Effective Field Theory approachesto Flavor Physics beyond the SM
Gino Isidori[ University of Zürich ]
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
Lecture I [The SM as an EFT]Lecture II [EFT tools for B Physics]Lecture III [Flavor Physics beyond the SM]
Effective Field Theory approachesto Flavor Physics beyond the SM
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
Gino Isidori[ University of Zürich ]
Lecture I [The SM as an EFT]The Standard Model and its flavor structureProperties of the CKM matrix and status of CKM fitsThe SM as an Effective Field Theory
Lecture II [EFT tools for B Physics] Lecture III [Flavor Physics beyond the SM]
The Standard Model and its flavor structure
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
Particle physics is described with good accuracy by a simple and economical theory:
ℒSM = ℒgauge (Aa, ψi) + ℒHiggs(ϕ, Aa, ψi )
The Standard Model and its flavor structure
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
ℒSM = ℒgauge (Aa, ψi) + ℒHiggs(ϕ, Aa, ψi )
Natural
Experimentally tested with high accuracy
Stable with respect to quantum corrections
Highly symmetric:
Σa - (Fμνa)2 + Σψ Σi ψi iD ψi
1
4ga2ℒgauge =
SU(3)c×SU(2)L×U(1)Y local symmetry
Global flavor symmetry
The Standard Model and its flavor structure
Particle physics is described with good accuracy by a simple and economical theory:
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
Natural
Experimentally tested with high accuracy
Stable with respect to quantum corrections
Highly symmetric
Ad hoc
Necessary to describe data [clear indication of a non-invariant vacuum] weakly tested in its dynamical form
Not stable with respect to quantum corrections
Origin of the flavor structure of the model [and of all the problems of the model...]
Particle physics is described with good accuracy by a simple and economical theory:
ℒSM = ℒgauge (Aa, ψi) + ℒHiggs(ϕ, Aa, ψi )
The Standard Model and its flavor structure
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
Natural
Experimentally tested with high accuracy
Stable with respect to quantum corrections
Highly symmetric
Ad hoc
Necessary to describe data [clear indication of a non-invariant vacuum] weakly tested in its dynamical form
Not stable with respect to quantum corrections
Origin of the flavor structure of the model [and of all the problems of the model...]
Particle physics is described with good accuracy by a simple and economical theory:
ℒSM = ℒgauge (Aa, ψi) + ℒHiggs(ϕ, Aa, ψi )
Elegant & stable, but also a bit boring...
Ugly & unstable, but is what makes nature interesting...!
The Standard Model and its flavor structure
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
3 identical replica of the basic fermion family [ψ = QL , uR, dR, LL, eR ] ⇒ huge flavor-degeneracy
The gauge Lagrangian is invariant under 5 independent U(3) global rotations for each of the 5 independent fermion fields
E.g.: QLi → Uij
QLj
U(1) flavor-independent phase +
SU(3) flavor-dependent mixing matrix
ℒSM = ℒgauge (Aa, ψi) + ℒHiggs(ϕ, Aa, ψi )
Σ ψ = QL , uR ,dR ,LL ,eR Σi=1..3 ψi iD ψi
QL = uL
dL
LL = νL
eL
, uR , dR , , eR
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
3 identical replica of the basic fermion family [ψ = QL , uR, dR, LL, eR ] ⇒ huge flavor-degeneracy: U(3)5 global symmetry
ℒSM = ℒgauge (Aa, ψi) + ℒHiggs(ϕ, Aa, ψi )
U(1)L × U(1)B × U(1)Y × SU(3)Q × SU(3)U × SU(3)D ×...
Flavor mixingLepton numberBarion number
Hypercharge
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
3 identical replica of the basic fermion family [ψ = QL , uR, dR, LL, eR ] ⇒ huge flavor-degeneracy: U(3)5 global symmetry
ℒSM = ℒgauge (Aa, ψi) + ℒHiggs(ϕ, Aa, ψi )
Within the SM the flavor-degeneracy is broken only by the Yukawa interaction:
QLi YD
ik dRk ϕ + h.c. → dL
i MDik dR
k + ...
QLi YU
ik uRk ϕc + h.c. → uL
i MUik uR
k + ...
in the quarksector:
_
_
_
_
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
3 identical replica of the basic fermion family [ψ = QL , uR, dR, LL, eR ] ⇒ huge flavor-degeneracy: U(3)5 global symmetry
ℒSM = ℒgauge (Aa, ψi) + ℒHiggs(ϕ, Aa, ψi )
Within the SM the flavor-degeneracy is broken only by the Yukawa interaction:
QLi YD
ik dRk ϕ + h.c. → dL
i MDik dR
k + ...
QLi YU
ik uRk ϕc + h.c. → uL
i MUik uR
k + ...
in the quarksector:
_
_
_
_
The Y are not hermitian → diagonalized by bi-unitary transformations:
VD+ YD
UD = diag(yb , ys , yd)
VU+ YU
UU = diag(yt , yc , yu)yi = ≈
2½ mqi
〈 ϕ〉
mqi
174 GeV
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
3 identical replica of the basic fermion family [ψ = QL , uR, dR, LL, eR ] ⇒ huge flavor-degeneracy: U(3)5 global symmetry
ℒSM = ℒgauge (Aa, ψi) + ℒHiggs(ϕ, Aa, ψi )
Within the SM the flavor-degeneracy is broken only by the Yukawa interaction:
QLi YD
ik dRk ϕ + h.c. → dL
i MDik dR
k + ...
