2. Glueball Searches and PWA at BESIII Shan JIN Institute of High Energy Physics (IHEP) jins@mail.ihep.ac.cn PWA Workshop Beijing, January 26, 2006

3. Outline  Physics goal of hadron spectroscopy at BESIII  What can we learn from BESII results?  Selected topics on glueball searches  PWA at BESIII (with discussions)

4. Physics goal of hadron spectroscopy at BESIII

5. Multi-quark State, Glueball and Hybrid  Hadrons consist of 2 or 3 quarks ： Naive Quark Model ：  New forms of hadrons: Multi-quark states ： Number of quarks > ＝ 4 Hybrids ： qqg ， qqqg … Glueballs ： gg ， ggg … Meson （ q q ） Baryon （ q q q ） How quarks/gluons form a hadron is far from being well understood.

6. Multi-quark states, glueballs and hybrids have been searched for experimentally for a very long time, but none is established.

7. J/  decays are an ideal factory to search for and study light exotic hadrons:  The production cross section of J/  is high.  The production BR of hadrons in J/  decays are one order higher than  ’ decays (“12% rule”).  The phase space to 1-3 GeV hadrons in J/  decays are larger than  decays.  Exotic hadrons are naively expected to have larger or similar production BR to conventional hadrons in J/  decays.  Clean background environment compared with hadron collision experiments, e.g., “J P, I” filter.

8. Physics Goal (I) With 10 10 J/psi events, we hope to answer:  Whether glueballs exist or not? Naively, we estimate in each exclusive decay mode: If the eff. is about 20%, we would have 20000 events for each decay mode  we should observe a relative narrow (width: 50~200MeV) glueball if it exists.

9. Physics Goal (II)  Is there any gluon content in hadrons – hybrid mesons and baryons?  Whether multiquark mesons and baryons exist in the nature?  Understanding conventional mesons and baryons  How quark/gluon form a hadron? QCD cannot “escape” from answering these fundamental questions finally.

10. Difficulties (I)  Theoretically (glueball as an example) Predictions on glueball masses from LQCD may be unreliable due to quench approximation. No predictions on the widths so far (even the order). No prediction on the production rate  (J/    G). Mix with qqbar mesons or even with 4q, qqg mesons? (dirty?)

11. Difficulties (II)  Experimentally: Data sample is not big enough (it is not a problem for BESIII) No good way modeling background at low energy, in many cases we have to study bck via data. Interferences among mesons make the mass/Dalitz plots very complicated   PWA is a must for hadron spectroscopy at BESIII  But PWA face many uncertainties (see the discussions on PWA)

12. What can we learn from BESII results?

13. A number of unexpected new observations at BESII  A possible bound state: mass threshold enhancement in and new observation of X(1835).  mass threshold enhancement in   mass threshold enhancement in J/     New observation of a broad 1 - - resonance in J/   K + K -  0

14. Observation of an anomalous enhancement near the threshold of mass spectrum at BES II M=1859 MeV/c 2  < 30 MeV/c 2 (90% CL) J/    pp M(pp)-2m p (GeV) 00.10.20.3 3-body phase space acceptance  2 /dof=56/56 acceptance weighted BW +3 +5  10  25 BES II Phys. Rev. Lett. 91, 022001 (2003)

15. Observation of X(1835) in The  +  -  mass spectrum for  decaying into  +  -  and   Statistical Significance 7.7 

16. Mass spectrum fitting 7.7  The  +  -  mass spectrum for  decaying into  +  -  and   BESII Preliminary

17. Re-fit to J/    p pbar including FSI Include FSI curve from A.Sirbirtsev et al. ( Phys.Rev.D71:054010, 2005 ) in the fit (I=0) M = 1830.6  6.7 MeV  = < 153 MeV @90%C.L. In good agreement with X(1835)

18. A Possible ppbar Bound State  X(1835) could be the same structure as ppbar mass threshold enhancement.  It could be a ppbar bound state since it dominantly decays to ppbar when its mass is above ppbar mass threshold.  Its spin-parity should be 0 -+ : this would be an important test  PWA is needed

19. Observation of an anomalous enhancement near the threshold of mass spectrum at BES II BES II 3-body phase space For a S-wave BW fit: M = 2075  12  5 MeV Γ = 90  35  9 MeV Phys. Rev. Lett. 93, 112002 (2004)

20. PS, eff. corrected Observation of a strong enhancement near the threshold of mass spectrum at BES II (Arbitrary normalization) BES II NX*NX*

21.  A strong enhancement is observed near the mass threshold of M K  at BES II.  Preliminary PWA with various combinations of possible N* and Λ* in the fits —— The structure N x *has: Mass 1500~1650MeV Width 70~110MeV J P favors 1/2 - The statistics is not high enough to tell what it is. The most important is: It has large BR(J/ψ  pN X *) BR(N X *  KΛ)  2 X 10 -4, suggesting N X * has strong coupling to KΛ. It could be an KΛ bound/resonant state (5-quark system).

