Hottopicsinthequarkmixingmatrix

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1 Hottopicsinthequarkmixingmatrix Technische Universität Dresden, June 1st, 26 Jérôme Charles CPT- Marseille in collaboration with the CKMfitter group

2 CP:adeepsymmetry C charge conjugation, P spatial parity, T time reversal C, P, T are fundamental discrete symmetries C and P are maximally violated (chiral fermions) CPandTareviolatedatthe 1 5 level C, P and CP are crucial ingredients of the Big- Bang theory(baryo- and/or leptogenesis) 2

3 CP:adeepsymmetry C charge conjugation, P spatial parity, T time reversal C, P, T are fundamental discrete symmetries C and P are maximally violated (chiral fermions) CPandTareviolatedatthe 1 5 level C, P and CP are crucial ingredients of the Big- Bang theory(baryo- and/or leptogenesis) History of the discoveries 1964 indirect CP violation in the neutral kaon system 1998 T violation in the neutral kaon system 1999 direct CP violation in the neutral kaon system 21 mixing-induced CP violation in the neutral B system 24 direct CP violation in the neutral B system 2

4 CP:adeepsymmetry C charge conjugation, P spatial parity, T time reversal C, P, T are fundamental discrete symmetries C and P are maximally violated (chiral fermions) CPandTareviolatedatthe 1 5 level C, P and CP are crucial ingredients of the Big- Bang theory(baryo- and/or leptogenesis) CPviolationisverywelldescribedbytheStandardModel,butwestilldon thaveanydynamical explanation of it History of the discoveries 1964 indirect CP violation in the neutral kaon system 1998 T violation in the neutral kaon system 1999 direct CP violation in the neutral kaon system 21 mixing-induced CP violation in the neutral B system 24 direct CP violation in the neutral B system 2

5 Quarkmixing Standard Model: the quark flavors are mixed by the weak interaction bi-diagonalization on the eigenstate basis via Cabibbo-Kobayashi-Maskawa(CKM) matrix V CKM = V ud V us V ub V cd V cs V cb V td V ts V tb 3

6 Quarkmixing Standard Model: the quark flavors are mixed by the weak interaction bi-diagonalization on the eigenstate basis via Cabibbo-Kobayashi-Maskawa(CKM) matrix V CKM = V ud V us V ub V cd V cs V cb V td V ts V tb thisunitarymatrix iscomplex(v ub V ub e iγ )assoonasthereareatleastthreegenerations of non-degenerate fermions CKM generates CP violation 3

7 CPviolation inmesondecays CPviolation inmixing: M l + X M l X ε K, A sl (B) 4

8 CPviolation inmesondecays CPviolation inmixing: M l + X M l X ε K, A sl (B) CPviolation indecay: M f M f ε /ε, B Kπ 4

9 CPviolation inmesondecays CPviolation inmixing: M l + X M l X ε K, A sl (B) CPviolation indecay: M f M f ε /ε, B Kπ CPviolation ininterferencebetweenmixinganddecay: M M f M M f B J/ψK S, B ππ, B ρρ 4

10 HierarchyandUnitarityTriangle(s) strong hierarchy of the CKM matrix: diagonal couplings 1 1st (resp. 2nd 3rd)generation λ.22(resp. λ 2 ) 1st 3rdgeneration λ 3 5

11 HierarchyandUnitarityTriangle(s) strong hierarchy of the CKM matrix: diagonal couplings 1 1st (resp. 2nd 3rd)generation λ.22(resp. λ 2 ) 1st 3rdgeneration λ 3 V ud V ub CKM unitarity six triangles in the complex plane,ofwhichfourarequasiflat,twoarenon flat and quasi degenerate (ρ, η) α V td V tb γ β V cd V cb (, ) (1, ) 5

12 unitarity-exact and convention-independent version of the Wolfenstein parametrization λ 2 V us 2 V ud 2 + V us 2 A 2 λ 4 V cb 2 V ud 2 + V us 2 6

13 unitarity-exact and convention-independent version of the Wolfenstein parametrization λ 2 V us 2 V ud 2 + V us 2 A 2 λ 4 ρ + i η V udv ub V cd V cb V cb 2 V ud 2 + V us 2 there is no need to stopat O(λ 4 )! V ud V ub (ρ, η) α V td V tb γ β V cd V cb (, ) (1, ) 6

14 ExtractingStandardModelparameters QCD and the extraction of CKM elements tree-level charged transitions are well constrained FCNC in mixing ( S = D = 2, B = D = 2andnow B = S = 2)arewellconstrained CP-conserving couplings are extracted from observables that also depend on hadronic matrix elements, which have to be computed from theory (e.g. lattice simulations) typically, Γ V CKM 2 f O i 2 in principle CP-violating CKM angles can be determined from experimental quantities only typically, A CP Im(V CKM/V CKM )(M QCD /M QCD ) 7

