[PPT] - CKM fits and nonleptonic decays S ebastien Descotes-Genon PowerPoint Presentation

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CKM fits and nonleptonic decays

S´ ebastien Descotes-Genon

Laboratoire de Physique Th´ eorique CNRS & Univ. Paris-Sud, Universit´ e Paris-Saclay, Orsay, France

Physikzentrum Bad Honnef, 8 February 2016

LPT Orsay

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 1

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CKMfitter

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 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)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 3

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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 Hadronic part treated as nuisance parameters

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 (∗) no penguin pollution α last WA ππ, ρπ, ρρ isospin γ last WA B → D(∗)K (∗) GLW/ADS/GGSZ as well as inputs on 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)

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 6

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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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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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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

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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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Nonleptonic decays in the global fit

Relevant constraints for the global fit Good experimental accuracy Hadronic contributions from experiment (CP-conjugate processes, flavour symmetries) or simple well-controlled theoretical inputs

γ α α β

β

α β γ

ρ η

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Nonleptonic decays in the global fit

Relevant constraints for the global fit Good experimental accuracy Hadronic contributions from experiment (CP-conjugate processes, flavour symmetries) or simple well-controlled theoretical inputs

γ α α 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

Nonleptonic B decays used for angles of the unitarity triangle γ from B → DK (several modes, charm input, Dalitz model) α from B → ππ (exploiting isospin relations) β from B → J/ψK (neglected penguin contribs) getting info on nuisance params. (i.e., hadronic params) along the way

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γ

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γ in B → DK

γ angle from interference between B− → D0K − and B− → ¯ D0K − colour allowed VcbV ∗

us ∼ Aλ3

colour suppressed VubV ∗

cs ∼ Aλ3(ρ − iη)

Sensitivity depending on size of hadronic ratio rBeiδB = Asupp Afav rB ∼

VubV ∗

cs

VcbV ∗

us

× 1/Nc ∼ 0.1 − 0.2

GLW: D into CP eigenstates (KK, ππ, KSπ0, KSω, KSφ) ADS: D(∗) into doubly Cabibbo suppressed states GGSZ: D(∗) into 3-body state and analysis

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GGSZ: D0, ¯ D0 → KSπ+π−

GGSZ: Dalitz amplitude: function of m2

+ = sKsπ+ and m2 − = sKSπ−

¯ D0 → KSπ+π− ∼ f(m2

+, m2 −)

D0 → KSπ+π− ∼ f(m2

−, m2 +)

B+ → (KSπ+π−)DK + : f(m2

+, m2 −) + rBei(δB+γ)f(m2 −, m2 +)

B− → (KSπ+π−)DK − : f(m2

−, m2 +) + rBei(δB−γ)f(m2 +, m2 −)

= ⇒simultaneous fit of γ, rB, δB + function f (model dependence)

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ADS and GLW

ADS: interf in rare B− → [K +π−]DK − normalised to common rate Colour suppressed + Cabibbo favoured VcsV ∗

ud

Colour allowed + Cabibbo suppressed VcdV ∗

us

RDK = Γ([K +π−]K −) + Γ([K −π+]K +) Γ([K −π+]K −) + Γ([K +π−]K +) = r 2

B + r 2 D + 2rBrD cos(δB + δD) cos γ

ADK = Γ([K +π−]K −) − Γ([K −π+]K +) Γ([K −π+]K −) + Γ([K +π−]K +) = 2rBrD sin(δB + δD) sin γ/RDK

with rDeiδD = A(D0 → K +π−)/A(¯ D0 → K +π−) and rD ≃ 0.06

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ADS and GLW

ADS: interf in rare B− → [K +π−]DK − normalised to common rate Colour suppressed + Cabibbo favoured VcsV ∗

ud

Colour allowed + Cabibbo suppressed VcdV ∗

us

RDK = Γ([K +π−]K −) + Γ([K −π+]K +) Γ([K −π+]K −) + Γ([K +π−]K +) = r 2

B + r 2 D + 2rBrD cos(δB + δD) cos γ

ADK = Γ([K +π−]K −) − Γ([K −π+]K +) Γ([K −π+]K −) + Γ([K +π−]K +) = 2rBrD sin(δB + δD) sin γ/RDK

with rDeiδD = A(D0 → K +π−)/A(¯ D0 → K +π−) and rD ≃ 0.06 GLW: decay into CP-eigenstate, with RCP,±, ACP,± same structure as ADS, but CP eigenstate (δD = 0, π, rD = 1)

