CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February...

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CKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban Kundu University of Calcutta CKM : Status and Prospects

Transcript of CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February...

Page 1: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

CKM : Status and Prospects

Anirban KunduUniversity of Calcutta

February 20, 2014IIT Guwahati, EWSB2014

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 2: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

Plan

The CKM matrix

|Vud |, |Vcd |, |Vcs |, |Vus ||Vtb|, |Vcb|, |Vub|Combinations

UT angles: α, β, γ, βs

BSM hints?

Summary: No spectacular deviation from SM

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 3: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

Plan

The CKM matrix

|Vud |, |Vcd |, |Vcs |, |Vus ||Vtb|, |Vcb|, |Vub|Combinations

UT angles: α, β, γ, βs

BSM hints?

Summary: No spectacular deviation from SM

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 4: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

The CKM matrix

Cabibbo [PRL 10, 532 (1963)]

Jµ = cos θ(j (0)µ + g (0)

µ ) + sin θ(j (1)µ + g (1)

µ )

(0): ∆S = 0,∆I = 1, (1): ∆S = 1,∆I = 12

“...the vector coupling constant for β decay is not G , but G cos θ. Thisgives a correction ... in the right direction to eliminate the discrepancybetween O14 and muon lifetimes.”

Kobayashi and Maskawa [PTP 49, 652 (1973)]d ′

s ′

b′

=

c1 −s1c3 −s1s3

s1c2 c1c2c3 − s2s3eiδ c1c2s3 + s2c3e

s1s2 c1s2c3 + c2s3eiδ c1s2s3 − c2c3e

dsb

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 5: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

The CKM matrix

The charged current Lagrangian is

Lwk = − g√2u′j(U†jiDik)γµPLd

′kW

+µ + h.c.

= − g√2Vjk u′jγ

µPLd′kW

+µ + h.c.

We can measure the elements of V but not the individual elementsof U or DPhysics depends only on the misalignment between these two bases

There is no way to know anything about the rotation matrices forright-handed quark fields

U and D are unitary, so the neutral current processes, involving U†Uor D†D, do not change generations — GIM mechanism

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 6: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

The CKM matrix

The charged current Lagrangian is

Lwk = − g√2u′j(U†jiDik)γµPLd

′kW

+µ + h.c.

= − g√2Vjk u′jγ

µPLd′kW

+µ + h.c.

We can measure the elements of V but not the individual elementsof U or DPhysics depends only on the misalignment between these two bases

There is no way to know anything about the rotation matrices forright-handed quark fields

U and D are unitary, so the neutral current processes, involving U†Uor D†D, do not change generations — GIM mechanism

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 7: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

The CKM matrix

The charged current Lagrangian is

Lwk = − g√2u′j(U†jiDik)γµPLd

′kW

+µ + h.c.

= − g√2Vjk u′jγ

µPLd′kW

+µ + h.c.

We can measure the elements of V but not the individual elementsof U or DPhysics depends only on the misalignment between these two bases

There is no way to know anything about the rotation matrices forright-handed quark fields

U and D are unitary, so the neutral current processes, involving U†Uor D†D, do not change generations — GIM mechanism

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 8: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

The CKM matrix

Q. Does the charged current Lagrangian violate CP?Ans.: If the coupling is real, hermitian conjugation is the same as CPconjugation, so no CP violation unless the coupling is complex.But the gauge coupling is real. Can V be complex?

It can be shown that an N × N quark mixing matrix has 12N(N − 1) real

angles and 12 (N − 1)(N − 2) complex phases

No CP violation for two generations. Only one unique CP violating phasefor N = 3

CP violation is not a small effect, but way too small to explain nb/nγ

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 9: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

The CKM matrix

Q. Does the charged current Lagrangian violate CP?Ans.: If the coupling is real, hermitian conjugation is the same as CPconjugation, so no CP violation unless the coupling is complex.But the gauge coupling is real. Can V be complex?

