Flavour physics (1)

Flavour physics (1)

S ´ebastien Descotes-Genon

Laboratoire de Physique Th ´eorique CNRS & Universit ´e Paris-Sud 11, 91405 Orsay, France

XLII International Meeting on Fundamental Physics Benasque, 27 January 2014

LPT Orsay

Outline

Why and how flavour is useful Basics of flavour physics CP-violation

Neutral-meson mixing Effective approaches Flavour in the Standard Model Hints of NP in flavour data

Flavour physics

Particle physics

Central question of QFT-based particle physics L=?

i.e. which degrees of freedom, symmetries, scales ?

H

3 générations

SM best answer up to now, but neutrino masses

dark matter dark energy

baryon asymmetry of the universe

hierarchy problem

=⇒3 generations playing a particular role in the SM

Particle physics

Central question of QFT-based particle physics L=?

i.e. which degrees of freedom, symmetries, scales ?

H

3 générations

SM best answer up to now, but neutrino masses

dark matter dark energy

baryon asymmetry of the universe

hierarchy problem

=⇒3 generations playing a particular role in the SM

Flavour in the SM

L_SM =L_gauge(Aa,Ψ_j)+L_Higgs(φ,Aa,Ψ_j) Gauge partL_gauge(Aa,Ψ_j)

Highly symmetric (gauge symmetry,flavour symmetry) Well-tested experimentally (electroweak precision tests) Stable with respect to quantum corrections

Higgs partL_Higgs(φ,Aa,Ψ_j) Ad hoc potential

Dynamics not fully tested

Not stable w.r.t quantum corrections

Origin offlavour structureof the Standard Model

Fermions in SM

SM:SU_C(3)⊗SU_L(2)⊗U_Y(1) Colour (for quarks only)

Weak isospin (for left-handed fermions only) Hypercharge (for everybody)

Standard Model is chiral: distinction between left- and right-chiralities Helicity: Projection of spin on momentum

but notion which is frame dependent for massive particle Chirality: Lorentz-invariant equivalent, identical form=0

P_R= (1+γ₅)/2 P_L= (1−γ₅)/2

=⇒Left chirality with weak isospin, right chirality without

SM fermion assignments

Covariant derivative for fermions, involvingW^1,2,3andB gauge bosons D_µψ= (∂_µ−igW_µ^aT^a−ig⁰YB_µ)ψ

Using the physicalW⁺,W⁻,Z⁰weak bosons andAµphoton Dµ=∂µ− ig

√

2(W_µ⁺T⁺+W_µ⁻T⁻)−ig²T³−g⁰²Y

pg²+g⁰² Zµ−i gg⁰

pg²+g⁰²(T³+Y)Aµ

whereQ=T₃+Y ande= √^gg0

g²+g⁰² Fields T3 Y Q=T3+Y

EL

„ νe

e

«

L

1/2 -1/2

„ 0

−1

«

eR eR 0 -1 -1

νR νR 0 0 0

QL

„ uL

dL

«

L

1/2 1/6

„ 2/3

−1/3

«

uR uR 0 2/3 2/3

dR dR 0 -1/3 -1/3

W^±couples only to left-handed fermions in doublets

ν_Rno quantum numbers (needed only to provide masses to neutrinos)

Electroweak currents

Lagrangian for masless 1st generation ψ∈ {E_L,e_R,Q_L,u_R,d_R} in terms of mass-eigenstates for bosons L_gauge,ψ =X

ψ

ψD¯ /ψ=X

ψ

ψ∂¯/ψ+g(W_µ⁺J_W^µ++W_µ⁻J_W^µ−+ZµJ_Z^µ)+eAµJ_em^µ

J_W^µ+ = 1

√2(¯νLγ^µeL+ ¯uLγ^µdL) J_W^µ− = 1

√2(¯eLγ^µνL+ ¯dLγ^µuL)

J_Z^µ = 1 cW

(1

2ν¯LγµνL+

„ s_W² −1

2

«

e¯LγµeL+s²_We¯RγµeR

+

„1 2−2

3s²_W

«

¯

uLγ^µuL−2

3s_W²¯uRγ^µuR+

„1 3s_W² −1

2

«

d¯Lγ^µdL+1

3s²_Wd¯Rγ^µdR

)