22. M 2 (  ) M2()M2() background X(1810) An  mass threshold enhancement is observed M(  ) Phys. Rev. Lett., 96 (2006) 162002 J PC favors 0 ++ It could be a multiquark/hybrid/glueball state.

23. Background New observation of a broad 1 - - X(1580) in J/   K + K -  0 Phys. Rev. Lett. 97 (2006) 142002

24. How to understand broad X(1580)?  Search of a similar structure in J/   K S K  will help to determine its isospin.  X(1580) could have different nature from conventional mesons: There are already many 1- - mesons nearby. Width is much broader than other mesons. Broad width is expected for a multiquark state.

25.  J/ψ decay is an ideal place to study exotic structures.  The statistics at BESII is not high enough yet.  We would expect: more unexpected discoveries on hadron spectroscopy at BESIII —— the more, the better ! What do we learn from BESII results

26. Selected topics on glueball searches

27.  J/   ,   2 ++ glueball candidates  Where to search for the 0 -+ glueball?

28. J/   ,   These two processes are believed to be an ideal place to tag the flavor of mesons.  BESII studied these two channels (PLB549, 47(2004)):  (1440) from J/  0 KK bck

29. J/   ,   At BESII, we only observe  ’,  (1440), f1(1285) in J/   , no clear peak in J/     At BESIII: The background could be very high when searching for other glueball candidates. Hope BESIII much better detector can strongly suppress the background  we will perform MC studies on this. PWA is needed.

30. 2 ++ glueball candidates  Lattice QCD predicts the 2 ++ glueball mass in the range of 2.2~2.4 GeV   (2230) was a candidate of 2 ++ glueball: It was first observed at MARKIII in J/  KK It was observed at BES I in J/  KK, ,  ppbar It was not observed at DM2.

31. BES-I  (2230) Result  (2230)

32. The situation at BESII  The mass plots shows no evident  (2230) peaks in J/  KK, ,  ppbar, which is different from BESI.  Difficult to draw firm conclusion at present.  PWA is needed to draw firm conclusion on it.

33.  (2230) could be similar to f 0 (980) at BESII  We saw a clear f 0 (980) mass peak in J/  at BESI, but we do not see a clear f 0 (980) peak in the mass plot at BESII.  However, we need a significant contribution of f 0 (980) in PWA of J/  at BESII BESII M(  +  - )  J/ 

34. Other 2 ++ glueball candidates  No other obvious good candidates have been observed in J/psi radiative decays in the mass range predicted by LQCD.  What does it mean: LQCD prediction is not very reliable, or BR(J/    G)xBR(G  hh) is small ( <10 -4 ) so that we don’t have the sensitivity to observe it ( quite possible ), or, The width of a glueball is very large ( ~1GeV, E.Klepmt ).

35. Where to search for the 0 -+ glueball?  Lattice QCD predicts the 0 -+ glueball mass in the range of 2.3~2.6 GeV.   (1440) and X(1835) were suggested being possible candidates, but their masses are much lower than LQCD predictions.

36. No 0 -+ glueball candidate observed in the mass range 2.3~2.6 GeV  No evidence for a relatively narrow state ( 100 ~ 200 MeV width ) above 2GeV in  Again: LQCD reliable? Production rate could be very low. Glueball width could be very large.

37. PWA at BESIII

38. PWA is crucial to most analyses at BESIII  Not only to the spin- parity determination of new hadrons  But also to the measurement of decay BR: e.g.: BR(J/   K*K) BR(J/   K*(1410) K) Also for D decays… From interference

39.  With huge data samples at BESIII, PWA is possible.  However, there are many difficult problems to be solved.  How to obtain robust PWA results with high speed ?

