Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014
Plan The CKM matrix V ud, V cd, V cs, V us V tb, V cb, V ub Combinations UT angles: α, β, γ, β s BSM hints? Summary: No spectacular deviation from SM
Plan The CKM matrix V ud, V cd, V cs, V us V tb, V cb, V ub Combinations UT angles: α, β, γ, β s BSM hints? Summary: No spectacular deviation from SM
The CKM matrix Cabibbo [PRL 10, 532 (1963)] J µ = 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 = 1 2...the vector coupling constant for β decay is not G, but G cos θ. This gives a correction... in the right direction to eliminate the discrepancy between O 14 and muon lifetimes. Kobayashi and Maskawa [PTP 49, 652 (1973)] d c 1 s 1 c 3 s 1 s 3 s = s 1 c 2 c 1 c 2 c 3 s 2 s 3 e iδ c 1 c 2 s 3 + s 2 c 3 e iδ b s 1 s 2 c 1 s 2 c 3 + c 2 s 3 e iδ c 1 s 2 s 3 c 2 c 3 e iδ d s b
The CKM matrix The charged current Lagrangian is L wk = g 2 ū j(u ji D ik)γ µ P L d kw + µ = g 2 V jk ū jγ µ P L d kw + µ + h.c. + h.c. We can measure the elements of V but not the individual elements of U or D Physics depends only on the misalignment between these two bases
The CKM matrix The charged current Lagrangian is L wk = g 2 ū j(u ji D ik)γ µ P L d kw + µ = g 2 V jk ū jγ µ P L d kw + µ + h.c. + h.c. We can measure the elements of V but not the individual elements of U or D Physics depends only on the misalignment between these two bases There is no way to know anything about the rotation matrices for right-handed quark fields U and D are unitary, so the neutral current processes, involving U U or D D, do not change generations GIM mechanism
The CKM matrix The charged current Lagrangian is L wk = g 2 ū j(u ji D ik)γ µ P L d kw + µ = g 2 V jk ū jγ µ P L d kw + µ + h.c. + h.c. We can measure the elements of V but not the individual elements of U or D Physics depends only on the misalignment between these two bases There is no way to know anything about the rotation matrices for right-handed quark fields U and D are unitary, so the neutral current processes, involving U U or D D, do not change generations GIM mechanism
The CKM matrix Q. Does the charged current Lagrangian violate CP? Ans.: If the coupling is real, hermitian conjugation is the same as CP conjugation, 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 1 2N(N 1) real angles and 1 2 (N 1)(N 2) complex phases No CP violation for two generations. Only one unique CP violating phase for N = 3 CP violation is not a small effect, but way too small to explain n b /n γ
The CKM matrix Q. Does the charged current Lagrangian violate CP? Ans.: If the coupling is real, hermitian conjugation is the same as CP conjugation, 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 1 2N(N 1) real angles and 1 2 (N 1)(N 2) complex phases No CP violation for two generations. Only one unique CP violating phase for N = 3 CP violation is not a small effect, but way too small to explain n b /n γ
The CKM matrix V = = V ud V us V ub V cd V cs V cb V td V ts V tb 1 1 2 λ2 λ Aλ 3 (ρ iη) λ 1 1 2 λ2 Aλ 2 + O(λ 4 ) Aλ 3 (1 ρ iη) Aλ 2 1 V td = V td exp( iβ), V ub = V ub exp( iγ) Wolfenstein parametrisation λ = 0.22457 +0.00186 0.00014, A = 0.823+0.012 0.033, ρ ρ(1 1 2 λ2 ) = 0.1289 +0.0176 0.0094, η η(1 1 2 λ2 ) = 0.348 ± 0.012 (CKMfitter 2013)
