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

SLIDE 1

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

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CKMfitter

S. Descotes-Genon (LPT-Orsay)

CKMfitter MITP15 - 19/1/16 2

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The CKM matrix

In SM, flavour dynamics related to weak charged transitions which mix quarks of different generations Encoded in unitary CKM matrix VCKM =   Vud Vus Vub Vcd Vcs Vcb Vtd Vts Vtb   3 generations = ⇒ 1 phase, only source of CP-violation in SM Wolfenstein parametrisation, defined to hold to all orders in λ and rephasing invariant λ2 = |Vus|2 |Vud|2 + |Vus|2 A2λ4 = |Vcb|2 |Vud|2 + |Vus|2 ¯ ρ + i ¯ η = −VudV ∗

ub

VcdV ∗

cb

= ⇒ 4 parameters describing the CKM matrix

S. Descotes-Genon (LPT-Orsay)

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Extracting the CKM parameters

CP-invariance of QCD to build hadronic-indep. CP-violating asym.

r to determine hadronic inputs from data

Statistical framework to combine data and assess uncertainties

Exp. uncert.

Theoretical uncertainties B(b) → D(c)ℓν |Vcb| vs form factor F B→D (OPE) Tree B → DK γ B(b) → π(u)ℓν |Vub| vs form factor F B→π (OPE) M → ℓν, M → Nℓν |VUD| vs fM (decay cst), F M→N Loop B → J/ΨKs β ǫK (K mix) (¯ ρ, ¯ η) vs BK (bag parameter) B → ππ, ρρ α ∆md, ∆ms (Bd, Bs mix) |VtbVtq| vs f 2

BBB (bag param)

S. Descotes-Genon (LPT-Orsay)

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The inputs

frequentist (≃ χ2 minim.) + Rfit scheme for theory uncert. data = weak ⊗ QCD = ⇒Need for hadronic inputs (mostly lattice)

+

(0) |Vcs| Ds → µν, Ds → τν, D → πℓν fDs = 248.2 ± 0.3 ± 1.9 MeV, f D→K

+

(0) |Vub| inclusive and exclusive B semileptonic |Vub| · 103 = 4.01 ± 0.08 ± 0.22 |Vcb| inclusive and exclusive B semileptonic |Vcb| · 103 = 41.00 ± 0.33 ± 0.74 B → τν (1.24 ± 0.22) · 10−4 fBs/fBd = 1.205 ± 0.003 ± 0.006 fBs = 224.0 ± 1.0 ± 2.0 MeV |Vub/Vcb| Λb semileptonic decays integrals of Λb form factors ∆md last WA Bd-¯ Bd mixing BBs/BBd = 1.023 ± 0.013 ± 0.014 ∆ms last WA Bs-¯ Bs mixing BBs = 1.320 ± 0.016 ± 0.030 β last WA J/ψK (∗) α last WA ππ, ρπ, ρρ isospin γ last WA B → D(∗)K (∗) GLW/ADS/GGSZ as well as mt, mc, αs(MZ ) !

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Statistical framework

q = (A, λ, ¯ ρ, ¯ η . . .) to be determined Omeas ± σO experimental values of observables Oth(q) theoretical description in a given model In case of statistical uncertainties σO, likelihoods and χ2 L(q) =

O

LO(q) χ2(q) = −2 ln L(q) =

O

Oth(q) − Omeas σO 2 Central value: estimator ˆ q max likelihood: χ2(ˆ q) = minq χ2(q) Range: confidence level for each q0 (p-value for q = q0) by: ∆χ2(q0) = χ2(q0) − min

q χ2(q)

assumed to obey χ2 law with N = dim(q) to yield CIs Pull: comparison of χ2

min with and without one measurement

pO =

minq χ2

with meas(q) − minq χ2 without meas(q)

= ⇒Specific scheme to treat theoretical uncertains (currently Rfit)

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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)

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Illustration for fK/fπ

Reference Nf Mean Stat Syst ETMC09 2 1.210 0.006 0.024 HPQCD/UKQCD07 2+1 1.189 0.002 0.014 MILC10 2+1 1.197 0.002

+0.003 −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 FNAL-MILC14 2+1+1 1.1956 0.0010

+0.0033 −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 (Nf = 2 FLAG), 1.192 ± 0.005 (Nf = 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. . .