15 ExtractingStandardModelparameters QCD and the extraction of CKM elements tree-level charged transitions are well constrained FCNC in mixing ( S = D = 2, B = D = 2andnow B = S = 2)arewellconstrained FCNCindecay( S = D = 1, B = D = 1 and B = S = 1) are not so well constrained because of hadronic and/or experimental uncertainties CP-conserving couplings are extracted from observables that also depend on hadronic matrix elements, which have to be computed from theory (e.g. lattice simulations) typically, Γ V CKM 2 f O i 2 in principle CP-violating CKM angles can be determined from experimental quantities only typically, A CP Im(V CKM/V CKM )(M QCD /M QCD ) 7

16 Examples (SM: presumably SM-dominated; SM B J/ψK s B ππ B DK β α γ 8

17 Examples (SM: presumably SM-dominated; SM B J/ψK s B ππ B DK β α γ SM QCD B(b) D(c)lν B(b) π(u)lν B lν V cb f BD + (OPE) V ub f Bπ + (OPE) V ub f B 8

18 Examples (SM: presumably SM-dominated; NP: potentially large NP contributions) SM B J/ψK s B ππ B DK β α γ SM QCD B(b) D(c)lν B(b) π(u)lν B lν V cb f BD + (OPE) V ub f Bπ + (OPE) V ub f B NP B φk s B s φφ K πν ν β β s ρ, η 8

19 Examples (SM: presumably SM-dominated; NP: potentially large NP contributions) SM B J/ψK s B ππ B DK β α γ SM QCD B(b) D(c)lν B(b) π(u)lν B lν V cb f BD + (OPE) V ub f Bπ + (OPE) V ub f B NP B φk s β NP QCD ε K ρ, η B K B s φφ β s M d,s V tb V td,s B B K πν ν ρ, η B l + l V td,s f B 8

20 Examples (SM: presumably SM-dominated; NP: potentially large NP contributions) SM B J/ψK s B ππ B DK β α γ SM QCD B(b) D(c)lν B(b) π(u)lν B lν V cb f BD + (OPE) V ub f Bπ + (OPE) V ub f B NP B φk s β NP QCD ε K ρ, η B K B s φφ β s M d,s V tb V td,s B B K πν ν ρ, η B l + l V td,s f B theoretical errors have to be controlled quantitatively in order to test the Standard Model; thereishowevernosystematic methodtodothat 8

21 Thestatistical framework weuseastandardfrequentistapproach: likelihoodmaximization (χ 2 minimization) where necessary, we treat non gaussian behavior by Monte-Carlo simulation of virtual experiments theoretical errors no model-independent treatment available, due to lack of precise definition; we use the Rfit model: atheoreticalparameterthathasbeencomputed(e.g. B K )isassumedtolie withina definite range, without any preference inside this range the best fit will thus be searched by moving uniformly in the theoretical parameter space references: A. Höcker et al., EPJC 21(21); JC et al., EPJC 41(25); 9

22 PartI theglobalckmfit

23 TheglobalCKMfit uses all constraints on which we think we have a good theoretical control 11

24 TheglobalCKMfit uses all constraints on which we think we have a good theoretical control V ud, V us, V cb PDG6 11

25 TheglobalCKMfit uses all constraints on which we think we have a good theoretical control V ud, V us, V cb PDG6 ε K exp: KTeV/KLOE,theo: CKM5 B K =.79 ±.4 ±.9 V ub PDG6 excl. (3.94 ±.28 ±.51) 1 3 incl. (4.45 ±.23 ±.39) 1 3 m d exp: lastwa,theo: CKM5 ξ = 1.24 ±.4 ±.6 m s dominatedbycdf6,theo: CKM5 f BB Bs = 271 ± 38GeV s note: we have splitted errors into stat. ± theo. 11

26 TheglobalCKMfit uses all constraints on which we think we have a good theoretical control V ud, V us, V cb PDG6 ε K exp: KTeV/KLOE,theo: CKM5 B K =.79 ±.4 ±.9 V ub PDG6 excl. (3.94 ±.28 ±.51) 1 3 incl. (4.45 ±.23 ±.39) 1 3 m d exp: lastwa,theo: CKM5 ξ = 1.24 ±.4 ±.6 m s dominatedbycdf6,theo: CKM5 f BB Bs = 271 ± 38GeV s β last WA α exp: lastwa,theo: ππ, ρπ, ρρandsu(2) γ exp: last WA, theo: GLW/ADS/GGSZ note: we have splitted errors into stat. ± theo. 11

27 TheglobalCKMfit uses all constraints on which we think we have a good theoretical control V ud, V us, V cb PDG6 ε K exp: KTeV/KLOE,theo: CKM5 B K =.79 ±.4 ±.9 V ub PDG6 excl. (3.94 ±.28 ±.51) 1 3 incl. (4.45 ±.23 ±.39) 1 3 m d exp: lastwa,theo: CKM5 ξ = 1.24 ±.4 ±.6 m s dominatedbycdf6,theo: CKM5 f BB Bs = 271 ± 38GeV s β last WA α exp: lastwa,theo: ππ, ρπ, ρρandsu(2) γ exp: last WA, theo: GLW/ADS/GGSZ B τν exp: lastwa,theo: CKM3-5 f Bd = 19 ± 25 ± 9MeV note: we have splitted errors into stat. ± theo. 11