J_em^µ = −¯eγ^µe+2

3¯uγ^µu−1 3d¯γ^µd cW =g/p

g²+g⁰²,sW = q

1−c_W² weak mixing(W_µ³,B_µ)↔(Z_µ⁰,A_µ) charged-currents only left-handedψ_L= [(1−γ5)/2]ψ

neutral currents both left- and right-handed (and vector for photon)

From BEH to CKM

General Yukawa interaction between Higgs and (3 families of) quarks LHiggs,quarks = ¯Q_LⁱY_D^ikd_R^kφ+ ¯Q_LⁱY_U^iku_R^kφc+h.c.+. . .

Vacuum expectation value for Higgshφi 6=0 yields mass matrices LHiggs,quarks = ¯d_LⁱM_D^ikd_R^k + ¯u_LⁱM_U^iku_R^k +. . .

Diagonalise the mass matrices to get mass eigenstatesψ⁰ m_q= yqhφi

√

2 M_D=diag(md,m_s,m_b) M_U =diag(mu,m_c,m_t) which are different from weak-interaction eigenstatesψ

U =



 u c t



=Vu



 u⁰ c⁰ t⁰



 D=



 d s b



=V_d



 d⁰ s⁰ b⁰





=⇒Potential misalignement between (unitary) rotations:V_u 6=V_d

CKM and flavour-changing charged currents

Charged currents in mass eigenstates involve matrixV J_W^µ = ¯u_Lⁱγ^µd_Lⁱ →u¯_L⁰V_u^†γ^µV_dd_L⁰ = ¯u_L⁰Vγ^µd_L⁰

Flavour-changing charged currents between generations at tree-level

W d_j

ui g

√

2[¯u_LiV_ijγ^µd_LjW_µ⁺+ ¯d_LjV_ij^∗γ^µu_LiW_µ⁻] unitaryCabibbo-Kobayashi-Maskawa matrix (linked to electroweak symmetry breaking) InSM_mν6=0, there is an equivalent mixing matrix for leptonsU_PMNS

FCNC or flavour-changing neutral currents

Neutral currents remain flavour-diagonal in mass eigenstates

¯uⁱ_Lγ^µu_Lⁱ →u¯_L⁰V_u^†γ^µV_uu_L⁰ = ¯u⁰_Lγ^µu_L⁰, d¯_Lⁱγ^µd_Lⁱ →d¯_L⁰V_d^†γ^µV_dd_L⁰ = ¯d_L⁰γ^µd_L⁰,

No flavour-changing neutral currents within or between generations . . . but only at tree level ! They can occur in loops

However, SM FCNC heavily suppressed by two mechanisms Loop: Higher order in pert. theory (suppr. by powers ofg,g⁰) GIM: Vanish in degenerate casem_u=m_c =m_t

(proportional toV_tb^∗V_ts+V_cb^∗ V_cs+V_ub^∗ V_us=0)

CP-violation

CP and CKM

C (Charge conjugation) and P (Parity) combined inCP

ψ¯₁γ_µ(1−γ₅)ψ₂→ψ¯₂γ_µ(1−γ₅)ψ₁ ψ¯1γµ(1+γ5)ψ2→ψ¯2γµ(1+γ5)ψ1

(at(~x,t)and(−~x,t)respectively) symmetry of QCD/QED, but symmetry for weak interactions ?

