Direct CP Violation in D  hh

1. Direct CP Violation in D  hh • Hai-Yang Cheng • Academia Sinica, Taipei • Diagrammatical approach • SU(3) breaking • CP violation at tree and loop levels Charm 2012, Hawaii, May 15, 2012

2. Stratage in search of NP • Null results in SM: ideal place to look for new physics in BSM • Bs +- • s : CP-odd phase in Bs system • CP violation in B--0 • Lepton number violation ( decay) • CP violation in charmed meson: D0-D0 mixing, DCPV • … • 2. Take a cue form the current anomalies: • B • sin2 • s • B-CP puzzles, especially AK • like-sign dimuon asymmetry • forward-backward asymmetry in B0 K*0+- • polarization puzzle • … 2

3. Experiment Time-dependent CP asymmetry Time-integrated asymmetry • LHCb: (11/14/2011) 0.92 fb-1based on 60% of 2011 data • ACP ACP(K+K-) - ACP(+-) = - (0.820.210.11)% • 3.5 effect: first evidence of CPV in charm sector CDF: (11/21/2011) 5.9 fb-1 ACP(K+K-)= - (0.240.220.09)%, ACP(+-) = (0.220.240.11)% ACP = - (0.460.310.11)% CDF: (2/29/2012) 9.7 fb-1 ACP= Araw(K+K-) - Araw(+-)= - (2.330.14)% - (-1.710.15)% = - (0.620.210.10)% will measure ACP(K+K-) & ACP(+-) separately

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

5. Why singly Cabibbo-suppressed decays ? In SM, CPV is expected to be very small in charm sector Consider DCPV in singly Cabibbo-suppressed decays Amp = V*cdVud (tree + penguin) + V*csVcs (tree’ + penguin) No CP violation in D decays if they proceed only through tree diagrams Penguin is needed in order to produce DCPV at tree & loop level : strong phase DCPV is expected to be the order of 10-3 10-4 Do LHCb and CDF measurements really imply NP in charm sector ?

6. Isidori, Kamenik, Ligeti, Perez [1111.4987] Brod, Kagan, Zupan [1111.5000] Wang, Zhu [1111.5196] 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] This talk is based on two papers in collaboration with Cheng-Wei Chiang 6

7. 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/mc 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

8. Diagrammatic Approach All two-body hadronic decays of heavy mesons can be expressed in terms of several distinct topological diagrams [Chau (’80); Chau, HYC(’86)] T (tree) A (W-annihilation) E (W-exchange) C (color-suppressed) HYC, Oh (’11) PA, PAEW PE, PEEW P, PcEW S, PEW 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. 8

9. Cabibbo-allowed decays For Cabibbo-allowed D→PP decays (in units of 10-6GeV) 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] CLEO (’10) 2=0.39/d.o.f Rosner (’99) Wu, Zhong, Zhou (’04) Bhattacharya, Rosner (’08,’10) HYC, Chiang (’10) • Phase between C & T ~ 150o • W-exchange Eis sizable with a large phase  importance of power corrections 1/mc • W-annihilaton A is smaller than Eand almost perpendicular to E E C A T The great merit & strong point of this approach  magnitude and strong phase of each topological tree amplitude are determined 9

10. 1/mc power corrections Sizable 1/mc power corrections are expected in D decays • Color-suppressed amplitude  a2= (0.820.02)exp[-i(1521)o] Naïve factorization  a2 = c2 + c1/Nc -0.11 • Weak annihilation vanishes in mc limit. Short-distance (SD) one is helicity suppressed. Sizable long-distance (LD) W-exchange can be induced via FSI’s FSIs: elastic or inelastic : quark exchange, resonance A E 10

11. In D PP decays, resonant FSIs are important due to existence of abundant resonances near D mesons Weinberg; Buccella et al. Mk Mi Ml Mj Cij(r) are normalized couplings of MiMj with resonance r Zenczykowski; HYC  |E| > |A| E, A receive sizable LD contributions even if SD “e” and “a” vanish For 0+ resonances K0*(1950) with mR=1945±22 MeV & ¡=201±86 MeV, contributing to amplitude E of D→K¼,Kη E=1.40 exp(i141o), in agreement with Eexpt = (1.53±0.08) exp (i122o) ⇒ Nearby resonances yield major contributions to weak annihilation in D PP 11

12. D VP decays Two different types of topological amplitudes: TP, TV, CP, CV, EP, EV, AP, AV TP, CP: P contains q of D meson; EP, AP: P contains q2 of q1q2 configuration 2 =0 Bhattacharya, Rosner HYC, Chiang assuming real TV & TP • There are one more solution for TV, CP, EP and five more possible solutions • for TP, CV, EV; but they are ruled out or disfavored mainly by SCS data • No solution found for AP & AV based on current data

13. SCS DCS 13

14. SU(3) flavor symmetry breaking A long standing puzzle: R=(D0 K+K-)/(D0+-)  2.8 p=V*cpVup Three possible scenarios for seemingly large SU(3) violation: • Large P • (i) If SU(3) symmetry for T & E, a fit to data yields P=1.54 exp(-i202o) • (ii) If (T+E)=(T+E)(1+T/2), (T+E)KK=(T+E)(1-T/2) • with |T| (0, 0.3)  |P/T|  0.5 Brod, Grossman, Kagan, Zupan Need a large P contributing constructively to K+K- & destructively to +- 14 14