40. Q1: How to speed up the PWA fit?  We will have 200 times larger data sample at BESIII: Typical size of a data sample at BESII: 10000 events. Usually it takes 1- 3 years to publish one PWA result (with more than 20 CPU fully used). From previous talks at BESII, we have leant how we obtained the PWA results, including how we dealt with systematic uncertainties Naively, we would have 2M events for one data sample at BESIII  The speed will be about 100 times slower  How many years do we need?

41. Q1: How to speed up the PWA fit?  PWA procedure at BESII: Global fit The PWA input contains 4-momentum of all events (the whole mass range). Various fits are tried with different combinations of the possible components/resonances/amplitudes, finding minimum –lnL of all these combinations.  One possible solution at BESIII: bin-by-bin fit Divide the mass spectrum into many (~100) bins. In each bin, we only fit various J PC components without BW structure. We can perform PWA fits for all bins on 100 CPU.

42. Bin-by-Bin Fit  Advantages Model independent for each J PC component in each mass bin. Phase shift measured automatically Fast  Disadvantages Detail mass information lost The constraint on the phase in nearby mass bin lost.

43. MC Input/Output Checks of Bin-by-Bin Fit  We have a working group to check whether the bin-by-bin fit can reproduce the input values based on extensive MC studies. Here I would only show some examples 

44. Example 1: One 0++ resonance & one 2++ resonance 2++ 0++ int All Generated KK mass plot in J/  KK (160K evts)

45. Error bar: bin-by-bin fit result Histogram: generated mass plot 0++ 2++ M KK

46. 0++GenFitDif Nevent65567 63874±8142.2σ Mass1750 1753.3±1.62.1σ Width 200 186.5±3.93.5σ 2++GenFitDif Nevent38099 39322±8141.5σ Mass1790 1690.1±1.10.1σ Width 80 83.4±2.81.2σ Fit mass plot based on bin-by-bin fit

47. 2++ B 2++ A All Example 2: Two 2++ resonances Generated KK mass plot in J/  KK (140K evts)

48. 0++ is not significant 2++ 0++

49. GenFitDif Nevent A 104514100936±7934.5σ Mass A 1950 1947.5±0.64.2σ Width A 150 144.3±1.63.6σ Nevent B 7746 6759±3752.6σ Mass B 2100 2099.7±0.90.3σ Width B 40 34.7±2.81.9σ

50.  Output (fitting the phase shift curve):  =61.49±6.90 M(0 ++ )=2.5012±0.005GeV  (0 ++ )=0.206±0.012GeV M(2++)=1.227±0.403GeV  (2++)=32.273±17.906GeV 0 ++ 2 ++  Input : 0++: m=2.5GeV,  =0.2GeV,  =60 2++: Phase Space  =0 Example 3: Phase Shift Measurement

51.  Bin-by-bin approach looks promising…  However 

52. 2++ Example 4: Two 2++ resonances (300K events) Error bar: bin-by-bin fit result Histogram: generated mass plot 2++ component cannot be reproduced. Resonance 1: M=1970 MeV Г=180 MeV Resonance 2: M=2040 MeV Г=20 MeV

53. 0++ 0++ component is significantly inconsistent with zero.

54.  Given this MC study, we really worry about bin-by-bin fit result (Fortunately, BESII did not have official results based on bin-by-bin analysis).

55. But in this case, global fit can well reproduce the Inputs. 2++

56.  Global fit results are more reliable than bin-by- bin fit.  More study are needed to understand this.  If bin-by-bin approach cannot obtain robust PWA results, what’s other solutions to speed up PWA fit? – Questions still remains.

57. Q2: How to treat background?  MC No reliable inclusive generator at low energy.  Sidebands More reliable than MC In some cases, maybe unreliable due to kinematic limits.

58. Q3: How to parameterizethe intermediate states?  e.g., the  mass shape in J/  process, FSI… M  In the  mass range of  (1760)

59. Q4: How to treat small components?  From PWA of J/   K + K -  0 at BESII, we see that small components could have big interference so as to affect the results significantly.