It can be shown that an N × N quark mixing matrix has 12N(N − 1) real

angles and 12 (N − 1)(N − 2) complex phases

No CP violation for two generations. Only one unique CP violating phasefor N = 3

CP violation is not a small effect, but way too small to explain nb/nγ

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 10: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

The CKM matrix

V =

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

=

1− 12λ

2 λ Aλ3(ρ− iη)−λ 1− 1

2λ2 Aλ2

Aλ3(1− ρ− iη) −Aλ2 1

+O(λ4)

Vtd = |Vtd | exp(−iβ),Vub = |Vub| exp(−iγ) Wolfenstein parametrisation

λ = 0.22457+0.00186−0.00014, A = 0.823+0.012

−0.033,

ρ ≡ ρ(1− 12λ

2) = 0.1289+0.0176−0.0094, η ≡ η(1− 1

2λ2) = 0.348± 0.012

(CKMfitter 2013)

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 11: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

The CKM matrix

V =

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

=

1− 12λ

2 λ Aλ3(ρ− iη)−λ 1− 1

2λ2 Aλ2

Aλ3(1− ρ− iη) −Aλ2 1

+O(λ4)

Vtd = |Vtd | exp(−iβ),Vub = |Vub| exp(−iγ) Wolfenstein parametrisation

λ = 0.22457+0.00186−0.00014, A = 0.823+0.012

−0.033,

ρ ≡ ρ(1− 12λ

2) = 0.1289+0.0176−0.0094, η ≡ η(1− 1

2λ2) = 0.348± 0.012

(CKMfitter 2013)

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 12: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

From VV † = V †V = 1, one can write

VudV∗us + VcdV

∗cs + VtdV

∗ts = 0 , (1, 1, 5)

VudV∗ub + VcdV

∗cb + VtdV

∗tb = 0 , (3, 3, 3)

VusV∗ub + VcsV

∗cb + VtsV

∗tb = 0 , (4, 2, 2)

VudV∗cd + VusV

∗cs + VubV

∗cb = 0 , (1, 1, 5)

VudV∗td + VusV

∗ts + VubV

∗tb = 0 , (3, 3, 3)

VcdV∗td + VcsV

∗ts + VcbV

∗tb = 0 . (4, 2, 2)

Unitarity trianglesThe entire CKM matrix can in principle be determined from 4 angles, twolarge, one small, and one even smaller. In practice, the smallest angle isimpossible to measure. (Aleksan et al. PRL 1994)

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 13: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

! "

#

($,%)

(0,0) (1,0)

VudVubVcdVcb

&

&VtdVtbVcdVcb

&

&

All UTs have same area. A nonzero area means CP violation

A good check of the 3-gen CKM paradigm is to see whetherα + β + γ = π, and whether the sides match

J = c12c213c23s12s23s13 sin δ = Im(VudV

∗usV

∗cdVcs)

Invariant and double the area of any UT (Jarlskog, 1973)

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 14: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

Evolution of the UT

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 15: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

α 88.5+2.8−1.5

β direct 21.38+0.79−0.77

β indirect 21.79+0.78−0.73

γ 69.7+1.3−2.8

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Page 16: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

The CKM matrix: summary

All physical observables are independent of CKM parametrization

φ = argA(B → f )

A(B → B)× A(B → f )

B → π+π− : φ = 2arg(VudV∗ubVtbV

∗td)

Direct measurements of sides and angles are consistent with fitresults (CKMfitter, UTfit)

All such measurements are consistent with the CKM paradigm,except a few minor hiccups

Any BSM that may show up at the LHC must have its CP violatingsector closely aligned to that of SM (e.g. MFV models)

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 17: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

The CKM matrix: summary

All physical observables are independent of CKM parametrization

φ = argA(B → f )

A(B → B)× A(B → f )

B → π+π− : φ = 2arg(VudV∗ubVtbV

∗td)

Direct measurements of sides and angles are consistent with fitresults (CKMfitter, UTfit)

All such measurements are consistent with the CKM paradigm,except a few minor hiccups

Any BSM that may show up at the LHC must have its CP violatingsector closely aligned to that of SM (e.g. MFV models)

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 18: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

The CKM matrix: summary

All physical observables are independent of CKM parametrization

φ = argA(B → f )

