1 Resolving B-CP puzzles in QCD factorization - An overview of charmless hadronic B decays - Hai-Yang Cheng Academia Sinica Based on 3 papers with Chun-Khiang Chua  B-CP puzzles in QCDF  B u,d decays  B  (K,K *,K 0 *,K 2 * )( ,  ’) May 6, 2010 at NTHU

Day in the life – The Emperor’s Tea : Murayama

3 Direct CP asymmetries   =A CP (K -   ) – A CP (K -   ) K -         K -  K *0  K -       A CP (%)    9 19  5 37   4  S 8.5  6.3  5.3  4.1  3.8  3.4  3.3   K* -     K -  K -             A CP (%) -18  7 15     6 S 2.6  2.5  2.0  1.9  1.8  CDF: A CP (B s  K +   )=0.39  0.17 (2.3  )

4 In heavy quark limit, decay amplitude is factorizable, expressed in terms of form factors and decay constants. Encounter several difficulties: Rate deficit puzzle: BFs are too small for penguin-dominated PP,VP,VV modes and for tree-dominated decays    ,     CP puzzle: CP asymmetries for K -  , K *-  , K -  ,     are wrong in signs Polarization puzzle: f T in penguin-dominated B  VV decays is too small  1/m b power corrections !

5 A(B 0  K -  + )  u a 1 + c (a 4 c +r  a 6 c ) Theory Expt Br 13.1x10 -6 (19.4  0.6)x10 -6 A CP Im  4 c   wrong sign for A CP penguin annihilation charming penguin, FSI penguin annihilation 1/m b corrections 4c4c

6 has endpoint divergence: X A and X A 2 with X A   1 0 dy/y Adjust   and   to fit BRs and A CP     1.10,    -50 o Im(   c +   c )  Beneke, Buchalla, Neubert, Sachrajda

77 New CP puzzles K -         K -  K *0  K -       A CP (%)    9 19  5 37   4  S 8.5  6.3  5.3  4.1  3.8  3.4  3.3  m b    3.3     PA  (  1.9)    K* -     K -  K -             A CP (%) -18  7 15  65.0    6 S 2.6  2.5  2.0  1.9  1.8  m b   PA  Penguin annihilation solves CP puzzles for K -  ,    ,…, but in the meantime introduces new CP puzzles for K - , K *0 , … Also true in SCET with penguin annihilation replaced by charming penguin

All “problematic” modes receive contributions from c’=C’+P’ EW. T’  a 1, C’  a 2, P’ EW  (-a 7 +a 9 ), P’ c EW  (a 10 +r  a 8 ), t’=T+P’ c EW  A K  puzzle is resolved, provided c’/t’ ~ with a large negative phase (naively, |c’/t’|  0.9)  a large complex C’ or P’ EW  A K   0 if c’ is negligible Large complex C’: Charng, Li, Mishima; Kim, Oh, Yu; Gronau, Rosner; … Large complex P’ EW needs New Physics for new strong & weak phases Yoshikawa; Buras et al.; Baek, London; G. Hou et al.; Soni et al.; Khalil et al.

9 Power corrections have been systematically studied by Beneke, Neubert: S2, S4 Ciuchini et al., Duraisamy & Kagan, Li & Mishima, The two distinct scenarios can be tested in tree-dominated modes where P EW <<C. CP puzzles of   ,     & large rates of    ,     cannot be explained by a large P EW

10 a 2  a 2 [1+  C exp(i  C )]  C  1.3,  C  -70 o for PP modes a 2 (K  )  0.51exp(-i58 o ) Two possible sources: spectator interactions NNLO calculations of V 2 & H 2 are now available Real part of a 2 comes from H and imaginary part from vertex a 2 (  )  i =0.34 exp(-i15 o ) for  = 250 MeV a 2 (K  )  0.51exp(-i58 o )    = 4.9 &    -77 o [Bell, Pilipp] final-state rescattering [ C.K. Chua] Neubert: In the presence of soft FSIs, there is no color suppression of C w.r.t. T

11 K -         K -  K *0  K -       A CP (%)    9 19  5 37   4  S 8.5  6.3  5.3  4.1  3.8  3.4  3.3  m b    3.3     PA   (  1.9)  large complex a 2   K* -     K -  K -             A CP (%) -18  7 15     6 S 2.6  2.5  2.0  1.9  1.8  m b   PA  large complex a 2  All new CP puzzles are resolved !

