Hadronic decays of (2S) Yuan Changzheng (苑 长 征) IHEP, Beijing June 26, 2008

The world of quarks

Onia cc J/y 0.09 3.1 Quarkonium is the bound state of quark and FORCES System Ground triplet state 13S1 (v/c)2 Number of states below dissociation energy binding decay Name G (MeV) Mass (GeV) n3S1 all POSITRONIUM EM e+e- Ortho- 5 10-15 0.001 ~0.0 2 8 QUARKONIUM S T R O N G uu,dd r 150.00 0.8 ~1.0 ss f 4.40 1.0 ~0.8 “1” “2” E M cc J/y 0.09 3.1 ~0.25 bb Υ 0.05 9.5 ~0.08 3 30 weak tt (3000.0) (360.) <0.01 Quarkonium is the bound state of quark and anti-quark by the gluon. Charmonium is charm anti-charm bound state!

Discovery of the J/ψ “November Revolution of Particle Physics!” Charm quark was proposed in 1964, first application in 1970! PRL33, 1404 (1974) PRL33, 1406 (1974) PRL33, 1408 (1974) ADONE confirmed! BNL SLAC 郁闷的Adone! Designed: Maximum Ecm~3 GeV!

Discovery of the ψ(2S) Predictions of the charmonium spectroscopy Argument and Potential model PRL33, 1453 (1974) PRL34, 365 (1975) PRL34, 369 (1975) SLAC From then on, there is a new field in HEP: Charmonium Physics.

Potential models Cornell potential： V(r) = -S/r + kr （库仑势+线性势） 解薛定谔方程能级, 波函数

Potential models vs experiments

This is the famous “12% rule”. The “12% rule” M. Appelquist and H. D. Politzer, PRL34, 43 (1975) This is the famous “12% rule”.

H.D.Politzer 和 “12%规则” 著名的“12%规则”! PRL30, 1346 (1973)通过检验2004年诺贝尔奖 +M. Appelquist, PRL34, 43 (1975)? 著名的“12%规则”! (2S)与J/唯一的差别是主量子数不同，“12%规则”是一个干净、简单的理论推论，预期普遍成立。 “规则”的破坏意味着强相互作用中非常基本的、不为人知的规律的存在！

“12% rule” and “ puzzle” Violation found by Mark-II , confirmed by BESI at higher sensitivity. Extensively studied by BESII/CLEOc VP mode:  , K*+K-+c.c., K*0K0+c.c., 0,… PP mode: KSKL, K+K-, +- BB mode: pp, , … VT mode: K*K*2, f2’, a2, f2 3-body: pp0, pp, +-0, … Multi-body: KSKShh, +-0 K+K- , 3(+-), … MARK-II K*K ρπ The assumptions: 1. pQCD is valid at c-quark mass 2. “pQCD rule” derived for inclusive decays holds for exclusive channels.

J/, (2S)衰变模式 衰变模式 J/ 分支比 (%) (2S) 跃迁 强子跃迁 辐射跃迁 0.0 1.3 51.5 26.3 跃迁 强子跃迁 辐射跃迁 0.0 1.3 51.5 26.3 轻子对衰变 11.8 1.7 强子衰变 电磁衰变 强衰变 13.5 69.1 17.7 辐射衰变 4.3 1.1 稀有衰变 <<1.0 总和 100.0

What we observed in experiment

连续态振幅对物理的显著影响 分支比 相角 与共振态之间的干涉应考虑 连续态贡献应被扣除 连续态贡献不能忽略!

A universal -90°phase? |φ| J/ψ Decays: ψ(2S) Decays: 1. AP: 90° M. Suzuki, PRD63, 054021 (2001) 2. VP: (106 ±10)° J. Jousset et al., PRD41, 1389 (1990) D. Coffman et al., PRD38, 2695 (1988) N. N. Achasov, talk at Hadron2001 3. PP: (90 ±10)° M. Suzuki, PRD60, 051501 (1999) (103±7)° BES, PRD69, 012003 (2004) 4. VV: (138 ±37)° L. Köpke and N. Wermes, Phys. Rep. 174, 67 (1989) 5. NN: (89 ±15)° R. Baldini et al., PLB444, 111 (1998) ψ(2S) Decays: 1. VP: φ=180° (± 90 ° ruled out!) M. Suzuki, PRD63, 054021 (2001) φ=180° or φ=-90° P. Wang et al., PRD69, 057502 (2004) 2. PP: (-82±29)° or (121±27)° BES, PRL92, 052001 (2004) & Yuan, Wang, Mo, PLB567, 73 (2003) |φ|=(95±15)°, CLEO, PRD74, 011105 (2006)

如何测量分支比 纯强衰变末态 纯电磁衰变末态 强+电磁衰变末态

φ ψ(2S)PP (赝标量介子对) ψ(2S) π+π- 电磁衰变 ψ(2S) KS KL 强衰变 ψ(2S) K+K- 强+电磁衰变 B’ (+-) and A’+B’ (K+K-) known, KS KL is needed to extract the phase between A’ and B’. φ When extract A’/B’ from experimental information, Continuum contribution should be considered!