28 theangle α Moreonselectedinputs... thebestconstraintcomesfromthe ρρmodes;thankstothebabarupdateon ρ + ρ thedataare now fully compatible with a closed isospin triangle C K M f i t t e r EPS 25 B ππ B ρπ B ρρ WA Combined CKM fit 1 CL α (deg) 12

29 theangle α Moreonselectedinputs... thebestconstraintcomesfromthe ρρmodes;thankstothebabarupdateon ρ + ρ thedataare now fully compatible with a closed isospin triangle newaverage α = ( ) C K M f i t t e r EPS 25 B ππ B ρπ B ρρ WA Combined CKM fit C K M f i t t e r FPCP 6 B ππ B ρπ B ρρ WA Combined 1 CL CL.8.6 CKM fit no α meas. in fit α (deg) α (deg) 12

30 theangle α Moreonselectedinputs... thebestconstraintcomesfromthe ρρmodes;thankstothebabarupdateon ρ + ρ thedataare now fully compatible with a closed isospin triangle newaverage α = ( ) C K M f i t t e r EPS 25 B ππ B ρπ B ρρ WA Combined CKM fit C K M f i t t e r FPCP 6 B ππ B ρπ B ρρ WA Combined 1 CL CL.8.6 CKM fit no α meas. in fit α (deg) α (deg) waitingforbelle: Dalitz ρπ,and ρ ρ modes! 12

31 the angle γ(preliminary) the analysis is non trivial: naive interpretation of χ 2 in terms of the error function underestimates the error on γ because of the bias on r B due to r B > ; both Babar and Belle use their own frequentist approach, while we use a different one meanwhile the central value of r B hasdecreasedsincelast summer...moreonselectedinputs... 13

32 the angle γ(preliminary)...moreonselectedinputs... the analysis is non trivial: naive interpretation of χ 2 in terms of the error function underestimates the error on γ because of the bias on r B due to r B > ; both Babar and Belle use their own frequentist approach, while we use a different one meanwhile the central value of r B hasdecreasedsincelast summer we find a somewhat looser constraint, with γ = ( ) 1 CL C K M f i t t e r FPCP 6 Full frequentist treatment on MC basis CKM fit no γ meas. in fit D ( * ) K ( * ) GLW + ADS D ( * ) K ( * ) GGSZ WA Combined γ (deg) 13

33 theoscillationfrequency m s...moreonselectedinputs Fermilab, winter 26: first two-sided bound by D first evidence for oscillation by CDF; 14

34 theoscillationfrequency m s...moreonselectedinputs 1.2 C K M f i t t e r FPCP 6 CKM fit w/o m s CDF measurement 1 Fermilab, winter 26: first two-sided bound by D first evidence for oscillation by CDF; justlookatthisplot! 1 CL m s 14

35 1.5 excluded area has CL >.95 Theglobal CKMfit: results... excluded at CL >.95 γ m d 1 sin 2β m s & m d.5 η -.5 ε K V ub /V cb γ α β α FPCP6 without m s (CDF) all constraints together -1 α sol. w/ cos 2β < (excl. at CL >.95) ε K C K M f i t t e r FPCP 6 γ ρ

36 1.5 excluded area has CL >.95 TheglobalCKMfit: results! excluded at CL >.95 γ m d 1 sin 2β m s & m d.5 η -.5 ε K V ub /V cb γ α β α FPCP6 with m s (CDF) all constraints together -1 α sol. w/ cos 2β < (excl. at CL >.95) ε K C K M f i t t e r FPCP 6 γ ρ

37 TestingtheCKMparadigm η excluded area has CL >.95 m d m s & m d α.1 V ub /V cb γ β CP-conserving... ρ C K M f i t t e r FPCP 6 η excluded area has CL >.95 sin 2β ε K γ α sol. w/ cos 2β < (excl. at CL >.95).1 γ β ρ α C K M f i t t e r FPCP 6...vs. CP-violating

38 TestingtheCKMparadigm η excluded area has CL >.95 m d m s & m d α.1 V ub /V cb γ β CP-conserving... η excluded area has CL >.95 m d ε K ρ m s & m d α C K M f i t t e r FPCP 6.1 V ub /V cb γ β noangles(withtheory)... ρ C K M f i t t e r FPCP 6 η excluded area has CL >.95 sin 2β ε K γ α sol. w/ cos 2β < (excl. at CL >.95).1 γ β η excluded area has CL >.95 sin 2β γ ρ α α C K M f i t t e r FPCP 6...vs. CP-violating sol. w/ cos 2β < (excl. at CL >.95).1 γ β ρ α C K M f i t t e r FPCP 6...vs. angles(withouttheory)

39 TestingtheCKMparadigm η excluded area has CL >.95 γ(α) α.1 V ub /V cb γ β tree... ρ C K M f i t t e r FPCP 6 η excluded area has CL >.95 sin 2β m d ε K m s & m d α sol. w/ cos 2β < (excl. at CL >.95).1 γ β ρ C K M f i t t e r FPCP 6...vs. loop 18

