Excited Charmonium in ee 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 n. Inclusive J/ cc{bar} production n. Exclusive J/ C ( C 0(1 P), C(2 S), …) production n. Search for excited C 0(2 P), C(3 S)… Has C 0(2 P) or C(3 S) been observed at 3. 94 Ge. V in e+e- J/ cc{bar} by Belle? 2. Charmonium in B exclusive decays with QCD factorization n. Predicted rates too small (but infrared safe) for B J/ +K, C 1+K, (3770)+K (with S-D mixing) n. Infrared divergences in B C 0+K, C 2+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/ ccbar Theory: via ONE virtual photon Cho-Leibovich (1996) Yuan-Qiao-Chao (1997) Baek-Ko-Lee-Song (1998) Ø p. QCD predicts: cross section at s 10. 6 Ge. V 0. 10 -0. 15 pb
ØBelle data 0. 9 pb, PRL 89(2002)142001 larger than theory by at least 5 times. Higher order relativistic and QCD radiative corrections?
Double Charm Production in e+e Annihilation EXCLUSIVE PROCESS e+e J/ C ( C 0, C(2 S), …) Theory: via ONE virtual photon (Braaten-Lee (2003) PRD 67, 054007) (Liu-He-Chao (2003) PLB 557, 45) (Hagiwara-Kou-Qiao (2003) PLB 570, 39) p. QCD prediction smaller again by an order of magnitude than Belle cross section 33 femto-barn for e+e J/ C (decaying to 4 charged) (PRL 89, 142001)
Double Charm Production in e+e Annihilation Theory: via TWO photons Ø Enhanced by photon fragmentation (small photon virtuality 4 mc 2 s ) Ø Suppressed by QED over QCD couplings Ø Exclusive J/ +J/ enhanced (Bodwinthe same order as for J/ + C (but ruled out later by data) Braaten-Lee, PRL 90, 162001), Ø Inclusive J/ ccbar via two photons prevail over via one photon when s 20 Ge. V (Liu-He-Chao, PRD 68, R 031501)
Double Charm Production in e+e Annihilation Ø Annihilation into TWO photons can NOT solve problems for both inclusive and exclusive double charm production Ø Both data larger than p. QCD predictions by about an order of magnitude Ø Color octet contributions are negligible Ø p. QCD factorization fails(? ) Ø C=+ glueballs misidentified as C (? ) (Brodsky et al. ) excluded!
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: PRL 89(2002)142001; hep-ex/0407009) See also: ICHEP 04/Belle, Pakhlov et al. In e+e- → J/ (cc)res e+e- → (2 S)(cc)res c, c 0, c(2 S) seen [ c 1, c 2, J/ , (2 S) not seen] Calculate the production cross sections, and Search for excited C 0(2 P), C(3 S)… Test the production mechanisms • Search for new charmonium states •
ICHEP 04/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/ , c 0, c 1, c 2, c’, (2 S) c J/ c 0 c 1 + c 2 c ’ (2 S) N 235 -14 89 10 164 -26 26 20 24 27 30 29 M [ Ge. V/c] 2. 972 0. 007 10. 7 fixed -3. 407 0. 011 3. 8 -fixed 3. 630 0. 008 6. 0 -fixed c, c 0, c’ confirmed seen Yields for J/ , c 1, c 2, (2 S) ~ 0 set UL J/ , c 1, c 2, (2 S) not
e+e- → (2 S)(cc)res Similar analysis for reconstructed (2 S) J/ Fit to Mrecoil ( (2 S)) spectrum: c J/ c 0 c 1 + c 2 c ’ (2 S) N 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, c 0, c ’ Similar tendency: c, c 0, c’ seen… J/ , c 1, c 2, (2 S) not seen
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 Ge. V/c 2 N=148 33 (4. 5 ) The width is surprisingly narrow <~ resolution (= 32 Me. V)
X(3940) could be C 0(2 P) or C(3 S)…? C 0(2 P) 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(3 S) 0 -+ mass: lower than potential model expected [close or even heavier than (3 S) = (4040)] decay: 0 -+ can not decay to DDbar, 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 C 1(2 P), why C 1(1 P) not observed? Another 1++? Is this X(3940) related to the J/ structure at 3940 Me. V in B decay? Branching ratio C 0(2 P) J/ seems too large? Width smaller than 90 Me. V.
Infrared Divergences in B CJ K and B h. CK Decays in QCD Factorization (Song, Chao, Phys. Lett. B 568 (2003)127) (Song, Meng, Gao, Chao, Phys. Rev. D 69(2003)054009) (Song, Meng, Chao, Eur. Phys. JC 36(2004)365) BBNS (Beneke et al. ) QCD factorization: Ø Good for B pi pi, B D pi. Ø Problems for B charmonium+K
Color transparency, cc-bar small size, viewed as a color (singlet) dipole, factorization might be good? ØS-wave: B J/ K (infrared safe) , but smaller than data by ~ 8 times (Chay-Kim, Cheng-Yang) ; ØS-wave: B C K (infrared safe) , but smaller than data by ~ 8 times (Song-Meng-Chao); P-wave: B CJ K and B h. CK , Infrared divergences (due to vertex corrections) in QCD factorization and NRQCD Ø
Z= M 2/MB 2 4 mc 2 /mb 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: (hc ggg)=5/6 ( c 1 qqg)
Too large branching ratio for B hc. 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-De. Fazio-Pham, PLB 542(2002)71; PRD 69(2004), 054023) LCSR: large for B J/psi+ K, Xc 1+K small for B etac+K, Xco+K (Melic, PRD 68(2003)034004) (Wang-Li-Huang, hep-ph/0311296)
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