QLi YU
ik uRk ϕc + h.c. → uL
i MUik uR
k + ...
in the quarksector:
_
_
_
_
YD = diag(yd ,ys ,yb)
YU = V+ × diag(yu ,yc ,yt)
The residual flavor symmetry let us to choose a (gauge-invariant) flavor basis where only one of the two Yukawas is diagonal:
unitary matrix
YD = V × diag(yd ,ys ,yb)
YU = diag(yu ,yc ,yt)
or
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
To diagonalize also the second mass matrix we need to rotate separately uL & dL (non gauge-invariant basis) ⇒ V appears in charged-current gauge interactions:
Jwμ = uL
γ μ dL → uL
V γμ dL
Cabibbo-Kobayashi-Maskawa(CKM) mixing matrix
_ _
MD = diag(md ,ms ,mb)
MU = V+ × diag(mu ,mc ,mt)
_
_
_
_
...however, it must be clear that this non-trivial mixing originates only from the Higgs sector: Vij → δij if we switch-off Yukawa interactions !
QLi YD
ik dRk ϕ → dL
i MDik dR
k + ...
QLi YU
ik uRk ϕc → uL
i MUik uR
k + ...
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
To diagonalize also the second mass matrix we need to rotate separately uL & dL (non gauge-invariant basis) ⇒ V appears in charged-current gauge interactions:
Jwμ = uL
γ μ dL → uL
V γμ dL
Cabibbo-Kobayashi-Maskawa(CKM) mixing matrix
_ _
MD = diag(md ,ms ,mb)
MU = V+ × diag(mu ,mc ,mt)
_
_
_
_QL
i YDik dR
k ϕ → dL
i MDik dR
k + ...
QLi YU
ik uRk ϕc → uL
i MUik uR
k + ...
V CKM = [V ud V us V ub
V cd V cs V cb
V td V ts V tb]
3 real parameters (rotational angles)
+
1 complex phase (source of CP violation)
Several equivalent parameterizations[unobservable quark phases] in terms of
V V+ = I
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
To diagonalize also the second mass matrix we need to rotate separately uL & dL (non gauge-invariant basis) ⇒ V appears in charged-current gauge interactions:
Jwμ = uL
γ μ dL → uL
V γμ dL
Cabibbo-Kobayashi-Maskawa(CKM) mixing matrix
_ _
MD = diag(md ,ms ,mb)
MU = V+ × diag(mu ,mc ,mt)
_
_
_
_QL
i YDik dR
k ϕ → dL
i MDik dR
k + ...
QLi YU
ik uRk ϕc → uL
i MUik uR
k + ...
V CKM = [V ud V us V ub
V cd V cs V cb
V td V ts V tb]
3 real parameters (rotational angles)
+
1 complex phase (source of CP violation)
The SM quark flavor sector is described by 10 observable parameters:
6 quark masses3+1 CKM parameters
Note that:
The rotation of the right-handed sector is not observableNeutral currents remain flavor diagonal
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
Properties of the CKM matrix & status of CKM fits
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
the area of these triangles is:always the samephase-convention independentzero in absence of CP violation
6 triangular relations:
Va1 (V+)1b
+Va2(V+)2b+Va3 (V
+)3b = 0
Some properties of the CKM matrix
3 real parameters (rotational angles)
+1 complex phase (source of CP violation)
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
V CKM = [V ud V us V ub
V cd V cs V cb
V td V ts V tb] V CKM V CKM
= I
Some properties of the CKM matrix
A, |ρ+iη| = O(1)
Wolfenstein, '83
λ = 0.22
1-λ2/2 λ Aλ3(ρ-iη)
- λ 1-λ2/2 Aλ2
Aλ3(1-ρ-iη) -Aλ2 1
≈
Experimental indication of a strongly hierarchical structure:
The b → d UT triangle:
Vub*Vud
+ Vcb
*Vcd + Vtb
*Vtd = 0
-Aλ3
Aλ3(ρ+iη)
only the 3-1 triangles have all sizes of the same order in λ
Aλ3(1-ρ-iη)
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
V CKM = [V ud V us V ub
V cd V cs V cb
V td V ts V tb] V CKM V CKM
= I
V CKM = [V ud V us V ub
V cd V cs V cb
V td V ts V tb] V CKM V CKM
= I
Some properties of the CKM matrix
1-λ2/2 λ Aλ3(ρ-iη)
- λ 1-λ2/2 Aλ2
Aλ3(1-ρ-iη) -Aλ2 1
≈
Experimental indication of a strongly hierarchical structure:
The b → d UT triangle:
Vub*Vud
+ Vcb
*Vcd + Vtb
*Vtd = 0
0 1
γ β
α
(ρ, η)η
ρ
Note: often you'll find experimental results shown as constraints in the ρ, η plane. These new parameters are defined by ρ = ρ (1-λ2/2)-½ (same for η) to keep into account higher-order terms in the expansion in powers of λ.