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ADS and GLW

ADS: interf in rare B− → [K +π−]DK − normalised to common rate Colour suppressed + Cabibbo favoured VcsV ∗

ud

Colour allowed + Cabibbo suppressed VcdV ∗

us

RDK = Γ([K +π−]K −) + Γ([K −π+]K +) Γ([K −π+]K −) + Γ([K +π−]K +) = r 2

B + r 2 D + 2rBrD cos(δB + δD) cos γ

ADK = Γ([K +π−]K −) − Γ([K −π+]K +) Γ([K −π+]K −) + Γ([K +π−]K +) = 2rBrD sin(δB + δD) sin γ/RDK

with rDeiδD = A(D0 → K +π−)/A(¯ D0 → K +π−) and rD ≃ 0.06 GLW: decay into CP-eigenstate, with RCP,±, ACP,± same structure as ADS, but CP eigenstate (δD = 0, π, rD = 1) Possible also with D∗ → D0π0 or D0γ

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Experimental inputs

GGSZ GLW ADS Babar DK, D∗K, DK ∗ DK, D∗K, DK ∗ DK, D∗K, DK ∗ (D → Kπ) Belle DK, D∗K DK, D∗K DK, D∗K (D → Kπ, Kππ0) LHCb DK DK DK (D → Kπ, K3π) +DK ∗0 (D → hh) +DK ∗0 (D → hh′) # obs 24 22 20+6 params rB, δB, γ rB, δB, γ rB, δB, γ f(sKh+, sKh−) rD, δD for A(D → f) Charged B decays, apart from DK ∗0 (LHCb)

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Experimental inputs

GGSZ GLW ADS Babar DK, D∗K, DK ∗ DK, D∗K, DK ∗ DK, D∗K, DK ∗ (D → Kπ) Belle DK, D∗K DK, D∗K DK, D∗K (D → Kπ, Kππ0) LHCb DK DK DK (D → Kπ, K3π) +DK ∗0 (D → hh) +DK ∗0 (D → hh′) # obs 24 22 20+6 params rB, δB, γ rB, δB, γ rB, δB, γ f(sKh+, sKh−) rD, δD for A(D → f) Charged B decays, apart from DK ∗0 (LHCb)

Charm hadronic parameters CLEO-c, BESIII : δD, rD but also coherence factor (between 0 and 1, coherence between intermediate states involved in the decay) includes also info on D mixing (Babar, Belle, CDF , LHCb. . . ) for D → KK, KSππ, Kℓν, Kππ0, Kπ . . . (incl CP-violation in charm) reproduces current experimental constraints

utcome used for hadronic params. in D → Kπ, D → Kππ, K3π
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Charm fit

) σ Pull (

1 2 3 4 5 2 4 6 8 10 12

CKM 14

CKM

f i t t e r

CP

y ( 1.82 )

Γ

A ( 0.68 ) (BaBar) π π

S

K ( 0.90 ) (Belle) π π

S

K ( 1.08 )

M

R ( 0.36 ) BES III ( 0.37 ) CLEO-c ( 1.88 ) (BaBar) π π K ( 3.37 ) (BaBar) π K ( 3.10 ) (Belle) π K ( 0.01 ) (CDF) π K ( 0.57 ) (LHCb) π K ( 1.64 )

) π (K

D

δ

50 100 150 200 250 300 350

p-value

0.0 0.2 0.4 0.6 0.8 1.0

CKM 14

CKM

f i t t e r Full Frequentist treatment on MC basis

ADS+GLW GGSZ+ADS+GLW All charm Combined

35 observables, 8 parameters, fit OK but not great (∼ 3σ) including charm information improves the determination of γ δKπ

D [charm]

= (191.4+8.2

−11.4)◦

δKπ

D [GGSZ + GLW + ADS]

= (193+18

−23)◦

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SLIDE 22

γ and B → D(∗)K (∗) hadronic parameters

Combined GLW+ADS

naive statistical treatment (for illustrative purpose only)