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Two decades of CKM

[LEP , KTeV, NA48, Babar, Belle, CDF, DØ, LHCb, CMS. . . ]

d

m

K
K
s

m

&

d

m

ub

V

1.0
0.5

0.0 0.5 1.0 1.5 2.0

1.5
1.0
0.5

0.0 0.5 1.0 1.5

excluded area has CL > 0.95 1995

CKM

f i t t e r d

m

K
K
s

m

&

d

m

ub

V

sin 2
1.0
0.5

0.0 0.5 1.0 1.5 2.0

1.5
1.0
0.5

0.0 0.5 1.0 1.5

excluded area has CL > 0.95 Summer 2001

CKM

f i t t e r

d

m

K
K
s

m

&

d

m

ub

V

sin 2
1.0
0.5

0.0 0.5 1.0 1.5 2.0

1.5
1.0
0.5

0.0 0.5 1.0 1.5

excluded area has CL > 0.95 2004

CKM

f i t t e r

1995 2001 2004

d

m

K
K
s

m

&

d

m

ub

V

sin 2

(excl. at CL > 0.95) < 0

sol. w/ cos 2

excluded at CL > 0.95

1.0
0.5

0.0 0.5 1.0 1.5 2.0

1.5
1.0
0.5

0.0 0.5 1.0 1.5

excluded area has CL > 0.95 2006

CKM

f i t t e r

d

m

K
K
s

m

&

d

m

ub

V

sin 2

(excl. at CL > 0.95) < 0

sol. w/ cos 2

excluded at CL > 0.95

1.0
0.5

0.0 0.5 1.0 1.5 2.0

1.5
1.0
0.5

0.0 0.5 1.0 1.5

excluded area has CL > 0.95 2009

CKM

f i t t e r

γ γ α α

d

m ∆

K

ε

K

ε

s

m ∆ &

d

m ∆

ub

V β sin 2

(excl. at CL > 0.95) < 0 β

sol. w/ cos 2

excluded at CL > 0.95 α β γ

ρ

1.0
0.5

0.0 0.5 1.0 1.5 2.0

η

1.5
1.0
0.5

0.0 0.5 1.0 1.5

excluded area has CL > 0.95 EPS 15

CKM

f i t t e r

2006 2009 2015

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SLIDE 10

EPS-HEP 2015

γ γ α α

d

m ∆

K

ε

K

ε

s

m ∆ &

d

m ∆

SL ub

V

ν τ ub

V

b

Λ ub

V

β sin 2

(excl. at CL > 0.95) < 0 β

sol. w/ cos 2

excluded at CL > 0.95

α β γ

ρ

1.0
0.5

0.0 0.5 1.0 1.5 2.0

η

1.5
1.0
0.5

0.0 0.5 1.0 1.5

excluded area has CL > 0.95 EPS 15

CKM

f i t t e r

|Vud|, |Vus| |Vcb|, |Vub|SL B → τν |Vub/Vcb|Λb ∆md, ∆ms ǫK sin 2β α γ A = 0.823+0.007

−0.014

λ = 0.2254+0.0004

−0.0003

¯ ρ = 0.150+0.012

−0.006

¯ η = 0.354+0.007

−0.008

(68% CL)

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Pulls

) σ Pull (

|

ud

|V

0.04

)

e3

B(K

0.00

)

e2

B(K

1.44

)

2 µ

B(K

0.03

)