40 TestingtheCKMparadigm η excluded area has CL >.95 γ(α) α.1 V ub /V cb γ β tree... ρ C K M f i t t e r FPCP sin 2β m d ε K m s & m d α sol. w/ cos 2β < (excl. at CL >.95).1 γ β the ( ρ, η)planeisnotthewholestory,still theoverallagreementisimpressive! η excluded area has CL >.95 ρ C K M f i t t e r FPCP 6...vs. loop 18

41 Theoreticaluncertainties... all non angle measurements uncertainties are now dominated by theory; however a lot of progress in analytical calculations and lattice simulations has been made recently excluded area has CL >.95 CKM fit m d excluded area has CL >.95 improved staggered fermions m d.5 B + τ + ν.5 B + τ + ν α α η γ β η γ β C K M f i t t e r FPCP 6 Constraint from B + τ + ν τ and m d using traditional approaches ρ C K M f i t t e r FPCP 6 Constraint from B + τ + ν τ and m d ρ using improved staggered fermions

42 andtheoreticalcorrelations from Okamoto et al. (25), splitting into stat. ± theo. f Bd = 216 ± 22MeV f Bs /f Bd = 1.2 ±.3 B Bd = ±.95 ±.21 B Bs = ±.93 ±.14 leadsto ξ = ±.71 ±.33and f Bd BBd = 242 ± 26 ± 2MeV,while f Bd = 216 ± 22GeV f Bs /f Bd = 1.2 ±.3 B Bs = ±.93 ±.14 B Bs /B Bd = 1.44 ±.23 ±.27 leadsto ξ = ±.35 ±.31, f Bd BBd = 242 ± 26 ± 9MeVand B Bd = ±.94 ±.45 2

43 the Wolfenstein parameters Selectedfitpredictions λ = A = ρ = η = the Jarlskog invariant J = (3.5 ±.18) 1 5 the UT angles α = ( ) β = ( ) γ = ( ) B s B s mixing B leptonic decay m s = ps 1 (indirect) ±.7ps 1 (CDF,direct) B(B τν) = (9.7 ± 1.3) 1 5 (indirect) ( ) 1 5 (WA,direct) 21

44 PartII Depuzzling B Kπ (in collaboration with J. Malclès, J. Ocariz, A. Höcker)

45 aswehaveseen, βand γcanbedeterminedfromtree-leveldecayswithoutanytheoreticalinput thisisnotthecasefor α,thatneeds(atleast)assumingisospin symmetry also many B-decays are sensitive to the CKM matrix through loop processes 23

46 aswehaveseen, βand γcanbedeterminedfromtree-leveldecayswithoutanytheoreticalinput thisisnotthecasefor α,thatneeds(atleast)assumingisospin symmetry also many B-decays are sensitive to the CKM matrix through loop processes theglobal"reference"fitisnotthewholestory! 23

47 Dynamicalapproachestonon-leptonic B-decays based on the heavy mass expansion: pqcd(diagrammatic) vs. QCDF(diagrammatic) and SCET(operator-based) 24

48 Dynamicalapproachestonon-leptonic B-decays based on the heavy mass expansion: pqcd(diagrammatic) vs. QCDF(diagrammatic) and SCET(operator-based) some theoretical issues need clarification theaccuracyoftheexpansionisnotsettledyet,becausetheerrorsarelargeandtheinput parameters poorly known chirally-enhancedterms 2m 2 π/[m b (m u + m d )]areformallysuppressedbutnumericallyof order one; no consensus about other possible sources of enhancement 24

49 Dynamicalapproachestonon-leptonic B-decays based on the heavy mass expansion: pqcd(diagrammatic) vs. QCDF(diagrammatic) and SCET(operator-based) some theoretical issues need clarification theaccuracyoftheexpansionisnotsettledyet,becausetheerrorsarelargeandtheinput parameters poorly known chirally-enhancedterms 2m 2 π/[m b (m u + m d )]areformallysuppressedbutnumericallyof order one; no consensus about other possible sources of enhancement despite recent progress, it is unsafe to use these calculations to obtain constraints on the CKM matrix and/or New Physics 24

50 Phenomenologicalmethods itissafetouseisospinsymmetrytoextractckmparameters e.g. determination of α 1 CL C K M f i t t e r FPCP 6 CKM fit no α meas. in fit B ππ B ρπ B ρρ WA Combined these constraints are not that strong; furthermore the sensitivity to New Physics is very weak ( I = 1/2 b d penguins disappear) α (deg) 25

51 Phenomenologicalmethods itissafetouseisospinsymmetrytoextractckmparameters e.g. determination of α 1 CL C K M f i t t e r FPCP 6 CKM fit no α meas. in fit B ππ B ρπ B ρρ WA Combined these constraints are not that strong; furthermore the sensitivity to New Physics is very weak ( I = 1/2 b d penguins disappear).2 whataboutsu(3)? α (deg) 25

