CKM fits and charm decays

Transcription

1 CKM fits and charm decays Sébastien Descotes-Genon Laboratoire de Physique Théorique CNRS & Université Paris-Sud 11, Orsay, France Beijing - 22 Oct 2010 Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/2010 1

2 Introduction End of the first B-factory era, Tevatron reign before LHC results High-precision data entangling electroweak and strong physics Stringent test of SM, and in particular of Kobayashi-Maskawa mechanism for CP violation Opportunity to test (and constrain) extensions of SM through flavour physics data Global CKM fits relevant players in this game both to check SM and provide directions for New Physics What can we learn from the weak interactions of charm? QCD : hard to compute analytically, but good prospects of improved accuracy from lattice SM : complementary K and D sectors (V ud V cs, V us V cd ) New Physics : investigating u-type sector, as b-factories for d-type Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/2010 2

3 Mapping CP-violation Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/2010 3

4 CP-violation : the four parameters In SM weak charged transitions mix quarks of different generations Encoded in unitary CKM matrix V CKM = λ 2 = V us 2 V ud 2 + V us 2 A 2 λ 4 = V ud V us V ub V cd V cs V cb V td V ts V tb 3 generations = 1 phase, only source of CP-violation in SM Wolfenstein parametrisation, defined to hold to all orders in λ and rephasing invariant V cb 2 V ud 2 + V us 2 ρ + i η = V udv ub V cd V cb = 4 parameters describing the CKM matrix, to extract from data Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/2010 4

5 The inputs CKM matrix within a frequentist framework ( χ 2 minimum) + specific scheme for systematic errors (Rfit) data = weak QCD = Need for hadronic inputs (often lattice) V ud superallowed β decays PRC79, (2009) V us K l3 (Flavianet) f + (0) = ± ± ɛ K PDG 08 ˆBK = ± ± V ub inclusive and exclusive V ub 10 3 = 3.92 ± 0.09 ± 0.45 V cb inclusive and exclusive V cb 10 3 = ± 0.38 ± 0.59 m d last WA B d - B d mixing B Bs /B Bd = 1.05 ± 0.01 ± 0.03 m s last WA B s - B s mixing B Bs = 1.28 ± 0.02 ± 0.03 β last WA J/ψK ( ) α last WA ππ, ρπ, ρρ isospin γ last WA B D ( ) K ( ) GLW/ADS/GGSZ B τν (1.68 ± 0.31) 10 4 f Bs /f Bd = ± ± f Bs = 228 ± 3 ± 17 MeV Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/2010 5

6 Lattice Consistent averages of lattice results for hadronic quantities needed = we perform our own averages of published N f = 2 and 2+1 results using Educated Rfit procedure central value : product of Gaussian (stat) + Rfit (syst) likelihoods combined stat uncertainty : product of Gaussian (stat) likelihoods combined syst uncertainty : the one of the most precise method Conservative, algorithmic procedure with internal logic for syst the present state of art cannot allow us to reach a better theoretical accuracy than the best of all estimates (combining 2 methods with similar syst does not reduce the intrinsic uncertainty encoded as a systematic) best estimate should not be penalized by less precise methods (opposed, e.g., to combined syst = dispersion of central values) Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/2010 6

7 The global fit ) excluded area has CL > 0.95 sin 2' $ K "! V ub SL V ub & %! " excluded at CL > 0.95 ' " & #m s #m d #m d V ud, V us V cb, V ub B τν m d, m s ɛ K sin 2β α γ -1.0 CKM f i t t e r ICHEP 10! ( $ K sol. w/ cos 2' < 0 (excl. at CL > 0.95) A = λ = ρ = η = (68% CL) Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/2010 7

8 Focus on γ γ angle from interference between B D 0 K and B D 0 K colour allowed Aλ 3 colour suppressed Aλ 3 (ρ + iη) r B = A suppr A favour V ubv cs V cb V us [1/N c] GLW : D into CP eigenstates (KK, ππ, K S π 0, K S ω, K S φ) ADS : D ( ) into doubly Cabibbo suppressed states GGSZ : D ( ) into 3-body state and Dalitz analysis Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/2010 8