K2

τ B(

2.22

not lattice

|

cd

|V

0.43

not lattice

|

cs

|V

0.00

) ν l π → B(D

0.04

) ν Kl → B(D

0.01

) ν τ →

s

B(D

1.64

) ν µ →

s

B(D

1.08

) ν µ → B(D

1.83

semilep

|

cb

|V

0.88

semilep

|

ub

|V

0.89

) ν τ → B(B

1.22

d

m ∆

1.29

s

m ∆

1.21

K

ε

0.05

β sin 2

1.66

α

0.84

γ

0.91

s

φ

0.65

µ µ →

s

B

0.91

0.5 1 1.5 2 2.5 3 3.5

Pulls for various observables (included in the fit or not) For 1D, pull obs =

χ2

min; with obs − χ2 min; w/o obs

If Gaussian errors, uncorrelated, random vars of mean 0 and variance 1 Here correlations, and some pulls = 0 due to the Rfit model for syst No indication of significant deviations from CKM picture

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Leptonic and semileptonic decays

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Leptonic and semileptonic kaon decays

Two type of constraints in the global fit from kaons tree-level decays: leptonic and semileptonic decays kaon mixing

|Vus|f K→π

+

(0) 0.21664 ± 0.00048

[PDG]

Br(K − → e−¯ νe) (1.581 ± 0.008) × 10−5

[PDG]

Br(K − → µ−¯ νµ) 0.6355 ± 0.0011

[PDG]

Br(τ − → K −¯ ντ) (0.6955 ± 0.0096) × 10−2

[HFAG]

Br(K − → µ−¯ νµ)/Br(π− → µ−¯ νµ) 1.3365 ± 0.0032

[PDG]

Br(τ − → K −¯ ντ)/Br(τ − → π−¯ ντ) (6.43 ± 0.09) × 10−2

[HFAG]

f K→π

+

(0) 0.9645 ± 0.0015 ± 0.0045

[our average]

fK (155.2 ± 0.2 ± 0.6) MeV

[our average]

fK/fπ 1.1952 ± 0.0007 ± 0.0029

[our average]

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|Vud| and |Vus|

Indirect ν π

>

τ / ν

>K

τ and

l2

π /

l2

K decays β ν

>K

τ and

l2

K

l3

K Direct (light green) All (yellow)

|

ud

|V

0.950 0.955 0.960 0.965 0.970 0.975 0.980 0.985 0.990

|

us

|V

0.210 0.215 0.220 0.225 0.230 excluded area has CL > 0.95

EPS 15

CKM

f i t t e r

“Direct” (semi- and leptonic) vs “indirect” (other sectors) (|Vud|, |Vus|): nuclear β + leptonic K, π and τ decays Same level of accuracy for exp and lattice inputs

Leptonic Semilep |Vus| |Vus/Vud| |Vus| Exp 0.1% 0.1% 0.2% Lattice 0.4% 0.3% 0.5%

|Vud| from superallowed β decays is 10 times more

accurate. . .
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Radiative corrections for K → eν, K → µν, τ → Kν

[Marciano-Sirlin, Decker-Finkemeier, Cirigliano-Rosell]

B = B0×short − dist. ew corr×long − dist. ew corr×struct − dep.corr

Short. dist. expressing W exchanges in terms of GF [universal]
Long. dist. using a point-like meson [universal]
Struct. dep. probing the structure of the meson [process-dep.]

B(K → ℓν) = G2

F|Vus|2

8π f 2

KmKm2 ℓ

1 − m2

ℓ

M2

K

2 1 + 2α π log MZ Mρ

1 + α

π F(mℓ/mK)

(1 + O(α))

B(τ → Kντ) = G2

F|Vus|2

16π f 2

KmKm2 ℓ

1 − m2

K

M2

τ

2 1 + 2α π log MZ Mτ

1 + α

π G(mK/mτ)

(1 + O(α))
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The importance of radiative corrections

Comparing the indirect fit results with the measurement for Br(K → ℓν) = ⇒Good test of radiative corrections and lattice QCD !