W_µ⁺¯u_iV_ijγ^µ(1−γ5)d_j+W_µ⁻d¯_jV_ij^∗γ^µ(1−γ5)u_i

→ W_µ⁻d¯_iV_ijγ^µ(1−γ₅)u_j+W_µ⁺u¯_jV_ij^∗γ^µ(1−γ₅)d_i Weak interactions are CP-invariant ifV is real ForN_ggenerations,V contains

(N_g−1)(N_g−2)/2 phases N_g(N_g−1)/2 moduli

Structure of CKM matrix

For two generations, 1 modulus, no phase, no CP violation (Cabbibo)

V =

V_ud V_us V_cd Vcs

=

cosθ sinθ

−sinθ cosθ

For three generations, 3 moduli and 1 phase, aunique source of CP

violationin quark sector (Kobayashi-Maskawa)

V= 2 4

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

3 5'

2 6 4

1−^λ₂² λ Aλ³( ¯ρ−iη)¯

−λ 1−^λ₂² Aλ² Aλ³(1−ρ¯−iη)¯ −Aλ² 1

3 7

5+O(λ⁴)

where we have exploited the observed hierarchy of matrix elements (V =1+O(λ), close to unity)

=⇒extremelypredictivemodel for CP violation embedded in SM

Unitarity triangles

Many unitarity relations, e.g., related to 4 neutral mesons (no top) B_d meson (bd) : V_udV_ub^∗ +V_cdV_cb^∗ +V_tdV_tb^∗ =0 (λ³, λ³, λ³) B_s meson (bs) : V_usV_ub^∗ +V_csV_cb^∗ +V_tsV_t^∗_b=0 (λ⁴, λ², λ²) K meson (sd) : V_udV_us^∗ +V_cdV_cs^∗ +V_tdV_t^∗_s=0 (λ, λ, λ⁵) Dmeson (cu) : V_udV_cd^∗ +V_usV_cs^∗ +V_ubV_cb^∗ =0 (λ, λ, λ⁵) Representation of (ρ, η) through rescaled triangles

(small but non squashed) B_D-meson triangle (bd)

(large but squashed) D-meson triangle (cu) In practice, alwaysB_d unitarity triangle (but only 2 parameters out of 4)

A handle on the CKM matrix

Measurements in terms of hadrons, not of quarks !

d →u: Nuclear physics (superallowedβdecays) s→u: Kaon physics (KLOE, KTeV, NA62)

c →d,s: Charm physics (CLEO-c, Babar, Belle, BESIII)

b→u,c andt→d,s: B physics (Babar, Belle, CDF, DØ, LHCb) t →b: Top physics (CDF/DØ, ATLAS, CMS)

Determine structure of CKM matrix from|V_ij|(CP-allowed processes) and/or arg(V_ij)(CP-violating processes)

Long-distance QCD

Take processes conjugate underCP b→u : A( ¯B⁰→π⁺`⁻ν)¯ ∝V_ub×F_B→π

¯b→¯u : A(B⁰→π⁻`⁺ν)∝V_ub^∗ ×FB→π

whereFB→π form factor defined fromhπ⁺|¯uγµ(1−γ5)b|Bi¯

encoding hadronisation of quarks into hadrons General feature : flavour processes with

weak part :odd under CP (phase from CKM)

strong part : even under CP (phase from strong interaction)

|V_ij|via CP-conserving quantity (|A|²)

from rates where hadronic quantities are crucial argV_ij via CP-violating quantity (Re(A1A^∗₂),Im(A1A^∗₂))

from asymmetries where hadronic quantities may cancel out CP-violation from relative phases between conjugate proc.

CP violation in decay

CP-conjugate processesB→f andB¯ →¯f (Bcharged or neutral) A_f =X

k

A_ke^iδke^iφk A¯¯f =X

k

A_ke^iδke^−iφk

δ_k:CP-even strong phases φ_k:CP-odd weak phases

A_f A¯¯f

6=1=⇒CP violation indecay

Asymmetry of the form Γ(B→f)−Γ( ¯B →¯f)

Γ(B→f) + Γ( ¯B →¯f) ∝sin(φ_i−φ_j)sin(δ_i−δ_j) need two different contributions with different strong phases strong and weak phases from decay

Observed inK-decays (⁰),B⁰→K⁺π⁻,π⁺π⁻,ηK^∗0. . . but weak phases do not only occur in decays

CP violation in decay

CP-conjugate processesB→f andB¯ →¯f (Bcharged or neutral) A_f =X

k

A_ke^iδke^iφk A¯¯f =X

k

A_ke^iδke^−iφk

δ_k:CP-even strong phases φ_k:CP-odd weak phases

A_f A¯¯f

6=1=⇒CP violation indecay

Asymmetry of the form Γ(B→f)−Γ( ¯B →¯f)