GGSZ γ

20 40 60 80 100 120 140 160 180

(DK)

B

δ

20 40 60 80 100 120 140 160 180

excluded area has CL > 0.95 CKM 14

CKM

f i t t e r

GGSZ GLW+ADS Combined

naive statistical treatment (for illustrative purpose only)

γ

20 40 60 80 100 120 140 160 180

(DK)

B

r

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

excluded area has CL > 0.95 CKM 14

CKM

f i t t e r

GLW : D into CP eigenstates (KK, ππ, KSπ0, KSη, KSω) rB, δB, γ ADS : D(∗) into doubly Cabibbo suppressed states rB, δB, γ + rD, δD for A(D → f) GGSZ : D(∗) into 3-body state and Dalitz analysis rB, δB, γ + A(D → KSh+h−) = f(sKh+, sKh−)

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Constraint on γ

γ

20 40 60 80 100 120 140 160 180

p-value

0.0 0.2 0.4 0.6 0.8 1.0

CKM 14

CKM

f i t t e r Full Frequentist treatment on MC basis

Belle LHCb BaBar Combined

γ

20 40 60 80 100 120 140 160 180

p-value

0.0 0.2 0.4 0.6 0.8 1.0

CKM 14

CKM

f i t t e r

GLW+ADS GGSZ Combined

Including all modes for B → D(∗)K(∗): γ[combined] = (73.2+6.3

−7.0)◦

compared to the indirect fit determination (not including these measurements): γ[ind] = (66.9+1.0−3.7)◦ with a pull = 0.91 σ

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B → D(∗)K (∗) hadronic parameters

(DK)

B

δ

20 40 60 80 100 120 140 160 180

p-value

0.0 0.2 0.4 0.6 0.8 1.0

CKM 14

CKM

f i t t e r Full Frequentist treatment on MC basis

Belle LHCb BaBar Combined

(DK)

B

r

0.00 0.05 0.10 0.15 0.20 0.25 0.30

p-value

0.0 0.2 0.4 0.6 0.8 1.0

CKM 14

CKM

f i t t e r Full Frequentist treatment on MC basis

Belle LHCb BaBar Combined

rB δB DK 0.0970+0.0062

−0.0063

(125.4+7.0

−7.8)◦

D∗K 0.119+0.018

−0.019

(−49+12

−15)◦

DK ∗ 0.137+0.051

−0.047

(112+32

−44)◦

DK ∗0 0.236+0.043

−0.052

(336+19

−23)◦ and (200+10 −9 )◦

Accurate experimental information on hadronic parameters

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SLIDE 25

α

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α in ππ

Tree Penguin A(B0 → π+π−) = VudV ∗

ubt +

q=u,c,t

VqdV ∗

qbpq = VudV ∗ ubt+− +VtdV ∗ tbp+−

Time-dependent CP asymmetry A(t) = S+− sin(∆mt) − C+− cos(∆mt) =

1 − (C+−)2 sin 2αeff sin(∆mt) − C+− cos(∆mt)

Combining CKM for t+− and B-¯ B mixing: S+− = sin(2α) + O(p+−

t+− )

= ⇒Penguin pollution: handle on p+− and t+− to extract sin(2α)

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Isospin analysis for B → ππ

In terms of isospin quantities Q(I)

Iz

Two operators for ¯ b → ¯ uu¯ d: O(3/2)

1/2

and O(1/2)

1/2

Two inital states: |B+ = |B(1/2)

1/2 and |B0 = |B(1/2) −1/2

Three final states: [I = 1 forbidden by Bose symmetry] π+π0| = ππ(2)

1 |

π+π−| =

1

3ππ(2)

0 | +

2

3ππ(0)

0 |

π0π0| =

2

3ππ(2)

0 | −

1

3ππ(0)

0 |

From B(1/2), O(3/2) can only yield I = 2 final states, and O(1/2) only I = 0, so two reduced amplitudes A2 = 1 2 √ 3 ππ(2)||O(3/2)||B(1/2) A0 = − 1 √ 6 ππ(0)||O(1/2)||B(1/2)