60. Q5:How can we include data/MC differences in the PWA fit?  Such differences may results in fake resonances in PWA based on our MC studies.  Example: Testing sample: J/  +  -  0 with two intermediate states  (770) and  (1450) Simulation of data/MC difference from MDC wire resolution  two different algorithms at BESII We add in  (1700),  (2100),  3 (1690) one by one and then check the significance ( -2  lnL ) of each resonance

61. 1.3M J/  +  -  0 events ~ BESII data sample Δs= -2  lnL as a function of the size of data sample

62.  When the data sample is as large as twice of the BESII sample,  (1700),  (2100),  3 (1690) will have a significance > 5  due to the data/MC difference from MDC wire resolution  They are fake resonances needed in PWA fit.  So We need to find a way to include the data/MC difference in our fit, or at least we need to make the correct judgment that whether the resonances are from the data/MC difference rather than physics resonance. Q5:How can we include data/MC differences in the PWA fit?

63. Q6: How to judge whether we have reached a real minimum in the PWA fit rather than local ones?  Especially when there are many resonances (parameters) in one fit.  Currently at BESII, we just tried hundreds of different combinations of initial values of the fitted parameters  very time consuming.

64. Summary  Based on the experience of BESII, we can expect much more unexpected discoveries and much more opportunities at BESIII on hadron spectroscopy.  With huge data samples at BESIII, we hope to answer some fundamental questions such as whether glueball/hybrids/multiquarks exist or not.  PWA is a crucial to most physics results at BESIII. There are many difficult problems to be solved in PWA —— Suggestions of the solutions are welcome!

65. 谢 谢！ Thank You!

66.  With threshold kinematic contributions removed, there are very smooth threshold enhancements in elastic “matrix element” and very small enhancement in annihilation “matrix element”:  much weaker than what BES observed ! NO strong dynamical threshold enhancement in cross sections (at LEAR) |M| 2 BES Both arbitrary normalization

67. Any inconsistency? NO!  For example: with M res = 1859 MeV, Γ = 30 MeV, J=0, BR(ppbar) ~ 10%, an estimation based on: At E cm = 2m p + 6 MeV ( i.e., p Lab = 150 MeV ), in elastic process, the resonant cross section is ~ 0.6 mb : much smaller than the continuum cross section ~ 94  20 mb.  D ifficult to observe it in cross sections experimentally.

68. Pure FSI disfavored (I) 1.Theoretical calculation (Zou and Chiang, PRD69 034004 (2003)) shows: The enhancement caused by one-pion-exchange (OPE) FSI is too small to explain the BES structure. 2.The enhancement caused by Coulomb interaction is even smaller than one-pion-exchange FSI. BES one-pion-exchange FSI |M| 2 Both arbitrary normalization BES Both arbitrary normalization Coulomb interaction

69. FSI Factors Most reliable full FSI factors are from A.Sirbirtsev et al. ( Phys.Rev.D71:054010, 2005 ) ， which fit ppbar elastic cross section near threshold quite well. ppbar elastic cross section near threshold I=1 S-wave I=0 S-wave P-wave

70.  J/  decays do not suffer large t-channel “background” as ppbar collision. >> In ppbar collision, the background is much lager (I)

71. A.Sibirtsev, J. Haidenbauer, S. Krewald, Ulf-G. Meißner, A.W. Thomas, Phys.Rev.D71:054010, 2005 P-wave I=0 S-wave I=1 S-wave In ppbar elastic scattering, I=1 S-wave dominant, while in J/  radiative decays I=0 S-wave dominant. ppbar elastic cross section near threshold In ppbar collision, the background is much lager (II)

72. So, the mechanism in ppbar collision is quite different from J/  decays and the background is much smaller in J/  decays It would be very difficult to observe an I=0 S-wave ppbar bound state in ppbar collisions if it exists. J/  decays (in e+e- collider) have much cleaner environment: “J P, I” filter

73.  pp near threshold enhancement is very likely due to some broad sub-threshold 0 -+ resonance(s) plus FSI. From B.S. Zou, Exotics 05: From A. Sirbirtsev :  FSI factors should be included in BW fit.

74. Discussion on I=1 S-wave FSI

75. Pure FSI disfavored (III) — I = 1 Pure I=1 S-wave FSI is disfavored by more than 3 . Pure FSI FSI + BW M = 1773  21 MeV  = 0  191 MeV

76. I=0 dominant in J/  radiative decays  Most I = 0 states have been observed in J/  radiative decays with big production rate ( especially for 0 -+ mesons ) such as ,  ’,  (1440),  (1760), f 2 (1270), f 2 (1525), f 0 (1500), f 0 (1710).  The only observed I=1 meson in J/  radiative decays is  0 with low production rate 4*10 – 5, e.g., no evidence for  (1800) in J/    3  process. It is unlikely to be from  (1800). I=1 S-wave FSI seems unlikely.