Γ(B→f) + Γ( ¯B →¯f) ∝sin(φ_i−φ_j)sin(δ_i−δ_j) need two different contributions with different strong phases strong and weak phases from decay

Observed inK-decays (⁰),B⁰→K⁺π⁻,π⁺π⁻,ηK^∗0. . . but weak phases do not only occur in decays

Neutral-meson mixing

Neutral-meson mixing

Loops allow∆F =2 FCNC

=⇒neutral-meson mixing possible id

dt

|M(t)i

|M(t)i¯

= M− i

2Γ |M(t)i

|M(t)i¯

Quantum-Mech. forM =K⁰,D⁰,B_d⁰,B_s⁰, withMandΓhermitian Γfrom restriction to 2 states

mixing due to non-diagonal termsM₁₂−iΓ₁₂/2

Diagonalisation: physical|M_H,Liof massesM_H,L, widthsΓ_H,L

|M_Li=p|Mi+q|Mi,¯ |M_Hi=p|Mi −q|Mi¯ |p|²+|q|²=1 In terms ofM₁₂,|Γ₁₂|andφ=arg

−^M_Γ¹²

12

Mass difference∆M =M_H−M_L=2|M₁₂| Width difference∆Γq= Γ_L−Γ_H =2|Γ₁₂|cos(φ) Mixing coefficientspandq

Neutral-meson mixing

Loops allow∆F =2 FCNC

=⇒neutral-meson mixing possible id

dt

|M(t)i

|M(t)i¯

= M− i

2Γ |M(t)i

|M(t)i¯

Quantum-Mech. forM =K⁰,D⁰,B_d⁰,B_s⁰, withMandΓhermitian Γfrom restriction to 2 states

mixing due to non-diagonal termsM₁₂−iΓ₁₂/2

Diagonalisation: physical|M_H,Liof massesM_H,L, widthsΓ_H,L

|M_Li=p|Mi+q|Mi,¯ |M_Hi=p|Mi −q|Mi¯ |p|²+|q|²=1 In terms ofM₁₂,|Γ₁₂|andφ=arg

−^M_Γ¹²

12

Mass difference∆M =M_H−M_L=2|M₁₂| Width difference∆Γq= Γ_L−Γ_H =2|Γ₁₂|cos(φ) Mixing coefficientspandq

Time evolution

Evolution of mass eigenstates in terms of CP-eigenstates

|M(t)i=g₊(t)|Mi+q

pg₋(t)|Mi¯ , |M(t)i¯ = p

qg₋(t)|Mi+g₊(t)|Mi¯ with time dependences [g₊(0) =1,g−(0) =1]

g₊(t) = e^−iMte^−Γt/2

cosh∆Γt

4 cos∆Mt

2 −isinh∆Γt

4 sin∆Mt 2

g−(t) = e^−iMte^−Γt/2

−sinh∆Γt

4 cos∆Mt

2 +icosh∆Γt

4 sin∆Mt 2

with average masses and widthsM,Γ, as well as differences∆Γ,∆M

Four very different mesons

1 2 3 4 5 tG

0.2 0.4 0.6 0.8 1.0 PHtL

K

1 2 3 4 5 6 tG

0.2 0.4 0.6 0.8 1.0 PHtL

D

1 2 3 4 5 tG

0.2 0.4 0.6 0.8 1.0 PHtL

B_d

1 2 3 4 5 tG

0.2 0.4 0.6 0.8 1.0 PHtL

B_s K:∆m∼∆Γ∼Γ:K_L(long) andK_S (short) rather than heavy-light D: very littleD¯ before decay

B:∆Γ'0

B_s:∆mΓ: very rapid oscillations

Oscillations

B-factories (Babar/Belle) Coherent production Υ(4S)→B_dB¯_d [idem with Bs atΥ(5S)]

Flavour tagged through one decay, which fixes the flavour of the otherB and starts the clock for its evolutiont =0