_ __
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
VCKM
= [V udV
usV
ub
Vcd
Vcs
Vcb
Vtd
Vts
Vtb]
Once we assume unitarity,the CKM matrix can be completely determinedusing only exp. info from processes mediated by tree-level c.c. amplitudes
l
di uk
ν W
Nuclear β decay K→ πlν
Excellent determination (error ~ 0.1%)Very good determination (error ~ 0.5%) Good determination (error ~ 2 %)Sizable error (5-15 %)Not competitive with unitarity constraints
|Vik |
1-λ2/2 λ Aλ3(ρ-iη)
- λ 1-λ2/2 Aλ2
Aλ3(1-ρ-iη) -Aλ2 1
N.B.: Also the phase γ = arg(Vub) can be obtained by (quasi-) tree-level processes
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
V CKM = [V ud V us V ub
V cd V cs V cb
V td V ts V tb]
Once we assume unitarity,the CKM matrix can be completely determinedusing only exp. info from processes mediated by tree-level c.c. amplitudes
l
di uk
ν W
Nuclear β decay K→ πlν
v + d c + l
Excellent determination (error ~ 0.1%)Very good determination (error ~ 0.5%) Good determination (error ~ 2 %)Sizable error (5-15 %)Not competitive with unitarity constraints
|Vik |
b → ulν
b → clν
t → blν
c → slν
1-λ2/2 λ Aλ3(ρ-iη)
- λ 1-λ2/2 Aλ2
Aλ3(1-ρ-iη) -Aλ2 1
N.B.: Also the phase γ = arg(Vub) can be obtained by (quasi-) tree-level processes
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
b (s) s (d)W
Z, γ
q
u = u,c,t
b (s)
ΔF =1 FCNC ΔF=2 (neutral-meson mixing)
GIM mechanism [ large top-quark contribution: A ~ mt
2 Vtq* Vtb ]
Rare B decays [ B → Xs γ, B → K(*)
l+l−, Bs,d → l
+l−, ...]
Rare K decays [ K → πνν, ...]
s (d)
b (s)s (d)
q
u = u,c,t
The only CKM elements we cannot access via tree-level processes are Vts & Vtd
Loop-induced amplitudes:
Bd(s)- Bd(s) mixing
K0- K0 mixing
_
_
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
Present status of CKM fits
At present all the measurements of quark flavor-violating observables show a remarkable success of the CKM picture: we have a redundant and consistent determination of various CKM elements.
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
Present status of CKM fits
At present all the measurements of quark flavor-violating observables show a remarkable success of the CKM picture: we have a redundant and consistent determination of various CKM elements.
The agreement between data and SM expectations is even more striking if we consider other observables, not appearing in CKM fits, such as BR(B → Xs γ) or the Bs mixing phase
Are there interesting measurements still to be done, within this field ?
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
The SM as an Effective Theory
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
The SM as an effective theory
Several theoretical arguments [inclusion of gravity, instability of the Higgs potential, neutrino masses, ...] and cosmological evidences [dark matter, inflation, cosmological constant, ... ] point toward the existence of physics beyond the SM.
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
The SM as an effective theory
Several theoretical arguments [inclusion of gravity, instability of the Higgs potential, neutrino masses, ...] and cosmological evidences [dark matter, inflation, cosmological constant, ... ] point toward the existence of physics beyond the SM.
Even the observed hierarchical structure of quark and lepton masses, and their mixing pattern, seems to points toward some new dynamics:
VCKM ~
It does not look “accidental”...
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
The SM as an effective theory
Several theoretical arguments [inclusion of gravity, instability of the Higgs potential, neutrino masses, ...] and cosmological evidences [dark matter, inflation, cosmological constant, ... ] point toward the existence of physics beyond the SM.
Even the observed hierarchical structure of quark and lepton masses, and their mixing pattern, seems to points toward some new dynamics.
If this new dynamics is not too far from the electroweak scale, we can expect modifications of the SM predictions for a few low-energy observables in the sector of flavor physics
still a lot of work to be done in this perspective
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
+ “heavy fields”
ℒSM = renormalizable part of ℒeff
All possible operators with d ≤ 4, compatible with the gauge symmetry, depending only on the “light fields” of the system
The modern point of view on the SM Lagrangian is that is only the low-energy limit of a more complete theory, or an effective theory.
New degrees of freedom are expected at a scale Λ above the electroweak scale.
ℒeff = ℒgauge (Aa, ψi) + ℒHiggs(ϕ, Aa, ψi )
The SM as an effective theory
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
+ “heavy fields”
The modern point of view on the SM Lagrangian is that is only the low-energy limit of a more complete theory, or an effective theory.
New degrees of freedom are expected at a scale Λ above the electroweak scale.
