Partial wave analysis of Jrc g K K p /

Transcription

1 9 March 2000 Phsics Letters B ž. 1 Partial wave analsis of Jrc g K K p / BE Collaboration J.Z. Bai a, Y. Ban f, J.G. Bian a, A.D. Chen a, G.P. Chen a, H.F. Chen b, H.. Chen a, J.C. Chen a, X.D. Chen a, Y. Chen a, Y.B. Chen a, B.. Cheng a, X.Z. Cui a, H.L. Ding a, L.Y. Dong a,h, Z.Z. Du a, C.. Gao a, M.L. Gao a,.q. Gao a, J.H. Gu a,.d. Gu a, W.X. Gu a, Y.N. Guo a, Z.J. Guo a,.w. Han a, Y. Han a,j.he a, J.T. He a, K.L. He a,m.he c, Y.K. Heng a, G.Y. Hu a, H.M. Hu a, J.L. Hu a, Q.H. Hu a,t.hu a, G.. Huang h, X.P. Huang a, Y.Z. Huang a, C.H. Jiang a, Y. Jin a,x.ju a, Z.J. Ke a, Y.F. Lai a, P.F. Lang a, C.G. Li a,d.li a, H.B. Li a,h, J. Li a, J.C. Li a, P.Q. Li a,w.li a, W.G. Li a, X.H. Li a, X.N. Li a, X.Q. Li i, Z.C. Li a, B. Liu a, F. Liu g, Feng Liu a, H.M. Liu a, J. Liu a, J.P. Liu k, R.G. Liu a, Y. Liu a, Z.X. Liu a, G.R. Lu j,f.lu a, J.G. Lu a, X.L. Luo a, E.C. Ma a, J.M. Ma a, H.. Mao a, Z.P. Mao a, X.C. Meng a, X.H. Mo a, J. Nie a, N.D. Qi a, X.R. Qi f, C.D. Qian e, J.F. Qiu a, Y.H. Qu a, Y.K. Que a, G. Rong a, Y.Y. hao a, B.W. hen a, D.L. hen a, H. hen a, H.Y. hen a, X.Y. hen a, F. hi a, H.Z. hi a, X.F. ong a, H.. un a, L.F. un a, Y.Z. un a,.q. Tang a, G.L. Tong a, F. Wang a, L. Wang a, L.. Wang a, L.Z. Wang a, P. Wang a, P.L. Wang a,.m. Wang a, Y.Y. Wang a, Z.Y. Wang a, C.L. Wei a,n.wu a, Y.G. Wu a, D.M. Xi a, X.M. Xia a, Y. Xie a, Y.H. Xie a, G.F. Xu a,.t. Xue a, J. Yan a, W.G. Yan a, C.M. Yang a, C.Y. Yang a, H.X. Yang a, X.F. Yang a, M.H. Ye a,.w. Ye b, Y.X. Ye b, C.. Yu a, C.X. Yu a, G.W. Yu a, Y.H. Yu d, Z.Q. Yu a, C.Z. Yuan a, Y. Yuan a, B.Y. Zhang a, C. Zhang a, C.C. Zhang a, D.H. Zhang a, Dehong Zhang a, H.L. Zhang a, J. Zhang a, J.W. Zhang a, L. Zhang a, Lei Zhang a, L.. Zhang a, P. Zhang a, Q.J. Zhang a,.q. Zhang a, X.Y. Zhang c, Y.Y. Zhang a, D.X. Zhao a, H.W. Zhao a, Jiawei Zhao b, J.W. Zhao a, M. Zhao a, W.R. Zhao a, Z.G. Zhao a, J.P. Zheng a, L.. Zheng a, Z.P. Zheng a, B.Q. Zhou a, L. Zhou a, K.J. Zhu a, Q.M. Zhu a, Y.C. Zhu a, Y.. Zhu a, Z.A. Zhu a, B.A. Zhuang a 1 Data analzed were taken prior to the participation of U members of the BE Collaboration r00r$ - see front matter q 2000 Published b Elsevier cience B.V. All rights reserved. PII:

2 26 ( ) J.Z. Bai et al.rphsics Letters B a Institute of High Energ Phsics, Beijing , People s Republic of China b UniÕersit of cience and Technolog of China, Hefei , People s Republic of China c handong UniÕersit, Jinan , People s Republic of China d Hangzhou UniÕersit, Hanzhou , People s Republic of China e hanghai Jiaotong UniÕersit, hanghai , People s Republic of China f Peking UniÕersit, Beijing , People s Republic of China g Hua Zhong Normal UniÕersit, Wuhan , People s Republic of China h China Center for AdÕanced cience and Technolog ( CCAT ), World Laborator, Beijing , People s Republic of China i Nankai UniÕersit, Tianjin , People s Republic of China j Henan Normal UniÕersit, Xinxiang , People s Republic of China k Wuhan UniÕersit, Wuhan , People s Republic of China l D.V. Bugg l, B.. Zou m,l Queen Mar and Westfield College, London E1 4N, UK m Institute of High Energ Phsics, Beijing , People s Republic of China Received 2 December 1999; received in revised form 26 Januar 2000; accepted 28 Januar 2000 Editor: L. Montanet Abstract BE data on Jrc g K K p.. are presented. There is a strong peak due to h ri, which is fitted with a Breit Wigner amplitude with s-dependent widths for decas to K ) K, kk, hpp and rr; k refers to the Kp -wave. At a P q KKp mass of ;2040 MeV, there is a second peak with width ;400 MeV; J s0 is preferred over 1 and 2 respectivel b 5.2 and 6.8 standard deviations. It is a possible candidate for a 0 ssg hbrid partner of p q 2000 Published b Elsevier cience B.V. All rights reserved. PAC: Cs; Mk; Jx; Hq There have been earlier data from Mark III wx 1 wx. and DM2 2 for Jrc radiative decas to K Kp, as well as K q K p 0. Recentl, the BE group has published data on the latter channel wx 3. Here we present BE data on decas to K " K 0 p.. These data have lower backgrounds than for K q K p 0, because of the identification of K 0 p q p. Consequentl, the partial wave analsis ma be extended up to a KKp mass of 2300 MeV, covering an interesting structure at ; 2040 MeV. The Beijing pectrometer BE. has collected 7.8 =10 6 Jrc triggers, used here. Details of the detecwx 4. We describe briefl those tor are given in Ref. detector elements plaing a crucial role in the present measurement. Tracking is provided b a 10 superlaer main drift chamber MDC.. Each superlaer contains four laers of sense wires measuring both the position and the ionization energ loss derdx. of charged particles. The momentum reso- ' 2 lution is s rp s 1.7% 1 q P, where P is the P momentum of charged tracks in GeVrc. The resolution of the derdx measurement is ;"9%, providing good prk separation and proton identification for momenta up to 600 MeVrc. An arra of 48 scintillation counters surrounding the MDC measures the time-of-flight TOF. of charged tracks with a resolution of 330 ps for hadrons. Outside the TOF sstem is an electromagnetic calorimeter made of lead sheets and streamer tubes and having a z positional resolution of 4 cm. The energ resolution ' scales as seres22%r E, where E is the energ in GeV. Outside the shower counter is a solenoidal magnet producing a 0.4 Tesla magnetic field. Each candidate event is required to have four charged tracks. Each track must have a good helix fit in the polar angle range 0.8-cosu-0.8 and a transverse momentum ) 60 MeVrc. A vertex is required within an interaction region "30 cm longitudinall and 3 cm radiall. A positive identification of just one K " is required using time of flight