纯强衰变末态 No continuum contribution Count number of events Use formula

纯强衰变末态 利用重建KS BESII, 58 Million J/ψ BESII, 14 Million ψ(2S) PRD 69, 012003 (2004) B (J/  Ks K L) = (1.82 ± 0.04 ± 0.13) ×10-4 B ((2S)  Ks K L) = (5.24 ± 0.47 ± 0.48) ×10-5 MC Bkg K*0KS+c.c. etc. Ks mass sidebands B ((2S)  Ks K L) = (28.8±3.7)% B (J/  Ks K L) PRL 92, 052001 (2004) 利用重建KS

纯电磁衰变末态 共振态与连续态间关系确定 在一个能量点采集数据，计算分支比

强+电磁衰变末态 K 共振态与连续态间关系不确定，依赖电磁与强衰变间的振幅比例和相角 至少在三个能量点采集数据，计算分支比

ψ(2S)PP 假设形状因子相同 三个测量，三个未知数 引进理论假设，利用共振峰数据，计算分支比和相角

’  PP First measurement of the phase in ’ decays! K+K– & + B (’ KS KL ) =5.810 – 5 K+K– & +  inputs ; Input 1: DASP; Input 2: BESI ; Input 3: K+K– from BESI & + by form factor. B (’ KS KL ) =5.2410 – 5 Yuan, Wang, Mo: PLB567 (2003)73 –(80??)° (120??)°

“ puzzle” MARK-II Violation found by Mark-II , confirmed by BESI at higher sensitivity. Further studied by BESII and CLEOc Can/should be improved at BESIII K*K ρπ

’ + - 0 BESII CLEOc BES and CLEOc in good agreement! 229 0s BESII: PLB619, 247 (2005) CLEOc: PRL94, 012005 (2005) 229 0s 196 0s BESII CLEOc BES and CLEOc in good agreement!

’ + - 0 Dalitz plots after applying 0 mass cut! Very different from J/ 3! CLEOc BESII J/ Similar Dalitz plots, different data handling techniques: PWA vs counting! ’ is observed, it is not completely missing, BR is at 10-5 level!

J/ + - 0 Make  mass cut, and count events PWA analysis assuming  interferes with excited  states L. P. Chen and W. Dunwoodie, Hadron’91, MRK3 data PDG04: 1.270.09% Very different!

J/ , ’  ρπ Greatly suppressed!

J/, ’ VP BESII : PLB614, 37 (2005); PRD73, 052007 (2006) CLEOc: PRL94, 012005 (2005) mode BESII: B(’)(×10-5) CLEOc: PDG06/BESII/… B(J/)(×10-4) B(’)/B(J/) (%)  5.1±0.7±1.1 2.4+0.8-0.7±0.2 234±26 0.13±03 (2150) 19.4±2.5+11.5-3.4 N/A +-0 18.1±1.8±1.9 18.8+1.6-1.5±2.8 200±9 0.92±11 K*0K0+c.c. 13.3±2.7±1.7 9.2+2.7-2.2±0.9 42±4 2.6±0.6 K*+K-+c.c. 2.9±1.7±0.4 1.3+1.0-0.7±0.3 50±4 0.34±0.20  1.87+0.68-0.62±0.28 2.5+1.2-1.0±0.2 5.38±0.66 3.7±1.2  1.78+0.67-0.62±0.17 3.0+1.1-0.9±0.2 1.93±0.23 10.9±3.4 ’ 1.87+1.64-1.11±0.33 1.05±0.18 18±16  <0.40 <0.064  3.3±1.1±0.5 2.0+1.5-1.1±0.4 8.98±0.92 3.0±1.2 ’ 3.1±1.4±0.7 5.46±0.64 5.7±3.0  <3.1 <1.1 23.5±2.7 <0.53 ’ 3.2+2.4-2.0±0.7 2.26±0.43 14±11

pQCD rule and “ρπ puzzle” VT ωf2(1270) Φf2’(1525) BESII, PRD69, 072001(2004) 14 Million ψ(2S) 6.0σ 4.3σ 3.6σ VT mode B(2S) X (10 – 4) (BES-II) B J/X (10 – 3) (PDG2002) Qh(%)  f2 2.05± 0.41 ± 0.38 4.3±0.6 4.8±1.5  a2 2.55± 0.73± 0.47 10.9±2.2 2.3±1.1 K* K*2 1.86± 0.32 ± 0.43 6.7±2.6 2.8±1.3  f2' 0.44 ± 0.12 ± 0.11 1.23±0.21 † 3.6±1.5 ρa2(1320) K*K2*(1430) † This value from DM2 only 5.3σ Suppressed!! BESII first observations! VT is suppressed less than VP!

