CKM fits and kaon decays S ebastien Descotes-Genon Laboratoire de - PowerPoint PPT Presentation

CKM fits and kaon decays S´ ebastien Descotes-Genon Laboratoire de Physique Th´ eorique CNRS & Universit´ e Paris-Sud, 91405 Orsay, France NA62 Kaon Physics Handbook Workshop 19 January 2016 LPT Orsay S. Descotes-Genon (LPT-Orsay) CKMfitter MITP15 - 19/1/16 1

CKMfitter S. Descotes-Genon (LPT-Orsay) CKMfitter MITP15 - 19/1/16 2

The CKM matrix In SM, flavour dynamics related to weak charged transitions which mix quarks of different generations  V ud V us V ub  Encoded in unitary CKM matrix V CKM = 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 us | 2 | V cb | 2 η = − V ud V ∗ λ 2 = A 2 λ 4 = ub ρ + i ¯ ¯ | V ud | 2 + | V us | 2 | V ud | 2 + | V us | 2 V cd V ∗ cb = ⇒ 4 parameters describing the CKM matrix S. Descotes-Genon (LPT-Orsay) CKMfitter MITP15 - 19/1/16 3

Extracting the CKM parameters CP -invariance of QCD to build hadronic-indep. CP -violating asym. or to determine hadronic inputs from data Statistical framework to combine data and assess uncertainties Exp. uncert. Theoretical uncertainties | V cb | vs form factor F B → D (OPE) B ( b ) → D ( c ) ℓν | V ub | vs form factor F B → π (OPE) Tree B → DK γ B ( b ) → π ( u ) ℓν | V UD | vs f M (decay cst), F M → N M → ℓν, M → N ℓν Loop B → J / Ψ K s β ǫ K ( K mix) (¯ ρ, ¯ η ) vs B K (bag parameter) | V tb V tq | vs f 2 B → ππ, ρρ α ∆ m d , ∆ m s ( B d , B s mix) B B B (bag param) S. Descotes-Genon (LPT-Orsay) CKMfitter MITP15 - 19/1/16 4

The inputs frequentist ( ≃ χ 2 minim.) + Rfit scheme for theory uncert. data = weak ⊗ QCD = ⇒ Need for hadronic inputs (mostly lattice) | V ud | superallowed β decays PRC79, 055502 (2009) | V us | K ℓ 3 f + ( 0 ) = 0 . 9645 ± 0 . 0015 ± 0 . 0045 K → ℓν, τ → K ν τ f K = 155 . 2 ± 0 . 2 ± 0 . 6 MeV | V us / V ud | K → ℓν/π → ℓν, τ → K ν τ /τ → πν τ f K / f π = 1 . 1952 ± 0 . 0007 ± 0 . 0029 ˆ ǫ K PDG B K = 0 . 7615 ± 0 . 0027 ± 0 . 0137 f D s / f D = 1 . 175 ± 0 . 001 ± 0 . 004, f D → π | V cd | D → µν , D → πℓν ( 0 ) + f D s = 248 . 2 ± 0 . 3 ± 1 . 9 MeV, f D → K | V cs | D s → µν , D s → τν , D → πℓν ( 0 ) + | V ub | · 10 3 = 4 . 01 ± 0 . 08 ± 0 . 22 | V ub | inclusive and exclusive B semileptonic | V cb | · 10 3 = 41 . 00 ± 0 . 33 ± 0 . 74 | V cb | inclusive and exclusive B semileptonic ( 1 . 24 ± 0 . 22 ) · 10 − 4 B → τν f B s / f B d = 1 . 205 ± 0 . 003 ± 0 . 006 f B s = 224 . 0 ± 1 . 0 ± 2 . 0 MeV | V ub / V cb | Λ b semileptonic decays integrals of Λ b form factors last WA B d - ¯ ∆ m d B d mixing B B s / B B d = 1 . 023 ± 0 . 013 ± 0 . 014 last WA B s - ¯ ∆ m s B s mixing B B s = 1 . 320 ± 0 . 016 ± 0 . 030 last WA J /ψ K ( ∗ ) β α last WA ππ, ρπ, ρρ isospin last WA B → D ( ∗ ) K ( ∗ ) γ GLW/ADS/GGSZ as well as m t , m c , α s ( M Z ) ! S. Descotes-Genon (LPT-Orsay) CKMfitter MITP15 - 19/1/16 5