5

) 10

e

ν e → BR(K

1.50 1.55 1.60 1.65 1.70

)

µ

ν µ → BR(K

0.620 0.625 0.630 0.635 0.640 0.645 0.650

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 p-value

EPS 15

CKM

f i t t e r

No radiative corrections

5

) 10

e

ν e → BR(K

1.50 1.55 1.60 1.65 1.70

)

µ

ν µ → BR(K

0.620 0.625 0.630 0.635 0.640 0.645 0.650

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 p-value

EPS 15

CKM

f i t t e r

Radiative corrections NB: Struct-dep corr not incuded but much smaller than the two others

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. . . but not in all cases

Ratios of K and π leptonic decays into µ or τ less sensitivity to the issue (part of radiative corrections cancel + heavy leptons)

) ν µ → π )/BR( ν µ → BR(K

1.30 1.32 1.34 1.36 1.38 1.40

) ν π → τ )/BR( ν K → τ BR(

0.060 0.062 0.064 0.066 0.068 0.070

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 p-value

EPS 15

CKM

f i t t e r

No radiative corrections

) ν µ → π )/BR( ν µ → BR(K

1.30 1.32 1.34 1.36 1.38 1.40

) ν π → τ )/BR( ν K → τ BR(

0.060 0.062 0.064 0.066 0.068 0.070

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 p-value

EPS 15

CKM

f i t t e r

Radiative corrections Radiative corrections needed in the global fit to get a decent fit χ2

min = 58 (naive p-value 0.002%) → χ2 min = 20 (naive p-value 49.3%)

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Kaon mixing

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ǫK

Two type of constraints in the global fit from kaons tree-level decays kaon mixing: ǫK

|ǫK| = κǫCǫ ˆ BK[Im[(VtsV ∗

td)2]ηttS(xt) + 2Im[(VcsV ∗ cdVtsV ∗ td)]ηctS(xc, xt)

+Im[(VcsV ∗

cd)2]ηccS(xc)]

Inami-Lim S0(xq = m2

x/m2 W)

Cǫ normalisation κǫ correcting factor (determination of Q6, higher order OPE)

|ǫK| (2.228 ± 0.011) × 10−3 PDG BK 0.7615 ± 0.0027 ± 0.0137

[our average]

ηcc 1.87 ± 0 ± 0.76

[Brod-Gorbahn]

ηct 0.497 ± 0 ± 0.047

[Brod-Gorbahn]

ηtt 0.5765 ± 0 ± 0.0065

[Nierste]

κǫ 0.940 ± 0.013 ± 0.023

[Buras, Guadagnoli, Isidori]

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ǫK

From time to time, issues with the compatibility of ǫK with the rest of the fit, related to the fact that ǫK has a strong dependence on BK : role of theoretical uncertainties |Vcb|: inclusive, exclusive or average

|

K

∈ |

0.0010 0.0015 0.0020 0.0025 0.0030 0.0035

p-value

0.0 0.2 0.4 0.6 0.8 1.0

EPS 15

CKM

f i t t e r

Gaussian Rfit Experiment

Rfit versus Gaussian treatment of theoretical uncertainties agreement of prediction with experiment in both cases

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|Vcb| from semileptonic B decays

Two ways of getting |Vcb|: Inclusive : b → cℓν + OPE for moments

[HFAG, Gambino and Schwanda]

Exclusive : B → D(∗)ℓν + Form factors

[J. A. Bailey et al., Fermilab-MILC]

|Vcb|inc = 42.42 ± 0.44 ± 0.74 |Vcb|exc = 38.99 ± 0.49 ± 1.17 |Vcb|ave = 41.00 ± 0.33 ± 0.74 with all values ×10−3 HFAG, with theory errors added linearly systematics combined using Educated Rfit

|

cb

|V

0.036 0.037 0.038 0.039 0.040 0.041 0.042 0.043 0.044 0.045 0.046

p-value

0.0 0.2 0.4 0.6 0.8 1.0

EPS 15

CKM

f i t t e r

semilept. aver.