12 B -  K -   A(B 0  K -  + ) = A  K (  pu  1 +  4 p +  3 p )= t’+p’  2 A(B -  K -  0 ) = A  K (  pu  1 +  4 p +  3 p )+A K  (  pu  2 +3/2  3,EW p )= t’+p’+c’ m b  penguin ann large complex a 2 Expt A CP (K-   )(%)  2.5  A K  (%)  2.8 In absence of C’ and P’ EW, K -   and K -   have similar CP violation   = a 1,   = a 2 arg(a 2 )=-58 o

13 Br(B  PP) Large K  ’ rates are naturally accounted for in QCDF partial NLO  A =1.10  A = -50 o  C =1.3  C = -70 o

14 B  K (*)  K   ’ In  q &  s flavor basis (  q =(uu+dd)/√2,  s =ss)  =39.3  BRs in units of Interference between (b) & (c)  K  ’  K  For K *, (b) is governed by a 4 -r   a 6, (c) by a 4 ; a 4, a 6 are negative and |a 4 |< |a 6 |; chiral factor r  is of order unity  additional sign difference between (b) & (c) for K *  (‘)

15 A CP (B  PP)(%) Several SCET predictions are in conflict with experiment

16 B 0  K 0   A(B -  K 0  - ) = A  K (  4 p +  3 p ) = p’  2 A(B 0  K 0  0 ) = A  K (-  4 p -  3 p ) + A K  (  pu  2 +  pc 3/2  3,EW c ) = -p’+c’ In absence of C’ and P’ EW, K 0   and K 0   have similar CP violation CP violation of both K 0   & K 0   is naively expected to be very small  A’ K  =A CP (K 0   ) – A CP (K 0   ) = 2sin  Imr C +…  -  A K  m b  penguin ann large complex a 2 Expt A CP (K 0   )(%)  10  A’ K  (%) BaBar:  0.13  0.03, Belle: 0.14  0.13  0.06 for A CP (K 0   )  A CP (K 0   )=  0.04  A CP (K 0   )=  An observation of A CP (K 0   )  - (0.10  0.15)  power corrections to c’ Toplogical quark diagram approach  A CP (K 0   )=  -0.12

17 B -  K -  Destructive interference  penguin amp is comparable to tree amp  more sizable CP asymmetry in K  than K  ’ Although f  c =-2 MeV is very small compared to f  q = 107 MeV, f  s = -112 MeV, it is CKM enhanced by V cb V cs * /(V ub V us * ) m b  penguin annlarge complex a 2 (w/o charm) large complex a 2 (with charm) Expt A CP (K -  )(%)  9 A CP (    )(%)  7 Charm content of  plays a crucial role for ACP(K -  ), but not for A CP (    ) Prediction of A CP (K -  ) still falls short of data

18 pQCD prediction is very sensitive to m qq, mass of  q A CP (K -  ) = , , for m qq = 0.14, 0.18, 0.22 GeV Two issues: (i) with anomaly: (ii) stability w.r.t. m qq Akeroyd,Chen,Geng Xiao et al. ( ) reply on NLO corrections to get a correct sign: A CP (K -  )= to LO, ( )% at NLO 1). If NLO effects flip the sign of A CP, pQCD calculations should be done consistently to NLO 2). Missing parts of NLO: hard spectator & weak annihilation

19 Time-dependent CP asymmetries: S B  PP  QCDF prediction for S(     ) agrees well with data  S(  ’K S ) is theoretically very clean in QCDF & SCET but not so in pQCD  Around 2005, CCS and Beneke got S(  ’K S )  0.74 in QCDF. Why 0.67 this time ?

