Flavor, Charm, CP Related Physics PASCOS, Taipei November 22, 2013 Hai-Yang Cheng Academia Sinica, Taipei

2 Outline: Quark and lepton mixing matrices Baryonic B decays Direct CP violation in D decays Direct CP violation in B decays See the talk of Rodrigues (11/21)

3 Quark & lepton mixing matrices

44 CP Violation in Standard Model V CKM is the only source of CPV in flavor-changing process in the SM. Only charged current interactions can change flavor Kobayashi & Maskawa (’72) pointed out that one needs at least six quarks in order to accommodate CPV in SM with one Higgs doublet Physics is independent of a particular parameterization of CKM matrix, but V KM has some disadvantages : Determination of  2 &  3 is not very accurate Some elements have comparable real & imaginary parts 1>>   >>   >>  

5 Maiani (’77) advocated by PDG (’86) as a standard parametrization. However, the coefficient of the imaginary part of V cb and V ts is O(10 -2 ) rather than O(10 -3 ) as s 23  In 1984 Ling-Lie Chau and Wai-Yee Keung proposed a new parametrization The same as V Maiani except for the phases of t & b quarks. The imaginary part is O(10 -3 ). This new CKM (Chau-Keung-Maiani) matrix is adapted by PDG as a standard parametrization since >>   >>   >>   s 13 ~ 10 -3

6 Some simplified parametrizations Wolfenstein (’83) used V cb =0.04  A 2,  0.22 Mixing matrix is expressed in terms of, A ~ 0.8,  and  Imaginary part = A 3  However, this matrix is valid only up to 3 6 Motivated by the boomerang approach of Frampton & He (’10), Qin & Ma have proposed a different parametrization (’10) Wolfenstein parameters A, ,   QM parameters f, h, 

7 Wolfenstein parametrization up to  Wolfenstein parametrization can also be obtained from KM matrix by making rotations: s  s e i , c  c e i , b  b e i( , t  t e -i(  and replacing A, ,  by A’,  ’,  ’ and ’ The original Wolfenstein parametrization is not adequate for the study of CP violation in charm decays, for example. Hence it should be expanded to higher order of

888 Look quite differently from those of V (CK) Wolf

99 Buras et al. (’94): As in any perturbative expansion, high order terms in are not unique in the Wolfenstein parametrization, though the nonuniquess of the high order terms does not change physics Now |V ub | ~ , |V cb | ~  |V ub | ~  |V cb |~ A  Wolfenstein (’83) used |V ub | ~ 0.2 |V cb | ~ A   ~ 0.129,  ~ not order of unity ! We define & of order unity

10 Most of the discrepancies are resolved via the definition of the parameters ,  of order unity Remaining discrepancies can be alleviated through 1.V us = = ’ 2.from V cb  3.from V ub  arXiv: Ahn, HYC, Oh

11 Lepton mixing matrix   = solar mixing angle,   = atmospheric mixing angle,   = reactor mixing angle Pontecorvo, Maki, Nakagawa, Sakata A different parametrization has been studied: Huang et al ;   ~ 19 o,   ~ 46 o,   ~ 29 o are quite different from   ~ 34 o,   ~ 38 o,   ~ 9 o

12 quark: lepton:   ~ 34 o,   ~ 38 o,   ~ 9 o   ~ 13 o,   ~ 2.4 o,   ~ 0.2 o 1>>   >>   >>  

13 Baryonic B Decays B  baryon + antibaryon B  baryon + antibaryon + meson B  baryon + antibaryon + 

14 A baryon pair is allowed in the final state of hadronic B decays. In charm decay, D s + →pn is the only allowed baryonic D decay. Its BR ~ (CLEO)

15 2-body charmless baryonic B decays Belle BaBar Belle CLEO ARGUS CLEO Belle ALEPH DLPHI CLEO Very rare !