excl. incl. |

cb

w/o |V

Indirect det. from global fit: |Vcb|fit = 43.0+0.4

−1.4 (4%)

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Exclusive versus inclusive for ǫK

|

K

∈ |

0.0010 0.0015 0.0020 0.0025 0.0030 0.0035

p-value

0.0 0.2 0.4 0.6 0.8 1.0

EPS 15

CKM

f i t t e r

excl

xb

V excl gauss

xb

V combined

xb

V Experiment

|Vxb| exclusive only

|

K

∈ |

0.0010 0.0015 0.0020 0.0025 0.0030 0.0035

p-value

0.0 0.2 0.4 0.6 0.8 1.0

EPS 15

CKM

f i t t e r

incl

xb

V incl gauss

xb

V combined

xb

V Experiment

|Vxb| inclusive only Exclusive slightly off compared to inclusive But good agreement in all cases

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ǫK at NNLO

QCD short-distance corrections computed up to NNLO ηtt: 0.5765 ± 0.0065 → 0.5765 ± 0.0065

[Buras, Jamin, Weisz]

ηct: 0.47 ± 0.04 → 0.496 ± 0.047

[Brod, Gorbahn]

ηcc: (1.46 ± δcc)

ˆ 1 − 1.2 `

¯ mc 1.25 GeV

´˜ [1 + 52(αs(MZ) − 0.118)] , δcc ≃ 0.22

→ 1.87 ± 0.76

[Brod, Gorbahn]

d

m

K
K
s

m

&

d

m

ub

V

sin 2

(excl. at CL > 0.95) < 0

sol. w/ cos 2

e x c l u d e d a t C L > . 9 5

1.0
0.5

0.0 0.5 1.0 1.5 2.0

1.5
1.0
0.5

0.0 0.5 1.0 1.5

excluded area has CL > 0.95 Summer 12

CKM

f i t t e r

η at NLO (Rfit)

d

m

K
K
s

m

&

d

m

ub

V

sin 2

(excl. at CL > 0.95) < 0

sol. w/ cos 2

e x c l u d e d a t C L > . 9 5

1.0
0.5

0.0 0.5 1.0 1.5 2.0

1.5
1.0
0.5

0.0 0.5 1.0 1.5

excluded area has CL > 0.95 Summer 12

CKM

f i t t e r

η at NNLO (Rfit)

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The role of lattice inputs

Compare input and fit result (without including the inputs) Fit results consistent, but not always competitive in accuracy, with lattice results

Input Fit [input not included] fK 155.2 ± 0.2 ± 0.6 (0.4%) 156.5+0.1

−0.8

(0.3%) fK/fπ 1.194 ± 0.001 ± 0.003 (0.3%) 1.191+0.006

−0.003

(0.4%) f K→π

+

(0) 0.9645 ± 0.0015 ± 0.0045 (0.5%) 0.9594+0.0024

−0.0029

(0.3%) ˆ BK 0.762 ± 0.003 ± 0.014 (1.9%) 0.70+0.28

−0.05

(24%)

Similarly for κǫ, we have

Input Fit [input not included] κǫ 0.940 ± 0.013 ± 0.023 (2.8%) 0.875+0.317

−0.069

(22%)

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SLIDE 25

K → πν¯ ν

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K → πν¯ ν

B[K + → π+ν¯ ν]SM = κ+ (1 + ∆em) "„Imλt λ5 Xt «2 + „Reλc λ (Pc + δPc,u) + Reλt λ5 Xt «2# B[KL → π0ν¯ ν]SM = κL „Imλt λ5 Xt «2 ,

[Buras et al.; Brod, Gorbahn; Mescia, Smith]

isospin-breaking parameter κ+,L from semileptonic K decays ∆em electromagnetic correction, Xt top-quark contributions, Pc and δPc,u light-quark contributions

