Excited Charmonium in e e- annihilation and B decay

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Excited Charmonium in ee- annihilation and
B decay

• K-T Chao
• Peking University
• QWG Workshop, Beijing, Oct. 12-15, 2004

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• 1. Double Charm Production in ee? 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 ee- ? 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, ?CK, ?C1K, ?(3770)K (with
  S-D mixing)
• Infrared divergences in
• B? ?C0K, ?C2K , hC K
• The role of NRQCD color-octet in
  exclusive processes?

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Double Charm Production in ee? Annihilation

• INCLUSIVE PRODUCTION
• ee?? 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

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• Belle data ? 0.9pb, PRL89(2002)142001

• larger than theory by at least 5 times. Higher
  order relativistic and QCD radiative corrections?

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Double Charm Production in ee? Annihilation

• EXCLUSIVE PROCESS
• ee? ? 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
• ee? ?J/??C (decaying to ? 4 charged) (PRL89,
  142001)

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Double Charm Production in ee? 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)

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Double Charm Production in ee? 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!

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• Search for excited charmonium states in ee-
  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 ee- ? J/?(cc)res ee- ? ?(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
  

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ee- ? J/?(cc)res with L155 fb-1
ICHEP04/Belle, Pakhlov et al.

• Study recoil mass against J/?
• Mrecoil ?((Ecms EJ/?)2 PJ/?2)½
• Include all known charmonium states
• ?c, J/?, ?c0, ?c1, ?c2, ?c, ?(2S)

N M GeV/c ?
?c J/? ?c0 ?c1 ?c2 ?c ?(2S) 235 ? 26 -14 ? 20 89 ? 24 10 ? 27 164 ? 30 -26 ? 29 2.972?0.007 fixed 3.407 ?0.011 fixed 3.630 ?0.008 fixed 10.7 -- 3.8 -- 6.0 --

• Yields for J/?, ?c1, ?c2, ?(2S) 0 ? set UL

?c, ?c0, ?c confirmed
J/?, ?c1, ?c2, ?(2S) not seen
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ee- ? ?(2S)(cc)res

• Similar analysis for reconstructed ?(2S)?J/???
• Fit to Mrecoil (?(2S)) spectrum

N ?
?c J/? ?c0 ?c1 ?c2 ?c ?(2S) 36.7? 10.4 6.9 ? 8.9 35.4 ? 10.7 6.6 ? 8.0 36.0? 11.4 -8.3 ? 8.5 4.2 -- 3.5 -- 3.4 --

• 5.3 ? observation of sum of ?c, ?c0, ?c

• Similar tendency ?c, ?c0, ?c seen J/?, ?c1,
  ?c2, ?(2S) not seen

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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 M3.940?0.011 GeV/c2
• N148?33 (4.5?)
• The width is surprisingly narrow lt resolution (
  32 MeV)

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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 DDbar. ?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.
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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?charmoniumK

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• 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

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Z M2/MB2 ? 4mc 2 /mb2 ? is the gluon mass for
infrared regularization
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If using the infrared divergence term to
estimate the B exclusive decay widths as in the
case of hadronic decay widths
?(hc ? ggg)5/6 ? (?c1?qqg)
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Too large branching ratio for B?hcK ! New method
and ingredients based on NRQCD are expected to
remove infrared divergences !
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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?
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Other approach to solve the problems

• Rescattering effects by intermediate charmed
  mesons, B? DDs?XcoK
• (Colangelo-DeFazio-Pham,PLB542(2002)71
  PRD69(2004),054023)
• LCSR large for B?J/psi K, Xc1K
• small for B?etacK, XcoK
• (Melic, PRD68(2003)034004)
• (Wang-Li-Huang, hep-ph/0311296)