52 FlavorSU(3)in B ππ, Kπ, KK a long story: Silva and Wolfenstein, 1993 Gronau et al., and 24 JC; Pirjol; Fleischer, 1999 JCetal.,24 Buras et al. (BFRS), manyotherworks! 26

53 FlavorSU(3)in B ππ, Kπ, KK a long story: Silva and Wolfenstein, 1993 Gronau et al., and 24 JC; Pirjol; Fleischer, 1999 JCetal.,24 Buras et al. (BFRS), manyotherworks! however due to lack of information on B s decays, most of these works assume in additionthatsomeorallofthefollowingannihilation/exchange topologies are negligible (exception: Wu and Zhou, 25) W W W 26

54 these topologies are power-suppressed Annihilation/exchangediagrams inheavymesondecays the amplitude ratios A(D K K ) A(D K + K ) and A(B D s K + ) A(B D π + ) arebothformallyoforder (1/N c )(Λ/m Q ); butthefirstoneis 43%whilethesecondoneis 12%! in charmless B-decays the only direct constraint is A(B K + K ) A(B π + π ) <.22 27

55 Theoriginofthe B Kπpuzzle measurement of branching ratios by CLEO, BaBar and Belle were found to be not completely consistent with naïve expectations based on a specific quark diagram hierarchy(buras and Fleischer,GronauandRosner,BFRS,...) theseargumentsareconfirmedbyamoredetailedanalysis(bfrs)takinginputfrom B ππand SU(3), but neglecting annihilation/exchange contributions theeffectisquiteinsensitive towhathappensin the S = 1, I = channelandwouldpoint towards non standard electroweak penguins however the discrepancy is not statistically convincing and the rôle of the neglected contributions isnotclear(yet) 28

56 Generalparametrization inthestrictsu(3)limit A(K + π ) = V us V ubt + + V ts V tbp A(K π + ) = V us V ubn + + V ts V tb( P + P EW C ) 2A(K + π ) = V us V ub(t + + T N + ) + V ts V tb(p + P EW P EW C ) 2A(K π ) = V us V ubt + V ts V tb( P + P EW ) A(π + π ) = V ud V ub(t + + T) + V td V tb(p + PA) 2A(π π ) = V ud V ub(t T) + V td V tb( P PA + P EW ) 2A(π + π ) = V ud V ub(t + + T ) + V td V tbp EW A(K + K ) = V ud V ub T + V td V tbpa A(K K ) = V ud V ub P + V td V tb( P PA + P EW C 1 3 PEW KK ) A(K + K ) = V ud V ubn + + V td V tb( P + P EW C ) 29

57 Electroweakpenguins the Q 7,8 operatorsaresuppressedbytheirwilsoncoefficientswithrespectto Q 9,1 (Neubertand Rosner; Buras and Fleischer; Gronau, Pirjol and Yan) so that their I = 3/2, 1 hadronic matrix elements are not independent parameters in the SU(3) limit P EW = R + (T + + T ) P EW C = R+ 2 (T+ + T + N + T P) R 2 (T+ T + N + + T + P) P EW KK = R+ (N + T P) with R ± = 3 2 c 9 ± c 1 c 1 ± c 2 = (1.35 ±.13)1 2 3

58 Parametercounting neglectingannihilation/exchangediagramswouldimply T = PA = N + P =,inwhich case there are 7 hadronic parameters(+( ρ, η)) and 15 independent measured observables the exact SU(3) limit need 6 additional parameters but introduces only 4 new measured observables(among which one upper limit) 31

59 Parametercounting neglectingannihilation/exchangediagramswouldimply T = PA = N + P =,inwhich case there are 7 hadronic parameters(+( ρ, η)) and 15 independent measured observables the exact SU(3) limit need 6 additional parameters but introduces only 4 new measured observables(among which one upper limit) thisseemshopeless! howeveritisnot... inadditionthereareusefulconstraintscomingfromratiosofbr sbycdf(amongwhichtwonew independentobservables, B s K + K and B s K + π ) in total we have 13+2 parameters for 21 independent observables 31