The CKM matrix V = = V ud V us V ub V cd V cs V cb V td V ts V tb 1 1 2 λ2 λ Aλ 3 (ρ iη) λ 1 1 2 λ2 Aλ 2 + O(λ 4 ) Aλ 3 (1 ρ iη) Aλ 2 1 V td = V td exp( iβ), V ub = V ub exp( iγ) Wolfenstein parametrisation λ = 0.22457 +0.00186 0.00014, A = 0.823+0.012 0.033, ρ ρ(1 1 2 λ2 ) = 0.1289 +0.0176 0.0094, η η(1 1 2 λ2 ) = 0.348 ± 0.012 (CKMfitter 2013)
From VV = V V = 1, one can write V ud Vus + V cd Vcs + V td Vts = 0, (1, 1, 5) V ud Vub + V cd Vcb + V td Vtb = 0, (3, 3, 3) V us Vub + V cs Vcb + V ts Vtb = 0, (4, 2, 2) V ud Vcd + V us Vcs + V ub Vcb = 0, (1, 1, 5) V ud Vtd + V us Vts + V ub Vtb = 0, (3, 3, 3) V cd Vtd + V cs Vts + V cb Vtb = 0. (4, 2, 2) Unitarity triangles The entire CKM matrix can in principle be determined from 4 angles, two large, one small, and one even smaller. In practice, the smallest angle is impossible to measure. (Aleksan et al. PRL 1994)
($,%) # & V ud V ub & V cd V cb & V td V tb & V cd V cb! " (0,0) (1,0) All UTs have same area. A nonzero area means CP violation A good check of the 3-gen CKM paradigm is to see whether α + β + γ = π, and whether the sides match J = c 12 c 2 13c 23 s 12 s 23 s 13 sin δ = Im(V ud V usv cdv cs ) 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 A(B f ) φ = arg A(B B) A( B f ) B π + π : φ = 2arg(V ud V ub V tbv td ) Direct measurements of sides and angles are consistent with fit results (CKMfitter, UTfit) All such measurements are consistent with the CKM paradigm, except a few minor hiccups
The CKM matrix: summary All physical observables are independent of CKM parametrization A(B f ) φ = arg A(B B) A( B f ) B π + π : φ = 2arg(V ud V ub V tbv td ) Direct measurements of sides and angles are consistent with fit results (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 violating sector closely aligned to that of SM (e.g. MFV models)
The CKM matrix: summary All physical observables are independent of CKM parametrization A(B f ) φ = arg A(B B) A( B f ) B π + π : φ = 2arg(V ud V ub V tbv td ) Direct measurements of sides and angles are consistent with fit results (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 violating sector closely aligned to that of SM (e.g. MFV models)
V ud V ud = 0.97425 ± 0.00022 (Hardy & Towner, 0812.1202) Average of 20 superallowed 0 + 0 + β-transitions ft(1 + δ R)(1 + δ NS δ C ) = K 2G 2 V (1 + V R ) K/( c) 6 = 8120.2787 10 11 GeV 4 -s δ R (E e, Z), δ NS (E e, Z, NS) : transition-dependent part of rad. corr. δ C (NS): isospin-symmetry breaking corrections V R : transition-independent part of rad. corr. G V = G F V ud PIBETA (π + π 0 e + ν): Tiny th. uncertainties but expt error large.
V cd ν scattering off nucleon: ν µ N µ cx and ν µ N µ + cx Double differential cross section ν + d µ + c, c s + µ + + ν µ d 2 σ(ν) dx dy [ v cd 2 d(x) + V cs 2 s(x) ] Compare 1µ and 2µ processes (CDHS, CCFR, CHARM-II, CHORUS) V cd = 0.230 ± 0.011 Compatible with semileptonic D decays D Klν, πlν V cd = 0.229 ± 0.006 ± 0.024 Second error is theoretical: form factor uncertainties (Indirect from CKM fit: 0.22443 +0.00186 0.00015 )
V cs From semileptonic D and leptonic D s decays: D Klν, D s µν, τν B(D s µν) = (5.90±0.33) 10 3, B(D s τν) = (5.29±0.28) 10 2 Use f Ds = (248.6 ± 3.0) MeV as lattice average, no more tension between µ and τ modes Leptonic and semileptonic average: V cs = 1.006 ± 0.023 Can also be obtained, less precisely, from on-shell W decays, assuming lepton universality: V cs = 0.94 0.26 +0.32 ± 0.13