Statistical framework q = ( A , λ, ¯ ρ, ¯ η . . . ) to be determined O meas ± σ O experimental values of observables O th ( q ) theoretical description in a given model In case of statistical uncertainties σ O , likelihoods and χ 2 � 2 � O th ( q ) − O meas � χ 2 ( q ) = − 2 ln L ( q ) = � L ( q ) = L O ( q ) σ O O O χ 2 (ˆ q ) = min q χ 2 ( q ) Central value: estimator ˆ q max likelihood: Range: confidence level for each q 0 ( p -value for q = q 0 ) by: ∆ χ 2 ( q 0 ) = χ 2 ( q 0 ) − min q χ 2 ( q ) assumed to obey χ 2 law with N = dim ( q ) to yield CIs Pull: comparison of χ 2 min with and without one measurement � min q χ 2 with meas ( q ) − min q χ 2 p O = without meas ( q ) ⇒ Specific scheme to treat theoretical uncertains (currently Rfit) = S. Descotes-Genon (LPT-Orsay) CKMfitter MITP15 - 19/1/16 6

Averaging lattice results Collecting lattice results follow FLAG to exclude limited results supplement with more recent published results with error budget Splitting error estimates into stat and syst Stat : essentially related to size of gauge conf Syst : fermion action, a → 0, L → ∞ , mass extrapolations. . . added linearly using error budget “Educated Rfit” used to combine the results no correlations assumed product of (Gaussian + Rfit) likelihoods for central value product of Gaussian (stat) likelihoods for stat uncertainty syst uncertainty of the combination = most precise method the present state of art cannot allow us to reach a better theoretical accuracy than the best of all estimates best estimate should not be penalized by less precise methods S. Descotes-Genon (LPT-Orsay) CKMfitter MITP15 - 19/1/16 7

Illustration for f K / f π Reference N f Mean Stat Syst ETMC09 2 1.210 0.006 0.024 HPQCD/UKQCD07 2+1 1.189 0.002 0.014 + 0 . 003 MILC10 2+1 1.197 0.002 − 0 . 007 BMW10 2+1 1.192 0.007 0.013 LVdW11 2+1 1.202 0.011 0.024 RBC-UKQCD12 2+1 1.1991 0.0116 0.0185 HPQCD13 2+1+1 1.1938 0.0015 0.0032 + 0 . 0033 FNAL-MILC14 2+1+1 1.1956 0.0010 − 0 . 0024 ETMC14 2+1+1 1.188 0.011 0.020 Our average 1.1952 0.0007 0.0029 Other values proposed: 1 . 194 ± 0 . 005 ( N f = 2 FLAG), 1 . 192 ± 0 . 005 ( N f = 3 FLAG). . . Results for QCD decay constants (further etm corrections in BRs) Strange for absolute reference + ratio of non-strange and strange Used for decay constants, bag parameters, form factors. . . S. Descotes-Genon (LPT-Orsay) CKMfitter MITP15 - 19/1/16 8

