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CKM : Status and Prospects
Anirban KunduUniversity of Calcutta
February 20, 2014IIT Guwahati, EWSB2014
Anirban Kundu University of Calcutta CKM : Status and Prospects
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
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
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
iδ
s1s2 c1s2c3 + c2s3eiδ c1s2s3 − c2c3e
iδ
dsb
Anirban Kundu University of Calcutta CKM : Status and Prospects
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
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
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
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
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
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
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
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
! "
#
($,%)
(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
Evolution of the UT
Anirban Kundu University of Calcutta CKM : Status and Prospects
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
Anirban Kundu University of Calcutta CKM : Status and Prospects
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
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
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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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