1. 1 Exclusive Baryonic B decays Hai-Yang Cheng Academia Sinica Two-body baryonic B decays Three-body baryonic B decays Radiative baryonic B decays 3 rd ICFP, NCU, Chung-li, Oct 3-8, 2005

2. 2 Baryonic B decays 3-body baryonic B deacys were found to have larger BRs than 2-body decays There are extensive studies of baryonic B decays in Taiwan both experimentally and theoretically B - →ppK - : first observation of charmless baryonic B decay B→pp(K,K *,  ) →  p( ,K) →  K B→pp, , p  stringent limits) B→p  : first observation of b→s  penguin in baryonic B decays Expt. Theory Chua, Geng, Hou, Hsiao, Tsai, Yang, HYC,… Publication after 2001: (hep-ph) 0008079, 0107110, 0108068, 0110263, 0112245, 0112294, 0204185, 0204186, 0208185, 0210275, 0211240, 0302110, 0303079, 0306092, 0307307, 0311035, 0503264, PRD(05, not on hep-ph) 0201015, 0405283 Belle group at NTU first paper on radiative baryonic B decays C.Q. Geng, this afternoon QCD05, Beijing

3. 3 History A baryon pair is allowed in the final state of hadronic B decays ARGUS (’87): stimulate extensive studies (16 theory papers) during 1988-92  pole model: Deshpande, Trampetic, Soni; Jarfi et al.  QCD sum rule: Chernyak, Zhitnitsky  diquark model: Ball, Dosch  symmetry: He, McKeller, Wu; Sheikholeslami, Khanna Experimental & theoretical activities faded away after 1992 and revived again mainly after 2000.

4. 4 1997: first measurement of B  c pX (X=0, ,  ) by CLEO 2000: first observation of B 0  D *- pn & B 0  D *- pp  + by CLEO 2001: first observation of charmless B -  ppK - by Belle 2002: observation of  c pX (X= ,  ) by Belle, CLEO, D (*)0 pp by Belle 2003: first observation of 2-body decay: B 0  c p (Belle), first evidence of J/  p (BaBar) 2004: first observation of b→s  penguin in baryonic B decays (Belle): B  p  2005: doubly charmed baryon modes B   c  c, B  c  c K (Belle) active theoretical studies since 2001

5. 5 Charmful baryonic B decays B -  J/  p (12 +9 -6 )  10 -6 by BaBar, (11.6  2.8 +1.8 -2.3 )  10 -6 by Belle

6. 6 2-body baryonic B decays Br(  c 0  -  + )=1.3%, Br(  c +  -  +  + )=7.1% (HYC,Tseng; Korner et al.)  Br(B -  c 0  c - )  4  10 -3, Br(B 0  c +  c - )  1.3  10 -3 charmless: charmful :  c  c  10 -3 >>  c p  10 -5 >>  p  10 -7

7. 7 Recently Belle has measured angular distribution and BaBar measured Dalitz plot asymmetry, providing information on the decay mechanism For charmless baryonic B decays,  (3-body)>  (2-body) e.g.  p  + (  10 -6 ) >>  p(  10 -7 ) For charmful decays, one also has  c + p  +  - (  10 -3 ) >  c + p  - (  10 -4 ) >  c + p(  10 -5 ) due mainly to resonant contributions to 3-body and 4-body decays For doubly charmful baryonic B decays  c  c K (  7  10 -4 )   c  c (  10 -3 ) first observation of charmless baryonic B decay Charmless 3-body baryonic B decays: Belle group at NTU has made major contributions

8. 8 Threshold or low mass enhancement effect B 0  p  -  Br(B 0  p  - ) >> Br(B -  p), Br(B - →ppK) >> Br(B 0 →pp) Threshold effect was conjectured by Hou & Soni (2001): energy release must be reduced in order to have larger baryonic B rate Dunietz (1999): In Dalitz plot for b  udu transition, the invariant mass of ud tends to peak at the highest possible value due to its (V- A) structure Spectrum of three-body baryonic B decays shows a low mass enhancement of the baryon pair B-c+pB-c+p

9. 9 2-body baryonic B decays B  B 1 B 2 via internal W-emission, b  d(s) penguin, annihilation Internal W emission is color suppressed in mesonic B decays, but not necessarily so in baryonic B decays due to baryon w.f. totally antisymmetric in color indices effective Hamiltonian approach  A(B  B 1 B 2 )  (c 1 -c 2 )  c 2 +c 1 /3 for tree-dominated 2-body decay mode

10. 10 Expt   c  c  10 -3 >>  c p  10 -5 >>  p  10 -7 Theoretical expectation:  B  B 1 B 2 )=|CKM| 2 f(energy release) -1 CKM(  c  c )=V cb V cs * and CKM(  c p)=V cb V ud * Br(  c + p)=Br(  c  c ) (dynamical suppression) ⇒ d.s.  10 -2 Br(  p) = Br(  c + p)|V ub /V cb | 2 (d.s.)’ = 2.2  10 -7 (d.s.)’ To have quantitative predictions, we use the pole model to evaluate the nonfactorizable decay amplitude and apply the MIT bag model to compute baryon-baryon transition (HYC,Yang 02) Other approaches: -- diquark model (Ball, Dosch 91) (Chang, Hou 01) -- sum rules (Chernyak, Zhitnisky 90) -- quark-diagram analysis: charmless baryonic B (Chua 03), charmful decay (Luo, Rosner 03)