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 23

SLIDE 28

Trapping the penguin in B → ππ

B+, B0 : A+0 = 3A2 A+− = √ 2(A2 − A0) A00 = 2A2 + A0 B−, B0 : ¯ A+0 = 3¯ A2 ¯ A+− = √ 2(¯ A2 − ¯ A0) ¯ A00 = 2¯ A2 + ¯ A0 A+0 is I = 2 ππ, only from tree and (negligible) I = 3/2 penguins Two triangular relations A+− + √ 2A00 = √ 2A+0 ¯ A+− + √ 2¯ A00 = √ 2¯ A+0 from BR (B+0, B+−, B00) and CP-asyms. (C+−, S+−, C00)

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 24

SLIDE 29

Trapping the penguin in B → ππ

B+, B0 : A+0 = 3A2 A+− = √ 2(A2 − A0) A00 = 2A2 + A0 B−, B0 : ¯ A+0 = 3¯ A2 ¯ A+− = √ 2(¯ A2 − ¯ A0) ¯ A00 = 2¯ A2 + ¯ A0 A+0 is I = 2 ππ, only from tree and (negligible) I = 3/2 penguins Two triangular relations A+− + √ 2A00 = √ 2A+0 ¯ A+− + √ 2¯ A00 = √ 2¯ A+0 from BR (B+0, B+−, B00) and CP-asyms. (C+−, S+−, C00) Introducing ˜ Aij = exp(−2iβ)¯ Aij, 2α between A+0 and ˜ A+0, 2αeff between A+− and ˜ A+− Measure mixed CP-asymmetry in π+π− as sin(2αeff) Reconstruct the triangles Up to discrete ambiguities, possible to determine sin(2α)

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 24

SLIDE 30

ππ triangle

2 /

π π +-

a

π π 00

a

= 1

00

+ a 2 /

+-

SU(2) : a

)

π π

Re(a

1.0
0.5

0.0 0.5 1.0

)

π π

Im(a

1.0
0.5

0.0 0.5 1.0

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

2 /

π π +-

a

π π 00

a

= 1

00

a + 2 /

+-

a SU(2) :

+-

α ∆ ±

)

π π

a Re(

1.0
0.5

0.0 0.5 1.0

)

π π

a Im(

1.0
0.5

0.0 0.5 1.0

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

The A triangle is flat, whereas the ¯ A triangle is not (two-fold degeneracy of the eight solutions : only four distinct solutions)

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 25

SLIDE 31

Extension to ρρ and ρπ

ρρ Analysis for each helicity state, dominated by longit. polarisation B+− and B+0 five times larger than ππ, B00 similar indicating a smaller penguin contamination than ππ same inputs + (loose) info from S00

S. Descotes-Genon (LPT-Orsay)

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SLIDE 32

Extension to ρρ and ρπ

ρρ Analysis for each helicity state, dominated by longit. polarisation B+− and B+0 five times larger than ππ, B00 similar indicating a smaller penguin contamination than ππ same inputs + (loose) info from S00 ρπ Dalitz plot for neutral B modes: A3π = f+A+− + f−A−+ + f0A00 with Aij = A(B0 → ρiπj) and ρi line-shape fi Γ(t): interferences f ∗

i fj and AijAij∗ (coefficients U and I)

Coefficients U and I yield Aij and ¯ Aij for +−, −+, 00 providing α as relative phase between combinations of amplitudes Similar analysis for charged B modes, and since distinguishable particles, isospin yields pentagonal relations A+− + A−+ + 2A00 = √ 2(A+0 + A0+) Pentagonal rels. + Charged and neutral Dalitz = ⇒full α constraint

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 26

SLIDE 33

ρρ triangle

2 /

ρ ρ +-

a

ρ ρ 00

a

= 1

00

+ a 2 /

+-

SU(2) : a

)

ρ ρ

Re(a

1.0
0.5

0.0 0.5 1.0

)

ρ ρ

Im(a

1.0
0.5

0.0 0.5 1.0

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

2 /

ρ ρ +-

a

ρ ρ 00

a

= 1

00

a + 2 /

+-

a SU(2) :

)

ρ ρ

a Re(

1.0
0.5

0.0 0.5 1.0

)

ρ ρ

a Im(

1.0
0.5

0.0 0.5 1.0

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

Both triangles are flat (four-fold degeneracy of the eight solutions : only two distinct solutions)