60 Parameter BABAR Belle CLEO CDF Average S + C + ππ.3 ±.17 ±.3 [1].67 ±.16 ±.6 [2].5 ±.12 ππ.9 ±.15 ±.4 [1].56 ±.12 ±.6 [2].37 ±.1 Cππ.12 ±.56 ±.6 [3] ±.17 [4] ±.39 SK S π ±.4 [5] +.22 ±.47 ±.8 [6] CK S π +.6 ±.18 ±.3 [5].11 ±.18 ±.8 [6].2 ±.13 A CP (π + π ).1 ±.1 ±.2 [3] +.2 ±.8 ±.1 [17].1 ±.6 A CP (K + π ).133 ±.3 ±.9 [8].113 ±.22 ±.8 [17].4 ±.16 ±.2 [9].13 ±.78 ±.12 [1].114 ±.18 A CP (K + π ) +.6 ±.6 ±.1 [3] +.4 ±.4 ±.2 [7].29 ±.23 ±.2 [9].4 ±.4 A CP (K π + ).9 ±.5 ±.1 [11] +.5 ±.5 ±.1 [17] +.18 ±.24 ±.2 [9].2 ±.4 A CP (K K + ) +.15 ±.33 ±.1 [11] +.15 ±.33 B(B π + π ) 5.5 ±.4 ±.3 [15] 4.4 ±.6 ±.3 [16] [14] (see ratios below) 5.1 ±.4 B(B + π + π ) 5.8 ±.6 ±.4 [3] 5. ± 1.2 ±.5 [16] [14] 5.5 ±.6 B(B π π ) 1.17 ±.32 ±.1 [3] [4] < 4.4 (not used) [14] 1.45 ± B(B K + π ) 19.2 ±.6 ±.6 [15] 18.5 ± 1. ±.7 [16] B(B + K + π ) 12. ±.7 ±.6 [3] 12. ± [16] B(B + K π + ) 26. ± 1.3 ± 1. [11] 22. ± 1.9 ± 1.1 [16] B(B K π ) 11.4 ±.9 ±.6 [5] 11.7 ± [16] [14] (see ratios below) 18.9 ±.7 [14] 12.1 ±.8 [14] ± 1.3 [14] 11.5 ± 1. B(B K + K ).4 ±.15 ±.8 [15] [13] <.8 (not used) [14] (see ratios below).5.9 B(B + K + K ) 1.5 ±.5 ±.1 [11] 1. ±.4 ±.1 [13] < 3.3 (not used) [14] 1.2 ±.3 B(B K K ) ±.13 [11].8 ±.3 ±.1 [13] < 3.3 (not used) [14].96 ±.24 B(B π + π ) B(B K + π ) f s B(B s K + K ) f d B(B K + π ) f d B(B π + π ) f s B(Bs K + K ) B(Bs π + π ) B(Bs K + K ) f s B(B s K π + ) f d B(B K + π ) B(B K + K ) B(B K + π ).21 ±.5 ±.3 [1].21 ±.6.46 ±.8 ±.7 [1].46 ± ±.13 ±.6 [1].45 ±.14 <.5 [1] <.5 <.8 [1] <.8 <.1 [1] <.1

61 SU(3)breaking dominant factorizable SU(3) breaking is easy to identify, it is related to ratios of decay constants; wenormalise B Kπ, B s K + K and B s K + π withrespectto B ππthroughthe factors N Kπ f K /f π, N K K (f Bs /f B )(f K /f π ) 2 and N s Kπ = (f B s /f B )(f K /f π );takeconservative theoretical errors N Kπ = 1.22 ±.22 N K K = 1.81 ±.34 N s Kπ = 1.48 ±.28 33

62 SU(3)breaking dominant factorizable SU(3) breaking is easy to identify, it is related to ratios of decay constants; wenormalise B Kπ, B s K + K and B s K + π withrespectto B ππthroughthe factors N Kπ f K /f π, N K K (f Bs /f B )(f K /f π ) 2 and N s Kπ = (f B s /f B )(f K /f π );takeconservative theoretical errors N Kπ = 1.22 ±.22 N K K = 1.81 ±.34 N s Kπ = 1.48 ±.28 remainingfactorizablesu(3)breaking,suchas (f π F B K )/(f K F B π )ismuchsmaller(afew%) and is neglected nonfactorizable Λ/m b -suppressedsu(3)breakingeffectsareneglected 33

63 Asideremark: directtestsofsu(3) inheavymesonobservables decayconstants: f Ds /f D (exp,latt)and f Bs /f B (latt)areofthesameorderas f K /f π once dominant sources are identified(phase space, pole contribution to the form factor), D π and D K semileptonic decays do not indicate large corrections(fajfer) still, information is incomplete and one cannot exclude new mechanisms of SU(3) breaking 34

64 Notation inthetreedominanceapproximation, B (t) π + π measures α,sowritethetime-dependent CP-asymmetry a CP (t) = Ccos mt + Ssin mt = Ccos mt + 1 C 2 sin 2α eff sin mt inthepenguindominanceapproximation, B (t) K S π measures β,sowrite the time-dependent CP-asymmetry a CP (t) = Ccos mt + 1 C 2 sin 2β eff sin mt 35

65 Understandingtheconstraintshape inthe ( ρ, η)plane thesubsystem B π + π, B K ± π, B K + K approximatelymeasures α neglecting annihilation and exchange, there is a simple analytical solution 1 C 2 ππ D cos(2α 2α eff ǫ) = (1 + λ 2 ) 2 2λ 2 sin 2 γ andbr(k + π )C(K + π ) +BR(π + π )C(π + π ) = where D D e iǫ = (1 + λ 2 )(1 + λ 2 e iγ ) [ 1 + BR(K+ π ) BR(π π + ) ] 36