V us K l3 gives V us f + (0), with f + (0) = 0.960 ± 0.005 (lattice) Is τ s(ūν) a statistical fluctuation? Compare BaBar: A CP (τ νk S π ) = ( 0.36 ± 0.23 ± 0.11)% with SM: A CP (τ νk S π ) = (0.36 ± 0.01)%... 2.8σ
V us K l3 gives V us f + (0), with f + (0) = 0.960 ± 0.005 (lattice) Is τ s(ūν) a statistical fluctuation? Compare BaBar: A CP (τ νk S π ) = ( 0.36 ± 0.23 ± 0.11)% with SM: A CP (τ νk S π ) = (0.36 ± 0.01)%... 2.8σ
V tb Top decays: R = Br(t Wb)/Br(t Wq 1/3 ) = V tb 2 V tb > 0.78 (CDF), [0.90 : 0.99] (D0), > 0.92 (CMS) Assumes unitarity Single top production (does not assume unitarity): V tb = 0.89 ± 0.07 (CDF, D0, CMS average) Z b b : larger errors but consistent with unitarity V tb = 0.999132 +0.000047 0.000024 (CKMfitter) V td and V ts can only be obtained in combination, unless we have ILC running as a top factory
V tb Top decays: R = Br(t Wb)/Br(t Wq 1/3 ) = V tb 2 V tb > 0.78 (CDF), [0.90 : 0.99] (D0), > 0.92 (CMS) Assumes unitarity Single top production (does not assume unitarity): V tb = 0.89 ± 0.07 (CDF, D0, CMS average) Z b b : larger errors but consistent with unitarity V tb = 0.999132 +0.000047 0.000024 (CKMfitter) V td and V ts can only be obtained in combination, unless we have ILC running as a top factory
V cb Consider the decays B D(D )lν Most of the meson momentum is carried by the heavy quark Momentum transfer q 2 (Λ QCD v Λ QCD v ) 2 = 2Λ 2 QCD (v.v 1) with p = mv and v 2 = 1 Define w = v.v = m2 B + m2 D ( ) q 2 2m B m ( ) D B D : h +, h B D : h V, h A1, h A2, h A3 There is only a single form factor ξ(v.v ) in the limit m b, m c Normalized to ξ(v.v = 1) = 1 h +, h V, h A1, h A3 = 1 + O(Λ 2 /m 2 c) +... h, h A2 = O(Λ 2 /m 2 c) +...
V cb Consider the decays B D(D )lν Most of the meson momentum is carried by the heavy quark Momentum transfer q 2 (Λ QCD v Λ QCD v ) 2 = 2Λ 2 QCD (v.v 1) with p = mv and v 2 = 1 Define w = v.v = m2 B + m2 D ( ) q 2 2m B m ( ) D B D : h +, h B D : h V, h A1, h A2, h A3 There is only a single form factor ξ(v.v ) in the limit m b, m c Normalized to ξ(v.v = 1) = 1 h +, h V, h A1, h A3 = 1 + O(Λ 2 /m 2 c) +... h, h A2 = O(Λ 2 /m 2 c) +...
V cb B D lν: about 2% precision, uncertainty from FF B Dlν: 5% V cb = (39.5 ± 0.8) 10 3 (exclusive) Inclusive b c: uses OPE and explicit quark-hadron duality for m b Λ QCD, inclusive B decay rates are the same as b decay rates Corrections are suppressed by powers of α s and Λ QCD /m b, can be estimated from moments of the distribution E n l (dγ/de l)de l V cb = (42.4 ± 0.9) 10 3 (inclusive) (41.51 +0.56 1.15 ) 10 3 (CKMfitter)
V cb B D lν: about 2% precision, uncertainty from FF B Dlν: 5% V cb = (39.5 ± 0.8) 10 3 (exclusive) Inclusive b c: uses OPE and explicit quark-hadron duality for m b Λ QCD, inclusive B decay rates are the same as b decay rates Corrections are suppressed by powers of α s and Λ QCD /m b, can be estimated from moments of the distribution E n l (dγ/de l)de l V cb = (42.4 ± 0.9) 10 3 (inclusive) Marginally consistent: V cb = (40.9 ± 1.5) 10 3 (41.51 +0.56 1.15 ) 10 3 (CKMfitter)