ℒeff = ℒgauge (Aa, ψi) + ℒHiggs(ϕ, Aa, ψi )
The concept of effective QFT allows us to give a more general meaning to the concept (request) of “renormalizability” in QFT
No fundamental distinction between renormalizable & non-renormalizable QFTs (once we consider them both as effective QFTs)
The SM as an effective theory
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
d=4 g Aμ ψ γμψ, λ ϕ4, ...
(ψ γμψ)2, ϕ6, ... 1
Λ21
Λ2d > 4
Contributions to scattering amplitudes:
mϕ2
E2
g(E), λ(E)
mψ
E dominant in the IR
potentially relevant at all energies
E2
Λ2irrelevant at low energies, but bad UV behavior
mϕ2 ϕ2, mψ ψ ψ, ... d < 4
S=∫ d 4 x ℒ
The concept of effective QFT allows us to give a more general meaning to the concept (request) of “renormalizability” in QFT:
Some general remarks on effective QFT
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
To define an effective QFT we need to define three basic ingredients:
I. The nature of the “light fields”, or the nature of the degrees of freedom we can directly excite in the validity regime of the theory [e.g. the SM fields]
II. The symmetries of the theory [e.g. the SU(3)×SU(2)×U(1) gauge symmetry]
III. The validity regime of the theory [typically an UV cut-off]
In general, the most general Lagrangian compatible with I & II contains and infinite set of operators; however, there is a finite number of operators with a given canonical dimension → at low-energies we can focus only on a finite sets of operators given terms of high dimension given small contributions
The concept of effective QFT allows us to give a more general meaning to the concept (request) of “renormalizability” in QFT:
Some general remarks on effective QFT
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
To define an effective QFT we need to define three basic ingredients:
I. The nature of the “light fields”, or the nature of the degrees of freedom we can directly excite in the validity regime of the theory [e.g. the SM fields]
II. The symmetries of the theory [e.g. the SU(3)×SU(2)×U(1) gauge symmetry]
III. The validity regime of the theory [typically an UV cut-off]
In general, the most general Lagrangian compatible with I & II contains and infinite set of operators; however, there is a finite number of operators with a given canonical dimension → at low-energies we can focus only on a finite sets of operators given terms of high dimension given small contributions
The concept of effective QFT allows us to give a more general meaning to the concept (request) of “renormalizability” in QFT:
“renormalizable” EFTs [e.g. SM]No clear indication about the validity
range of the theory
“non-renormalizable” EFTs [e.g. Fermi theory, CHPT, ...]
Clear indication about the maximal validity range of the theory
Some general remarks on effective QFT
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
+ Σ On(d) (ϕ, Aa, ψi)
cn
Λd-4
The modern point of view on the SM Lagrangian is that is only the low-energy limit of a more complete theory, or an effective theory.
New degrees of freedom are expected at a scale Λ above the electroweak scale.
ℒeff = ℒgauge (Aa, ψi) + ℒHiggs(ϕ, Aa, ψi )
Operators of d ≥ 5 containing SM fields only (compatible with the SM gauge symmetry)
heavy dynamics
SM field
SM field SM field
SM field
This is the most general parameterization of the new (heavy) degrees of freedom, as long as we do not have enough energy to directly produce them.
ℒSM = renormalizable part of ℒeff
The SM as an effective theory
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
+ Σ On(d) (ϕ, Aa, ψi)
cn
Λd-4 ℒeff = ℒgauge (Aa, ψi) + ℒHiggs(ϕ, Aa, ψi )
(LLi σ2 ϕ)( LL
j σ2 ϕ
T )gν
ij
ΛLN
gνij v2
ΛLN
(mν)ij =
v =〈 ϕ〉
T
A clear evidence of a non-vanishing term in the series of higher-dim. ops. (so far the only one...) comes from neutrino masses:
Neutrino masses are well described by the only d=5 term allowed by the SM gauge symmetry.
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
The SM as an effective theory & neutrino masses
(→ Exercise: check in detail)
+ Σ On(d) (ϕ, Aa, ψi)
cn
Λd-4 ℒeff = ℒgauge (Aa, ψi) + ℒHiggs(ϕ, Aa, ψi )
(LLi σ2 ϕ)( LL
j σ2 ϕ
T )gν
ij
ΛLN
gνij v2
ΛLN
(mν)ij =
v =〈 ϕ〉
Possible dynamical origin of this d=5 ops.:
TLL LL
νR
ϕ ϕ
A clear evidence of a non-vanishing term in the series of higher-dim. ops. (so far the only one...) comes from neutrino masses:
In this case (see-saw mechanism):
gν
Λ
YνTYν
MRN=
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
The SM as an effective theory & neutrino masses
+ Σ On(d) (ϕ, Aa, ψi)
cn
Λd-4 ℒeff = ℒgauge (Aa, ψi) + ℒHiggs(ϕ, Aa, ψi )
(LLi σ2 ϕ)( LL
j σ2 ϕ
T )gν
ij
ΛLN
gνij v2
ΛLN
(mν)ij =
v =〈 ϕ〉
T
A clear evidence of a non-vanishing term in the series of higher-dim. ops. (so far the only one...) comes from neutrino masses:
The smallness of mν seems to point toward a veryhigh value of Λ (that fits well with the idea of an underlying GUT at very high energies):
O(1) ×(246 GeV)2
1015 TeVLN
~ 0.06 eV
0.3 eV < mνmax < 0.04 eV ~ ~
(cosmological bounds)
(atmosphericoscillations)
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
The SM as an effective theory & neutrino masses
+ Σ On(d) (ϕ, Aa, ψi)
cn
Λd-4 ℒeff = ℒgauge (Aa, ψi) + ℒHiggs(ϕ, Aa, ψi )
(LLi σ2 ϕ)( LL
j σ2 ϕ
T )gν
ij
ΛLN
gνij v2
ΛLN
(mν)ij =
v =〈 ϕ〉
T
A clear evidence of a non-vanishing term in the series of higher-dim. ops. (so far the only one...) comes from neutrino masses:
However, this d=5 ops. violates lepton number, which is a global symmetry of the SM → the high value of Λ may be related to the breaking of LN.