) ν ν

+

π →

+

BR(K ×

10

1 2 3 4 5 6

p-value

0.0 0.2 0.4 0.6 0.8 1.0

EPS 15

CKM

f i t t e r

E787+E949 ν ν

+

π →

+

CKM prediction for K

Br(K + → π+ν¯ ν) = (0.89+0.09

−0.10) × 10−10

) ν ν π →

L

BR(K ×

10

0.0 0.1 0.2 0.3 0.4 0.5 0.6

p-value

0.0 0.2 0.4 0.6 0.8 1.0

EPS 15

CKM

f i t t e r

ν ν π →

L

CKM prediction for K

Br(KL → π0ν¯ ν) = (0.31+0.02

−0.02) × 10−10

S. Descotes-Genon (LPT-Orsay)

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SLIDE 27

Prospective

NA62 : Br(K + → π+ν¯ ν) at 10% accuracy KOTO : Phase 1 ∼ 3σ constraint on the branching ratio (SM), Phase 2 stage with Br(KL → π0ν¯ ν) at 10% accuracy

(NA62) ν ν

+

π →

+

K

Phase 1 Phase 2

(KOTO) ν ν π →

L

K

(th. uncertainty)

α β γ

ρ

1.0 − 0.5 − 0.0 0.5 1.0 1.5 2.0

η

1.5 − 1.0 − 0.5 − 0.0 0.5 1.0 1.5

excluded area has CL > 0.95 EPS 15

CKM

f i t t e r

Prospective study on rare Kaons

NA62: in grey the role played by theoretical uncertainties KOTO : phases 1 and 2 indicated

S. Descotes-Genon (LPT-Orsay)

CKMfitter MITP15 - 19/1/16 27

SLIDE 28

More information

More on http://ckmfitter.in2p3.fr

J. Charles, Theory
O. Deschamps, LHCb

SDG, Theory

H. Lacker, ATLAS/BaBar
A. Menzel, ATLAS
S. Monteil, LHCb
V. Niess, LHCb
J. Ocariz, ATLAS/BaBar
J. Orloff, Theory
A. Perez, Babar
W. Qian, LHCb
V. Tisserand, BaBar/LHCb
K. Trabelsi, Belle/LHCb

P . Urquijo, Belle/Belle II

L. Vale Silva, Theory
S. Descotes-Genon (LPT-Orsay)

CKMfitter MITP15 - 19/1/16 28

SLIDE 29

Spares

S. Descotes-Genon (LPT-Orsay)

CKMfitter MITP15 - 19/1/16 29

SLIDE 30

Rfit scheme

: Treatment of systematics within the Rfit scheme modify likelihood L = exp(−χ2/2) to get a χ2 with flat bottom (syst) and parabolic walls (stat) all values within range of syst treated on the same footing

5 5 2 4 6 8 Χ2

S. Descotes-Genon (LPT-Orsay)

CKMfitter MITP15 - 19/1/16 30

SLIDE 31

|Vub| from semileptonic B decays

Two ways of getting |Vub|: Inclusive : b → uℓν + Operator Product Expansion

[HFAG BLNP]

Exclusive : B → πℓν + Form factors

[J. A. Bailey et al., Fermilab-MILC]

|Vub|inc = 4.45 ± 0.18 ± 0.31 |Vub|exc = 3.72 ± 0.09 ± 0.22 |Vub|ave = 4.01 ± 0.08 ± 0.22 with all values ×10−3 HFAG, with theory errors added linearly systematics combined using Educated Rfit

|

ub

|V

0.0025 0.0030 0.0035 0.0040 0.0045 0.0050 0.0055

p-value

0.0 0.2 0.4 0.6 0.8 1.0

EPS 15

CKM

f i t t e r

semilept. aver.

excl. incl. |

ub

w/o |V

Indirect det. from global fit: |Vub|fit = 3.57+0.15

−0.14 (4%)