V cb B D lν: about 2% precision, uncertainty from FF B Dlν: 5% V cb = (39.5 ± 0.8) 10 3 (exclusive) Inclusive b c: uses OPE and explicit quark-hadron duality for m b Λ QCD, inclusive B decay rates are the same as b decay rates Corrections are suppressed by powers of α s and Λ QCD /m b, can be estimated from moments of the distribution E n l (dγ/de l)de l V cb = (42.4 ± 0.9) 10 3 (inclusive) Marginally consistent: V cb = (40.9 ± 1.5) 10 3 (41.51 +0.56 1.15 ) 10 3 (CKMfitter)
V ub Inclusive B X u lν Have to take leptons beyond charm threshold, possibly large nonperturbative effects LO in Λ QCD /m b : Only one parameter, can be extracted from photon energy spectrum of B X s γ. More parameters at higher order, have to be modeled Low-q 2 : can use OPE but have to know B X c lν background V ub = (4.41 ± 0.15 +0.15 0.19 ) 10 3 (inclusive) Exclusive B π(ρ)lν Form factors from unquenched lattice, reliable at high-q 2 V ub = (3.23 ± 0.31) 10 3 (exclusive) V ub = (4.15 ± 0.49) 10 3 (average) (3.55 +0.16 0.13 ) 10 3 (CKMfitter)
V ub Inclusive B X u lν Have to take leptons beyond charm threshold, possibly large nonperturbative effects LO in Λ QCD /m b : Only one parameter, can be extracted from photon energy spectrum of B X s γ. More parameters at higher order, have to be modeled Low-q 2 : can use OPE but have to know B X c lν background V ub = (4.41 ± 0.15 +0.15 0.19 ) 10 3 (inclusive) Exclusive B π(ρ)lν Form factors from unquenched lattice, reliable at high-q 2 V ub = (3.23 ± 0.31) 10 3 (exclusive) V ub = (4.15 ± 0.49) 10 3 (average) Br(B τν) = (1.67 ± 0.30) 10 4 f B = (190.6 ± 4.6) MeV V ub = (5.10 ± 0.47) 10 3 (BSM hint? H +?) (3.55 +0.16 0.13 ) 10 3 (CKMfitter)
V ub Inclusive B X u lν Have to take leptons beyond charm threshold, possibly large nonperturbative effects LO in Λ QCD /m b : Only one parameter, can be extracted from photon energy spectrum of B X s γ. More parameters at higher order, have to be modeled Low-q 2 : can use OPE but have to know B X c lν background V ub = (4.41 ± 0.15 +0.15 0.19 ) 10 3 (inclusive) Exclusive B π(ρ)lν Form factors from unquenched lattice, reliable at high-q 2 V ub = (3.23 ± 0.31) 10 3 (exclusive) V ub = (4.15 ± 0.49) 10 3 (average) Br(B τν) = (1.67 ± 0.30) 10 4 f B = (190.6 ± 4.6) MeV V ub = (5.10 ± 0.47) 10 3 (BSM hint? H +?) (3.55 +0.16 0.13 ) 10 3 (CKMfitter)
V td and V ts No way to determine directly M d = (0.507 ± 0.004) ps 1, V td V tb 2 M s = (17.719 ± 0.043) ps 1, V ts V tb 2 Lattice for f B and V tb = 1 V td = (8.4 ± 0.6) 10 3, V ts = (42.9 ± 2.6) 10 3 Lots of uncertainties cancel in the ratio V td / V ts = 0.211 ± 0.001 ± 0.006
V td and V ts No way to determine directly M d = (0.507 ± 0.004) ps 1, V td V tb 2 M s = (17.719 ± 0.043) ps 1, V ts V tb 2 Lattice for f B and V tb = 1 V td = (8.4 ± 0.6) 10 3, V ts = (42.9 ± 2.6) 10 3 Lots of uncertainties cancel in the ratio V td / V ts = 0.211 ± 0.001 ± 0.006 Can also use B K γ, B ργ, and their ratio V td / V ts = 0.21 ± 0.04
V td and V ts No way to determine directly M d = (0.507 ± 0.004) ps 1, V td V tb 2 M s = (17.719 ± 0.043) ps 1, V ts V tb 2 Lattice for f B and V tb = 1 V td = (8.4 ± 0.6) 10 3, V ts = (42.9 ± 2.6) 10 3 Lots of uncertainties cancel in the ratio V td / V ts = 0.211 ± 0.001 ± 0.006 Can also use B K γ, B ργ, and their ratio V td / V ts = 0.21 ± 0.04 K + π + ν ν gives V tsv td, theoretically clean, need more events