Very small in ’’ decays ’’ + - 0 Very small in ’’ decays φ phase interference interference Continuum contribution is crucial in ’’ analysis: Total ’’ charmless decays (<2nb) is much less than total continuum process (~16nb), Inteference between amplitudes BESII

’’ + - 0 3.773GeV 3.670GeV 3.773GeV 3.650GeV BESII: PRD72, 072007 (2005) CLEO: PRD73, 012002 (2006) BESII CLEOc 3.773GeV 3.670GeV 3.773GeV 3.650GeV BES and CLEOc are in good agreement! X-section at ’’ peak is smaller than at continuum!

BESII: PRD72, 072007 (2005) CLEO: PRD73, 012002 (2006) ’’ + - 0 BESII CLEOc 3.773 3.65 3.773 3.67 Subtle difference in handling efficiency and ISR correction. BES and CLEOc are in good agreement! X-section at ’’ peak is smaller than at continuum! non-zero ’’ amplitude.

’’   Total cross section Three unknowns with two equations --- Wang, Yuan and Mo:PLB574,41(2003) Total cross section Three unknowns with two equations --- One can plot the BR versus phase . B depends on efficiency and ISR correction, efficiency and ISR correction depends on B(s) ! Iteration is necessary!

’’   BES data restrict BR and phase in a wide range (@90% C.L.): BESII: PRD72, 072007 (2005) CLEOc: PRD73, 012002 (2006) ’’   BES data restrict BR and phase in a wide range (@90% C.L.): CLEOc data further restrict BR and phase in a ring*. At =-90: *Toy MC is used to get BR from CLEOc data (not CLEO official results)!

pQCD rule and “ρπ puzzle” Models Recent review: Mo X. H., Yuan C. Z., Wang P., HEP&NP31,686(2007) Models before BES: J/-vector glueball mixing; BLT model Hou-Soni (1983) Brodsky et al. (1987) 2. Sequential quark pair creation Karl-Roberts (1984) Exponentially falling form factor Chaichian & Tornqvist (1989) Generalized hindered M1 transition Pinsky (1990)

pQCD rule and “ρπ puzzle” Models Models after BES: Final-state interactions Li-Bugg-Zou (1997) Intrinsic charm |qqcc> Fock components of the light vector mesons Brodsky-Karlin (1997) 3. Fock state with ccbar pair in a color-octet Chen-Braaten (1998) cc annihilation into 5g via 2 steps Gerard-Weyers (1999) 5. Decays thru light-quark Fock component by a soft mechanism Feldmann-Kroll (2000) 6.  (2S)-vector glueball mixing Suzuki (2001) 7. (2S)-(1D) mixing Rosner (2001)

pQCD rule and “ρπ puzzle” Models Model predictions Test results Theo. Exp. HS/BLT Glueball at Not seen   M3.0 GeV. 0 not all VP suppressed. suppressed. CT All two-body (2S) (2S) b1 decays suppressed. not suppressed.  B()710-5 <310-5 Pinsky Q()210-3 3.610-2 !  f2 suppressed No f2 not suppressed Suppressed KR B() small Big   cross section btwn (2S) & J/ No data !

pQCD rule and “ρπ puzzle” Models Model predictions Test results Theo. Exp. LBZ Big rates for Not seen ! (2S)  a1, K1*K* BK All VP suppressed 0 not suppressed   CB Many VP BRs Agree ! b1 not suppressed Agree a2 a bit suppressed Agree Angular distributions No data !

pQCD rule and “ρπ puzzle” Models Model predictions Test results Theo. Exp. GW Copious h1(1170) in (2S) No ? ! FK VP BRs Agree  cVV BRs Agree cVV suppressed No data Suzuki Vector glueball at M3.7 GeV No data ! Rosner Measurable VP No data !

“12%” rule ’ VP suppressed ’ PP enhanced ’ VT suppressed ’ BB obey/enh Multi-body –obey/sup Seems no obvious rule to categorize the suppressed, the enhanced, and the normal decay modes of J/ and ’. The models developed for interpreting specific mode may hard to find solution for other (all) modes. Model to explain J/, ’ and ’’ decays naturally and simultaneously? S-D mixing in ’ and ’’ [J. L. Rosner, PRD64, 094002 (2001)] DD-bar reannihilation in ’’ (J. L. Rosner, hep-ph/0405196) Four-quark component in ’’ [M. Voloshin, PRD71, 114003 (2005)] Survival cc-bar in ’ (P. Artoisenet et al., PLB628, 211 (2005)) Other model(s)?

pQCD rule and “ρπ puzzle” Conclusions Many experimental results Many theoretical models Explanation still not satisfactory ضء@#$%^&* *()&%*)(#%дмфёЊ حشع٣ؤضء ž¤&ùÐ… Questions need to be fixed: Is the abnormal in J/ψ or in ψ(2S) decays or in both? Are there assumptions behind the experiments and/or theories? What is the key issue to solve the problem? The puzzle remains a puzzle … Both experimentalists and theorists are working hard …

Outlook The End Lots of fun in charmonium physics, Lots of fun in charmonium decays, Lots of puzzles in hadronic final states, All wait for you, a smart guy To solve them by joining us, And to win the ??? prize! 联系电话：8823 3199 (O) Email: yuancz@ihep.ac.cn The End 阿基米德牌浴缸