We can expect lower values of Λ for effective operators that do not violate any of the symmetries of the SM Lagrangian
The smallness of mν seems to point toward a veryhigh value of Λ
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
The SM as an effective theory & neutrino masses
+ Σ On(d) (ϕ, Aa, ψi)
cn
Λd-4 ℒeff = ℒgauge (Aa, ψi) + ℒHiggs(ϕ, Aa, ψi )
Indeed an indication of a much lower value of Λ comes from the only d=2 term in this Lagrangian, namely from the Higgs sector:
If the effective theory is “natural” we should expect some new degrees of freedom (respecting SM symmetries and coupled to the Higgs sector) not far from the TeV scale to stabilize the Higgs mass term.
μ2 ϕ
+ ϕ Λ2 ϕ
+ ϕ quantum
corrections
The“naturalness” problem
A clear evidence of a non-vanishing term in the series of higher-dim. ops. (so far the only one...) comes from neutrino masses:
μ2(tree)
= ½ mh2
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
N.B.: the quadratic sensitivity of the Higgs mass from the cut-off is not a pure “technical” issue: it implies a quadratic sensitivity to the the new degrees of freedom (if we assume there is something else beyond the SM, such e.g. RH neutrinos):
ΔmH2 ~ Σb cbMb
2 – Σf cf Mf2
boson
fermion
If the effective theory is “natural” we should expect some new degrees of freedom (respecting SM symmetries and coupled to the Higgs sector) not far from the TeV scale to stabilize the Higgs mass term.
μ2 ϕ
+ ϕ Λ2 ϕ
+ ϕ quantum
corrections
If Λ >> mh, either mh is “fine-tuned” or the NP does not couple to the Higgs sector
The“naturalness” problem
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
N.B.: the quadratic sensitivity of the Higgs mass from the cut-off is not a pure “technical” issue: it implies a quadratic sensitivity to the the new degrees of freedom
If the effective theory is “natural” we should expect some new degrees of freedom (respecting SM symmetries and coupled to the Higgs sector) not far from the TeV scale to stabilize the Higgs mass term.
μ2 ϕ
+ ϕ Λ2 ϕ
+ ϕ quantum
corrections
N.B. (II): a “warning” that the naturalness argument should be taken with some care comes from the cosmological constant
V0 + μ2 ϕ
+ ϕ Λ4 + Λ2 ϕ
+ ϕ quantum
corrections
“exp”
~ (100 MeV)2~ (0.002 eV)4
The“naturalness” problem
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
The modern point of view on the SM Lagrangian is that is only the low-energy limit of a more complete theory, or an effective theory.
New degrees of freedom are expected at a scale Λ above the electroweak scale.
+ Σ On(d) (ϕ, Aa, ψi)
cn
Λd-4 ℒeff = ℒgauge (Aa, ψi) + ℒHiggs(ϕ, Aa, ψi )
Which is the energy scale of New Physics (or the value of Λ)
Which is the symmetry structure of the new degrees of freedom (or the structure of the cn)
Two key questions of particle physics today:
High-energy searches [the high-energy frontier]
High-precision measurements [the high-intensity frontier]
The key questions of particle physics
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
More precisely, on both “frontiers” we have two independent sets of questions, a “difficult one” and a “more pragmatic one”:
What determines the Higgs mass term (or the Fermi scale)?
Is there anything else beyond the SM Higgs at the TeV scale?
What determines the observed pattern of masses and mixing angles of quarks and leptons?
Which are the sources of flavor symmetry breaking accessible at low energies? [Is there anything else beside SM Yukawa couplings & neutrino mass matrix?]
High-energy searches[the high-energy frontier]
High-precision measurements [the high-intensity frontier]
The key questions of particle physics
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
More precisely, on both “frontiers” we have two independent sets of questions, a “difficult one” and a “more pragmatic one”:
What determines the Higgs mass term (or the Fermi scale)?
Is there anything else beyond the SM Higgs at the TeV scale?
What determines the observed pattern of masses and mixing angles of quarks and leptons?