A(B → B)× A(B → f )

B → π+π− : φ = 2arg(VudV∗ubVtbV

∗td)

Direct measurements of sides and angles are consistent with fitresults (CKMfitter, UTfit)

All such measurements are consistent with the CKM paradigm,except a few minor hiccups

Any BSM that may show up at the LHC must have its CP violatingsector closely aligned to that of SM (e.g. MFV models)

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 19: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

|Vud |

|Vud | = 0.97425± 0.00022(Hardy & Towner, 0812.1202)

Average of 20 superallowed 0+ → 0+ β-transitions

ft(1 + δ′R)(1 + δNS − δC ) =K

2G 2V (1 + ∆V

R )

K/(~c)6 = 8120.2787× 1011 GeV−4-sδ′R(Ee ,Z ), δNS(Ee ,Z ,NS) : transition-dependent part of rad. corr.δC (NS): isospin-symmetry breaking corrections∆V

R : transition-independent part of rad. corr.

GV = GF |Vud |

PIBETA (π+ → π0e+ν): Tiny th. uncertainties but expt error large.

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 20: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

|Vcd |ν scattering off nucleon: νµN → µ−cX and νµN → µ+cX

ν + d → µ− + c , c → s + µ+ + νµ

Double differential cross section

d2σ(ν)

dx dy∝[|vcd |2d(x) + |Vcs |2s(x)

]Compare 1µ and 2µ processes (CDHS, CCFR, CHARM-II, CHORUS)

|Vcd | = 0.230± 0.011

Compatible with semileptonic D decays D → K`ν, π`ν

|Vcd | = 0.229± 0.006± 0.024

Second error is theoretical: form factor uncertainties(Indirect from CKM fit: 0.22443+0.00186

−0.00015)

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 21: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

|Vcs |

From semileptonic D and leptonic Ds decays: D → K`ν, Ds → µν, τν

B(Ds → µν) = (5.90±0.33)×10−3 , B(Ds → τν) = (5.29±0.28)×10−2

Use fDs = (248.6± 3.0) MeV as lattice average, no more tensionbetween µ and τ modesLeptonic and semileptonic average: |Vcs | = 1.006± 0.023Can also be obtained, less precisely, from on-shell W decays, assuminglepton universality:

|Vcs | = 0.94+0.32−0.26 ± 0.13

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 22: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

|Vus |

K`3 gives |Vus |f+(0), with f+(0) = 0.960± 0.005 (lattice)Is τ → s(uν) a statistical fluctuation?Compare BaBar: ACP(τ− → νKSπ

−) = (−0.36± 0.23± 0.11)% withSM: ACP(τ− → νKSπ

−) = (0.36± 0.01)% ..... 2.8σ

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 23: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

|Vus |

K`3 gives |Vus |f+(0), with f+(0) = 0.960± 0.005 (lattice)Is τ → s(uν) a statistical fluctuation?Compare BaBar: ACP(τ− → νKSπ

−) = (−0.36± 0.23± 0.11)% withSM: ACP(τ− → νKSπ

−) = (0.36± 0.01)% ..... 2.8σ

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 24: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

|Vtb|

Top decays: R = Br(t →Wb)/Br(t →Wq−1/3) = |Vtb|2Vtb > 0.78 (CDF), [0.90 : 0.99] (D0), > 0.92 (CMS)Assumes unitarity

Single top production (does not assume unitarity):|Vtb| = 0.89± 0.07 (CDF, D0, CMS average)

Z → bb : larger errors but consistent with unitarity

|Vtb| = 0.999132+0.000047−0.000024 (CKMfitter)

Vtd and Vts can only be obtained in combination, unless we have ILCrunning as a top factory

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 25: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

|Vtb|

Top decays: R = Br(t →Wb)/Br(t →Wq−1/3) = |Vtb|2Vtb > 0.78 (CDF), [0.90 : 0.99] (D0), > 0.92 (CMS)Assumes unitarity

Single top production (does not assume unitarity):|Vtb| = 0.89± 0.07 (CDF, D0, CMS average)