16 CZ=Chernyak & Zhitnitsky (’90), CY= Cheng & Yang (’02) CY What is the theory expectation of Br(B 0  pp) ?

17 Talk presented at 7 th Particle Physics Phenomenology Workshop, 2007

18 Br(B 0  pp)= ( )  Br(B s 0  pp)= ( )  LHCb ( ) 3.3  The pQCD calculation of B 0  pp is similar to the pQCD calculation of B→  c p (46 Feynman diagrams) by X.G.He, T.Li, X.Q.Li, Y.M.Wang (’06) LHCb ( ) observed a resonance  (1520) in B -  ppK - decays Br(B -   (1520)p)= (  0.1  0.3)   (1520)  pK - Why is Br(B -   (1520)p) >> Br(B 0  pp) ? first evidence see the talk of Prisciandaro (22C1b)

19 Angular distribution Measurement of angular distributions in dibaryon rest frame will provide further insight of the underlying dynamics SD picture predict a stronger correlation of the meson with the antibaryon than to the baryon in B→B 1 B 2 M B - →pp  - b u -- p p B-B- - u B rest frame p -- p p -- p pp -- p p pp rest frame Belle(’08) (’13)

20 Belle(’04) BaBar(’05) Angular distribution in penguin-dominated B -  ppK - BaBar measured Dalitz plot asymmetry Belle: K - is preferred to move collinearly with p in pp rest frame !  a surprise in correlation SD picture predicts a strong correlation between K - and p ! pp K-K- p p _ - b u u s K-K- p - - u p b s - u u K-K- p p unsolved enigma ! (’13)

21 Angular distribution in B -  p  - b s  p B0B0 - d ++ u - u SD picture: Both  & p picks up energetic s and u quarks, respectively ⇒ on the average, pion has no preference for its correlation with  or p ⇒ a symmetric parabola that opens downward Belle(’07): M.Z. Wang et al. shows a slanted straight line ⇒ another surprise !! Tsai, thesis (’06) pp p _ ++  Correlation enigma occurs in penguin-dominated modes B→ppK,  p  Cannot be explained by SD b→ sg * picture Needs to be checked by LHCb & BaBar Theorists need to work hard !

22 Radiative baryonic B decays At mesonic level, b  s  electroweak penguin transition manifests in B  K * . Can one see the same mechanism in baryonic B decays ? 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   Br(B -  0 p  )= 2.9  Penguin-induced B -  p  and B -  0  -  should be readily accessible to B factories Br(B -  p  ) = (  0.22)  Br(B -  0 p  ) < 4.6  first observation of b  s  in baryonic B decay Belle [ Lee & Wang et al. PRL 95, (’05) ] HYC,Yang (’02)

23 Extensive studies of baryonic B decays in Taiwan both experimentally and theoretically B - →ppK - : first observation of charmless baryonic B decay (’01) B→pp(K,K *,  ) →  p( ,K) →  K B→pp, , p  stringent limits) B→p  : first observation of b→s  penguin in baryonic B decays (’04) Expt. Theory Chen, Chua, Geng, He, Hou, Hsiao, Tsai, Yang, HYC,… Publication after 2000: (hep-ph) , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , PRD(05,not on hep-ph), , , , , , , , , , Belle group at NTU (Min-Zu Wang,…) Taiwan contributes to 86% of theory papers Publication after 2002: 15 papers (first author) so far: 7PRL, 2PLB, 6PRD; 2 in preparation

24 Direct CP violation in charm decays

25 Amp = V* cd V ud (tree + penguin) + V* cs V us (tree’ + penguin) DCPV is expected to be the order of  !  : strong phase DCPV requires nontrival strong and weak phase difference In SM, DCPV occurs only in singly Cabibbo-suppressed decays. It is expected to be very small in charm sector within SM Penguin is needed in order to produce DCPV at tree & loop level No CP violation in D decays if they proceed only through tree diagrams CP violation in charm decays