Which are the sources of flavor symmetry breaking accessible at low energies? [Is there anything else beside SM Yukawa couplings & neutrino mass matrix?]
High-energy searches[the high-energy frontier]
High-precision measurements [the high-intensity frontier]
The key questions of particle physics
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
Lecture I [The SM as an EFT] Lecture II [EFT tools for B Physics]
PremiseEFT tools for B PhysicsΔF=2 amplitudes and the gauge-less limitRare B decays
Lecture III [Flavor Physics beyond the SM]
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
More precisely, on both “frontiers” we have two independent sets of questions, a “difficult one” and a “more pragmatic one”:
What determines the Higgs mass term (or the Fermi scale)?
Is there anything else beyond the SM Higgs at the TeV scale?
What determines the observed pattern of masses and mixing angles of quarks and leptons?
Which are the sources of flavor symmetry breaking accessible at low energies? [Is there anything else beside SM Yukawa couplings & neutrino mass matrix?]
High-energy searches[the high-energy frontier]
High-precision measurements [the high-intensity frontier]
Premise
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
3 identical replica of the basic fermion family ⇒ huge flavor-degeneracy [U(3)5 symmetry]
Flavor-degeneracy broken only by the Yukawa interaction
several new sources of flavor symmetry breaking are, in principle, allowed
What we have only started to investigate is the flavor structure of the new degrees of freedom
which hopefully will show up above the electroweak scale
+ Σ On(d) (ϕ, Aa, ψi)
cn
Λd-4 ℒeff = ℒgauge (Aa, ψi) + ℒHiggs(ϕ, Aa, ψi )
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
Premise
Probing the flavor structure of physics beyond the SM requires the following three main steps:
Identify processes where the SM is calculable with good accuracy using the tree-level inputs, or sufficiently suppressed for null tests.
Determine the CKM elements from theoretically clean and non-suppressed tree-level processes, where the SM is likely to be largely dominant.
Measure with good accuracy these rare processes and determine the allowed room
for new physics.
ΔF=2 Neutral meson mixing [ K, Bd, Bs]
Rare decays
Exclusive and inclusive semi-leptonic b→u decays ( |Vub| )
Selected non-leptonic B decays sensitive to γ
1
Λ2 A = A0 cSM + cNP
1
MW2
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
EFT tools for B Physics
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
b s
newd.o.f.
γ, l+l-, νν
B Xs
q
No SM tree-level contribution
Strong suppression within the SM because of CKM hierarchy
Low-energy tools: general considerations
ΔF=2 meson-antimeson mixing amplitudes & rare decays mediated by Flavour Changing Neutral Current (FCNC) amplitudes are, in principle, the best probes for precision tests of flavor dynamics beyond the SM
newd.o.f.
b q
bq
B B_
b s
newd.o.f.
γ, l+l-, νν
B Xs
q
In both cases the key point to be addresses for a good TH control is a proper “scale separation” (from the e.w. scale down to the hadronic scale) by means of suitable EFT approaches
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
In general, this involves a 3-step procedure:
1st step: Construction of a local (partonic) eff. Hamiltonian at the electroweak scale “integrating out” all the heavy fields around mW (including the heavy SM fields)
Heff = Σi Ci(MW) Qi
b s
c c
Low-energy tools: general considerations
“Matching procedure”(Perturb. Theory,
within the SM)
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
In general, this involves a 3-step procedure:
1st step: Construction of a local (partonic) eff. Hamiltonian at the electroweak scale “integrating out” all the heavy fields around mW (including the heavy SM fields)
Heff = Σi Ci(MW) Qi
b s
c c
“Matching procedure”(Perturb. Theory,
within the SM)
Low-energy tools: general considerations
2nd step: Evolution of Heff down to low scales using RGE
Heff = Σi Ci(μ) Qi
RGE evolution dictated by light SM
d.o.f. only (QCD, QED)[ ΛQCD << μ < MW ]
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
In general, this involves a 3-step procedure:
1st step: Construction of a local (partonic) eff. Hamiltonian at the electroweak scale “integrating out” all the heavy fields around mW (including the heavy SM fields)
Heff = Σi Ci(MW) Qi
b s
c c
Low-energy tools: general considerations
2nd step: Evolution of Heff down to low scales using RGE
Heff = Σi Ci(μ) Qi
RGE evolution dictated by light SM
d.o.f. only (QCD, QED)[ ΛQCD << μ < MW ]
3rd step: Evaluation of the hadronic matrix elements
A(i → f ) = Σi Ci(μ) ⟨ f | Qi
|i ⟩ (μ)non-perturbative effects...