Z → bb : larger errors but consistent with unitarity

|Vtb| = 0.999132+0.000047−0.000024 (CKMfitter)

Vtd and Vts can only be obtained in combination, unless we have ILCrunning as a top factory

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 26: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

|Vcb|

Consider the decays B → D(D∗)`νMost of the meson momentum is carried by the heavy quarkMomentum transfer q2 ∼ (ΛQCDv − ΛQCDv

′)2 = 2Λ2QCD(v .v ′ − 1)

with p = mv and v2 = 1

Define

w = v .v ′ =m2

B + m2D(∗) − q2

2mBm(∗)D

B → D : h+, h−B → D∗ : hV , hA1 , hA2 , hA3

There is only a single form factor ξ(v .v ′) in the limit mb,mc →∞Normalized to ξ(v .v ′ = 1) = 1h+, hV , hA1 , hA3 = 1 +O(Λ2/m2

c) + ...h−, hA2 = O(Λ2/m2

c) + ...

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 27: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

|Vcb|

Consider the decays B → D(D∗)`νMost of the meson momentum is carried by the heavy quarkMomentum transfer q2 ∼ (ΛQCDv − ΛQCDv

′)2 = 2Λ2QCD(v .v ′ − 1)

with p = mv and v2 = 1

Define

w = v .v ′ =m2

B + m2D(∗) − q2

2mBm(∗)D

B → D : h+, h−B → D∗ : hV , hA1 , hA2 , hA3

There is only a single form factor ξ(v .v ′) in the limit mb,mc →∞Normalized to ξ(v .v ′ = 1) = 1h+, hV , hA1 , hA3 = 1 +O(Λ2/m2

c) + ...h−, hA2 = O(Λ2/m2

c) + ...

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 28: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

|Vcb|

B → D∗`ν: about 2% precision, uncertainty from FFB → D`ν: ∼ 5%|Vcb| = (39.5± 0.8)× 10−3 (exclusive)

Inclusive b → c : uses OPE and explicit quark-hadron duality—formb � ΛQCD , inclusive B decay rates are the same as b decay ratesCorrections are suppressed by powers of αs and ΛQCD/mb, can beestimated from moments of the distribution

∫E n` (dΓ/dE`)dE`

|Vcb| = (42.4± 0.9)× 10−3 (inclusive)

Marginally consistent: |Vcb| = (40.9± 1.5)× 10−3

(41.51+0.56−1.15)× 10−3 (CKMfitter)

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 29: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

|Vcb|

B → D∗`ν: about 2% precision, uncertainty from FFB → D`ν: ∼ 5%|Vcb| = (39.5± 0.8)× 10−3 (exclusive)

Inclusive b → c : uses OPE and explicit quark-hadron duality—formb � ΛQCD , inclusive B decay rates are the same as b decay ratesCorrections are suppressed by powers of αs and ΛQCD/mb, can beestimated from moments of the distribution

∫E n` (dΓ/dE`)dE`

|Vcb| = (42.4± 0.9)× 10−3 (inclusive)

Marginally consistent: |Vcb| = (40.9± 1.5)× 10−3

(41.51+0.56−1.15)× 10−3 (CKMfitter)

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 30: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

|Vcb|

B → D∗`ν: about 2% precision, uncertainty from FFB → D`ν: ∼ 5%|Vcb| = (39.5± 0.8)× 10−3 (exclusive)

Inclusive b → c : uses OPE and explicit quark-hadron duality—formb � ΛQCD , inclusive B decay rates are the same as b decay ratesCorrections are suppressed by powers of αs and ΛQCD/mb, can beestimated from moments of the distribution

∫E n` (dΓ/dE`)dE`

|Vcb| = (42.4± 0.9)× 10−3 (inclusive)

Marginally consistent: |Vcb| = (40.9± 1.5)× 10−3

(41.51+0.56−1.15)× 10−3 (CKMfitter)