26 Experiment Time-dependent CP asymmetry Time-integrated asymmetry LHCb: (11/14/2011) 0.92 fb -1 based on 60% of 2011 data  A CP  A CP (D 0  K + K - ) – A CP (D 0      ) = - (0.82  0.21  0.11)%  3.5  effect: first evidence of CPV in charm sector Belle: (ICHEP2012) 540 fb -1  A CP  - (0.87  0.41  0.06)% CDF: (2/29/2012) 9.7 fb -1  A CP = A raw (K + K - ) - A raw (    - )= - (2.33  0.14)% - (-1.71  0.15)% = - (0.62  0.21  0.10)% 2.7  effect see Mohanty’s talk (11/25)

27 World averages of LHCb + CDF + BaBar + Belle in 2012  a CP dir = -(0.678  0.147)%, 4.6  effect a CP ind = -(0.027  0.163)% Theory estimate is much smaller than the expt’l measurement of |  a CP dir |  0.7%  New physics ?

28 Isidori, Kamenik, Ligeti, Perez [ ] Brod, Kagan, Zupan [ ] Wang, Zhu [ ] Rozanov, Vysotsky [ ] Hochberg, Nir [ ] Pirtskhalava, Uttayarat [ ] Cheng, Chiang [ ] Bhattacharya, Gronau, Rosner [ ] Chang, Du, Liu, Lu, Yang [ ] Giudice, Isidori, Paradisi [ ] Altmannshofer, Primulando, C. Yu, F. Yu [ ] Chen, Geng, Wang [ ] Feldmann, Nandi, Soni [ ] Li, Lu, Yu [ ] Franco, Mishima, Silvestrini [ ] Brod, Grossman, Kagan, Zupan [ ] Hiller, Hochberg, Nir [ ] Grossman, Kagan, Zupan [ ] Cheng, Chiang [ ] Chen, Geng, Wang [ ] Delaunay, Kamenik, Perez, Randall [ ] Da Rold, Delaunay, Grojean, Perez [ ] Lyon, Zwicky [ ] Atwood, Soni [ ] Hiller, Jung, Schacht [ ] Delepine, Faisel, Ramirez [ ] Li, Lu, Qin, Yu [ ] Buccella, Lusignoli, Pugliese, Santorelli [ ] 28 theory papers !

29 All two-body hadronic decays of heavy mesons can be expressed in terms of several distinct topological diagrams [Chau (’80); Chau, HYC(’86)] All quark graphs are topological and meant to have all strong interactions encoded and hence they are not Feynman graphs. And SU(3) flavor symmetry is assumed. Diagrammatic Approach T (tree) C (color-suppressed) E (W-exchange) A (W-annihilation) P, P c EW S, P EW PE, PE EW PA, PA EW HYC, Oh (’11)

For Cabibbo-allowed D →PP decays (in units of GeV) T = 3.14 ± 0.06 (taken to be real) C = (2.61 ± 0.08) exp[i(-152±1) o ] E = ( ) exp[i(122±2) o ] A= ( ) exp[i( ) o ] Rosner (’99) Wu, Zhong, Zhou (’04) Bhattacharya, Rosner (’08,’10) HYC, Chiang (’10) T C A E 30  Phase between C & T ~ 150 o  W-exchange E is sizable with a large phase  importance of 1/m c power corrections  W-annihilaton A is smaller than E and almost perpendicular to E CLEO (’10) Cabibbo-allowed decays The great merit & strong point of this approach  magnitude and strong phase of each topological tree amplitude are determined   =0.39/d.o.f

31 Tree-level direct CP violation DCPV can occur even at tree level A(D s +  K 0   ) = d (T + P d + PE d ) + s (A + P s + PE s ), p =V* cp V up DCPV in D s +  K 0   arises from interference between T & A  Larger DCPV at tree level occurs in decay modes with interference between T & C (e.g. D s +    ) or C & E (e.g. D 0     ) DCPV at tree level can be reliably estimated in diagrammatic approach as magnitude & phase of tree amplitudes can be extracted from data