20 sin2  extracted from charmonium data is  circ 2005, and  today. It is more sensible to consider the difference  S f = -  f S f - sin2   S f = 2|r f |cos2  sin  cos  f with r f =( u A f u )/( c A f c ) small and could be + or –  S  Ks positive

21 B  VV decays Branching fractions tree-dominated decays: VV>PV>VP>PP (due to f V > f P ) penguin-dominated decays: PP>PV~VV>VP (due to amplitudes  a 4 +r  P a 6, a 4 +r  V a 6, a 4 -r  P a 6, a 4 +r  V a 6 Polarization puzzle in charmless B→VV decays Why is f T so sizable ~ 0.5 in B → K * Á decays ? In transversity basis

22 A 00 >> A -- >> A ++

23 B → K * Á ® 3 =a 3 +a 5, ® 4 =a 4 -r  Á a 6, ® 3,EW =a 9 +a 7, ¯ 3 = penguin ann h=0 h= - h=0 h= - Coefficients are helicity dependent ! constructive (destructive) interference in A - (A 0 ) ⇒ f L ¼ 0.58 with ¯ 3 =0 NLO corrections alone can lower f L and enhance f T significantly ! Yang, HYC

24 Although f L is reduced to 60% level, polarization puzzle is not resolved as the predicted rate, BR» 4.3£10 -6, is too small compared to the data, » 10£10 -6 for B →K * Á Br & f L are fitted by ½ A =0.60, Á A = -50 o Kagan f || ¼ f ? » 0.25 (S-P)(S+P) (S-P)(S+P) penguin annihilation contributes to A -- & A 00 with similar amount

25   =0.78,   =-43 o for K * ,   =0.65,   =-53 o for K *   Rate for    is very small However, pQCD prediction is larger than QCDF by a factor of 20 ! Br(B 0  K *0 K *0 )=  0.11 by BaBar, 0.3  0.3  0.1 by Belle Br(B 0     )= is obtained with  C =0  soft corrections to a 2 are large for PP, moderate for VP and very small for VV r  V <<r  P doesn’t help! or due to Goldstone nature of the pion ? [Duraisamy, Kagan]

26 Conclusions  In QCDF one needs two 1/m b power corrections (one to penguin annihilation, one to color-suppressed tree amplitude) to explain decay rates and resolve CP puzzles.  CP asymmetries are the best places to discriminate between different models.

27       ’ is the other way around

28 Spare slides

29 Br(B  VP)  A (VP)=1.07  A (VP)=  A (PV)=0.87  A (PV)= -30 o  A (K  )=0.70  A (K  )= -40 o  C =0.8  C = - 70 o Br(B -   )=Br(B -   ) sin    is an  -  mixing angle  3.3 o Belle: C.C. Chiang

30 Br(B  VP)  A (VP)=1.09  A (VP)=  A (PV)=0.87  A (PV)= -30 o  A (K  )=0.70  A (K  )= -40 o  C =0.8  C = - 70 o In heavy quark limit, K*  rates are too small by (15  50)%, while K  are too small by a factor of 2  3    (  K * )>   (  K * ) QCDF predictions for K*  ’ too small compared to BaBar but consistent with Belle: Br(K *-  ’)<2.9, Br(K *0  ’)<2.6

31 A CP (B  VP)(%) K *0  -,  - K 0 have small A CP as they are pure penguin processes  A K*  =A CP (K *-   ) - A CP (K *-   )= -2sin  Imr c (K *  )+….   A’ K *  =A CP (K *0   )- A CP (K *0   )= 2sin  Imr c (K *  ) +…  Data of A CP (K *0  ) is in better agreement with QCDF than pQCD & SCET. The SCET predictions are ruled out by experiment.

32 S B  VP  S B  VP  S  is negative and sensitive to soft corrections on a 2 Expt’l errors of S  are very large

33    is expected to have larger f T as its tree contribution is small b  d penguin-dominated modes K *0 K *0, K *0 K *- are expected to have f L  0.5. Experimentally, f L  (why ?) For K *-  0, recent BaBar measurement gives f L =0.9  0.2 with 2.5 significance QCDF leads to