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 31: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

|Vub|

Inclusive B → Xu`νHave to take leptons beyond charm threshold, possibly largenonperturbative effectsLO in ΛQCD/mb: Only one parameter, can be extracted from photonenergy spectrum of B → Xsγ. More parameters at higher order,have to be modeledLow-q2: can use OPE but have to know B → Xc`ν background|Vub| = (4.41± 0.15+0.15

−0.19)× 10−3 (inclusive)

Exclusive B → π(ρ)`νForm factors from unquenched lattice, reliable at high-q2

|Vub| = (3.23± 0.31)× 10−3 (exclusive)|Vub| = (4.15± 0.49)× 10−3 (average)

Br(B → τν) = (1.67± 0.30)× 10−4

fB = (190.6± 4.6) MeV ⇒ |Vub| = (5.10± 0.47)× 10−3 (BSMhint? H+?)

(3.55+0.16−0.13)× 10−3 (CKMfitter)

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|Vub|

Inclusive B → Xu`νHave to take leptons beyond charm threshold, possibly largenonperturbative effectsLO in ΛQCD/mb: Only one parameter, can be extracted from photonenergy spectrum of B → Xsγ. More parameters at higher order,have to be modeledLow-q2: can use OPE but have to know B → Xc`ν background|Vub| = (4.41± 0.15+0.15

−0.19)× 10−3 (inclusive)

Exclusive B → π(ρ)`νForm factors from unquenched lattice, reliable at high-q2

|Vub| = (3.23± 0.31)× 10−3 (exclusive)|Vub| = (4.15± 0.49)× 10−3 (average)

Br(B → τν) = (1.67± 0.30)× 10−4

fB = (190.6± 4.6) MeV ⇒ |Vub| = (5.10± 0.47)× 10−3 (BSMhint? H+?)

(3.55+0.16−0.13)× 10−3 (CKMfitter)

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|Vub|

Inclusive B → Xu`νHave to take leptons beyond charm threshold, possibly largenonperturbative effectsLO in ΛQCD/mb: Only one parameter, can be extracted from photonenergy spectrum of B → Xsγ. More parameters at higher order,have to be modeledLow-q2: can use OPE but have to know B → Xc`ν background|Vub| = (4.41± 0.15+0.15

−0.19)× 10−3 (inclusive)

Exclusive B → π(ρ)`νForm factors from unquenched lattice, reliable at high-q2

|Vub| = (3.23± 0.31)× 10−3 (exclusive)|Vub| = (4.15± 0.49)× 10−3 (average)

Br(B → τν) = (1.67± 0.30)× 10−4

fB = (190.6± 4.6) MeV ⇒ |Vub| = (5.10± 0.47)× 10−3 (BSMhint? H+?)

(3.55+0.16−0.13)× 10−3 (CKMfitter)

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 34: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

Vtd and Vts

No way to determine directly

∆Md = (0.507± 0.004) ps−1, ∝ |VtdVtb|2∆Ms = (17.719± 0.043) ps−1, ∝ |VtsVtb|2

Lattice for f√B and Vtb = 1

|Vtd | = (8.4± 0.6)× 10−3 , |Vts | = (42.9± 2.6)× 10−3

Lots of uncertainties cancel in the ratio|Vtd |/|Vts | = 0.211± 0.001± 0.006

Can also use B → K∗γ, B → ργ, and their ratio|Vtd |/|Vts | = 0.21± 0.04

K+ → π+νν gives V ∗tsVtd , theoretically clean, need more events

All numbers consistent with CKM unitarity

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 35: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

Vtd and Vts

No way to determine directly

∆Md = (0.507± 0.004) ps−1, ∝ |VtdVtb|2∆Ms = (17.719± 0.043) ps−1, ∝ |VtsVtb|2

Lattice for f√B and Vtb = 1

|Vtd | = (8.4± 0.6)× 10−3 , |Vts | = (42.9± 2.6)× 10−3

Lots of uncertainties cancel in the ratio|Vtd |/|Vts | = 0.211± 0.001± 0.006

Can also use B → K∗γ, B → ργ, and their ratio|Vtd |/|Vts | = 0.21± 0.04

K+ → π+νν gives V ∗tsVtd , theoretically clean, need more events

All numbers consistent with CKM unitarity

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 36: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

