1. Theory of Direct CP Violation in D  hh Chongqing, May 8, 2012 Hai-Yang Cheng ( 鄭海揚 ) Academia Sinica, Taipei Diagrammatical approach SU(3) breaking CP violation at tree and loop levels 2012 年兩岸粒子物理與宇宙學研討會

2. 22 1.Null results in SM: ideal place to look for new physics in BSM B s       s : CP-odd phase in B s system CP violation in B -      Lepton number violation (  decay) CP violation in charmed meson: D 0 -D  mixing, DCPV … 2. Take a cue form the current anomalies: B    sin2   s B-CP puzzles, especially  A K  like-sign dimuon asymmetry forward-backward asymmetry in B 0  K *0     polarization puzzle … Stratage in search of NP

3. 3 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 (K + K - ) - A CP (     ) = - (0.82  0.21  0.11)%  3.5  effect: first evidence of CPV in charm sector CDF: (11/21/2011) 5.9 fb -1 A CP (K + K - )= - (0.24  0.22  0.09)%, A CP (     ) = (0.22  0.24  0.11)%  A CP  - (0.46  0.31  0.11)% 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)% will measure A CP (K + K - ) & A CP (    - ) separately

4. 4 4 New world averages of LHCb + CDF + BaBar + Belle  a CP dir = -(0.656  0.154)%, 4.3  effect a CP ind = -(0.025  0.235)% Before claiming new physics effects, it is important to have a reliable SM estimate of  A CP Can we have reliable estimate of strong phases and hadronic matrix elements ? Can the LHCb result be accommodated in SM ? Given the expt’l results, can one predict DCPV in other modes ?

5. 5 V cs V ud V cd V ud V cd V us V cs V us Cabibbo favored singly Cabibbo-suppressed doubly Cabibbo-suppressed D

6. 6 Why singly Cabibbo-suppressed decays ? Amp = V * cd V ud (tree + penguin) + V* cs V cs (tree’ + penguin) DCPV is expected to be the order of 10 -3  10 -4  : strong phase In SM, CPV is expected to be very small in charm sector Consider DCPV in singly Cabibbo-suppressed decays Penguin is needed in order to produce DCPV at tree & loop level Common folklore: CPV is at most 10 -3 in SM; 10 -2 is a “smoking gun” signature of NP

7. 77 Isidori, Kamenik, Ligeti, Perez [1111.4987] (11/21/2011) Brod, Kagan, Zupan [1111.5000] (11/21/2011) Wang, Zhu [1111.5196] (11/22/2011) Rozanov, Vysotsky [1111.6949] Hochberg, Nir [1112.5268] Pirtskhalava, Uttayarat [1112.5451] Cheng, Chiang [1201.0785] Bhattacharya, Gronau, Rosner [1201.2351] Chang, Du, Liu, Lu, Yang [1201.2565] Giudice, Isidori, Paradisi [1201.6204] Altmannshofer, Primulando, C. Yu, F. Yu [1202.2866] Chen, Geng, Wang [1202.3300] Feldmann, Nandi, Soni [1202.3795] Li, Lu, Yu [1203.3120] Franco, Mishima, Silvestrini [1203.3131] Brod, Grossman, Kagan, Zupan [1203.6659] Hiller, Hochberg, Nir [1204.1046] Grossman, Kagan, Zupan [1204.3557] Cheng, Chiang [1205.0580] Forthcoming papers: Hiller, Jung, Schacht Delaunay, Kamenik, Perez, Randall …

8. 8 Theoretical framework  Effective Hamiltonian approach pQCD: Li, Tseng (’97); Du, Y. Li, C.D. Lu (’05) QCDF: Du, H. Gong, J.F. Sun (’01) X.Y. Wu, X.G. Yin, D.B. Chen, Y.Q. Guo, Y. Zeng (’04) J.H. Lai, K.C. Yang (’05); D.N. Gao (’06) Grossman, Kagan, Nir (’07) X.Y. Wu, B.Z. Zhang, H.B. Li, X.J. Liu, B. Liu, J.W. Li, Y.Q. Gao (’09) However, it doesn’t make much sense to apply pQCD & QCDF to charm decays due to huge 1/m c power corrections QCD sum rules: Blok, Shifman (’87); Khodjamirian, Ruckl; Halperin (’95)  Lattice QCD: ultimate tool but a formidable task now  Model-independent diagrammatical approach