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 27

SLIDE 34

ρπ analysis

Constraint on the reduced amplitude (A+− + A−+)/(A+0 + A0+) One of the two triangles is flat

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 28

SLIDE 35

Determination of α

Four-fold ambiguity for ππ Two-fold ambiguity for ρρ No ambiguity for ρπ (agreement only at 3σ with other determinations)

(deg) α

20 40 60 80 100 120 140 160 180

p-value

0.0 0.2 0.4 0.6 0.8 1.0

EPS 15

CKM

f i t t e r

(WA) ρ ρ → B (WA) π π → B (WA) π ρ → B Combined CKM fit

(deg) α

20 40 60 80 100 120 140 160 180

p-value

0.0 0.2 0.4 0.6 0.8 1.0

EPS 15

CKM

f i t t e r

(BABAR) π ρ / ρ ρ / π π (Belle) π ρ / ρ ρ / π π (WA) π ρ / ρ ρ / π π CKM fit

Including all modes: α[combined] = (87.6+3.5

−3.3)◦

compared to the indirect fit determination (not including these measurements): α[ind] = (90.6+3.9

−1.1)◦

with a pull = 0.84 σ

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 29

SLIDE 36

Isospin breaking by penguins

Broken by electroweak ∆I = 1/2 penguins in B+ → h+h0

A+− = T +−e−ıα + P+− √ 2A00 = T 00e−ıα − P+− + P+0

EW

√ 2A+0 = (T +− + T 00)e−ıα + P+0

EW

Model-independent constraint from effective Hamiltonian analysis P+0

EW

T +0e−ıα ∼ −3 2 C9 + C10 C1 + C2

VtdV ∗

tb

VudV ∗

ub

[Buras,Fleischer,Neubert,Rosner]

neglecting small ew ops O7 and O8, leading to theoretical estimate rPEW = P+0

EW

T +0 = (3.23 ± 0.30) · 10−2 ∆α = α − α|rPEW =0 = arcsin[rPEW sin α] < 1.9◦ Indirect constraint from the fit rPEW (ππ) = (−8 ± 16) · 10−2 rPEW (ρρ) = (−2.3+10.5

−7.7 ) · 10−2

s

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 30

SLIDE 37

Penguin-to-tree ratio

π π → B

:

+-

R ) σ (1

0.07

+0.06

0.40 :

00

R ) σ 0.14(1 ± 0.63

ρ ρ → B

:

+-

R ) σ (1

0.04

+0.05

0.04 :

00

R ) σ (1

0.20

+0.27

0.20

π ρ → B

:

+-

R ) σ (1

0.45

+0.51

0.45 :

+

R ) σ (1

0.53

+0.09

0.53

|

ij

/T

ij

|P 0.2 0.4 0.6 0.8 1 1.2 1.4

Phases well constrained only for ππ, and not very different from 0 or π

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 31

SLIDE 38

Colour suppression

For the colour-suppressed ratio RCeiδC = T 00/T +− RC(ππ) = 0.45 ± 0.05 δC(ππ) = (−45.8+12.6

−11.5) ◦

RC(ρρ) = 0.16 ± 0.02 δC(ρρ) = (3.4+37.2

−42.4) ◦

(no accurate constraint on ρπ due to limited statistics) Experimental information on hadronic parameters

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 32

SLIDE 39

β and more

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 33

SLIDE 40

β in Bd → J/ψKS

Interf between Bd ¯ Bd mixing and ¯ b → ¯ cs¯ s decay Γ(¯ B0(t) → fCP) − Γ(B0(t) → fCP) Γ(¯ B0(t) → fCP) + Γ(B0(t) → fCP) = S sin(∆mt) − C cos(∆mt) S weak phases due to mixing + decay (dominated by a single phase) tree c,t penguins u penguins VcbV ∗

cs

VcbV ∗

cs and VtbV ∗ ts

VubV ∗

us

O(λ2) real O(αsλ2) real O(αsλ4) S = sin(φBd) = sin(2β) in SM: golden channel for B factories

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 34

SLIDE 41

Penguin pollution for β ?

