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Excited Charmonium in e + e - annihilation and B decay

Excited Charmonium in e + e - annihilation and B decay. K-T Chao Peking University QWG Workshop, Beijing, Oct. 12-15, 2004. 1. Double Charm Production in e + e  Annihilation Inclusive J/  cc{bar} production Exclusive J/   C ( C0 (1P),  C (2S), … ) production

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Excited Charmonium in e + e - annihilation and B decay

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  1. Excited Charmonium in e+e- annihilation and B decay K-T Chao Peking University QWG Workshop, Beijing, Oct. 12-15, 2004

  2. 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 , hC +K The role of NRQCD color-octet in exclusive processes?

  3. 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 0.10-0.15pb

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

  5. Double Charm Production in e+e Annihilation EXCLUSIVEPROCESS e+e J/ C (C0, C(2S),…) Theory: via ONE virtual photon (Braaten-Lee (2003) PRD67, 054007) (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, 142001)

  6. Double Charm Production in e+e Annihilation Theory: via TWO photons • Enhanced by photon fragmentation (small photon virtuality 4mc2 s ) • Suppressed by QED over QCD couplings • Exclusive J/ +J/ enhanced (Bodwin-Braaten-Lee, PRL90, 162001), 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)

  7. 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!

  8. Search for excited charmonium states in e+e- annihilation • (Liu, He & Chao, hep-ph/0408141) • Predicted relative production rates seem to be compatible with data (Belle: PRL89(2002)142001; hep-ex/0407009) • 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

  9. ICHEP04/Belle, Pakhlov et al. e+e-→ J/(cc)res with L=155 fb-1 • Study recoil mass against J/: Mrecoil((Ecms–EJ/)2–PJ/2)½ • Include all known charmonium states: c, J/, c0, c1, c2, c’, (2S) • Yields for J/, c1, c2, (2S) ~ 0  set UL c, c0, c’ confirmed J/, c1, c2, (2S) not seen

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

  11. 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0.011 GeV/c2 • N=14833 (4.5) • The width is surprisingly narrow <~ resolution (= 32 MeV)

  12. 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.

  13. Infrared Divergences in B CJ K and B hCK 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

  14. 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 hCK , Infrared divergences (due to vertex corrections) in QCD factorization and NRQCD

  15. Z=M2/MB2  4mc 2 /mb2  is the gluon mass for infrared regularization

  16. If usingthe infrared divergence term to estimate the B exclusive decay widthsas in the case of hadronic decay widths: (hc ggg)=5/6  (c1qqg)

  17. Too large branching ratio for BhcK ! New method and ingredients based on NRQCD are expected to remove infrared divergences !

  18. 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?

  19. 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/0311296)

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