9 Combined results on γ Increased statistics on GGSZ (DK ±, D K ±, DK ± with D Dπ 0, D 0 γ and D K 0 S π+ π ) (Babar takes also neutral D into K 0 S K + K ) Belle [arxiv: ] BaBar[arXiv: ] All methods combined : γ = ( ) From the global fit : γ = ( ) (68%CL) 1 - CL CKM f i t t e r FPCP 10 D(*) K(*) GLW + ADS D(*) K(*) GGSZ Full Frequentist treatment on MC basis WA Combined CKM fit ! (deg) Far less precise than α and β, = and driven by one methode (GGSZ) : why is it so? Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/2010 9

10 Hadronic inputs for γ methods Not only γ in 3 methods, also A(B DK )/A(B DK ) = r B e iδ B GLW (D CP K, D CP K, D CPK ) R CP± = 1 ± 2r B cos δ B cos γ + r 2 B ADS (DK, D K, DK for K π...) R ADS = r 2 B + r 2 D +2r B r D cos(δ B + δ D ) cos γ A ADS = 2r Br D sin(δ B +δ D ) sin γ R ADS GGSZ (DK, D K, DK ) x ± = r B cos(δ B ± γ) y ± = r B sin(δ B ± γ) Needs agreement on had. qties to increase accuracy on γ (DK) r B A CP± = ±2r B sin δ B sin γ/r CP± excluded area has CL > 68.3, 95 % CKM f i t t e r FPCP 10 GGSZ Combined GLW+ADS preliminary naive statistical treatment (for illustrative purpose only) ! (D(*)K(*)) (deg) Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

11 The three methods w.r.t hadronic inputs excluded area has CL > 68.3, 95 % 150 ADS 0.20 excluded area has CL > 68.3, 95 % 0.15 (DK) (deg) " B GGSZ GLW (DK) r B ADS GGSZ GLW 0 CKM f i t t e r FPCP 10 preliminary naive statistical treatment (for illustrative purpose only) 0.00 CKM f i t t e r FPCP 10 preliminary naive statistical treatment (for illustrative purpose only) ! (D(*)K(*)) (deg) ! (D(*)K(*)) (deg) R GLW,CP± = 1 ± 2r B cos δ B cos γ + rb 2 A GLW,CP± = ± 2r B sin δ B sin γ R ADS,CP± R ADS = rb 2 + r D 2 + 2r Br D cos(δ B + δ D ) cos γ A ADS = 2r Br D sin(δ B +δ D ) sin γ R ADS Symmetry (δ B, δ D, γ) ( δ B, δ D, γ) For ADS: (r B, δ B ) not enough, (r D, δ D ) nuisance parameters Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

12 Impact of charm on ADS+GLW (deg) CKM f i t t e r Charm CL (deg) CKM f i t t e r Charm CL " D " D ! (DK) (deg) R GLW,CP± = 1 ± 2r B cos δ B cos γ + r 2 B R ADS = r 2 B + r 2 D + 2r Br D cos(δ B + δ D ) cos γ ! (D(*)K(*)) (deg) A GLW,CP± = ± 2r B sin δ B sin γ R ADS,CP± A ADS = 2r Br D sin(δ B +δ D ) sin γ R ADS r D e iδ D = A(D 0 K + π )/A(D 0 K π + ) (and in particular δ D ) needed to put GLW+ADS on a par with GGSZ 0.0 Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

13 D-meson and the unitarity triangle(s) Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

14 The D-meson unitarity triangle Unitarity of the CKM matrix for (b, d) V ud V ub V cd V cb +1+ V tdv tb V cd V cb O(1) O(1) = 0 = 0 Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

15 The D-meson unitarity triangle Unitarity of the CKM matrix for (c, u) V ud Vcd V us Vcs +1+ V ubvcb V us Vcs = 0 O(1) O(λ 4 ) = 0 can be used to define a (squashed) D-meson unitarity triangle ρ D + i η D = V ud Vcd V ( usvcs ) ( ) α D = arg V ubvcb V ud Vcd = arg V ubvud V cb Vcd = γ ( ) γ D = arg V ud Vcd V usvcs = O(λ 4 ) ( ) β D = arg = π α D γ D = π + γ + O(λ 4 ) VusV cs V ub V cb Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