Low statistics, but very good control of kinematics

Hadronic machines (CDF/DØ/LHCb)

Incoherent production of b-hadrons frompp collisions

Possibility of oscillations for both tagging and signal b-hadrons (40%B_d, 10%

Bs)

High statistics, but less good control of kinematics

Time-dependent decay rates

Γ(M(t)→f) = N_f²|Af|²e^−Γt

(1+|λf|²

2 cosh∆Γt

2 +1− |λf|²

2 cos(∆Mt)

−Reλfsinh∆Γt

2 −Imλfsin(∆Mt) )

Γ( ¯M(t)→f) = N_f²|Af|²

˛

˛

˛

˛ p q

˛

˛

˛

˛

2

e^−Γt

(1+|λf|²

2 cosh∆Γt

2 −1− |λf|²

2 cos(∆Mt)

−Reλfsinh∆Γt

2 +Imλfsin(∆Mt) )

Decay amplitudesA_f =A(M→f),A¯_f =A( ¯M →f) Ratio of mixing and decay amplitude parameters

λ_f = q p

A¯_f A_f

Similar possibilities withf replaced byCP-conjugate¯f

CP violation in mixing

Neutral mass eigenstates not necessarily CP-eigenstates

|M_Li=p|Mi+q|Mi¯ |M_Hi=p|Mi −q|Mi¯

q p

6=1=⇒CPviolation inmixing

flavour-specific decays (A¯_f =A¯f =0) with no CP-violation in decay (|A_f|=|A¯¯f|) weak phase from mixing only

“Wrong-sign” semileptonic decays (`<sup>−</sup>←B(b¯ d¯)↔B(¯bd)→`⁺) a_SL= Γ( ¯B⁰(t)→`<sup>+</sup>νX)−Γ(B<sup>0</sup>(t)→`⁻νX¯ )

Γ( ¯B⁰(t)→`<sup>+</sup>νX) + Γ(B<sup>0</sup>(t)→`⁻νX¯ ) = |p|⁴− |q|⁴

|p|⁴+|q|⁴ Seen forK meson (_K),

but tiny asymmetry in SM forB_d,smesons,q/p almost a pure phase

CP violation in mixing

Neutral mass eigenstates not necessarily CP-eigenstates

|M_Li=p|Mi+q|Mi¯ |M_Hi=p|Mi −q|Mi¯

q p

6=1=⇒CPviolation inmixing

flavour-specific decays (A¯_f =A¯f =0) with no CP-violation in decay (|A_f|=|A¯¯f|) weak phase from mixing only

“Wrong-sign” semileptonic decays (`<sup>−</sup>←B(b¯ d¯)↔B(¯bd)→`⁺) a_SL= Γ( ¯B⁰(t)→`<sup>+</sup>νX)−Γ(B<sup>0</sup>(t)→`⁻νX¯ )

Γ( ¯B⁰(t)→`<sup>+</sup>νX) + Γ(B<sup>0</sup>(t)→`⁻νX¯ ) = |p|⁴− |q|⁴

|p|⁴+|q|⁴ Seen forK meson (_K),

but tiny asymmetry in SM forB_d,smesons,q/palmost a pure phase

CPV in interf. between decay with & w/o mixing

For decays intoCP-eigenstate:M→f_CPandM →M¯ →f_CPinterfere λ_f = q

p A¯_f

A_f 6=±1=⇒CP-violation ininterference. . .

Γ( ¯M(t)→f)−Γ(M(t)→f)

Γ( ¯M(t)→f) + Γ(M(t)→f) = − A^dir_CPcos(∆Mt) +A^mix_CP sin(∆Mt)

cosh(∆Γt/2) +A^∆Γ_CPsinh(∆Γt/2)+O 1−

˛

˛

˛

˛ q p

˛

˛

˛

˛

2!