66 Understandingtheconstraintshape inthe ( ρ, η)plane thesubsystem B π + π, B K ± π, B K + K approximatelymeasures α neglecting annihilation and exchange, there is a simple analytical solution 1 C 2 ππ D cos(2α 2α eff ǫ) = (1 + λ 2 ) 2 2λ 2 sin 2 γ andbr(k + π )C(K + π ) +BR(π + π )C(π + π ) = where D D e iǫ = (1 + λ 2 )(1 + λ 2 e iγ ) [ 1 + BR(K+ π ) BR(π π + ) taking power-suppressed contributions into account, the system of equations remain closed and solvable,andcanbeapproximatelyviewedasaboundon α α eff. theboundwouldbecomeanequalityifthetime-dependentcp-asymmetryin B K + K is measured ] 36

67 Fitresultfor"α" CL CKM Fit η.6.4 perfect agreement with the standard constraints C K M f i t t e r EPS 25 α from h + h (h=π, K) in SU(3) ρ 37

68 The"β"subsystem replace B π + π by B K S π, B K ± π by B π π,and αby β 1 C 2 K S π D cos(2β 2β eff + ǫ) = (1 + λ 2 ) 2 2λ 2 sin 2 γ andbr(k S π )C(K S π ) +BR(π π )C(π π ) = [ 1 + BR(π π ) BR(K s π ) taking annihilation/exchange into account, this translates into a bound that improves the result of Gronau, Grossman and Rosner that is not optimal ] 38

69 Fitresultfor"β" CL CKM Fit.8.6 η a discrepancy? -1 C K M f i t t e r EPS 25 β from h h, K + K in SU(3) ρ.2 39

70 Combining αand β CL CKM Fit.8.6 η C K M f i t t e r EPS 25 h + h, h h (h=π, K) in SU(3) ρ combination of constraints stronger than the naïve product α β: the correlation comes mainly fromtheelectroweakpenguincoefficients R ± 4

71 Combining αand β CL CL CKM Fit.6.5 CKM Fit.6 η η C K M f i t t e r EPS 25 h + h, h h (h=π, K) in SU(3) C K M f i t t e r EPS 25 With π + π, B s K + h - (h=π, K) ρ combination of constraints stronger than the naïve product α β: the correlation comes mainly fromtheelectroweakpenguincoefficients R ± adding the observables that depend on the same parameters is useful ρ 4

72 Constraint inthe ( ρ, η)plane fromthefullinputset CL 1 η 1.5 CKM Fit.8.6 the α and β subsystems dominate the constraint; other inputs help in disfavouring mirror solutions C K M f i t t e r EPS 25 hh (h=π, K) in SU(3) ρ 41

73 Constraint inthe ( ρ, η)plane fromthefullinputset CL 1 η C K M f i t t e r EPS 25 hh (h=π, K) in SU(3) CKM Fit the α and β subsystems dominate the constraint; other inputs help in disfavouring mirror solutions the main contributions to the χ 2 come from BR(K ± π ), BR(K S π ) and the CPasymmetry S(K S π ) ρ 41

74 ThepValueoftheanalysis withinthestandardmodel infrequentiststatistics,thepvalueisawell-definedinterpretationof χ 2 min /N dof;assumingagiven theory(here, ( ρ, η) SM +SU(3)),thepValueistheprobabilitythatoneobtainsalessgoodfitifone performs many similar experiments 42

75 ThepValueoftheanalysis withinthestandardmodel infrequentiststatistics,thepvalueisawell-definedinterpretationof χ 2 min /N dof;assumingagiven theory(here, ( ρ, η) SM +SU(3)),thepValueistheprobabilitythatoneobtainsalessgoodfitifone performs many similar experiments the larger the pvalue, the better the compatibility of the observed data with respect to the assumed theory 42

76 ThepValueoftheanalysis withinthestandardmodel infrequentiststatistics,thepvalueisawell-definedinterpretationof χ 2 min /N dof;assumingagiven theory(here, ( ρ, η) SM +SU(3)),thepValueistheprobabilitythatoneobtainsalessgoodfitifone performs many similar experiments the larger the pvalue, the better the compatibility of the observed data with respect to the assumed theory herethepvalueifoforder3 4%andthusthecompatibilityofthedatawiththeSM+SU(3) hypothesis is very good 42

77 ThepValueoftheanalysis withinthestandardmodel infrequentiststatistics,thepvalueisawell-definedinterpretationof χ 2 min /N dof;assumingagiven theory(here, ( ρ, η) SM +SU(3)),thepValueistheprobabilitythatoneobtainsalessgoodfitifone performs many similar experiments the larger the pvalue, the better the compatibility of the observed data with respect to the assumed theory herethepvalueifoforder3 4%andthusthecompatibilityofthedatawiththeSM+SU(3) hypothesis is very good howeverthe χ 2 min isnotalwaysthebestmeasureofthecompatibilityofthedatawiththetheory; let slookatthedominantcontributionstothe χ 2 in moredetail 42

