Excited Charmonium in e + e - annihilation and B decay K-T Chao Peking University QWG Workshop, Beijing, Oct , 2004

1. Double Charm Production in e + e  Annihilation Inclusive J/  cc{\bar} production Exclusive J/   C (  C0 (1P),  C (2S), … ) production Search for excited  C0 (2P),  C (3S) … Has  C0 (2P) or  C (3S) been observed at 3.94GeV in e+e-  J/  cc{\bar} by Belle? 2. Charmonium in B exclusive decays with QCD factorization Predicted rates too small (but infrared safe) for B  J/  +K,  C +K,  C1 +K,  (3770)+K (with S-D mixing) Infrared divergences in B   C0 +K,  C2 +K, h C +K The role of NRQCD color-octet in exclusive processes?

Double Charm Production in e + e  Annihilation INCLUSIVE PRODUCTION : e + e   J/  cc \ bar Theory: via ONE virtual photon Cho-Leibovich (1996) Yuan-Qiao-Chao (1997) Baek-Ko-Lee-Song (1998)  pQCD predicts: cross section at  s  10.6 GeV  pb

larger than theory by at least 5 times. Higher order relativistic and QCD radiative corrections?  Belle data  0.9pb, PRL89(2002)142001

Double Charm Production in e + e  Annihilation EXCLUSIVE PROCESS e + e   J/   C (  C0,  C (2S), … ) Theory: via ONE virtual photon (Braaten-Lee (2003) PRD67, ) (Liu-He-Chao (2003) PLB557, 45) (Hagiwara-Kou-Qiao (2003) PLB570, 39) pQCD prediction smaller again by an order of magnitude than Belle cross section  33 femto-barn for e + e   J/  C (decaying to  4 charged) (PRL89, )

Double Charm Production in e + e  Annihilation Theory: via TWO photons  Enhanced by photon fragmentation (small photon virtuality 4m c 2  s )  Suppressed by QED over QCD couplings  Exclusive J/  +J/  enhanced (Bodwin- Braaten-Lee, PRL90, ), the same order as for J/  +  C (but ruled out later by data)  Inclusive J/  cc\bar via two photons prevail over via one photon when  s  20GeV (Liu-He-Chao, PRD68, R031501)

Double Charm Production in e + e  Annihilation  Annihilation into TWO photons can NOT solve problems for both inclusive and exclusive double charm production  Both data larger than pQCD predictions by about an order of magnitude  Color octet contributions are negligible  pQCD factorization fails(?)  C=+ glueballs misidentified as  C (?) (Brodsky et al.) excluded!

Search for excited charmonium states in e+e- annihilation (Liu, He & Chao, hep-ph/ ) Predicted relative production rates seem to be compatible with data (Belle: PRL89(2002)142001; hep-ex/ ) See also: ICHEP04/Belle, Pakhlov et al. In e+e- → J/  (cc)res e+e- →  (2S)(cc)res  c,  c0,  c (2S) seen [  c1,  c2, J/ ,  (2S) not seen] Calculate the production cross sections, and Search for excited  C0 (2P),  C (3S) … Test the production mechanisms Search for new charmonium states

e + e - → J/  (cc) res with L=155 fb -1 Yields for J/ ,  c1,  c2,  (2S) ~ 0  set UL  c,  c0,  c ’ confirmed J/ ,  c1,  c2,  (2S) not seen NM [ GeV/c]   c J/   c0  c1 +  c2  c ’  (2S) 235        fixed  fixed  fixed Study recoil mass against J/  : M recoil  ((E cms – E J/  ) 2 – P J/  2 ) ½ Include all known charmonium states:  c, J/ ,  c0,  c1,  c2,  c ’,  (2S) ICHEP04/Belle, Pakhlov et al.

e + e - →  (2S)(cc) res Similar analysis for reconstructed  (2S)  J/  Fit to M recoil (  (2S)) spectrum : N   c J/   c0  c1 +  c2  c ’  (2S) 36.7       Similar tendency:  c,  c0,  c ’ seen … J/ ,  c1,  c2,  (2S) not seen 5.3  observation of sum of  c,  c0,  c ’

Evidence for new charmonium The reconstruction and selection procedure is not changed since the first Belle paper Extend the studied region No signal of X(3872) Significant peak at M=3.940  GeV/c 2 N=148  33 (4.5  ) The width is surprisingly narrow <~ resolution (= 32 MeV)

X(3940) could be  C0 (2P) or  C (3S)…?  C0 (2P) 0 ++ mass: consistent with potential model estimate. narrow width: node in wave function may cause suppression for DDbar (see e.g. Eichten et al); but 0 ++ can not decay to DD*bar.  C (3S) 0 -+ mass: lower than potential model expected [close or even heavier than  (3S) =  (4040)] decay: 0 -+ can not decay to DD\bar, and the allowed DD*\bar could be suppressed by the node structure--natural explanation for the observed decay width and modes? Unkonw 1 ++ : if it is  C1 (2P), why  C1 (1P) not observed? Another 1 ++ ? Is this X(3940) related to the J/  structure at 3940 MeV in B decay? Branching ratio  C0 (2P)  J/  seems too large? Width smaller than 90 MeV.

Infrared Divergences in B   CJ K and B  h C K Decays in QCD Factorization (Song, Chao, Phys.Lett. B568 (2003)127) (Song, Meng, Gao, Chao, Phys.Rev.D69(2003)054009) (Song, Meng, Chao, Eur.Phys.JC36(2004)365) BBNS (Beneke et al.) QCD factorization:  Good for B  pi pi, B  D pi.  Problems for B  charmonium+K

Color transparency, cc-bar small size, viewed as a color (singlet) dipole, factorization might be good?  S-wave: B  J/  K (infrared safe), but smaller than data by ~ 8 times (Chay-Kim, Cheng-Yang) ;  S-wave: B   C K (infrared safe), but smaller than data by ~ 8 times (Song-Meng-Chao) ;  P-wave: B   CJ K and B  h C K, Infrared divergences (due to vertex corrections ) in QCD factorization and NRQCD

Z= M 2 /M B 2  4m c 2 /m b 2 is the gluon mass for infrared regularization

If using the infrared divergence term to estimate the B exclusive decay widths as in the case of hadronic decay widths:  (h c  ggg)=5/6  (  c1  qqg)

Too large branching ratio for B  h c K ! New method and ingredients based on NRQCD are expected to remove infrared divergences !

Questions about NRQCD color-octet mechanism Color octet components in charmonium should help, as in the INCLUSIVE B decays, to enhance the decay rates and remove the infrared divergences, but HOW to do it in EXCLUSIVE decays?

Other approach to solve the problems Rescattering effects by intermediate charmed mesons, B  D+Ds  Xco+K (Colangelo-DeFazio-Pham,PLB542(2002)71; PRD69(2004),054023) LCSR: large for B  J/psi+ K, Xc1+K small for B  etac+K, Xco+K (Melic, PRD68(2003)034004) (Wang-Li-Huang, hep-ph/ )