15. Nominal SU(3) breaking in T plus a small P  R=1.6 P=0.49 exp(-i129o) |P/T|  0.15 Assuming EKK=E Bhattacharya et al. obtained • Nominal SU(3) breaking in both T & E; P negligible (common wisdom) SU(3) symmetry must be broken in amplitudes E & PA A(D0 K0K0)=d(Ed + 2PAd) + s(Es+ 2PAs) almost vanishes in SU(3) limit Neglecting P, Ed & Es fixed from D0 K+K-, +-, 00, K0K0 to be Accumulation of several small SU(3) breaking effects leads to apparently large SU(3) violation seen in K+K- and +- modes

16. Singly Cabibbo-suppressed D PP decays

17. Tree-level direct CP violation DCPV can occur even at tree level A(Ds+ K0+) =d(T + Pd+ PEd) + s(A + Ps+ PEs), p=V*cpVup DCPV in Ds+ K0+ arises from interference between T & A  10-4 DCPV at tree level can be reliably estimated in diagrammatic approach as magnitude & phase of tree amplitudes can be extracted from data Larger DCPV at tree level occurs in decay modes with interference between T & C (e.g. Ds+K+) or C & E (e.g. D00)

18. Tree-level DCPV aCP(tree) in units of per mille LLY: Li, Lu, Yu 10-3 > adir(tree) > 10-4 • Largest tree-level DCPV PP: D0K0K0, VP: D0’ • Signs of aCP(tree) obtained by LLY are opposite to ours for most of D  PP decays E (our) T Es Eq (LLY)

19. Penguin-induced CP violation DCPV in D0+-, K+K- arises from interference between tree and penguin In SU(3) limit, aCPdir(+-) = -aCPdir(K+K-) 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 D0 K+K- & +- due to almost trivial strong phase ~ 170o

20. 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 D0 K+K- followed by a resonantlike final-state rescattering It is reasonable to assume PE ~ E, PEP ~ EP, PEV ~ EV • Two other approaches for PE: • PE=(c3/c1)E+ GF/2(ifDfM1fM2)[c3A3i +(c5+Ncc6)A3f] • A3f -2<P1P2|(uq)S+P|0><0|(qc)S-P|D> • Apply large-Nc argument to get • PE ~ (2Ncc6eff /c1) E Li, Lu, Yu Brod, Kagan, Zupan major FSI effects not considered

21. aCPdir (10-3) aCPdir= -0.1390.004% (I) -0.1510.004% (II) about 3.3 away from -(0.6560.154)% A similar result aCPdir=-0.128% obtained by Li, Lu, Yu Even for PE  T aCPdir = -0.27%, an upper bound in SM, still 2 away from data

22. 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 : Pb 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

23. New Physics interpretation Before LHCb: Grossman, Kagan, Nir (’07) Bigi, Paul, Recksiegel (’11) After LHCb : • Model-independent analysis of NP effects Isidori, Kamenik, Ligeti, Perez • Tree level (applied to some of SCS modes) • 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 • 4th generation Giudice, Isidori, Paradisi; Altmannshofer, Primulando, C. Yu, F. Yu Wang, Zhu; Altmannshofer, Primulando, C. Yu, F. Yu Altmannshofer et al. Hochberg, Nir Altmannshofer et al; Chen, Geng, Wang Altmannshofer et al. Rozanov, Vysotsky; Feldmann, Nandi, Soni

24. 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. Loop level (applied to all SCS modes) Large C=1 chromomagnetic operator with large imaginary coefficient is least constrained by low-energy data and can accommodate large ACP.<PP|O8g|D> is enhanced by O(v/mc). However, D0-D0 mixing induced by O8g is suppressed by O(mc2/v2). Need NP to enhance c8g by O(v/mc) Giudice, Isidori, Paradisi • It can be realized in SUSY models • gluino-squark loops • new sources of flavor violation from disoriented A terms, split families • trilinear scalar coupling Grossman, Kagan, Nir Giudice, Isidori, Paradisi Hiller, Hochberg, Nir

25. aCPdir (10-3) Consider two scenarios in which aCPdir is accommodated: (i) large penguin with ½P ~3T (ii) large chromomagnetic dipole operator with c8g =0.012exp(i14o) Bhattacharya, Gronau, Rosner Brod, Grossman, Kagan, Zupan Giudice, Isiori, Paradisi, Altamannshofer et al. Large c.d.o. predicts large CP asymmetry for 00,0, but small ones for D00’, D++’, K+K0, Ds++K0, K+’; other way around in large penguin scenario.

26. 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 aCP = -(0.1390.004)% and • -(0.1510.004)% • New physics models are highly constrained by D0-D0 mixing, ’/, … Chromomagnetic dipole operator is least constrained by experiment.

27. Back-up Slides

28. Weak penguin annihilation in QCDF PE  fDfP1fP2 [c3 A1i +c5 (A3i+A3f)+Ncc6A3f] PA  fDfP1fP2 (c4 +c6)A1i E  fDfP1fP2 c1A1i A  fDfP1fP2 c2A1i Ann. amplitude contains XA and XA2 A/E= c2/c1= -0.34 PA=(c4+ c6)/c2A= 0.22A PE=(c3/c1)E+ GF/2(ifDfM1fM2)[c3A3i +(c5+Ncc6)A3f]