Vtd and Vts

No way to determine directly

∆Md = (0.507± 0.004) ps−1, ∝ |VtdVtb|2∆Ms = (17.719± 0.043) ps−1, ∝ |VtsVtb|2

Lattice for f√B and Vtb = 1

|Vtd | = (8.4± 0.6)× 10−3 , |Vts | = (42.9± 2.6)× 10−3

Lots of uncertainties cancel in the ratio|Vtd |/|Vts | = 0.211± 0.001± 0.006

Can also use B → K∗γ, B → ργ, and their ratio|Vtd |/|Vts | = 0.21± 0.04

K+ → π+νν gives V ∗tsVtd , theoretically clean, need more events

All numbers consistent with CKM unitarity

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 37: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

Vtd and Vts

No way to determine directly

∆Md = (0.507± 0.004) ps−1, ∝ |VtdVtb|2∆Ms = (17.719± 0.043) ps−1, ∝ |VtsVtb|2

Lattice for f√B and Vtb = 1

|Vtd | = (8.4± 0.6)× 10−3 , |Vts | = (42.9± 2.6)× 10−3

Lots of uncertainties cancel in the ratio|Vtd |/|Vts | = 0.211± 0.001± 0.006

Can also use B → K∗γ, B → ργ, and their ratio|Vtd |/|Vts | = 0.21± 0.04

K+ → π+νν gives V ∗tsVtd , theoretically clean, need more events

All numbers consistent with CKM unitarity

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 38: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

Vtd and Vts

No way to determine directly

∆Md = (0.507± 0.004) ps−1, ∝ |VtdVtb|2∆Ms = (17.719± 0.043) ps−1, ∝ |VtsVtb|2

Lattice for f√B and Vtb = 1

|Vtd | = (8.4± 0.6)× 10−3 , |Vts | = (42.9± 2.6)× 10−3

Lots of uncertainties cancel in the ratio|Vtd |/|Vts | = 0.211± 0.001± 0.006

Can also use B → K∗γ, B → ργ, and their ratio|Vtd |/|Vts | = 0.21± 0.04

K+ → π+νν gives V ∗tsVtd , theoretically clean, need more events

All numbers consistent with CKM unitarity

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 39: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

UT angle: α ≡ φ2

α = arg(−VtdV∗tb/VudV

∗ub)

From B → ππ, πρ, ρρ (B → ρρ: fL ≈ 1, CP-even)

α = (85.4+4.0−3.8)◦ (direct)

α = (94.9+4.8−6.8)◦ (CKM fit)

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 40: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

UT angle: β ≡ φ1

β = arg(−VcdV∗cb/VtdV

∗tb) ≈ −arg(Vtd)

B → J/ψKS , φKS , ... no discrepancy between ccs and sss modessin(2β) = 0.689± 0.019 , β = (21.39± 0.78)◦ (direct)

β = (21.79+0.78−0.73)◦ (CKM fit)

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 41: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

UT angle: γ ≡ φ3

Option 1: Consider B∓ → DCPK∓ (or excitations),

DCP → DCP+,DCP−Interference between b → cus and b → ucs

(Gronau,London,Wyler)Rate and CP asymmetries depend on γ, as well asrB = A(b → u)/A(b → c) and arg(rB)

Option 2: Consider B− → DK−,D → K+π− and its chargeconjugated channels(allowed, suppressed) ↔ (suppressed, allowed)

(Atwood, Dunietz, Soni)Rate and CP asymmetries depend on γ, rB , arg(rB), rD , arg(rD)rD has been measured from D decays ≈ 0.06

Option 3: Use a Dalitz plot analysis forB− → DK−,D → KSπ

+π−, ... and its charge conjugateSimultaneous determination of γ, rB , arg(rB)

(Giri, Grossman, Sofer, Zupan)

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 42: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

UT angle: γ ≡ φ3

Option 1: Consider B∓ → DCPK∓ (or excitations),

DCP → DCP+,DCP−Interference between b → cus and b → ucs

(Gronau,London,Wyler)Rate and CP asymmetries depend on γ, as well asrB = A(b → u)/A(b → c) and arg(rB)

