CKMfitter keynote (well, beamer. . . ) talk S ebastien - PowerPoint PPT Presentation

CKMfitter keynote (well, beamer. . . ) talk S´ ebastien Descotes-Genon Laboratoire de Physique Th´ eorique CNRS & Universit´ e Paris-Sud, 91405 Orsay, France Fundamental parameters from Lattice QCD 31 August 2015 LPT Orsay S. Descotes-Genon (LPT-Orsay) CKMfitter MITP15 - 31/8/15 1

The name of the game S. Descotes-Genon (LPT-Orsay) CKMfitter MITP15 - 31/8/15 2

Why flavour ? L SM = L gauge ( A a , Ψ j ) + L Higgs ( φ, A a , Ψ j ) Gauge part L gauge ( A a , Ψ j ) Highly symmetric (gauge symmetry, flavour symmetry) Well-tested experimentally (electroweak precision tests) Stable with respect to quantum corrections Higgs part L Higgs ( φ, A a , Ψ j ) Ad hoc potential Dynamics not fully tested (more room for NP) Not stable w.r.t quantum corrections Origin of flavour structure of the Standard Model Flavour structure: Quark masses and CKM matrix from diagonalisation of Yukawa couplings after EWSB S. Descotes-Genon (LPT-Orsay) CKMfitter MITP15 - 31/8/15 3

Quark flavours, SM and NP γ g W Z Gauge φ Higgs Fermions ν e ud μ s c τ b t NP? i Important, unexplained hierarchy among 10 of 19 params of SM m ν = 0 Mass (6 params, a lot of small ratios of scales) CP violation (4 params, strong hierarchy between generations) With interesting phenomenological consequences Hierarchy of CP asymmetries according to generations Quantum sensitivity (via loops) to large range of scales GIM suppression of Flavour-Changing Neutral Currents Potential to unravel patterns of deviations from NP (in a time where direct searches have not succeeded) S. Descotes-Genon (LPT-Orsay) CKMfitter MITP15 - 31/8/15 4

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 - 31/8/15 5

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 B ( b ) → D ( c ) ℓν | V cb | vs form factor (OPE) Tree B → DK γ B ( b ) → π ( u ) ℓν | V ub | vs form factor (OPE) M → ℓν | V UD | vs f M (decay cst) Loop B → J / Ψ K s β ǫ K ( K mixing) (¯ 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 mixings) B B B (bag param) S. Descotes-Genon (LPT-Orsay) CKMfitter MITP15 - 31/8/15 6

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 (Flavianet) 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 - 31/8/15 7

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 ) S. Descotes-Genon (LPT-Orsay) CKMfitter MITP15 - 31/8/15 8

Rfit scheme : Treatment of systematics within the Rfit scheme modify likelihood L = exp ( − χ 2 / 2 ) to get a χ 2 with flat bottom (syst) and parabolic walls (stat) all values within range of syst treated on the same footing Χ 2 8 6 4 2 � 5 5 [More in J´ erˆ ome Charles’ talk on Wednesday] S. Descotes-Genon (LPT-Orsay) CKMfitter MITP15 - 31/8/15 9

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 - 31/8/15 10

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 corrections in BRs) Used for decay constants, bag parameters, form factors. . . Some assumptions on correlations for B B s and B B d / B B s since √ some collaborations quote only f B B S. Descotes-Genon (LPT-Orsay) CKMfitter MITP15 - 31/8/15 11

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 - 31/8/15 12

Where we are now S. Descotes-Genon (LPT-Orsay) CKMfitter MITP15 - 31/8/15 13