16 Current constraints on D unitarity triangle In the SM, kaon and B-processes constrain strongly D-UT, squashed with two almost parallel sides ) excluded area has CL > 0.95 sin 2' $ K! #m d " & #m s #m d $ K V ub & % CKM f i t t e r ICHEP 10 sol. w/ cos 2' < 0 (excl. at CL > 0.95) " 0.1 V ub! SL " ' ( Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

17 Current constraints on D unitarity triangle In the SM, kaon and B-processes constrain strongly D-UT, squashed with two almost parallel sides excluded area has CL > 0.95 γ sol. w/ cos 2β < 0 (excl. at CL > 0.95) D η α V ub τ ν V ub SL α ε K CKM f i t t e r Charm 2010 sin 2β γ m d & m s m d ρ D Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

18 What on CKM from charm? CP-violating observables CP-violation very difficult to observe in D meson... and hard to control theoretically Diffcult to extract information from D 0 - D 0 mixing Constraining loop NP effects C = 2 but issue of long distances CP-conserving observables Provide V cd and V cs Accessible through leptonic and semileptonic D-decays Hadronic part controlled through lattice simulations Constraining for NP in tree decays = Focus on latter observables both for SM and NP Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

19 Direct non-lattice constraints on V cd and V cs V cd : deep-inelastic scattering of ν, ν on nucleons d 3 σ(ν µ N µ + µ X) dξdydx = d 2 σ(ν µ N cx) D dξdy c hadron (z)b c (c µ + X) D hadronisation of c, B c weighted average of cross-sections of charm mesons d 2 σ LO (ν µ N cx) dξdy [ V cd 2 d(ξ) + V cs 2 s(ξ)] νn vs νn: s cancel and V cd up to modelling of d parton distribution V cs : charmed-tagged W decays W cs V cd = ± σ( V cd )/ V cd = 5% V cs = ± 0.13 σ( V cs )/ V cs = 34% (!) Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

20 Direct (non-lattice) vs indirect measurements cs V B physics Indirect Direct (no lattice) K and nucleon: not so constraining V ud V cs and V cd V us only at first non trivial order in λ (need b-sector to fix the higher orders) 0.80 Nucleon & Kaon CKM f i t t e r excluded area has CL > 0.95 Charm V cd Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

21 Direct (non-lattice) vs indirect measurements cs V Nucleon & Kaon CKM f i t t e r B physics V cd Indirect Direct (no lattice) excluded area has CL > 0.95 Charm K and nucleon: not so constraining V ud V cs and V cd V us only at first non trivial order in λ (need b-sector to fix the higher orders) B alone: rather constraining V cd = V cs = Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

22 Direct (non-lattice) vs indirect measurements cs V Nucleon & Kaon CKM f i t t e r B physics V cd Indirect Direct (no lattice) excluded area has CL > 0.95 Charm K and nucleon: not so constraining V ud V cs and V cd V us only at first non trivial order in λ (need b-sector to fix the higher orders) B alone: rather constraining V cd = V cs = Indirect (combination of the two above): already quite well determined: V cd = ± V cs = Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

23 Direct (non-lattice) vs indirect measurements cs V Nucleon & Kaon CKM f i t t e r B physics V cd Indirect Direct (no lattice) excluded area has CL > 0.95 Charm K and nucleon: not so constraining V ud V cs and V cd V us only at first non trivial order in λ (need b-sector to fix the higher orders) B alone: rather constraining V cd = V cs = Indirect (combination of the two above): already quite well determined: V cd = ± V cs = Direct (no lattice inputs): poorly known (ellipse deformed by V cd 2 + V cs 2 1) Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

24 V cs from leptonic decays Γ(D s lν) = G2 F 8π V cs 2 f 2 D s m 2 l m D s ( 1 m2 l m 2 D s ) 2 +O(α) Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

25 V cs from leptonic decays ( ) 2 Γ(D s lν) = G2 F 8π V cs 2 fd 2 s ml 2 m D s 1 m2 l md 2 +O(α) s f Ds (MeV) Reference Article N f Mean Stat Syst CP-PACS MILC ETMC HPQCD FNAL-MILC HPQCD Our average Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