3 ( ) J.Z. Bai et al.rphsics Letters B andror derdx. Events are fitted kinematicall to the ". q 4C hpothesis Jrc g K p p p., requiring a confidence level )5%. Backgrounds arise mainl from p 0 K " p. p q p and K " p. p q p. Those events giving a better fit to these channels are rejected. Next, we require NU NsNE P N-0.15 GeVrc 2, so as to miss miss miss reject the events with multi-photons or more or less than one charged kaon; here, Emiss and Pmiss are, respectivel, the missing energ and missing momentum of all charged particles. The momentum of the K " p. p q p sstem transverse to the photon 2 2 P 2 tg s4npmissn sin umgr GeVrc 2 is required in order to remove the background Jrc p 0 K " p. p q p ; here umg is the angle between the missing momentum and the photon direction. Finall, K s 0 are selected with a cut on the p q p invariant mass, NM q M 0 N-25 MeV. Fig. 1. p p K s a shows the p q p invariant mass closest to the K 0 mass before the K s 0 are selected; a ver strong signal K 0 is seen. The number of surviving events is 1095 with 57 " 5 non-k 0 background under the K 0. For our final fit, we use 683 events below a KKp mass of 2.3 GeV. A constraint to the K 0 vertex does not improve the signalrbackground ratio further, but loses some events. The effects of the various selection cuts on the data is simulated with a full Monte Carlo of the BE detector including the deca path of the K s 0 ; 250,000 Monte Carlo events are successfull fitted to Jrc g K K p... All background reactions are similarl fitted to this channel. The estimated background 0 is 29" 7%, mostl from Jrc p K K p.., some from non-k 0 events. It peaks at about 2.3 GeV, and follows phase space closel. We have included it in the amplitude analsis, but it has little effect, since all genuine signals have a characteristic dependence on either or both of production and deca angles... Fig. 1 b shows the K Kp mass spectrum; the dark histogram shows the estimated background in the analsis region. There is a conspicuous and somewhat asmmetric peak due to h ri, similar to the earlier data from Mark III, DM2 and BE. At high mass, there is a distinct peak at 2040 MeV. Fig. 2 shows Dalitz plots for three mass ranges:. a MeV,. b MeV, and. c MeV; fits are shown in. d,. e and. f. There is a conspicuous K ) K deca mode in the first region of the h At higher masses, it disappears rapidl, and the mass projections shown in Fig. 3 are consistent with decas to kk onl; above 1560 MeV, there is no significant evidence for a K, a0 KK. We have carried out a partial wave analsis using amplitudes constructed from Lorentz-invariant combinations of the 4-vectors and the photon polarization for Jrc initial states with helicit "1. Cross sections are summed over photon polarisations. The relative magnitudes and phases of the amplitudes are determined b a maximum likelihood fit. We include q KKp states with quantum numbers 0, 1, 2 and 2 q. There are two helicit amplitudes for 1 q, three for 2 and three for 2 q. Because production is via an electromagnetic transition, the same phase is used for different helicit amplitudes to the same final. q 0. Fig. 1. a the p p invariant mass with invariant mass closest to the K mass; b KKp mass spectrum. The dark dashed histogram of. b shows the estimated background in the analsis region KKp mass below 2.3 GeV..

4 28 ( ) J.Z. Bai et al.rphsics Letters B Fig. 2. Dalitz plots for KKp mass ranges a MeV, b MeV, c MeV; d, e and f show fitted Dalitz plots. state. Different phases are allowed for different deca channels, e.g K ) K and kk, because of strong interaction effects due to rescattering. The analsis is discussed separatel for the mass region of h and the 2040 MeV peak. The h has been fitted using a Breit Wigner amplitude with s-dependent width: L f s 2 M sim wg ) s. q G s. q G s. q G. s. x K K hs rr k K 1. The numerator L is a complex coupling constant. The G s. are taken to be proportional to the available phase space for each channel, evaluated numeriwx 5. The hpp phase space is taken from hs, call the dominant channel, but a p phase space is similar and both are slowl varing over this mass region. The magnitude of each G is adjusted iterativel so that cross sections integrated over the resonance agree with the branching ratios determined experimentall. The magnitude of Ghs has been obtained from BE data on radiative decas to hpp

5 ( ) J.Z. Bai et al.rphsics Letters B Fig. 3. Projections on to a c K K mass, d f Kp mass for the three mass intervals of Fig. 2; histograms show the fit. wx 6. That for Grr has been obtained b fitting BE data on radiative decas to 4p wx 7, including in the fit h and the broad h Here h refers to the ver broad 0 signal G, 1 GeV. derived b Bugg and Zou wx 8 from an analsis of several channels of Jrc radiative deca. Values of G ) K K and Gk K are obtained from the present data. In the mass region of the h 1440., half the kk signal comes from the low mass tail of h and its constructive interference with h That is, if h is removed from the fit, the kk width of h needs to be doubled. Removing the h has a significant, but not dramatic, effect on log likelihood, which changes b 4.8 for 2 extra parameters. The f is also included in the amplitude analsis, and a small component due to f Both optimise close to the masses and widths quoted b the Particle Data Group PDG. wx 9, so we fix them at PDG values. The amplitude analsis distinguishes cleanl between quantum numbers 1 q and ) 0 for K K decas. If the whole h signal is P fitted with J s1 q optimising its mass and width., log likelihood is worse b 11.4, a significant amount. Our definition of log likelihood is such that it increases b 0.5 for a one standard deviation change in one parameter.. In the earlier analsis of BE data on the q 0 K K p final state wx 3, a fairl large amplitude was fitted for h The smaller background in present data and the wider mass range allow us to show that this component should in fact be rather small. Its effects on the h ma be replaced with some increase in the total width of that resonance and an increase in its width for decas to K ) K. Present results for the fitted widths are shown in Fig. 4 and