Option 2: Consider B− → DK−,D → K+π− and its chargeconjugated channels(allowed, suppressed) ↔ (suppressed, allowed)

(Atwood, Dunietz, Soni)Rate and CP asymmetries depend on γ, rB , arg(rB), rD , arg(rD)rD has been measured from D decays ≈ 0.06

Option 3: Use a Dalitz plot analysis forB− → DK−,D → KSπ

+π−, ... and its charge conjugateSimultaneous determination of γ, rB , arg(rB)

(Giri, Grossman, Sofer, Zupan)

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 43: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

UT angle: γ ≡ φ3

Option 1: Consider B∓ → DCPK∓ (or excitations),

DCP → DCP+,DCP−Interference between b → cus and b → ucs

(Gronau,London,Wyler)Rate and CP asymmetries depend on γ, as well asrB = A(b → u)/A(b → c) and arg(rB)

Option 2: Consider B− → DK−,D → K+π− and its chargeconjugated channels(allowed, suppressed) ↔ (suppressed, allowed)

(Atwood, Dunietz, Soni)Rate and CP asymmetries depend on γ, rB , arg(rB), rD , arg(rD)rD has been measured from D decays ≈ 0.06

Option 3: Use a Dalitz plot analysis forB− → DK−,D → KSπ

+π−, ... and its charge conjugateSimultaneous determination of γ, rB , arg(rB)

(Giri, Grossman, Sofer, Zupan)

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 44: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

UT angle: γ ≡ φ3

γ = arg(−VudV∗ub/VcdV

∗cb) ≈ −arg(Vub)γ = (68.0+8.0

−8.5)◦ (direct)

γ = (69.7+1.3−2.8)◦ (CKM fit)

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 45: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

Lesser known angles: βs

∆Vts = 12A(1− 2ρ)λ4 − iηAλ4

βs = arg

(−VcbV

∗cs

VtbV ∗ts

)Comes in Bs–Bs mixing, not to be confused with

φs = arg(−M12/Γ12)

SM: βs = 0.019± 0.001Exp: 0.020± 0.045 (direct), 0.0182(8) (fit)

VusV∗ub + VcsV

∗cb + VtsV

∗tb = 0 ⇒ (αs , βs , γ)

αs ≈ π − γ, can be extracted from Bs → K+K− .... LHCb? Super-B?

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 46: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

Lesser known angles: βs

0.25

CDF

LHCb

ATLAS

Combined

SM

0.20

0.15

0.10

0.05

0-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

68% CL contours( )

HFAGPDG 2013

LHCb 1.0 fb–1+ CDF 9.6 fb –1 + ATLAS 4.9 fb 1+ D 8 fb– –1

D

φccss = −2βsThe mirror image (−∆Γs , π − φccss ) ruled out by LHCb, ∆Γs > 0

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 47: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

BSM? What BSM?

Nobody knows.

Circumstantial evidence is occasionallyvery convincing, as when you finda trout in the milk.— Arthur Conan Doyle

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 48: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

BSM? What BSM?

Nobody knows.

Circumstantial evidence is occasionallyvery convincing, as when you finda trout in the milk.— Arthur Conan Doyle

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 49: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

Circumstantial evidence for BSM

New physics in mixing? M12 = MSM12 exp(i∆)

1.5σ from SM,coming from Vub

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 50: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

Circumstantial evidence for BSM

Even better fit for Bs

Perfect fit withSM but does notinclude Ab

sl fromthe D0 dimuonresult, 3.4σ away

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 51: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

Circumstantial evidence for BSM

(Absl)SM = (−2.4± 0.4)× 10−4, (Ab

sl)D0 = (−7.87± 1.96)× 10−3

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 52: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

Circumstantial evidence for BSM

R(D(∗)) =Br(B → D(∗)τν)

Br(B → D(∗)`ν)

SM : R(D) = 0.297± 0.017 , R(D∗) = 0.252± 0.003

BaBar : R(D) = 0.440±0.058±0.042 , R(D∗) = 0.332±0.024±0.018 .