32 Decay theory Decay theory D0 D0  0 D0 D0  0 D0 D0  0 D0 D0  0 D 0    0.82 D0 D0  0 D 0    ’ D 0  K + K *- 0 D 0  D 0  K - K *+ 0 D 0  ’ D 0  K 0 K * D 0  K + K - 0 D 0  K 0 K * D 0     D0 D0  0 D +     0 D 0    0 D +    0.36 D 0   0.19 D+ ’D+ ’ D0 ’D0 ’ D +  K + K D 0  0 D s +  + K D 0    Ds+ K+Ds+ K D0 ’D0 ’ 0.59 D s +  K +  D s +  K +  ’ > a dir (tree) > Largest tree-level DCPV PP: D 0  K 0 K 0, VP: D 0   ’  Tree-level DCPV a CP (tree) in units of per mille a CP (tree) vanishes in D 0     , K + K -

33 Short-distance penguin contributions are very small. How about power corrections to QCD penguin ? SD weak penguin annihilation is also very small; typically, PE / T  0.04 and PA / T  Large LD contribution to PE can arise from D 0  K + K - followed by a resonantlike final- state rescattering It is reasonable to assume PE ~ E, PE P ~ E P, PE V ~ E V Power corrections to P from PE via final-state rescattering cannot be larger than T

34 Decay a CP dir Decay a CP dir D0 +-D0 +  0.04 D 0     D0 00D0 0  0.04 D 0     D0 0D0 0 0.06  0.04 D0  D0   D0 0’D0 0’ 0.01  0.02 D 0  K + K * D 0     0.02 D 0  K - K * D 0   ’ 0.53   0.02 D 0  K 0 K * D 0  K + K   0.02 D 0  K 0 K * D 0  K 0 K   0.01 D0 D0  0.37 D+ + D+ +   0.06 D0 D0  0 D+ +’D+ +’ 0.34  0.07 D 0   0.50 D +  K + K  0.04 D 0  ’  Ds+ +K0Ds+ +K  0.03 D 0  0 Ds+ 0K+Ds+ 0K  0.10 D 0   D s +  K +   0.05 D 0  ’   0.20 D s +  K +  ’  0.12 a CP dir (10 -3 )  a CP dir =  0.004% (I)  0.004% (II) about 3.3  away from -(0.678  0.147)% Even for PE  T  a CP dir = -0.27%, an upper bound in SM A similar result  a CP dir =-0.128% obtained by Li, Lu, Yu see Hsiang-nan Li’s talk (11/25) If  a CP dir ~ -0.68%, it is definitely a new physics effect !

35 Attempts for SM interpretation Golden, Grinstein (’89): hadronic matrix elements enhanced as in  I=1/2 rule. However, D   data do not show large  I=1/2 enhancement over  I=3/2 one. Moreover, |A 0 /A 2 |=2.5 in D decays is dominated by tree amplitudes. Brod, Kagan, Zupan: PE and PA amplitudes considered Pirtskhalava, Uttayarat : SU(3) breaking with hadronic m.e. enhanced Bhattacharya, Gronau, Rosner : P b enhanced by unforeseen QCD effects Feldmann, Nandi, Soni : U-spin breaking with hadronic m.e. enhanced Brod, Grossman, Kagan, Zupan: penguin enhanced Franco, Mishima, Silvestrini: marginally accommodated We have argued that power corrections to P from PE via final-state rescattering cannot be larger than T

36  A CP = - (0.34  0.15  0.10)% D * tagged  A CP = (0.49  0.30  0.14)% B  D 0  X, muon tagged - (0.15  0.16)% combination LHCb in 2013: World average:  a CP dir = -(0.333  0.120)%, 2.8  a CP ind = (0.015  0.052)% Recall that  a CP dir = -(0.678  0.147)%, 4.6  in 2012 ! It appears that SM always wins ! See D. Tonelli’s talk (11/25)