6 30 ( ) J.Z. Bai et al.rphsics Letters B Fig. 4. The s-dependence of widths fitted to h branching fractions in Table 1. The fit is compared with the KKp mass spectrum b the histogram in Fig. 5. A free fit to the mass gives 1440 MeV. However, hpp data give a resonance mass of 1405"5 MeV, according to the summar b the Particle Data Group wx 9. The s-dependent width we use for h explains naturall a mass difference of 20 MeV between hpp and KKp data; the rapidl increasing ) phase space for K K makes the KKp channel peak higher and explains also the asmmetric shape of the peak, which rises rapidl on the lower side of the peak and falls more slowl on the upper side. A small ; 15 MeV. discrepanc remains between the peaks fitted to hpp and KKp. We adopt a compromise between fitting these data and hpp b using a mass of 1432 MeV, but the effect on other conclusions is negligible. Interferences between h and the broad h depend on their relative phases and can shift the peak in different data sets; so we do not regard this small discrepanc as a matter for concern. Around 1650 MeV, there is some indication for a narrow KKp peak. However, fitting it requires an unreasonabl narrow width ; 30 MeV. An ss state at this mass has no obvious non-strange partners. If fitted, it is onl a two standard deviation effect. Therefore we discard it as a statistical fluctuation. Including it has negligible effects on parameters fitted to h and the peak at 2040 MeV. We now turn to the latter peak. It cannot be explained b the ver broad h 1800., which has a completel different and much flatter shape, illustrated b the shaded area in Fig. 5. b below. We fit it with a simple Breit Wigner amplitude of constant width. Its mass and width optimise at M s 2040" 50 MeV, Gs400"90 MeV. We have tried fits to this peak with resonances having quantum numbers 0, q 1 and 2 ; for standard qq states, one does not expect 3 q in kaonic channels until 2300 MeV. We find that log likelihood is better for 0 than 1 q b The latter has one additional parameter, so it is a poorer fit b 5.2 standard deviations. If a combination of 0 and 1 q amplitudes is used, log likelihood improves onl b 0.6, and the fitted 1 q component is ver small: 4.4% of 0 in cross section. These results are not sensitive to the h contribution: removing it, the distinction between quantum numbers 0 and 1 q for the 2040 MeV peak remains at a log likelihood difference of We have also tried adding or substituting 2. Alone it gives a poor fit, worse in log likelihood than 0 b This demonstrates that 2 and 0 are well separated b their distinctivel different angular distributions. If it is added freel to the fit, it improves log likelihood b 3.2 for three extra parameters; this cannot be considered significant. Fig. 5 shows magnitudes of components fitted in the amplitude analsis when the 2040 MeV peak is fitted as 0. The slight differences between Fig. 5. b and. d is due to interferences of h and h with the broad h in Fig. 5 b.. Branching fractions for production and deca, including the dominant interferences, are given in Table 2. Values are integrated up to a KKp mass of 2.3 GeV. Decas to K " K p. have a branching ratio 1r3 of all KKp decas. We correct all measured branching ratios b this factor 3, so as to quote branching fractions for all KKp charge states. The overall branching fraction, summed over all final states is 6.0"0.4"2.1 =10. Table 1 Branching ratios BR. of h integrated over its width Deca channel BR % ) K K 0.70"0.05 kk 0.13"0.03 hpp 0.09"0.03 rr 0.08"0.03