26 V cs from leptonic decays ( ) 2 Γ(D s lν) = G2 F 8π V cs 2 fd 2 s ml 2 m D s 1 m2 l md 2 +O(α) s f Ds (MeV) Reference Article N f Mean Stat Syst CP-PACS MILC ETMC HPQCD FNAL-MILC HPQCD Our average V cs f Ds (MeV) CLEO-c, Belle (D s µν) ± 9.6 ± 1.8 Babar (D s µν) ± 16.3 ± 1.7 CLEO-c, Babar (D s τν) ± 7.4 ± 1.8 HFAG Average ± 5.7 (last error correlated, from τ Ds ) Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

27 V cd from leptonic decays Γ(D lν) = G2 F 8π V cd 2 f 2 D m2 l m D ( 1 m2 l m 2 D ) 2 +O(α) f Ds /f D Reference Article N f Mean Stat Syst CP-PACS MILC ETMC HPQCD FNAL-MILC Our average V cd f D (MeV) CLEO-c (D µν) + PDG 46.4 ± 1.9 ± 0.6 MeV = A lot to gain from more measurements... Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

28 Leptonic decays 1.00 B physics Indirect 0.95 Direct (leptonic) 0.90 cs V Nucleon & Kaon CKM f i t t e r Charm 2010 excluded area has CL > V cd Leptonic decays: V cd = , V cs = Indirect: V cd = ± , V cs = Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

29 V cd from semileptonic decays Differential decay rate dγ(d πeν) dq 2 = G2 F V cd 2 24π 3 p 3 π F π +(q 2 ) 2 F π + vector from factor (neglecting scalar contribution m 2 e) Several parametrisations of q 2 -dependence equivalent since smooth functions of q 2 (BK, modified pole, z-expansion... ) Γ(D πeν) F π +(0) 2 V cd 2 Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

30 V cd from semileptonic decays Differential decay rate dγ(d πeν) dq 2 = G2 F V cd 2 24π 3 p 3 π F π +(q 2 ) 2 F π + vector from factor (neglecting scalar contribution m 2 e) Several parametrisations of q 2 -dependence equivalent since smooth functions of q 2 (BK, modified pole, z-expansion... ) Γ(D πeν) F π +(0) 2 V cd 2 F+(0) π Reference Article N f Mean Stat Syst MILC Our average F+(0) V π cd CLEO-c ± ± Belle ± ± Our average ± Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

31 V cs from semileptonic decays Similarly, up to parametrisation of q 2 -dependence (part of exp. syst.) Γ(D Keν) F K + (0) 2 V cs 2 F+ K (0) Reference Article N f Mean Stat Syst MILC HPQCD Our average F+ K (0) V cs CLEO-c ± ± Belle ± ± Babar ± ± Our average ± Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

32 Semileptonic decays 1.00 B physics Indirect Direct (semileptonic) cs V Nucleon & Kaon CKM f i t t e r Charm 2010 excluded area has CL > V cd Semileptonic decays: V cd = , V cs = Indirect: V cd = ± , V cs = Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

33 Altogether 1.00 B physics Indirect 0.95 Direct (All) 0.90 cs V Nucleon & Kaon CKM f i t t e r Charm 2010 excluded area has CL > V cd Altogether: V cd = , V cs = Indirect: V cd = ± , V cs = Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

34 The importance of being a ratio Unitarity powerful 1D constraint V cd 2 + V cs 2 = 1 V cb 2 [even if discrepancy between incl. and excl. determination of V cb ] orthogonal constraint from V cd V cs Γ(D lν) Γ(D πeν), Γ(D s lν) Γ(D Keν) reduced systematics reduced both exp and theo f Ds /f D U-spin breaking, F π +(0)/F K + (0)... vector modes? for instance, take ratio of D πlν with D s φlν, very narrow s s state, good control on lattice = Think in terms of D s /D ratios for V cd and V cs! Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