37 Direct CP violation in charmless B decays

38 Direct CP asymmetries (2-body)    A CP (K -   ) – A CP (K -   ) Bu/Bd Bu/Bd K -       K -  K *0  K* -   K - f 2 (1270)  K -       A CP (%) -8.2    8 19     4  S 13.7  5.8  4.6  3.8  3.6  3.4  3.3  Bu/BdBu/Bd     K -   K* -  K -       K -          *  A CP (%) -14  5 10  431    9 20  1143   645  25 S 2.8  2.5  2.4  1.9  1.8    12.2   B s K +  - A CP (%) 26  4 S 7.2  LHCb K  puzzle:  A K  is naively expected to vanish

39 A CP (B -  K -  ) BaBar Belle CDF Average A CP (%) 12.8  4.4   12  5 -7   4.2 QCDF pQCD SCET A CP (%) 0.6   0 LHCb observed CP violation in B -  K - K + K - but not around  resonance LHCb ( ) obtained A CP = (2.2  2.1  0.9)% Expt: Theory: arXiv:

40 Bu/Bd Bu/Bd K -       K -  K *0  K* -    K -       A CP (%) -8.2    8 19   6 37   4  S 13.7  5.8  4.6  3.8  3.4  3.3  m b         B s K +  - A CP (%) 26  4 S 7.2  m b   In heavy quark limit, decay amplitude is factorizable, expressed in terms of form factors and decay constants. See Beneke & Neubert (’03) for m b  results Bu/BdBu/Bd  -   K -  0 K* - K -  0  +  + K -  0  0  -  +  K* 0 A CP (%) -14  5 10  431    9 20  1143   645  25 S 2.8  2.5  2.4  1.9  1.8  m b           sign

41 A(B 0  K -  + )  u a 1 + c (a 4 c +r  a 6 c ) Theory Expt Br 13.1x10 -6 (19.55  0.54)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

42 New CP puzzles in QCDF 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 Bu/Bd Bu/Bd K -       K -  K *0  K* -    K -       A CP (%) -8.2    819   6 37   4  S 13.7  5.8  4.6  3.8  3.4  3.3  m b         PA       12.2    3.3  (  1.9) Bu/BdBu/Bd  -   K -  0 K* - K -  0  +  + K -  0  0  -  +  K* 0 A CP (%) -14  5 10  431    9 20  1143   645  25 S 2.8  2.5  2.4  1.9  1.8  m b           PA         

43 All “problematic” modes receive contributions from u C+ c P EW P EW  (-a 7 +a 9 ), P c EW  (a 10 +r  a 8 ), u =V ub V* us, c =V cb V* cs  A K  puzzle can be resolved by having a large complex C (C/T  0.5e –i55 ) or a large complex P EW or the combination  A K   0 if C, P EW, A are negligible   A K  puzzle 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;… o

44 The two distinct scenarios can be tested in tree-dominated modes where ’ c P EW << ’ u C. CP puzzles of   ,     & large rates of    ,     cannot be explained by a large complex P EW     puzzle: A CP =(43  24)%, Br = (1.91  0.22)    12.2    3.3  (  1.9)  Bu/Bd Bu/Bd K -       K -  K *0  K* -    K -       A CP (%) -8.2    8 19   6 37   4  S 13.7  5.8  4.6  3.8  3.4  3.3  m b         PA     large complex a 2   Bu/BdBu/Bd  -   K -  0 K* - K -  0  +  + K -  0  0  -  +  K* 0 A CP (%) -14  5 10  431    9 20  1143   645  25 S 2.8  2.5  2.4  1.9  1.8  m b           PA          large complex a 2         

45 Direct CP asymmetries (3-body) LHCb found evidence of inclusive CP asymmetry in B -       , K + K - K -, K + K -   BaBar(%) Belle(%) LHCb(%) Average       3.2   2.1   2.2 K + K - K   0.9   1.0 K -     2.8  2.0   2.6   0.8   1.0 K + K -   0  10   4.0   4.1 Large asymmetries observed in localized regions of p.s. A CP (KK  ) =    for m KK 2 <1.5 GeV 2 A CP (KKK) =    for 1.2< m KK, low 2 <2.0 GeV 2, m KK, high 2 <15 GeV 2 A CP (  ) = for m , low 2 15 GeV 2 A CP (K  ) =    for 0.08< m , low 2 <0.66 GeV 2, m K  2 <15 GeV 2