9. 99 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)

10. For Cabibbo-allowed D →PP decays (in units of 10 -6 GeV) T = 3.14 ± 0.06 (taken to be real) C = (2.61 ± 0.08) exp[i(-152±1) o ] E = (1.53 +0.07 -0.08 ) exp[i(122±2) o ] A= (0.39 +0.13 -0.09 ) exp[i(31 +20 -33 ) o ] Rosner (’99) Wu, Zhong, Zhou (’04) Bhattacharya, Rosner (’08,’10) HYC, Chiang (’10) T C A E 10  Phase between C & T ~ 150 o  W-exchange E is sizable with a large phase  importance of power corrections 1/m c  W-annihilation 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 amplitude are determined   =0.39/d.o.f

11. 11 1/m c power corrections 11 E Short-distance (SD) weak annihilation is helicity suppressed. Sizable long-distance (LD) W-exchange can be induced via FSI’s FSIs: elastic or inelastic : quark exchange, resonance A Sizable 1/m c power corrections are expected in D decays  a 2 = (0.82  0.02)exp[-i(152  1) o ] Naïve factorization  a 2 = c 2 + c 1 /N c  -0.11 Color-suppressed amplitude

12. 12 SCS DCS

13. SU(3) flavor symmetry breaking Three possible scenarios for seemingly large SU(3) violation: p =V* cp V up A long standing puzzle: R=  (D 0  K+K - )/  (D 0      )  2.8 13 Large  P (i) If SU(3) symmetry for T & E, a fit to data yields  P=1.54 exp(-i202 o )  (ii) If (T+E)  =(T+E)(1+   /2), (T+E) KK =(T+E)(1-   /2)  with |     (0, 0.3)  |  P/T|  0.5 Brod, Grossman, Kagan, Zupan Need large  P contributing constructively to K + K - & destructively to    

14. 14  R=1.6 Nominal SU(3) breaking in T plus a small  P  P=0.49 exp(-i129 o ) |  P/T|  0.15 Bhattacharya et al. obtained Nominal SU(3) breaking in both T & E;  P negligible SU(3) symmetry must be broken in amplitudes E & PA Accumulation of several small SU(3) breaking effects leads to apparently large SU(3) violation seen in K + K - and     modes  T KK /T  =1.32 Assuming E KK =E  A(D 0  K 0 K 0 )= d (E d + 2PA d ) + s (E s + 2PA s ) almost vanishes in SU(3) limit Neglecting  P, E d & E s fixed from D 0  K + K -,    ,    , K 0 K 0 to be

15. 15 Singly Cabibbo-suppressed D  PP decays

16. 16 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  10 -4 Large 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

17. 17 Decay CC LLY Decay CC D0 D0  0 0 D0 D0  0 D0 D0  0 0 D0 D0  0 D 0    0.82 -0.29 D0 D0  0 D 0    ’ -0.39 0.43 D 0  K + K *- 0 D 0  -0.28 -0.42 0.29 D 0  K - K *+ 0 D 0  ’ 0.49 0.38 -0.30 D 0  K 0 K *0 0.73 D 0  K + K - 0 0 D 0  K 0 K *0 -0.73 D 0     -0.73 -1.73 0.90 D0 D0  0 D +     0 0 D 0    0 D +    0.36 -0.46 D 0   0.19 D+ ’D+ ’ -0.20 0.30 D0 ’D0 ’ -1.07 D +  K + K 0 -0.08 D 0  0 D s +  + K 0 0.08 -0.01 D 0    -0.53 Ds+ K+Ds+ K+ 0.01 0.17 D0 ’D0 ’ 0.59 D s +  K +  -0.70 0.75 D s +  K +  ’ 0.35 -0.48 10 -3 > a dir (tree) > 10 -4  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 CC: Chiang, HYC LLY: Li, Lu, Yu T E (CC) EsEs E q (LLY)  Signs of a CP (tree ) obtained by LLY are opposite to ours

18. Penguin-induced CP violation DCPV in D 0     , K + K - arises from interference between tree and penguin In SU(3) limit, a CP dir (  +  - ) = -a CP dir (K + K - ) 18 Apply QCD factorization to estimate QCD-penguin amplitude to NLO a (t+p) (     )  - 4  10 -5, a (t+p) (K + K - )  2  10 -5, DCPV from QCD penguin is small for D 0  K + K - &     due to almost trivial strong phase ~ 170 o

