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

CKM : Status and Prospects

Anirban KunduUniversity of Calcutta

February 20, 2014IIT Guwahati, EWSB2014

Anirban Kundu University of Calcutta CKM : Status and Prospects

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

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

The CKM matrix

Cabibbo [PRL 10, 532 (1963)]

Jµ = cos θ(j (0)µ + g (0)

µ ) + sin θ(j (1)µ + g (1)

(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 ′

c1 −s1c3 −s1s3

s1c2 c1c2c3 − s2s3eiδ c1c2s3 + s2c3e

s1s2 c1s2c3 + c2s3eiδ c1s2s3 − c2c3e

The CKM matrix

The charged current Lagrangian is

Lwk = − g√2u′j(U†jiDik)γµPLd

+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

The CKM matrix

+µ + h.c.

µPLd′kW

+µ + h.c.

The CKM matrix

+µ + h.c.

µPLd′kW

+µ + h.c.

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

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

The CKM matrix

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)

The CKM matrix

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)

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)

(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)

Evolution of the UT

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

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)

φ = argA(B → f )

A(B → B)× A(B → f )

∗td)

φ = argA(B → f )

A(B → B)× A(B → f )

∗td)

|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

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.

|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)

|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

|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

|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

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

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

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) + ...

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) + ...

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)

|Vcb| = (42.4± 0.9)× 10−3 (inclusive)

(41.51+0.56−1.15)× 10−3 (CKMfitter)

|Vcb| = (42.4± 0.9)× 10−3 (inclusive)

(41.51+0.56−1.15)× 10−3 (CKMfitter)

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)

−0.19)× 10−3 (inclusive)

Br(B → τν) = (1.67± 0.30)× 10−4

(3.55+0.16−0.13)× 10−3 (CKMfitter)

−0.19)× 10−3 (inclusive)

Br(B → τν) = (1.67± 0.30)× 10−4

(3.55+0.16−0.13)× 10−3 (CKMfitter)

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