Whysingly Cabibbo-suppressed decays?InSM,CPisexpectedtobeverysmallincharmsectorConsiderDCPVinsinglyCabibbo-suppresseddecaysAmp= V*cdVud (tree + penguin)+ V*csVcs (tree'+ penguin)PenguinisneededinordertoproduceDcPVattree&looplevelA2 Im(Vsin8=1.2×10-3sino:strongphaseIVaVuaPDCPV is expected to be the orderof 10-3~10-4Common folklore: CPV is at most 10-3 in SM; 10-2 is a “smokinggunsignatureofNp6
6 Why singly Cabibbo-suppressed decays ? Amp = V* cdVud (tree + penguin) + V*csVcs (tree’ + penguin) sin d 2 sin sin d 1.2 10 sin d | | 2Im( ) 3 * * * 2 * * T A T A V V V V T A V V V V V V a cd u d cb u b cd u d dir cd u d cs u s CP - = = = DCPV is expected to be the order of 10-3 10-4 d: 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
Isidori,Kamenik,Ligeti,Perez[1111.49871(11/21/2011)Forthcoming papers:Brod, Kagan, Zupan [1111.5000] (11/21/2011)Hiller, Jung, SchachtWang, Zhu [1111.5196] (112/2011)Delaunay,Kamenik,Perez,RandallRozanov, 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]7Cheng, Chiang [1205.0580]
7 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
TheoreticalframeworkEffectiveHamiltonianapproachpQcD: Li, Tseng('97); Du, Y. Li, C.D. Lu ('05)QcDF:Du,H.Gong,J.F.Sun('o1)X.Y. Wu, X.G. Yin, D.B. Chen, Y.Q. Guo, Y. Zeng ('O4)J.H. Lai, K.C. Yang ('05); D.N. Gao (06)Grossman,Kagan,Nir('o7)X.Y. Wu, B.Z. Zhang, H.B. Li, X.J. Liu, B. Liu, J.W. Li, Y.Q. Gao (o9)However,itdoesn'tmakemuchsensetoapplypQcD&QcDFtocharmdecaysduetohuge1/m.powercorrectionsQcD sumrules: Blok, Shifman (87);Khodjamirian, Ruckl; Halperin (95)LatticeQCD: ultimate tool but a formidable tasknowModel-independentdiagrammaticalapproach8
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/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
DiagrammaticApproachAlltwo-bodyhadronicdecaysofheawymesonscanbeexpressedinterms of several distinct topological diagrams [Chau ('80); Chau, HYC('86)]T (tree)E(W-exchange)C(color-suppressed)A(W-annihilation)HYC, Oh(11)PE, PEewPA, PAewP, P°EWS, PewAll quarkgraphs aretopological and meantto haveall strong interactionsencoded and hence they are not Feynman graphs.And SU(3) flavorsymmetryis assumed.9
9 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, Pc EW S, PEW PE, PEEW PA, PAEW HYC, Oh (’11)