeV/c gg M(0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 ) E v en t s / ( . G e V / c (b) Figure 3. Unbinned fitting results of γγ invariant mass spectra: (a) for the signal region events; (b) for theside-band region events, where the signal shape is obtained from the MC γγ invariant mass distributionand the background shape is a third order Chebyshev polynomial. ) GeV/c *K M(K*1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 ) E v en t s / ( . G e V / c ) GeV/c *K M(K*1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 ) E v en t s / ( . G e V / c Figure 4. The K ∗ K ∗ invariant mass spectrum, where points with error bars are candidate events, thedashed histogram is from MC phase space for J /ψ → η K ∗ K ∗ , the shaded histogram is from side-bandevents, and the solid curve is the fitting result, where the Y(2175) shape used is from MC simulation.ing these contributions, 16.3% is obtained as thesystematic error from fitting. We used different side-band regions to estimatethe backgrounds both in section III.A and III.B,and take the difference as a source of systematicerror. The result is 10.0% for the measurement ofbranching fraction and 4.2% for the upper limit.
To estimate the systematic error from the re-quirement of two good photons, we compare theefficiency difference for this requirement betweendata and MC sample, and obtain 4.4%, which istaken as the systematic error from the two photonrequirement. K ∗ simulation The K ∗ is simulated with a P-wave relativisticBreit-Wigner function BW = Γ( s ) m ( s − m ) +Γ( s ) m ,with the width Γ( s ) = Γ m m r p r p [ pp ] , where ris the interaction radius and the value (3 . ± . ± . GeV /c ) − measured by a K − π + scatteringexperiment [20] is used. Varying the value of r by1 σ , the difference of the detection efficiencies for J /ψ → η K ∗ K ∗ , J /ψ → ηY (2175) → η K ∗ K ∗ is taken as the systematic error from the uncer-tainty of the r value.The systematic errors from the different sourcesand the total systematic errors are shown in TableI.
5. Summary
With 58M BESII J /ψ events, the branchingfraction of J /ψ → η K ∗ K ∗ is measured for thefirst time: Br ( J /ψ → η K ∗ K ∗ ) = (1 . ± . ± . × − . No obvious enhancement near 2.175 GeV/ c in the invariant mass spectrum of K ∗ K ∗ isobserved. The upper limit on Br ( J /ψ → ηY (2175)) · Br ( Y (2175) → K ∗ K ∗ ) at the 90%C.L. is 2 . × − . Due to the limited statistics,we can not distinguish whether the Y (2175) is ahybrid or quarkonium state. The BES collaboration thanks the staff ofBEPC and computing center for their hard ef-forts. This work is supported in part by the Na-tional Natural Science Foundation of China undercontracts Nos. 10491300, 10225524, 10225525,10425523, 10625524, 10521003, 10821063,10825524, the Chinese Academy of Sciencesunder contract No. KJ 95T-03, the 100 Tal-ents Program of CAS under Contract Nos. U-11, U-24, U-25, and the Knowledge InnovationProject of CAS under Contract Nos. U-602, U-34(IHEP), the National Natural Science Foundationof China under Contract No. 10225522 (TsinghuaUniversity), and the Department of Energy underContract No. DE-FG02-04ER41291 (U. Hawaii). REFERENCES
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