Two decades of CKM [LEP , KTeV, NA48, Babar, Belle, CDF, DØ, LHCb, CMS. . . ] 1.5 1.5 1.5 excluded area has CL > 0.95 excluded area has CL > 0.95 excluded area has CL > 0.95 � m � m d � m 1.0 d 1.0 1.0 m & m d � � d s � m & � m m & m s sin 2 � � � sin 2 � d d s 0.5 0.5 0.5 � � � � K � � K K � � � � � � � � � 0.0 0.0 0.0 V V ub V ub ub -0.5 -0.5 -0.5 � � � -1.0 -1.0 -1.0 K � CKM CKM CKM K f i t t e r f i t t e r f i t t e r 1995 Summer 2001 2004 � K -1.5 -1.5 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 � � � 1995 2001 2004 1.5 1.5 1.5 excluded at CL > 0.95 excluded at CL > 0.95 excluded at CL > 0.95 excluded area has CL > 0.95 excluded area has CL > 0.95 excluded area has CL > 0.95 � � γ 1.0 1.0 1.0 m m & m m � m & � m ∆ m & ∆ m � � � � s d d s d d s d sin 2 � sin 2 � sin 2 β 0.5 0.5 0.5 ∆ m d � � ε � � α K K K � � � � � � η γ β 0.0 0.0 0.0 α � � V V V α ub ub ub � � -0.5 -0.5 -0.5 ε � � γ -1.0 -1.0 -1.0 K K K CKM CKM CKM � sol. w/ cos 2 � < 0 � sol. w/ cos 2 � < 0 sol. w/ cos 2 β < 0 f i t t e r f i t t e r f i t t e r 2006 (excl. at CL > 0.95) 2009 (excl. at CL > 0.95) EPS 15 (excl. at CL > 0.95) -1.5 -1.5 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 � � ρ 2006 2009 2015 S. Descotes-Genon (LPT-Orsay) CKMfitter MITP15 - 19/1/16 9

EPS-HEP 2015 | V ud | , | V us | 1.5 excluded at CL > 0.95 excluded area has CL > 0.95 | V cb | , | V ub | SL γ B → τν 1.0 ∆ m & ∆ m s d | V ub / V cb | Λ b sin 2 β ∆ m d , ∆ m s 0.5 ∆ m ǫ K d ε α K sin 2 β γ β η 0.0 α α V ub V Λ b ub SL γ α V ub τ ν -0.5 A = 0 . 823 + 0 . 007 ε − 0 . 014 γ K -1.0 λ = 0 . 2254 + 0 . 0004 CKM − 0 . 0003 sol. w/ cos 2 β < 0 f i t t e r ρ = 0 . 150 + 0 . 012 ¯ EPS 15 (excl. at CL > 0.95) − 0 . 006 -1.5 η = 0 . 354 + 0 . 007 ¯ -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 − 0 . 008 ρ (68% CL) S. Descotes-Genon (LPT-Orsay) CKMfitter MITP15 - 19/1/16 10

Pulls Pulls for various observables B → µ µ 0.91 s φ 0.65 s (included in the fit or not) γ 0.91 α 0.84 sin 2 β 1.66 For 1D, pull obs = ε 0.05 K ∆ m 1.21 s � χ 2 min ; with obs − χ 2 ∆ m 1.29 d B(B → τ ν ) 1.22 min ; w / o obs |V | 0.89 ub semilep |V | 0.88 If Gaussian errors, cb semilep B(D → µ ν ) 1.83 B(D → µ ν ) 1.08 s uncorrelated, random vars of B(D → τ ν ) 1.64 s B(D → Kl ν ) 0.01 B(D → π l ν ) mean 0 and variance 1 0.04 |V | 0.00 cs not lattice |V | 0.43 cd not lattice Here correlations, and some B( τ ) 2.22 K2 B(K ) 0.03 µ 2 B(K ) 1.44 pulls = 0 due to the Rfit model e2 B(K ) 0.00 e3 |V | 0.04 ud for syst 0 0.5 1 1.5 2 2.5 3 3.5 Pull ( σ ) No indication of significant deviations from CKM picture S. Descotes-Genon (LPT-Orsay) CKMfitter MITP15 - 19/1/16 11

Leptonic and semileptonic decays S. Descotes-Genon (LPT-Orsay) CKMfitter MITP15 - 19/1/16 12