19. 19 How about power corrections to QCD penguin ? SD weak penguin annihilation is very small; typically, PE / T  0.04 and PA / T  -0.02 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 Two other approaches for PE: 1.PE=(c 3 /c 1 )E+ G F /  2(if D f M1 f M2 )[c 3 A 3 i +(c 5 +N c c 6 )A 3 f ] A 3 f  -2 2.Apply large-N c argument to get PE ~ (2N c c 6 /c 1 ) E Li, Lu, Yu Brod, Kagan, Zupan valid only for SD contributions !

20. 20 Decay a CP dir Decay a CP dir D0 +-D0 +- 0.96  0.04 D 0     -0.51 D0 00D0 00 0.83  0.04 D 0     -0.27 D0 0D0 0 0.06  0.04 D0  D0   -0.74 D0 0’D0 0’ 0.01  0.02 D 0  K + K *- 0.50 D 0   -0.58  0.02 -0.74  0.02 D 0  K - K *+ 0.29 D 0   ’ 0.53  0.03 0.33  0.02 D 0  K 0 K *0 0.73 D 0  K + K - -0.42  0.01 -0.54  0.02 D 0  K 0 K *0 -0.73 D 0  K 0 K 0 -0.67  0.01 -1.90  0.01 D0 D0  0.37 D+ + D+ +  -0.78  0.06 D0 D0  0 D+ +’D+ +’ 0.34  0.07 D 0   0.50 D +  K + K 0 -0.40  0.04 D 0  ’  -0.89 Ds+ +K0Ds+ +K0 0.46  0.03 D 0  0 Ds+ 0K+Ds+ 0K+ 0.98  0.10 D 0   -0.23 D s +  K +  -0.61  0.05 D 0  ’   0.20 D s +  K +  ’ -0.29  0.12 a CP dir (10 -3 )  a CP dir = -0.139  0.004% (I) -0.151  0.004% (II) about 3.3  away from -(0.656  0.154)% Even for PE  T  a CP dir = -0.27%, an upper bound in SM, still 2  away from data A similar result  a CP dir =-0.128% obtained by Li, Lu, Yu

21. 21 Attempts for SM interpretation Golden, Grinstein (’89): hadronic matrix elements enhanced as in  I=1/2 rule. However, D   data do not show  I=1/2 enhancement over  I=3/2 one 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

22. 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 : 22

23. 23 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. It can be realized in SUSY models gluino-squark loops new sources of flavor violation from disoriented A terms, split families trilinear scalar coupling Giudice, Isidori, Paradisi Grossman, Kagan, Nir Giudice, Isidori, Paradisi Loop level (applied to all SCS modes) Hiller, Hochberg, Nir

24. 24 Consider two scenarios in which  a CP dir is accommodated: (i) large penguin with  ½  P ~3T (ii) large chromomagnetic dipole operator with c 8g =0.012exp(i14 o ) Large c.d.o. predicts large CP asymmetry for    , but small ones for D 0     ’, D +     ’, K + K 0, D s +    K 0 ; other way around in large penguin scenario. Bhattacharya, Gronau, Rosner Brod, Grossman, Kagan, Zupan Giudice, Isiori, Paradisi, Altamannshofer et al. Decay Large penguin Large c 8g D0 D0  4.4 3.7 D0 D0  1.0 6.2 D 0    0.03-4.2 D 0    ’ 2.7-0.4 D 0  -1.6-2.0 D 0  ’ 1.5-1.1 D 0  K + K - -2.4-2.9 D +    -3.6-3.7 D+ ’D+ ’ 3.3 0.6 D +  K + K 0 -3.3 0.3 D s +  + K 0 3.7-0.4 Ds+ K+Ds+ K+ 5.1 3.1 D s +  K +  -0.6 0.9 D s +  K +  ’ -5.8 1.4

25. 25 Conclusions The diagrammatical approach is very useful for analyzing hadronic D decays DCPV in charm decays is studied in the diagrammatic approach. Our prediction is  a CP dir = -(0.139  0.004)% & -(0.151  0.004)% New physics models are highly constrained by D 0 -D 0 mixing,  ’/ , … Chromomagnetic dipole operator is least constrained by experiment.