7 ( ) J.Z. Bai et al.rphsics Letters B ".... q Fig. 5. Projections from all events below a K Kp mass of 2.3 GeV of a all contributions, b 0 including interferences, c 1 and d. h full curve. and h dotted. without interferences; the dark shaded histogram of b. is the contribution of h Crosses are data and histograms the fit. We now discuss possible interpretations for the 2040 MeV peak. Our data for Jrc radiative decas q to hp p wx 6 were fitted using an h with a width of 250 MeV and an h The h is entirel distinct from h 1800., which has a much larger width. A possible interpretation is that it is the ns3 qq state. Then the h observed here could be its ss partner. However, the VE collaboration has identified a p w10x with curious deca modes to f p, f 980. p and K K, but not rp. There has been speculation that this is an I s 1 hbrid w11 x. The h would make a natural partner; its decas to hs and a p are to be expected for a hbrid. It is natural to expect a corresponding ssg state decaing to kk in the KKp Table 2 Branching fractions BF. for production and deca. Values are corrected for all charge states in KKp Process BF %. 1 Jrc gh 1440, h 1440 KKp =10. 2 Jrc g f1 1285, f KKp =10. 3 Jrc g f1 1420, f KKp =10. 4 Jrc gh 1800, h 1800 kk 0.58"0.03"0.20 =10. 5 Interference between 1 and =10 6. Interference between 1. and =10. 7 Jrc gh 2040, h 2040 kk 2.1"0.1"0.7 =10

8 32 ( ) J.Z. Bai et al.rphsics Letters B channel roughl MeV above the peak in hpp. In Jrc radiative decas, the amplitude for production of qq states is suppressed b two powers of a, required to couple intermediate gluons to s quarks; at 2040 MeV, a s, Production of a hbrid will onl be suppressed b one power of a s in amplitude. We therefore examine the possible interpretation of h as a qqg hbrid. For a hbrid, the branching fraction expected in the KKp channel is half that for hpp, since in Jrc decas intermediate gluons couple equall to uu, dd and ss. If fitted as 0, the branching ratio for the 2040 MeV peak in KKp is = 10 ; this value is obtained after allowing for interferences with h and includes the error in the overall normalisation. It is to be compared with the branching ratio for h in hpp of =10 wx 6. These values are consistent within the sizable errors with the expectation for hbrids. The magnitude of branching ratio we now fit to h 1800 kk is = 10. Again, the error includes the overall normalisation uncertaint. It compares with = 10 fitted to hpp decas wx 6. Within the errors, these values are now consistent with flavour-blind decas of a glueball. In summar, present data contain less background q than earlier data on Jrc g K K p 0. and allow a somewhat improved determination of the properties of h Its dominant deca mode is to K ) K. This suggests it is the first radial excitation of h 958., probabl mixed with the broad h 1800., in order to account for its strong production in Jrc radiative decas. We now find a small component of h decaing to kk. We observe a peak at 2040 MeV which ma be fitted with a 0 resonance of width 400 MeV. J P s0 is preferred over 1 q and 2 respectivel b 5.2 and 6.8 standard deviations. Its branching fraction, when compared with the hpp channel, would 2 be consistent with interpretation as a 0 ssg hbrid. Acknowledgements The BE group thanks the staff of IHEP for technical support in running the experiment. This work is supported in part b China Postdoctoral cience Foundation and National Natural cience Foundation of China under contract Nos , and ; and b the Chinese Academ of ciences under contract No. KJ 95T- 03 IHEP.. We also acknowledge financial support from the Roal ociet for collaboration between Chinese and UK groups. References wx 1 J.Z. Bai et al., Phs. Rev. Lett wx 2 J.-E. Augustin et al., Phs. Rev. D wx 3 J.Z. Bai et al., Phs. Lett. B wx 4 BE Collaboration, Nucl. Instr. Methods A wx 5 D.V. Bugg, A.V. arantsev, B.. Zou, Nucl. Phs. B , see Eq wx 6 J.Z. Bai et al., Phs. Lett. B wx 7 J.Z. Bai et al., Phs. Lett. B wx 8 D.V. Bugg, B.. Zou, Phs. Lett. B wx 9 Particle Data Group, Euro. Phs. J. C w10x D. Amelin et al., Phs. Lett. B w11x F.E. Close, P.R. Page, Nucl. Phs. B ; Phs. Rev. D w12x J. Adomeit et al., Zeit. Phs. C w13x J.Z. Bai et al., Phs. Lett. B w x Refs. 12,13 were not cited in the text of the article.