35 New Physics searches Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

36 sin(2β) vs B τν Global fit χ 2 min drops by 2.6[2.8]σ if sin 2β c c [B τν] removed CL CKM f i t t e r ICHEP 10 BR(B $ #") CKM f i t t e r ICHEP sin 2! (GeV) f Bd B # "! All $m d LQCD f Bd Sqrt[B ] (GeV) B d Change in measured Br(B τν) (2.8 σ) Correlated change in lattice values for f Bd and B Bd (2.8 σ) New Physics in mixing ( F = 2) or in tree ( F = 1) Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

37 Two-Higgs doublet model of type II vs SM Simple and predictive extension of SM (embedded in susy models) One doublet coupling to down quarks, one to up s (and leptons) SM-like Yukawa terms for the quark sector No flavour-changing neutral currents at tree level CKM matrix only source of flavour-changing interactions, but new interactions : H + rather than W (S P vs V A) M q d q d l q u W + l H + M W + H + b s b s! l q u! l Additional d.o.f. and parameters: 5 scalars : H ± (charged), A (pseudoscalar), h 0 and H 0 (scalar) masses of H ±, H and A, ratio of Higgs vacuum expectation values tan β = v 2 /v 1 angle describing the mixing between h 0 and H 0 Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

38 F = 1 for 2HDM(II) Analysis for F = 1 or electroweak processes with H + contributions Potential problems with leptonic decays (B τν, D s lν... ) Parameters : CKM matrix, M H +, tan β (none from neutral Higgses) O. Deschamps et al., % excluded area has CL > 0.95 V ub "! "(!) # CKM matrix inputs where H + contribution suppressed, prop to m lightm heavy M 2 H + or m2 light M 2 H CKM f i t t e r 2HDM "(!) $ selects V ud, V ub, V cb, γ (as a combination of α and β, not from B DK ) Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

39 Leptonic decays For any meson M, SM leptonic decay rate ( B[M lν l ] SM = G2 F m Mm 2 l 8π 1 m2 l m 2 M ) 2 V quqd 2 f 2 M τ M(1 + δ Ml2 em ) Charged Higgs contributions (helicity suppressed, vanish as m M 0) B[M lν] = B[M lν] SM (1 + r H ) 2 ( ) ( m qu m qd tan 2 ) β 2 mm r H = m qu + m qd m H + If perfect agreement SM-data, two distinct solutions in 2HDM(II) decoupling : r H = 0 (m H +, tan β small) fine-tuned : r H = 2 (linear correlation between m + H and large tan β, depends on meson mass Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

40 Leptonic decays : B τν and K lν/π lν excluded area has CL > 0.95 CKM f i t t e r 2HDM excluded area has CL > 0.95 CKM f i t t e r 2HDM log 10 (mh +/GeV) B!" log 10 (mh +/GeV) K µ2 /! µ2 L "K2 /"! !1.0! log 10 (tan(#)) !1.0! log 10 (tan(#)) Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

41 The 4 leptonic decays : D µν and D s lν excluded area has CL > 0.95 CKM f i t t e r 2HDM excluded area has CL > 0.95 CKM f i t t e r 2HDM log 10 (mh +/GeV) log 10 (mh +/GeV) D µ! 0.5 D s l! 0.0!1.0! log 10 (tan(")) !1.0! log 10 (tan(")) Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

42 Leptonic decays combined log 10 (mh +/GeV) excluded area has CL > 0.95 All B "# K µ2 /! µ2 L "K2 /"!2 D s l# CKM f i t t e r 2HDM 0.0!1.0! log 10 (tan($)) D µ# Overlap of non-decoupling regions (an overlap of fine-tuned solutions would be much more exciting!) Leptonic D and D s decays useful to discard some of the fine-tuned solutions and to enhance the one from B τν Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

43 Leptonic decays combined log 10 (mh +/GeV) !1.0 excluded area has CL > 0.95!0.5 All log 10 (tan(!)) CKM 1.5 f i t t e r 2HDM 2.0 Overlap of non-decoupling regions (an overlap of fine-tuned solutions would be much more exciting!) Leptonic D and D s decays useful to discard some of the fine-tuned solutions and to enhance the one from B τν Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