“Matching procedure”(Perturb. Theory,
within the SM)
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
ΔF=2 amplitudes and the gauge-less limit
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
b d
bd Vqd Vq'b*
Vqb* Vq'd
Highly suppressed amplitude potentially very sensitive
to New PhysicsB B
_
q'
q
No SM tree-level contributionStrong suppression within the SM because of CKM hierarchy Calculable with good accuracy since dominated by short-distance dynamics [power-like GIM mechanism → top-quark dominance]Measurable with good accuracy from the time evolution of the neutral meson system
ΔF=2 mixing
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
b d
bd Vqd Vq'b*
Vqb* Vq'd
q'
power-like GIM mechanism:
AΔF=2 = Σq,q'=u,c,t (Vqb*Vqd) (Vq'b
*Vq'd) Aq'q q
Aqq' ~
mq mq'
mW2
g4
16π2mW2
Const. + + ... × (dL γμ bL)2
1st step: Construction of a local (partonic) eff. Hamiltonian at the electroweak scale “integrating out” all the heavy fields around mW (including the heavy SM fields)
_
Only d=6 operator generated within the SM
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
b d
bd Vqd Vq'b*
Vqb* Vq'd
q'
power-like GIM mechanism:
AΔF=2 = Σq,q'=u,c,t (Vqb*Vqd) (Vq'b
*Vq'd) Aq'q q
AΔF=2 = Σq=u,c,t (Vqb*Vqd) [ Vtb
*Vtd (Atq-Auq) + Vcb*Vcd (Acq-Auq) ]
Vub*Vud = - Vtb
*Vtd - Vcb*Vcd [CKM unitarity]
Aqq' ~
mq mq'
mW2
g4
16π2mW2
Const. + + ... × (dL γμ bL)2
1st step: Construction of a local (partonic) eff. Hamiltonian at the electroweak scale “integrating out” all the heavy fields around mW (including the heavy SM fields)
_
Only d=6 operator generated within the SM
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
b d
bd Vqd Vq'b*
Vqb* Vq'd
q'
power-like GIM mechanism:
AΔF=2 = Σq,q'=u,c,t (Vqb*Vqd) (Vq'b
*Vq'd) Aq'q q
AΔF=2 = Σq=u,c,t (Vqb*Vqd) [ Vtb
*Vtd (Atq-Auq) + Vcb*Vcd (Acq-Auq) ]
Vub*Vud = - Vtb
*Vtd - Vcb*Vcd [CKM unitarity]
Aqq' ~
mq mq'
mW2
g4
16π2mW2
Const. + + ... × (dL γμ bL)2
1st step: Construction of a local (partonic) eff. Hamiltonian at the electroweak scale “integrating out” all the heavy fields around mW (including the heavy SM fields)
_
HΔF=2 ~ (Vtb*Vtd)2
g4mt2
16π2mW4
[expansion of the loop amplitude for small
(internal) quark masses]
(dL γμ bL)2(d=6) _
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
bL dL
bLdL Yqd Yq'b*
Yqb* Yq'd
q'R
qRThe structure of this result can be better
understood “switching-off” gauge interactionsϕ+
dLi YU
ik uRk ℒYukawa →
_ϕ- + h.c.
YU = V+ × diag(yu, yc, yt)
The “gauge-less” limit:
HΔF=2 ~ (Vtb*Vtd)2
g4mt2
16π2mW4
(dL γμ bL)2(d=6) _
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
bL dL
bLdL Yqd Yq'b*
Yqb* Yq'd
tR
tR ϕ+
dLi YU
ik uRk ℒYukawa →
_ϕ- + h.c.
YU = V+ × diag(yu, yc, yt)
≈ V+ × diag(0, 0, yt)
ADF=2 ~ (Vtb*Vtd)2 ~ (Vtb
*Vtd)2(yt)
4
16π2mt2
This way we obtain the exact result of the amplitude in the limit mt ≫mW :
gaugeless g4 mt2
16π2mW4
mt = yt v / √2
mW = g v / 2
ADF=2 = ADF=2 × [ 1 + O(g2) ]full gauge-less
The “gauge-less” limit:
The structure of this result can be better understood “switching-off” gauge interactions
HΔF=2 ~ (Vtb*Vtd)2
g4mt2
16π2mW4
(dL γμ bL)2(d=6) _
(→ Exercise: check in detail)
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
1st step: Construction of a local (partonic) eff. Hamiltonian at the electroweak scale “integrating out” all the heavy fields around mW (including the heavy SM fields)
HΔF=2 (MW) =
(Vtb*Vtd)2
16π2mW2
Q0 = (dL γμ bL)2(d=6)_
C0(MW) Q0
C0(MW) = g4 mt
2
mW2 × [ 1 + O(g2, gs
2) ]
2nd step: Evolution of Heff down to low scales using RGE
In this case the RGE evolution is particularly simple since there is only one effective operator (even beyond the 1-loop level) at d=6 → “multiplicative” renormalization of C0 (dictated by the anomalous dimension of Q0)
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
1st step: Construction of a local (partonic) eff. Hamiltonian at the electroweak scale “integrating out” all the heavy fields around mW (including the heavy SM fields)
HΔF=2 (MW) =
(Vtb*Vtd)2
16π2mW2
Q0 = (dL γμ bL)2(d=6)_
C0(MW) Q0
C0(MW) = g4 mt
2
mW2 × [ 1 + O(g2, gs
2) ]
2nd step: Evolution of Heff down to low scales using RGE
3rd step: Evaluation of the hadronic matrix element
⟨ B | Qi | B ⟩
In this case the RGE evolution is particularly simple since there is only one effective operator (even beyond the 1-loop level) at d=6 → “multiplicative” renormalization of C0 (dictated by the anomalous dimension of Q0)
_All non-perturbative effects are encoded into a single hadronic parameter,
→ reliable estimates (~20%) by means of Lattice QCD
N.B.: the “weak phase of the amplitude” has negligible hadronic uncertainties
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
Rare B decays
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
Similarly to ΔF=2 mixings, rare decays mediated by Flavour Changing Neutral Current (FCNC) amplitudes are useful probes for precision tests of flavor dynamics beyond the SM
b s (d)
newd.o.f.