11. 11 (CZ=Chernyak & Zhitnitsky) charmless 2-body baryonic B decays

12. 12 CZ Jarfi et al. HYC, Yang Expt B0c+pB0c+p 4  10 -4 1.1  10 -3 1.1  10 -5 (2.19  0.84)  10 -5 B-c0pB-c0p 3  10 -3 1.5  10 -2 6.0  10 -5 (3.67 +0.56 -0.51  0.18)  10 -5 B0c0nB0c0n 5.8  10 -3 6.0  10 -7 B -  c +  -- 2  10 -4 3.6  10 -2 1.9  10 -5 (0.65 +0.56 -0.51  0.18)  10 -5 All previous predictions based on QCD sum rule, pole model and diquark model are too large compared to experiment 2-body singly charmed baryonic B decays 2-body doubly charmed baryonic B decays Earlier predictions based on QCD sum rule and diquark model ⇒  c 0 p  c  c ⇒ dynamical suppression effect for the former is missing We (Chua, Tsai, HYC) are now working on the d.s. effect

13. 13 3-body baryonic B decays Internal W-emission diagrams (c), (d) are color suppressed (e.g. J/  p), but (e) and (f) are not. The decays B 0  c 0 p  + (  0 ) that proceed only via the latter have rates similar to  c ++ p  - which proceeds via external W-emission (a). 8 distinct quark diagrams: 2 external W-emission, 4 internal W-emission, and 2 annihilation

14. 14 Factorizable contributions to 3-body baryonic B decays: current-induced process: can be related to some measurable quantities (e.g. nucleon EM form factors) for octet baryon pair can be readily evaluated under factorization and QCD counting rule for form factors (Chua, Hou, Tsai 01,02) transition process: use QCD counting rule to make power expansion of 1/m 2 12 for form factors in 3-body matrix element and then use charmless 3- body decay data to fit form factors (Chua, Hou, Tsai) use pole model to evaluate 3-body matrix element: a dynamical calculation (HYC, Yang 02)

15. 15 Chua, Hou, Tsai -- charmful: B  D * pn -- charmless: B  np  (  ), ppK(  ),  )p  HYC, Yang (pole model) -- charmful: B   c p ,  c p  D * pn, D * pp  -- charmless: B  np  (  ), ppK(  ),  p  Geng, Hsiao -- B   K(  ) -- T violation in B   p  see Geng, Hsiao parallel session (Thursday)

16. 16 b u b s u s K-K- p p K-K- p p B-B- B-B- p p p p K-K- K-K- b,bb,b  ’, ,… - - u - u Threshold effect in pnguin-dominated B -  ppK - + (a) (b) (a): Invariant mass of Kp tends to be small, supported by Belle observation that p prefers to be parallel to K and BaBar measurement that K is correlated more strongly to p than to p ⇒ dominance of penguin contribution (b): maximal propagator when invariant mass pp is close to the threshold  low mass enhancement effect -

17. 17 Low mass enhancement effect from near-threshold resonances ? gluonic resonance  pp in B  ppK (Chua, Hou, Tsai 02) not favored by measurements of angular distribution (Belle) & Dalitz plot asymmetry (BaBar) structure of  c p in B  c p  can be parametrized as a Breit-Wigner with m=3.35 +0.02 -0.03 GeV & width=0.07 +0.06 -0.05 GeV (Belle) Br(B→  c  c K)  10 -8 vs 7  10 -4 (expt.) due to tiny phase space available & color suppression ! A big surprise ! ⇒ a charmonium (  4.65 GeV)→  c  c with large coupling and narrow width ? (Chua,Tsai, HYC 05) B-c+pB-c+p

18. 18 Radiative baryonic B decays Owing to large m t, b  s  penguin transition is neither quark mixing nor loop suppressed. At mesonic level, it manifests as B  K * . What happens at baryonic level ? Consider  b pole diagram and apply HQS and static b quark limit to relate the tensor matrix element with  b  form factors  Br(B -  p  )  Br(B -  0  -  ) = 1.2  10 -6 (HYC, Yang, 2002)  Br(B -  0 p  )= 2.9  10 -9 We concluded three years ago that penguin-induced B -  p  and B -  0  -  should be readily accessible to B factories

19. 19 Br(B -  p  ) = (2.16 +0.58 -0.53  0.20)  10 -6 Br(B -  0 p  ) < 3.3  10 -6 Geng & Hsiao [PL B610, 67 (2005)] use QCD counting rules and data of charmless baryonic B to constrain the relevant matrix elements Br(B -  p  ) = (0.9  0.2)  10 -6 Br(B -  0 p  ) = (1.7  1.5)  10 -7 Quark diagram analysis (Kohara 04) first observation of b  s  in baryonic B decay Belle [Lee & Wang et al. PRL 95, 061802 (2005)] Measurement of B -  0 p  could be used to discriminate between different models see Min-ru Wang’s talk tomorrow

20. 20 Conclusions Threshold effect is a key ingredient for understanding 2- body and 3-body baryonic B decays BR of charmless 2-body decay is predicted to be of order 10 -7 Penguin-induced radiative baryonic B decays should be explored more both experimentally and theoretically