78 RemovingBR(K ± π ),BR(K S π )and S(K S π ) CL 1 define R n = 2BR(K S π )/BR(K ± π ) both observables are very sensitive to electroweak 1.8 penguins assuming SM+SU(3), and determining the pa-.8.6 rameters with the other inputs, there is a discrepancy between the fit prediction and the direct R n.6.4 measurement of R n and S(K S π ) BFRSfitforNewPhysicsinthe S = I = 1sec-.4 torandobtainagoodresultfor R n,but Sremains.2 C K M f i t t e r EPS somewhat too large the experimental error on S is large, while R n could be affected by larger than expected non factorizable SU(3)-breaking effects S(K s π ) 43

79 DirectCPviolation: B K ± π vs. B ± K ± π 1 1 CL C(K + π - ) a small discrepancy between the fit result and the direct measurement C K M f i t t e r EPS C(K + π ).2 44

80 Apuzzle? the discrepancies for the specific observables explicited above do not exceed the 2σ level however these discrepancies were already there, at about the same significance level, in the simplified analysis where one neglects the 6 parameters related to annihilation/exchange contributions: this is intriguing! we do not know yet to which extent the residual SU(3)-breaking effects could improve the theoretical description of the data within the Standard Model(see however Feldmann and Hurth, 24) 45

81 Outlook inthenearfuture,thankstocdfandlhcb,theremaybeupto38measuredobservables dependingontheverysame13+2parameters;thiswill allowtofitpartofsu(3)breakingandto study different New Physics scenarios 46

82 Outlook inthenearfuture,thankstocdfandlhcb,theremaybeupto38measuredobservables dependingontheverysame13+2parameters;thiswill allowtofitpartofsu(3)breakingandto study different New Physics scenarios naïve extrapolation for 28 two B-factorieswith1ab 1 each;scalestatistical errorsaccordingtoluminosity,leave systematics unchanged CDF BR ratios: errors unchanged threecpin B s inputsfromlhcb,takenfromtdr23 central values: output from the present SM full fit there will certainly be other measurements available 46

83 From25to28 η.7 1 CL.6 CKM Fit C K M.1 f i t t e r 28 EPS LHCb ρ

84 From25to28 η.7 1 CL.6 CKM Fit C K M.1 f i t t e r 28 EPS LHCb η C K M f i t t e r ca CL CKM Fit ρ ρ η C K M f i t t e r 28 LHCb 1 CL CKM Fit ρ 47

85 Conclusion the global CKM fit, which uses very well controlled inputs only, does confirm the CKM mechanism as the dominant contribution to flavor- and CP-violating transitions thethreemainfcnctransitions(s d, b dand b s)havenowbeentestedandarein good to excellent agreement with SM predictions someimportantobservables(veryrarekaonand Bdecays,CPviolation in B s decays...) remain to be measured and interpreted: will be done at future experiments! 48

86 Conclusion the global CKM fit, which uses very well controlled inputs only, does confirm the CKM mechanism as the dominant contribution to flavor- and CP-violating transitions thethreemainfcnctransitions(s d, b dand b s)havenowbeentestedandarein good to excellent agreement with SM predictions someimportantobservables(veryrarekaonand Bdecays,CPviolation in B s decays...) remain to be measured and interpreted: will be done at future experiments! the overall pattern of B decays to two pseudoscalars is reasonably described by simple phenomenological approaches, but its details and dynamics challenges the theory present understanding makes unclear the disentanglement of statistical fluctuations, hadronic effects(flavor symmetry breaking) and possible New Physics effects however due to the large number of experimentally accessible observables, new information from nonleptonic Bdecaysisexpectedin aclosefuture 48

87 Yadurab

88 Thestatistical methodtoextract γ theobservablesdependon γand µwhere µ = (r B, δ) 1. minimize χ 2 (γ, µ)withrespectto µandsubstracttheminimum χ 2 (γ) 2. assumethatthetruevalueof µis µ t PDF [ χ 2 (γ) γ, µ t ] 3. compute (1 CL) µt (γ)viatoymonte-carlo 4. maximizewithrespectto µ t (1 CL)(γ) this is a quite general, but very expensive, procedure; coverage must be(and is being) checked beforeweassumedthat µ t wasgivenbythevaluethatminimizes χ 2 (γ, µ)ontherealdata: studieshaveshownusthatthiscanleadtoanunderestimateoftheerror 5

89 sin(2β + γ) from b cūd, u cd C K M f i t t e r FPCP 6 D + π + D* + π + D + ρ + Partial. + fully rec. Combined CKM fit 1 CL WA sin(2β + γ) 51

90 Electroweakpenguinsincharmlessdecays fit output for R + vs. R compared to the theoretical calculation 52

91 model-independent parametrization Bq H SM+NP B=2 NewPhysicsinmixing B q Bq H B=2 SM B q (1 + hq e 2iσ q ) 18 1 CL CL σ d (deg) σ s (deg) C K M f i t t e r FPCP C K M f i t t e r FPCP h d h s 53

92 assuming m s = 2. ±.11ps 1 andsin 2β s =.36 ±.28(oneyearLHCb running) CL 1.8 σ s (deg) C K M f i t t e r LHCb h s 54

93 from B τν Constraint onsupersymmetric chargedhiggs CL 1.8 m H + (GeV/c 2 ) tan β C K M f i t t e r FPCP