77. ppbar bound state in NNbar potential  Paris NNbar potential: ( Paris 93, B. Loiseau et al., hep-ph/0411218, 0501112 ) For 11 S 0, there is a bound state: E = - 4.8 - i 26.3 MeV quite close to the BES observation.  However, Julich NNbar model: ( A. Sibirtsev et al., hep-ph/0411386 ) For 11 S 0 : E = - 104 - i 413 MeV seems quite far away from BES observation. They both predict an 11 S 0 ppbar bound state, although they are quantitatively different.

78. BES II Preliminary No  (1800)

79.  With threshold kinematic contributions removed, there are very smooth threshold enhancements in elastic “matrix element” and very small enhancement in annihilation “matrix element”:  much weaker than what BES observed ! NO strong dynamical threshold enhancement in cross sections (at LEAR) |M| 2 BES Both arbitrary normalization

80. The large BR to ppbar suggest it could be an unconventional meson  For a conventional qqbar meson, the BRs decaying into baryons are usually at least one order lower than decaying into mesons. There are many examples in PDG. E.g.  So the large BR to ppbar (with limited phase space from the tail of X(1860)) seems very hard to be explained by a conventional qqbar meson.

81. Analysis of X(1835) 5.1 

82. Analysis of X(1835) 6.0 

83. Comparison of two decay modes  Mass and width from m=1827.4  8.1MeV/c 2,  =54.2  34.5MeV/c 2  Mass and width from m=1836.3  7.9MeV/c 2,  =70.3  23.1MeV/c 2      The mass, width and branching fractions obtained from two different decay modes are consistent with each other.

84. Similar enhancement also observed in 4  away from phase space.

85. This enhancement is NOT observed in process at SAPHIR

86. Discussion on KΛ mass threshold enhancement N X (1610)  N X (1610) has strong coupling to KΛ: From (S&D-wave decay) and is a P-wave decay, we can estimate From BESII, The phase space of N X to KΛ is very small, so such a big BR shows N X has very strong coupling to KΛ, indicating it has a big hidden ssbar component. (5-quark system)

87. Non-observation of N X in suggests an evidence of new baryon :  It is unlikely to be N*(1535). If N X were N*(1535), it should be observed in process, since: From PDG, for the N* in the mass range 1535~1750 MeV, N*(1535) has the largest, and from previous estimation, N X would also have almost the largest BR to KΛ.  Also, the EM transition rate of N X to proton is very low.

88. Clear  and  signals    recoiling against 

89. Side-bands do not have mass threshold enhancement Side-bands

91.  Four decay modes are included :  Amplitudes are defined by Covariant tensor formalism B.S. Zhou and D.V. Bugg, Eur. Phys. J. A16, 537(2003)  BW with energy-dependent width J.H. Kuhn, A. Satamaria, Z. Phys. C48, 445 (1990). Partial Wave Analysis of J/   K + K -  0 events

92. Angular distributions for events with from PWA fit  Figures on the right:  (a),(c),(e) are polar angles in lab. reference frame  (b),(d),(f) are polar angles in CM frames of respectively

93. Broad X cannot be fit with known mesons or their interference  It is unlikely to be  (1450), because: The parameters of the X is incompatible with  (1450).  (1450) has very small fraction to KK. From PDG:  It cannot be fit with the interference of  (770),  (1900) and  (2150): The log-likelihood value worsens by 85 (  2 =170).

94. Summary (I)  BES II has observed several strong mass threshold enhancements in J/  decays.  Why strong mass threshold structures are important? Multiquark states may be only observable near mass thresholds with limited decay phase space.  Otherwise, it might be too wide to be observed as a resonance since it can easily fall apart into two or more mesons. I can see f 0 (980) broad resonance or phase space? any broad resonance under other peaks? I can see broad  under other peaks

95. Summary (II)  A very narrow and strong mass threshold enhancement is uniquely observed in decays at BES II: It is NOT observed in B or Y(1S) decays. Its large BR to suggests it be a bound state.  X(1835) is observed in It could be same structure as the ppbar mass threshold enhancement, i.e., it could be a ppbar bound state.