V td and V ts No way to determine directly M d = (0.507 ± 0.004) ps 1, V td V tb 2 M s = (17.719 ± 0.043) ps 1, V ts V tb 2 Lattice for f B and V tb = 1 V td = (8.4 ± 0.6) 10 3, V ts = (42.9 ± 2.6) 10 3 Lots of uncertainties cancel in the ratio V td / V ts = 0.211 ± 0.001 ± 0.006 Can also use B K γ, B ργ, and their ratio V td / V ts = 0.21 ± 0.04 K + π + ν ν gives V tsv td, theoretically clean, need more events All numbers consistent with CKM unitarity
V td and V ts No way to determine directly M d = (0.507 ± 0.004) ps 1, V td V tb 2 M s = (17.719 ± 0.043) ps 1, V ts V tb 2 Lattice for f B and V tb = 1 V td = (8.4 ± 0.6) 10 3, V ts = (42.9 ± 2.6) 10 3 Lots of uncertainties cancel in the ratio V td / V ts = 0.211 ± 0.001 ± 0.006 Can also use B K γ, B ργ, and their ratio V td / V ts = 0.21 ± 0.04 K + π + ν ν gives V tsv td, theoretically clean, need more events All numbers consistent with CKM unitarity
UT angle: α φ 2 α = arg( V td V tb /V udv ub ) From B ππ, πρ, ρρ (B ρρ: f L 1, CP-even) α = (85.4 3.8 +4.0 ) (direct) α = (94.9 6.8 +4.8 ) (CKM fit)
UT angle: β φ 1 β = arg( V cd V cb /V tdv tb ) arg(v td) B J/ψK S, φk S,... no discrepancy between c cs and s ss modes sin(2β) = 0.689 ± 0.019, β = (21.39 ± 0.78) (direct) β = (21.79 +0.78 0.73 ) (CKM fit)
UT angle: γ φ 3 Option 1: Consider B D CP K (or excitations), D CP D CP+, D CP Interference between b cūs and b u cs (Gronau,London,Wyler) Rate and CP asymmetries depend on γ, as well as r B = A(b u)/a(b c) and arg(r B ) Option 2: Consider B DK, D K + π and its charge conjugated channels (allowed, suppressed) (suppressed, allowed) (Atwood, Dunietz, Soni) Rate and CP asymmetries depend on γ, r B, arg(r B ), r D, arg(r D ) r D has been measured from D decays 0.06
UT angle: γ φ 3 Option 1: Consider B D CP K (or excitations), D CP D CP+, D CP Interference between b cūs and b u cs (Gronau,London,Wyler) Rate and CP asymmetries depend on γ, as well as r B = A(b u)/a(b c) and arg(r B ) Option 2: Consider B DK, D K + π and its charge conjugated channels (allowed, suppressed) (suppressed, allowed) (Atwood, Dunietz, Soni) Rate and CP asymmetries depend on γ, r B, arg(r B ), r D, arg(r D ) r D has been measured from D decays 0.06 Option 3: Use a Dalitz plot analysis for B DK, D K S π + π,... and its charge conjugate Simultaneous determination of γ, r B, arg(r B ) (Giri, Grossman, Sofer, Zupan)
UT angle: γ φ 3 Option 1: Consider B D CP K (or excitations), D CP D CP+, D CP Interference between b cūs and b u cs (Gronau,London,Wyler) Rate and CP asymmetries depend on γ, as well as r B = A(b u)/a(b c) and arg(r B ) Option 2: Consider B DK, D K + π and its charge conjugated channels (allowed, suppressed) (suppressed, allowed) (Atwood, Dunietz, Soni) Rate and CP asymmetries depend on γ, r B, arg(r B ), r D, arg(r D ) r D has been measured from D decays 0.06 Option 3: Use a Dalitz plot analysis for B DK, D K S π + π,... and its charge conjugate Simultaneous determination of γ, r B, arg(r B ) (Giri, Grossman, Sofer, Zupan)
UT angle: γ φ 3 γ = arg( V ud Vub /V cdvcb ) arg(v ub) γ = (68.0 +8.0 8.5 ) (direct) γ = (69.7 +1.3 2.8 ) (CKM fit)
Lesser known angles: β s V ts = 1 2 A(1 2ρ)λ4 iηaλ 4 ( β s = arg V cbvcs ) V tb Vts Comes in B s B s mixing, not to be confused with φ s = arg( M 12 /Γ 12 ) SM: β s = 0.019 ± 0.001 Exp: 0.020 ± 0.045 (direct), 0.0182(8) (fit) V us V ub + V cs V cb + V ts V tb = 0 (α s, β s, γ) α s π γ, can be extracted from B s K + K... LHCb? Super-B?