A^dir_CP =1− |λf|²

1+|λf|² A^mix_CP =−2Imλf

1+λf|² A^∆Γ_CP =− 2Reλf

1+λf|² |A^dirCP|²+|A^mixCP|²+|A^∆ΓCP|²=1

weak phase from both mixing and decay

if one weak phase dominates decay amplitudes [“golden modes”]

|A_f|=|A¯_f|andA^dir_CP=0

λ_f pure weak phase andA^mix_CP =Imλ_f Bd →J/ψK_S,Bs→J/ψφ ifAhas comparable amplitudes with different weak phases, interpretation more difficult B→πK. . .

Two decades of CKM

md

K

K ms &

md

Vub

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

excluded area has CL > 0.95

1995 CKMf i t t e r

md

K

K ms &

md

Vub sin 2

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

excluded area has CL > 0.95

Summer 2001 CKMf i t t e r

md

K

K ms &

md

Vub sin 2

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

excluded area has CL > 0.95

2004 CKMf i t t e r

1995 2001 2004

md

K

K ms &

md

Vub sin 2

(excl. at CL > 0.95) < 0 sol. w/ cos 2 excluded at CL > 0.95

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

excluded area has CL > 0.95

2006 CKMf i t t e r

md

K

K ms &

md

Vub sin 2

(excl. at CL > 0.95) < 0 sol. w/ cos 2 excluded at CL > 0.95

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

excluded area has CL > 0.95

2009 CKMf i t t e r

md K

K ms &

md

Vub sin 2

(excl. at CL > 0.95) < 0 sol. w/ cos 2 ex cl uded at CL >

0.

95

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

excluded area has CL > 0.95

FPCP 13 CKMf i t t e r

2006 2009 2013

The current status of CKM

md K

K

ms

&

md

ubSL

V Vub

sin 2

(excl. at CL > 0.95) < 0 sol. w/ cos 2 ex

cluded

at CL >

0.95

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

excluded area has CL > 0.95

FPCP 13

CKMf i t t e r

|V_ud|,|V_us|,|V_cb|,|V_ub|_SL B→τ ν

∆m_d,∆m_s,K

α, sin 2β,γ

A=0.823^+0.012_−0.033 λ=0.2246^+0.0019_−0.0001

¯

ρ=0.129^+0.018_−0.009

¯

η =0.348^+0.012_−0.012 (68% CL)

Effective approaches

Quark flavour parameters and SM

Gauge Higgs Fermions

γg

t b

c s

W Z

ud ν_i

φ

μ τ

e NP?

Important, unexplained hierarchy among 10 of 19 params of SM_mν=0 Mass (6 params, a lot of small ratios of scales)

CP violation (4 params, strong hierarchy between generations)

With interesting phenomenological consequences CP asymmetries from a single parameter

Quantum sensitivity (via loops) to large range of scales Suppression of Flavour-Changing Neutral Currents

Very significant constraints on any NP extension

Good track record: charm (no K_L→µµ), 3rd family (_K), m_c (∆m_K), m_t (∆m_B)

Quark flavour parameters and SM

Gauge Higgs Fermions

γg

t b

c s

W Z

ud ν_i

φ

μ τ

e NP?

Important, unexplained hierarchy among 10 of 19 params of SM_mν=0 Mass (6 params, a lot of small ratios of scales)

CP violation (4 params, strong hierarchy between generations) With interesting phenomenological consequences

CP asymmetries from a single parameter

Quantum sensitivity (via loops) to large range of scales Suppression of Flavour-Changing Neutral Currents

Very significant constraints on any NP extension

Good track record: charm (no K_L→µµ), 3rd family (_K), m_c (∆m_K), m_t (∆m_B)

A multi-scale problem

Gauge Higgs Fermions

γg

t b

c s

W Z

ud ν_i

φ

μ τ

e

NP?

Heavy quarks

Non-perturb. QCD Electroweak

Tough multi-scale challenge with 3 interactions intertwined Several steps to separate/factorise scales

BSM→SM+1/Λ(Λ_EW/Λ)→H_eff (m_b/Λ_EW)→eff. th. (Λ_QCD/m_b)

Th problem from hadronisation of quarks into hadrons:

description/parametrisation in terms of QCD quantities decay constants, form factors, bag parameters. . . Long-distance non-perturbative QCD: source of uncertainties

lattice QCD simulations, effective theories. . .