44 Further observables and combined fit log 10 (mh +/GeV) M (X)l" excluded area has CL > !1.0! All b s#!mq L Z b b semileptonic decays, with helicity-suppr scalar terms B[B Dτν]/B[B Dlν] B[K 0 πµν]/b[k 0 πeν] b sγ (very powerful drive towards SM) Z b b and B B mixing (similar shapes) LEP all agree with SM and select large m H +, apart CKM f i t t e r 2HDM from large B[B τν] favouring fine-tuned sol at log 10 (tan($)) low m H + Limit on m H + > 316 GeV at 95% CL (LEP searches > 78.6 GeV)... but no constraint on tan β at 95%CL Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

45 Outlook Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

46 Outlook CKM mechanism unifying scheme for flavour physics D-decays should have an impact in reducing uncertainty on γ Weak part of charm decays constrained by B and K... As long as one knows strong interaction part (lattice) Two different ways of seeing the charm contribution CP-violation : D-unitarity triangle Semileptonic and leptonic decays : [V cd, V cs ] plot Progress in lattice and exp start making this CKM row relevant NP searches Only loose constraints on loop processes due to hadronic uncert Strong constraints on tree decays, in competition with B, K Useful if NP connects the different corners (e.g., 2HDM) Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

47 More CKM_FPCP10.html file:///users/descotes/documents/talks/2010/fpcp10/plots/num/ckm_fpcp10.html 5/21/10 9:55 PM Page 1 of 4 CKMfitter global fit results as of FPCP 10: Wolfenstein parameters UT angles and sides UT sangle and apex CKM elements Theory parameters Rare branching fractions (B l, B ll) Wolfenstein parameters and Jarlskog invariant: Observable Central ± 1 ± 2 ± 3 A [ ] [ ] [ ] [ ] [ ] [ ] bar [ ] [ ] [ ] bar [ ] [ ] [ ] J [10-5 ] 2.98 [ ] 2.98 [ ] 2.98 [ ] UT angles and sides: Observable Central ± 1 ± 2 ± [ sin [ ] [ ] 0.14] sin 2 (meas. not [ [ ] [ ] in the fit) ] [ sin [ ] [ ] ] sin 2 (meas. not [ [ ] [ ] in the fit) ] [ sin (2 + ) [ ] [ ] ] 90.5 [ [deg] 90.5 [ ] 90.5 [ ] 3.6] [deg] (meas. not 97.4 [ [ ] 97.4 [ ] in the fit) 9.5] [deg] (dir [ [ ] [ [+21-13] [ meas.) 4.2] -5.6] 0 [+5-0] 13.8] 0 [+12-0] [ [deg] 21.7 [ ] 21.7 [ ] 0.75] [deg] (meas. not [ [ ] 28.1 [ ] in the fit) 1.84] [deg] (dir [ [ ] 21.1 [ ] meas.) 0.88] More plots and results available on J. Charles, Theory O. Deschamps, LHCb SDG, Theory R. Itoh, Belle A. Jantsch, ATLAS H. Lacker, ATLAS A. Menzel, ATLAS S. Monteil, LHCb V. Niess, LHCb J. Ocariz, BaBar S. T Jampens, LHCb V. Tisserand, BaBar/LHCb K. Trabelsi, Belle Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

48 Back-up Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

49 Statistics : Framework q = (A, λ, ρ, η...) to be determined O exp experimental values of the observables O th (q) theoretical description in a model In case of experimental (Gaussian) uncertainties, likelihoods and χ 2 L(q) = O L O (q) χ 2 (q) = 2 ln L(q) = O ( Oth (q) O exp σ O ) 2 Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

50 Statistics : Framework q = (A, λ, ρ, η...) to be determined O exp experimental values of the observables O th (q) theoretical description in a model In case of experimental (Gaussian) uncertainties, likelihoods and χ 2 L(q) = O L O (q) χ 2 (q) = 2 ln L(q) = O ( Oth (q) O exp σ O ) 2 Estimator ˆq maximum likelood: χ 2 (ˆq) = min q χ 2 (q) Confidence level for a given q 0 (p-value for q = q 0 ) obtained from χ 2 (q 0 ) = χ 2 (q 0 ) min q χ 2 (q) (distributed like χ 2 law of dim(q)) What to do in the case of systematic uncertainties, which stand out of this picture? Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