S. Descotes-Genon (LPT-Orsay)

CKMfitter MITP15 - 19/1/16 31

SLIDE 32

|Vub|, |Vcb|

SL,excl cb

V

SL,incl cb

V SL cb

V

b

Λ cb

V /

ub

V

SL,excl ub

V

SL,incl ub

V SL ub

V

|

cb

|V

0.032 0.034 0.036 0.038 0.040 0.042 0.044 0.046 0.048

|

ub

|V

0.0020 0.0025 0.0030 0.0035 0.0040 0.0045 0.0050 0.0055 0.0060

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

p-value

excluded area has CL > 0.95

EPS 15

CKM

f i t t e r

Information on |Vub| from Br(B → τν) New LHCb result on |Vub/Vcb| from Γ(Λb → pµν)/ Γ(Λb → Λcµν) at high q2

[Detmold, Lehner and Meinel]

Global fit favours exclusive |Vub|SL but inclusive |Vcb|SL

S. Descotes-Genon (LPT-Orsay)

CKMfitter MITP15 - 19/1/16 32

SLIDE 33

From 2014 to 2015

γ α α

d

m ∆

K

ε

K

ε

s

m ∆ &

d

m ∆

SL ub

V β sin 2

(excl. at CL > 0.95) < 0 β

sol. w/ cos 2

ν τ ub

V

α β γ

ρ

0.4
0.2

0.0 0.2 0.4 0.6 0.8 1.0

η

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

excluded area has CL > 0.95 Winter 14

CKM

f i t t e r

γ α α

d

m ∆

K

ε

s

m ∆ &

d

m ∆

SL ub

V

ν τ ub

V

b

Λ ub

V β sin 2

(excl. at CL > 0.95) < 0 β

sol. w/ cos 2

α β γ

ρ

0.4
0.2

0.0 0.2 0.4 0.6 0.8 1.0

η

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

excluded area has CL > 0.95 EPS 15

CKM

f i t t e r

β sin 2

0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 SL

|

ub

|V

0.0025 0.0030 0.0035 0.0040 0.0045 0.0050

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 p-value

EPS 15

CKM

f i t t e r

Increase in the average used as input for |Vub|SL slight tension between |Vub|SL and sin(2β) (1.5 σ for 2D hyp) reducing uncertainty on CKM params (mostly ¯ η)

S. Descotes-Genon (LPT-Orsay)

CKMfitter MITP15 - 19/1/16 33

SLIDE 34

Consistency of the KM mechanism

d

m ∆

s

m ∆ &

d

m ∆

ub

V

α β γ

ρ

0.4
0.2

0.0 0.2 0.4 0.6 0.8 1.0

η

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 excluded area has CL > 0.95

EPS 15

CKM

f i t t e r

γ α α

K

ε β sin 2

(excl. at CL > 0.95) < 0 β

sol. w/ cos 2

α β γ

ρ

0.4
0.2

0.0 0.2 0.4 0.6 0.8 1.0

η

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 excluded area has CL > 0.95

EPS 15

CKM

f i t t e r

CP-allowed only CP-violating only

) α ( γ

ub

V

α β γ

ρ

0.4
0.2

0.0 0.2 0.4 0.6 0.8 1.0

η

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 excluded area has CL > 0.95

EPS 15

CKM

f i t t e r d

m ∆

K

ε

s

m ∆ &

d

m ∆ β sin 2

(excl. at CL > 0.95) < 0 β

sol. w/ cos 2

α β γ

ρ

0.4
0.2

0.0 0.2 0.4 0.6 0.8 1.0

η

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 excluded area has CL > 0.95

EPS 15

CKM

f i t t e r

Tree only Loop only Validity of Kobayashi-Maskawa picture of CP violation

S. Descotes-Genon (LPT-Orsay)

CKMfitter MITP15 - 19/1/16 34