A multi-scale problem

Gauge Higgs Fermions

γg

t b

c s

W Z

ud ν_i

φ

μ τ

e

NP?

Heavy quarks

Non-perturb. QCD Electroweak

Tough multi-scale challenge with 3 interactions intertwined Several steps to separate/factorise scales

BSM→SM+1/Λ(Λ_EW/Λ)→H_eff (m_b/Λ_EW)→eff. th. (Λ_QCD/m_b) Th problem from hadronisation of quarks into hadrons:

description/parametrisation in terms of QCD quantities decay constants, form factors, bag parameters. . . Long-distance non-perturbative QCD: source of uncertainties

lattice QCD simulations, effective theories. . .

H

: From Fermi to electroweak

Fermi-like approach : separation between different scales Short distances : numerical coefficients

Long distances : local operator

b b

V_udV_cb^{∗ G√F}

2 m²_W

m²_W−p²_W uγ¯ _µ(1−γ5)dbγ¯ ^µ(1−γ5)c

Before/below SM, Fermi theory carried info on yesterday’s NP (=EW) G_F: scale of “new physics”

O_i: interaction with left-handed fermions, through charged spin 1 Obviously not all info (gauge structure,Z⁰. . . ), but a good start, especially if you cannot excite the NP degrees of freedom directly

H

: From Fermi to electroweak

Fermi-like approach : separation between different scales Short distances : numerical coefficients

Long distances : local operator

b b

V_udV_cb^{∗ √GF}

2 uγ¯ _µ(1−γ5)dbγ¯ ^µ(1−γ5)c

Before/below SM, Fermi theory carried info on yesterday’s NP (=EW) G_F: scale of “new physics”

O_i: interaction with left-handed fermions, through charged spin 1 Obviously not all info (gauge structure,Z⁰. . . ), but a good start, especially if you cannot excite the NP degrees of freedom directly

H

: From heavy quarks to SM (1)

SM

→

H_eff Taking into account one (or more) gluons

H_eff = G_F

√

2V_cb^∗V_ud[C₁(µ)Q₁(µ)+C₂(µ)Q₂(µ)]

Q₁ = (¯b_αc_β)_V−A(¯u_βd_α)_V−A (¯bc)_V−A= ¯bγ_µ(1−γ₅)c Q₂ = (¯b_αc_α)_V−A(¯u_βd_β)_V−A

new colour structures (flipped indicesα, β) divergences absorbed by renormalisation

C₁andC₂calculable fonctions ofµas perturbative series inα_s µseparation scale between short- and long-distance physics

H

: From heavy quarks to SM (2)

Gauge Higgs Fermions

γg

t b

c s

W Z

ud ν_i

φ

μ τ

e

NP?

Heavy quarks

Non-perturb. QCD Electroweak

A(B→H) =P

iV_CKM,iC_i(µ)hQ_ii(µ)

Simplification of the problem, keeping only relevant d.o.f.

Matching to fundamental theory at a high scaleµ0=O(M_W,mt) Evolution down toµ_b=O(m_b)done by renormalisation group

=⇒resummation of large logsα_s(µ_b)ⁿlog^k(µ²_b/µ²₀)inC(µ_b)

V_udV_ub^∗ (¯bu)_V−A(¯ud)_V−A V_qdV_qb^∗ (¯bd)_V−AP

q(¯qq)_V±A

H

: From heavy quarks to SM (2)

Gauge Higgs Fermions

γg

t b

c s

W Z

ud ν_i

φ

μ τ

e

NP?

Heavy quarks

Non-perturb. QCD Electroweak

A(B→H) =P

iV_CKM,iC_i(µ)hQ_ii(µ)

Simplification of the problem, keeping only relevant d.o.f.

Matching to fundamental theory at a high scaleµ0=O(M_W,mt) Evolution down toµ_b=O(m_b)done by renormalisation group

=⇒resummation of large logsα_s(µ_b)ⁿlog^k(µ²_b/µ²₀)inC(µ_b)

V_udV_ub^∗ (¯bu)V−A(¯ud)_V−A V_qdV_qb^∗ (¯bd)_V−AP

q(¯qq)V±A

H

: From heavy quarks to SM (2)

Gauge Higgs Fermions

γg

t b

c s

W Z

ud ν_i

φ

μ τ

e

NP?