51 Statistics : Rfit scheme : Treatment of systematics within the Rfit scheme χ 2 with flat bottom (syst) and parabolic walls (stat), and corresponding likelihood L = exp( χ 2 /2) all values within range of syst treated on the same footing Χ Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

52 V ub inclusive and exclusive Not all tensions are New Physics! Two ways of getting V ub : Inclusive : b ulν + Operator Product Expansion Exclusive : B πlν + Form factors V ub inc = ± 0.45 V ub exc = 3.51 ± 0.10 ± CKM f i t t e r FPCP 10 average excl. incl. CKM fit w/o V ub V ub ave = 3.92 ± 0.09 ± 0.45 with all values CL Vub Tension depends on statistical treatment: discrepancy solved once systematics combined in Educated Rfit same problem for V cb Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

53 V cb inclusive and exclusive V cb inc = ± 0.43 ± 0.59 V cb exc = ± 0.77 ± CL CKM f i t t e r FPCP 10 average excl. incl. CKM fit w/o V cb V cb ave = ± 0.38 ± with all values to be multiplied by 10 3 Tension depends on statistical treatment: discrepancy solved once systematics combined in Educated Rfit same problem for V ub Vcb Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

54 Selected inputs: ɛ K ɛ K defined in K ππ [dominated by I = 0 from I = 1/2 rule] η ab = A(K L π a π b ) A(K S π a π b ) ɛ K = η 00+2η + 3 ɛ K = η 00+η + 3 related to K K mixing: K S(L) = [(1 + ɛ) K 0 (1 ɛ) K 0 ]/ 1 + ɛ 2 ɛ K = ɛ + ξ = sin φ ɛ e iφɛ [ ImM12 M + ξ ] with strong-phase separation A(K 0 (ππ) I ) = A I e iδstrong I ξ = ImA 0 ReA 0 Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

55 Selected inputs: ɛ K ɛ K defined in K ππ [dominated by I = 0 from I = 1/2 rule] η ab = A(K L π a π b ) A(K S π a π b ) ɛ K = η 00+2η + 3 ɛ K = η 00+η + 3 related to K K mixing: K S(L) = [(1 + ɛ) K 0 (1 ɛ) K 0 ]/ 1 + ɛ 2 ɛ K = ɛ + ξ = sin φ ɛ e iφɛ [ ImM12 M + ξ ] with strong-phase separation A(K 0 (ππ) I ) = A I e iδstrong I ξ = ImA 0 ReA 0 ɛ K, M K from experiment, φ ɛ = arctan( 2 M/ Γ) π/4 ImM 12 from effective Hamiltonian keep only lowest-dimension contribution ImM (6) 12 top boxes ˆB K K 0 ( sd) V A ( sd) V A K 0 ɛ K C ɛ ˆBK λ 2 η 2 V cb 2 [ V cb 2 (1 ρ)η tt S 0 (x t ) + η ct S 0 (x t, x c ) η cc S 0 (x c )] Inami-Lim functions S 0 (x q = m 2 q/m 2 W ) and C ɛ normalisation Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

56 Selected inputs: κ ɛ (1) ɛ K = sin φ ɛ e iφɛ [ ImM12 M ] + ξ e iφɛ ImM (6) = κ ɛ 12 with κ ɛ 1 2 M K 1) φ ɛ = 43.5 ± (κ ɛ ) φ = 0.97 ± ) ξ = ImA 0 /ReA 0 [Buras Guadagnoli 2008,2009] ReA I from experiment (no theory for I = 1/2 rule) ImA I from H S=1 eff : ImA I y i (ππ) I Q i K with y i Wilson coefficients and Q i S = 1 operators ImA 0 (ξ) dominated by QCD penguin Q 6 0 (not known) ImA 2 dominated by electroweak penguin Q 8 2 (lattice, sum rules) ɛ /ɛ involves both ImA 0 and ImA 2 Q 6 0 = f [(ɛ /ɛ) exp, Q 8 2 ] ξ = g[ Q 6 0 ] = g [(ɛ /ɛ) exp, Q 8 2 ] (κ ɛ ) φ+ξ = ± ɛ /ɛ,φ ɛ ± Q6,Q 8 Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