46 Correlation: A CP (K - K + K - )  – A CP (K -     ), A CP (   K + K - )  – A CP (       ) Relative signs between CP asymmetries of K - K + K - &      ,   K + K - & K -     are consistent with U-spin prediction. It has been conjectured that CPT theorem & final-state rescattering of      K + K - may play important roles Zhang, Guo, Yang [ ] Bhattacharya, Gronau, Rosner [ ] Xu, Li, He [ ] Bediaga, Frederico, Lourenco [ ] Cheng, Chua [ ] Zhang, Guo, Yang [ ] Lesniak, Zenczykowski [ ] Xu, Li, He [ ]

47 Conclusion of this section  CP asymmetries are the ideal places to discriminate between different models.  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  Can we understand the correlation ? A CP (K - K + K - )  – A CP (K -     ), A CP (   K + K - )  – A CP (       )

48 Conclusions To expand Wolfenstein parametrization to higher order of, it is important to use  &  parameters order of unity. First evidence of charmless baryonic B decays: time for updated theory studies. Correlation puzzle in penguin- dominated decays needs to be resolved. DCPV in charm decays is studied in the diagrammatic approach. It can be reliably estimated at tree level. Our prediction is  a CP = -(0.139  0.004)%

49 Backup Slides

50  : strong phase To accommodate  a CP one needs P  T~ 3 for maximal strong phase, while it is naively expected to be of order  s /  Bhattacharya, Gronau, Rosner Brod, Grossman, Kagan, Zupan Can penguin be enhanced by some nonperturbative effects or unforeseen QCD effects ? We have argued that power corrections to P from PE via final-state rescattering cannot be larger than T

51 In D   decays In absence of penguin contribution & SU(3) breaking, this ratio is predicted to be 3.8, larger than the expt’l result. This means  P should contribute destructively to A 0 /A 2. In kaon decays, the predicted ratio due to tree amplitudes is too small compared to experiment  large enhancement of penguin matrix element. ( 22.4  0.1 in K 

52 Before LHCb: Grossman, Kagan, Nir (’07) Bigi, Paul, Recksiegel (’11) New Physics interpretation FCNC Z FCNC Z’ (a leptophobic massive gauge boson) 2 Higgs-doublet model: charged Higgs Color-singlet scalar Color-sextet scalar (diquark scalar) Color-octet scalar 4 th generation Wang, Zhu; Altmannshofer, Primulando, C. Yu, F. Yu Hochberg, Nir Altmannshofer et al; Chen, Geng, Wang Rozanov, Vysotsky; Feldmann, Nandi, Soni Tree level (applied to some of SCS modes) Giudice, Isidori, Paradisi; Altmannshofer, Primulando, C. Yu, F. Yu Model-independent analysis of NP effects Isidori, Kamenik, Ligeti, Perez Altmannshofer et al. After LHCb :

53 Large  C=1 chromomagnetic operator with large imaginary coefficient is least constrained by low-energy data and can accommodate large  A CP. is enhanced by O(v/m c ). However, D 0 -D 0 mixing induced by O 8g is suppressed by O(m c 2 /v 2 ). Need NP to enhance c 8g by O(v/m c ) NP models are highly constrained from D-D mixing, K-K mixing,  ’/ ,… Tree-level models are either ruled out or in tension with other experiments. Giudice, Isidori, Paradisi Grossman, Kagan, Nir Giudice, Isidori, Paradisi Loop level (applied to all SCS modes) Hiller, Hochberg, Nir Delaunay, Kamenik, Perez, Randall It can be realized in SUSY models gluino-squark loops new sources of flavor violation from disoriented A terms, split families trilinear scalar coupling RS flavor anarchy warped extra dimension models