Lesser known angles: β s 0.25 0.20 0.15 LHCb 1.0 fb 1 + CDF 9.6 fb 1 + D 8 fb 1 + ATLAS 4.9 fb 1 D LHCb HFAG PDG 2013 68% CL contours ( ) 0.10 Combined 0.05 CDF SM ATLAS 0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 = 2β s The mirror image ( Γ s, π φ c cs s ) ruled out by LHCb, Γ s > 0 φ c cs s
BSM? What BSM? Nobody knows. Circumstantial evidence is occasionally very convincing, as when you find a trout in the milk. Arthur Conan Doyle
BSM? What BSM? Nobody knows. Circumstantial evidence is occasionally very convincing, as when you find a trout in the milk. Arthur Conan Doyle
Circumstantial evidence for BSM New physics in mixing? M 12 = M SM 12 exp(i ) 1.5σ from SM, coming from V ub
Circumstantial evidence for BSM Even better fit for B s Perfect fit with SM but does not include A b sl from the D0 dimuon result, 3.4σ away
Circumstantial evidence for BSM (A b sl ) SM = ( 2.4 ± 0.4) 10 4, (A b sl ) D0 = ( 7.87 ± 1.96) 10 3
Circumstantial evidence for BSM R(D ( ) ) = Br(B D( ) τν) Br(B D ( ) lν) 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) exp R(D) SM = 1.481 (1 ± 0.173), R(D ) exp R(D ) SM = 1.317 (1 ± 0.091).
Circumstantial evidence for BSM R(D ( ) ) = Br(B D( ) τν) Br(B D ( ) lν) 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) exp R(D) SM = 1.481 (1 ± 0.173), R(D ) exp R(D ) SM = 1.317 (1 ± 0.091).
Circumstantial evidence for BSM A I = Br(B0 K 0( ) µ + µ ) τ0 τ + Br(B + K +( ) µ + µ ) Br(B 0 K 0( ) µ + µ ) + τ0 τ + Br(B + K +( ) µ + µ ) A I = 0 in naive factorization ISR from spectator can contribute up to 1% unless q 2 is very small B K µµ is consistent with SM B Kµµ: 4.4σ away from zero, integrated over all q 2 [LHCb, 1205.3422] A I 1 0.5 0-0.5-1 + - B Kµ µ LHCb -1.5 0 5 10 15 20 25 2 q 2 [GeV /c 4 ] A I 0.5 Theory Data 0.4 * + - B K µ µ LHCb 0.3 0.2 0.1 0-0.1-0.2-0.3-0.4-0.5 0 5 10 15 20 2 q 2 [GeV /c 4 ]
Where to? CKM matrix seems to be unitary V uq 2 = 0.9999 ± 0.0006, q V qd 2 = 1.002 ± 0.005, q V cq 2 = 1.067 ± 0.047 q V qs 2 = 1.065 ± 0.046 q Also, α + β + γ = (178 +11 12 ) (direct), consistent with triangle New physics must be aligned Flav. structure a few TeV > a few TeV Anarchy O(1) X small ( < O(1)) Small small tiny misalignment (O(0.1)) (O(0.01-0.1)) Alignment tiny out of reach (MFV) (O(0.01)) < O(0.01)
Where to? CKM matrix seems to be unitary V uq 2 = 0.9999 ± 0.0006, q V qd 2 = 1.002 ± 0.005, q V cq 2 = 1.067 ± 0.047 q V qs 2 = 1.065 ± 0.046 q Also, α + β + γ = (178 +11 12 ) (direct), consistent with triangle New physics must be aligned Flav. structure a few TeV > a few TeV Anarchy O(1) X small ( < O(1)) Small small tiny misalignment (O(0.1)) (O(0.01-0.1)) Alignment tiny out of reach (MFV) (O(0.01)) < O(0.01)
Where to? 4th gen (constraint from S and T) V t b can still be significant (Soni et al. PRD 2010) New operator of the form (1/Λ 2 )( qγ µ P L q ) 2 is constrained from mixing: Λ > 100 TeV from B s, 10 4 TeV from K, comparable bounds from other structures If BSM is at 1 TeV, we hardly expect any drastically new source of CP violation β s consistent with SM, more from Super-B? Thank you.
Where to? 4th gen (constraint from S and T) V t b can still be significant (Soni et al. PRD 2010) New operator of the form (1/Λ 2 )( qγ µ P L q ) 2 is constrained from mixing: Λ > 100 TeV from B s, 10 4 TeV from K, comparable bounds from other structures If BSM is at 1 TeV, we hardly expect any drastically new source of CP violation β s consistent with SM, more from Super-B? Thank you.