57 Selected inputs: κ ɛ (2) 3) Higher-dim corr to ImM 12 [Buras Guadagnoli Isidori 2010] M 12 = K 0 H S =2 eff K 0 K 0 d 4 xre[it [H S =1 eff (x)h S =1 eff (0)]] K 0 Leading from d = 6 operator ( sd) V A ( sd) V A in H S =2 eff d = 8 corr from H S =2 eff m 2 K /m2 c-suppressed wrt d = 6 charm [2%] d = 8 corrections from two insertions of H S =1 eff s u, c d s u, c d K0 K0 K0 K0 d s d s computed using χpt for S = 1 transitions: ξ ρξ with ρ = 0.6 ± 0.3 K 0 π 0, η (η ) K 0 K 0 π K 0 (κ ɛ ) tot = ± ± slightly more conservative than BGI (0.94 ± 0.2) Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/ π

58 Selected inputs: ɛ K in global fit (1) Assume something on κ ɛ, compute ɛ K and compare with expt Use measurement of ɛ K and the global fit to study κ ɛ 1.0 CKM 0.94 ± ± f i t t e r FPCP ± 0.02 (Rfit) 0.94 ± 0.02 (Gauss) meas. 1.0 CKM 0.94 ± ± f i t t e r FPCP ± 0.02 (Rfit) 0.94 ± 0.02 (Gauss) prediction CL CL ! K (meas. not in the fit) "! = The correction κ ɛ does not spoil the quality of the global fit κ ɛ = 0.94 ± 0.02 (Gaussian) κ ɛ = 0.94 ± 0.02 (Rfit) κ ɛ = ± ± Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

59 Selected inputs: ɛ K in global fit (2) Impact of the statistical treatment of theoretical inputs on ɛ K κ ɛ and V cb, ˆB K, η ct,cc,tt, m c,t 1.0 CKM f i t t e r FPCP 10 on V, B K, #!, ", m cb cc,ct,tt c,t Gaussian uncer. Rfit uncer. meas CL ! K (meas. not in the fit) Gaussian error : 1.3 σ tension Rfit error : no tension Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

60 2HDM(II): Semileptonic decays + / GeV ] [ m H 10 Log excluded area has CL > 0.95 K#" l! B#D$! CKM f i t t e r Hints 2009 Semileptonic decays help to remove fined-tuned solutions at 95% CL B[B Dτν]/B[B Dlν] and B[K 0 πµν]/b[k 0 πeν] Log [ tan(%) ] 10 Easier to study experimentally than purely leptonic decays Sensitive to scalar contributions through helicity-suppressed terms, enhanced by mass of the charged lepton = hence comparison between τ, µ, e Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

61 2HDM(II): b sγ + / GeV ] [ m H 10 Log NNLO BR from public package SusyBSG B[ B X sγ] = Vts V tb 2 6αEM B[ B X cl ν] V cb πc (P + N), [Misiak, Gambino, Haisch... ] excluded area has CL > 0.95 CKM f i t t e r 2HDM Log [ tan(β) ] 10 b sγ P leading term in 1/m b expansion, perturbative N non-perturbative, higher orders (starting at 1/m 2 b ) P + N = (C eff,(0) 7,SM + B Ceff,(0) 7,H + ) 2 + A C eff,(0) 7,H + models H + impact, dependence on (m H +, tan β), fitted from SusyBSG NNLO SM estimate: Br(B X s γ) = (3.15 ± 0.23) 10 4 [Misiak et al.] Measurement: B(B X s γ) = (3.57 ± 0.24) 10 4 [2009 WA] Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/

62 2HDM(II): Further observables Further observables added : R b = Γ[Z b b]/γ[z hadrons] and B B mixing Charged Higgs contrib = shift in (perturbative) coeff describing decays 3.0 Δ M d + Δ M s CKM f i t t e r 2HDM / GeV ] + [ m H 10 Log R b excluded area has CL > Log [ tan(β) ] 10 Sébastien Descotes-Genon (LPT-Orsay) CKM fits and charm decays 22/10/