R(D)expR(D)SM

= 1.481× (1± 0.173) ,R(D∗)expR(D∗)SM

= 1.317× (1± 0.091) .

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 53: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

Circumstantial evidence for BSM

R(D(∗)) =Br(B → D(∗)τν)

Br(B → D(∗)`ν)

SM : R(D) = 0.297± 0.017 , R(D∗) = 0.252± 0.003

BaBar : R(D) = 0.440±0.058±0.042 , R(D∗) = 0.332±0.024±0.018 .

R(D)expR(D)SM

= 1.481× (1± 0.173) ,R(D∗)expR(D∗)SM

= 1.317× (1± 0.091) .

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 54: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

Circumstantial evidence for BSM

AI =Br(B0 → K 0(∗)µ+µ−)− τ0

τ+Br(B+ → K+(∗)µ+µ−)

Br(B0 → K 0(∗)µ+µ−) + τ0

τ+Br(B+ → K+(∗)µ+µ−)

AI = 0 in naive factorization

ISR from spectator can contribute up to ∼ 1% unless q2 is very small

B → K∗µµ is consistent with SM

B → Kµµ: 4.4σ away from zero, integrated over all q2

[LHCb, 1205.3422]

]4c/2 [GeV2q0 5 10 15 20 25

IA

-1.5

-1

-0.5

0

0.5

1

LHCb-µ+µ K→B

]4c/2 [GeV2q0 5 10 15 20

IA

-0.5-0.4-0.3-0.2-0.1

00.10.20.30.40.5

Theory Data

LHCb-µ+µ K →B *

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 55: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

Where to?

CKM matrix seems to be unitary

∑q

|Vuq|2 = 0.9999± 0.0006 ,∑q

|Vcq|2 = 1.067± 0.047

∑q

|Vqd |2 = 1.002± 0.005 ,∑q

|Vqs |2 = 1.065± 0.046

Also, α + β + γ = (178+11−12)◦ (direct), consistent with triangle

New physics must be aligned

Flav. structure a few TeV > a few TeVAnarchy O(1) X small ( < O(1))

Small small tinymisalignment (O(0.1)) (O(0.01-0.1))

Alignment tiny out of reach(MFV) (O(0.01)) < O(0.01)

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 56: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

Where to?

CKM matrix seems to be unitary

∑q

|Vuq|2 = 0.9999± 0.0006 ,∑q

|Vcq|2 = 1.067± 0.047

∑q

|Vqd |2 = 1.002± 0.005 ,∑q

|Vqs |2 = 1.065± 0.046

Also, α + β + γ = (178+11−12)◦ (direct), consistent with triangle

New physics must be aligned

Flav. structure a few TeV > a few TeVAnarchy O(1) X small ( < O(1))

Small small tinymisalignment (O(0.1)) (O(0.01-0.1))

Alignment tiny out of reach(MFV) (O(0.01)) < O(0.01)

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 57: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

Where to?

4th gen (constraint from S and T) — Vt′b can still be significant(Soni et al. PRD 2010)

New operator of the form (1/Λ2)(qγµPLq′)2 is constrained from

mixing: Λ > 100 TeV from Bs , 104 TeV from K , comparable boundsfrom other structures

If BSM is at 1 TeV, we hardly expect any drastically new source ofCP violation

βs consistent with SM, more from Super-B?

Thank you.

Anirban Kundu University of Calcutta CKM : Status and Prospects

Page 58: CKM : Status and ProspectsCKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Anirban KunduUniversity of Calcutta CKM : Status

Where to?

4th gen (constraint from S and T) — Vt′b can still be significant(Soni et al. PRD 2010)

New operator of the form (1/Λ2)(qγµPLq′)2 is constrained from

mixing: Λ > 100 TeV from Bs , 104 TeV from K , comparable boundsfrom other structures

If BSM is at 1 TeV, we hardly expect any drastically new source ofCP violation

βs consistent with SM, more from Super-B?

Thank you.

Anirban Kundu University of Calcutta CKM : Status and Prospects