All charmonium modes (KL, KS, K ∗0(→ KSπ0) and ψ(nS), χc, ηc) sin(2β) = 0.691 ± 0.017 [HFAG] sin(2β)[ind] = 0.748+0.030

−0.032

not significant source of tension in global fit (pull=1.66 σ) currently no systematics included related to penguin pollution (hard to establish a model-independent tight constraint)

sin(2β) ≡ sin(2φ1)

2
1

1 2 3 BaBar

PRD 79 (2009) 072009 0.69 ± 0.03 ± 0.01

BaBar χc0 KS

PRD 80 (2009) 112001 0.69 ± 0.52 ± 0.04 ± 0.07

BaBar J/ψ (hadronic) KS

PRD 69 (2004) 052001 1.56 ± 0.42 ± 0.21

Belle

PRL 108 (2012) 171802 0.67 ± 0.02 ± 0.01

ALEPH

PLB 492, 259 (2000) 0.84 +

1

. . 8 2 4 ± 0.16

OPAL

EPJ C5, 379 (1998) 3.20 +

1

2 . . 8 0 ± 0.50

CDF

PRD 61, 072005 (2000) 0.79 +

.

. 4 4 1 4

LHCb

PRL 115 (2015) 031601 0.73 ± 0.04 ± 0.02

Belle5S

PRL 108 (2012) 171801 0.57 ± 0.58 ± 0.06

Average

HFAG 0.69 ± 0.02

H F A G H F A G

Moriond 2015 PRELIMINARY

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

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 35

SLIDE 42

B0 → D(∗)−π+, ρ−

Interfer. between Cabibbo Fav. and Doubly Cabbibo-Supp. + mixing

leading to a relative strong phase δ and weak 2β + γ

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 36

SLIDE 43

B0 → D(∗)−π+, ρ−

Interfer. between Cabibbo Fav. and Doubly Cabbibo-Supp. + mixing

leading to a relative strong phase δ and weak 2β + γ Similar to γ, but r = |ADCS/ACF| ≃ 2% only not possible to extract from experiment exploit SU(3) symmetry to relate this mode to B(B0 → D(∗)+

s

π−) r(D(∗)π) =

Vcd

Vcs

fD(∗)

fD(∗)

s

B(B0 → D(∗)+

s

π−) B(B0 → D(∗)−π+) SU(3) and factorisation breakings : 1 ± 0.10 ± 0.05 (soft rescattering, W-exchange, non-factorisable corr)

[M. Baak]

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 36

SLIDE 44

2β + γ

)| γ + β |sin(2

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

p-value

0.0 0.2 0.4 0.6 0.8 1.0

Summer 14

CKM

f i t t e r

+

π

+-

D

+

π

+-

D*

+

ρ

+-

D Combined CKM fit

(deg) γ

20 40 60 80 100 120 140 160 180

p-value

0.0 0.2 0.4 0.6 0.8 1.0

Summer 14

CKM

f i t t e r

D(*) K(*) ALL )| γ + β |sin(2 Combined CKM fit

As expected, not competive with respect to

ther determinations of the angles
S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 37

SLIDE 45

Outlook

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 38

SLIDE 46

Outlook

Two-body nonleptonic decays Very rich phenomenology, but hadronic parameters “Restricted” use for CKM fits to the angle side Need to determine hadronic parameters from somewhere else γ from B → DK: several modes, charm input, Dalitz model α from B → ππ: isospin relations β from B → J/ψK: neglected penguins Upcoming CKMfitter update notes for both α and γ with results from B-factories + LHCb Run I Non-leptonic decays interesting probes of strong interactions Test underlying assumptions for the three angles ? [U. Nierste, M. Jung. . . ] Other non-leptonic modes to understand QCD dynamics ? [A. Perez. . . ] Many results from B-factories and LHCb, not all exploited to their full potential

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 39

SLIDE 47

More information

More in Phys.Rev. D91 (2015) 7, 073007 [arXiv:1501.05013] and 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

With special thanks to Karim and Olivier for the content of this talk !

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 40

SLIDE 48

Bonus track

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 41

SLIDE 49

|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%)

S. Descotes-Genon (LPT-Orsay)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 42

SLIDE 50

|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)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 43

SLIDE 51

|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)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 44

SLIDE 52

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)

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SLIDE 53

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)

CKM fits and nonleptonic decays Bad Honnef, 8/2/16 46