Heavy quarks

Non-perturb. QCD Electroweak

A(B→H) =P

iV_CKM,iC_i(µ)hQ_ii(µ)

Simplification of the problem, keeping only relevant d.o.f.

Matching to fundamental theory at a high scaleµ0=O(M_W,mt) Evolution down toµ_b=O(m_b)done by renormalisation group

=⇒resummation of large logsα_s(µ_b)ⁿlog^k(µ²_b/µ²₀)inC(µ_b)

V_udV_ub^∗ (¯bu)V−A(¯ud)_V−A V_qdV_qb^∗ (¯bd)_V−AP

q(¯qq)V±A

H

: From heavy quarks to SM (3)

Current-curent (¯bu)V−A(¯ud)_V−A, (¯biuj)_V−A(¯ujdi)_V−A

QCD penguins (¯bd)V−AP

q(¯qq)_V±A, (¯b_id_j)_V−AP

q(¯q_jq_i)_V±A Electroweak penguins

(¯bd)V−AP

qeq(¯qq)V±A, (¯b_id_j)_V−AP

qe_q(¯q_jq_i)_V±A Magnetic operators

e

8π²mb¯sσ^µν(1+γ₅)bFµν,

g

8π²m_b¯sσ^µν(1+γ₅)bGµν

∆B=2 operators (¯bd)V−A(¯bd)_V−A Semileptonic operators

(¯bs)V−A(¯ee)_V/A

H

: From heavy quarks to SM (3)

Current-curent (¯bu)V−A(¯ud)_V−A, (¯biuj)_V−A(¯ujdi)_V−A QCD penguins

(¯bd)V−AP

q(¯qq)_V±A, (¯b_id_j)_V−AP

q(¯q_jq_i)_V±A

Electroweak penguins (¯bd)V−AP

qeq(¯qq)V±A, (¯b_id_j)_V−AP

qe_q(¯q_jq_i)_V±A Magnetic operators

e

8π²mb¯sσ^µν(1+γ₅)bFµν,

g

8π²m_b¯sσ^µν(1+γ₅)bGµν

∆B=2 operators (¯bd)V−A(¯bd)_V−A Semileptonic operators

(¯bs)V−A(¯ee)_V/A

H

: From heavy quarks to SM (3)

Current-curent (¯bu)V−A(¯ud)_V−A, (¯biuj)_V−A(¯ujdi)_V−A QCD penguins

(¯bd)V−AP

q(¯qq)_V±A, (¯b_id_j)_V−AP

q(¯q_jq_i)_V±A Electroweak penguins

(¯bd)V−AP

qeq(¯qq)V±A, (¯b_id_j)_V−AP

qe_q(¯q_jq_i)_V±A

Magnetic operators

e

8π²mb¯sσ^µν(1+γ₅)bFµν,

g

8π²m_b¯sσ^µν(1+γ₅)bGµν

∆B=2 operators (¯bd)V−A(¯bd)_V−A Semileptonic operators

(¯bs)V−A(¯ee)_V/A

H

: From heavy quarks to SM (3)

Current-curent (¯bu)V−A(¯ud)_V−A, (¯biuj)_V−A(¯ujdi)_V−A QCD penguins

(¯bd)V−AP

q(¯qq)_V±A, (¯b_id_j)_V−AP

q(¯q_jq_i)_V±A Electroweak penguins

(¯bd)V−AP

qeq(¯qq)V±A, (¯b_id_j)_V−AP

qe_q(¯q_jq_i)_V±A Magnetic operators

e

8π²mb¯sσ^µν(1+γ₅)bFµν,

g

8π²m_b¯sσ^µν(1+γ₅)bGµν

∆B=2 operators (¯bd)V−A(¯bd)_V−A Semileptonic operators

(¯bs)V−A(¯ee)_V/A