γ, l+l-, νν
Rare B decays
No SM tree-level contribution
Strong suppression within the SM because of CKM hierarchy
Predicted with high precision within the SM at the partonic level: NNLO pert. calculations available for all the main B modes (mb ≫ ΛQCD)
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
The key point is the relation between patonic & hadronic worlds
Fully inclusive decays usually good precision thanks
to heavy-quark symmetry
Γ(b → sγ) Γ(B → Xs γ) mb ∞
Exclusive decays generally more difficult than inclusive,
with some notable exceptions:
B → (0, K, K*) + μ-μ+
Similarly to ΔF=2 mixings, rare decays mediated by Flavour Changing Neutral Current (FCNC) amplitudes are useful probes for precision tests of flavor dynamics beyond the SM
b s (d)
newd.o.f.
γ, l+l-, νν
Rare B decays
No SM tree-level contribution
Strong suppression within the SM because of CKM hierarchy
Predicted with high precision within the SM at the partonic level: NNLO pert. calculations available for all the main B modes (mb ≫ ΛQCD)
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
Heff = Σi Ci(MW) Qi
The interesting short-distance info is encoded in the Ci(MW) (initial conditions) of the FCNC operators (NP effects expected to be small in the four-quark ops.)
Q9V
=Qf(b s)
V−A( f f )
V
Q10A
=Qf(b s)
V−A( f f )
A
FCNC operators: Four-quark (tree-level) ops.:
Q1=(b s)
V−A(c c)
V−A
Q2=(bc)
V−A(c s)
V−A
b sb s
c c
⋮Q
6=(b s)
V −A(q q)
V
⋮
[Gluon penguins]
[E.W. penguins]
1st step: Construction of a local eff. Hamiltonian at the electroweak scale
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
Heff = Σi Ci(MW) Qi
The interesting short-distance info is encoded in the Ci(MW) (initial conditions) of the FCNC operators (NP effects expected to be small in the four-quark ops.)
N.B.: Only one of the FCNC ops. (Q10A) exhibits the power-like GIM behavior seen in the ΔF=2 case (→ Exercise: try to understand why. Help: gauge-less limit)
Q9V
=Qf(b s)
V−A( f f )
V
Q10A
=Qf(b s)
V−A( f f )
A
FCNC operators: Four-quark (tree-level) ops.:
Q1=(b s)
V−A(c c)
V−A
Q2=(bc)
V−A(c s)
V−A
b sb s
c c
⋮Q
6=(b s)
V −A(q q)
V
⋮
[Gluon penguins]
[E.W. penguins]
1st step: Construction of a local eff. Hamiltonian at the electroweak scale
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
Sources of long-distance effects: [dilution of the interesting short-distance info]:
Mixing of the four-quark Qi into the FCNC Qi [perturbative long-distance contribution]
g
Q2 c, u
p ~ μ
b
s
e.g.:
2nd step: Evolution of Heff down to low scales using RGE
Penguin operators: Four-quark (tree-level) ops.:
Q9V =Q f b sV−A f f VQ10A=Q f b sV−A f f A
Q1=b s V−Ac c V−A
Q2=b cV−Ac sV−A⋮Q6 =b sV−Aq qV
⋮
Small in the case of electroweak penguins (Q10A) because of the power-like GIM mechanism [mixing parametrically suppressed by O(mc
2/ mt
2)]
Sizable for photon penguinsHuge for gluon penguins
Heff = Σi Ci(MW) Qi
Heff = Σi Ci(μ ~ mb) Qi
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
3rd step: Evaluation of the hadronic matrix elements
sensitivity to long-distances (cc threshold, mc dependence,...) distinction between inclusive (OPE + 1mb,c expansion) and exclusive modes (hadronic form factors) irreducible large theory errors in the case of exclusive non-leptonic final states
A(B → f ) = Σi Ci(μ) ⟨ f | Qi |B ⟩ (μ) [ μ ~ mb ]
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
3rd step: Evaluation of the hadronic matrix elements
A(B → f ) = Σi Ci(μ) ⟨ f | Qi
|B ⟩ (μ)
sensitivity to long-distances (cc threshold, mc dependence,...) distinction between inclusive (OPE + 1mb,c expansion) and exclusive modes (hadronic form factors) irreducible large theory errors in the case of exclusive non-leptonic final states
NNLO SM th. estimate: To be compared with: B(B → Xs γ) = (3.57±0.24)×10
-4
Putting all the ingredients together in the case of B → Xs γ[best inclusive mode so far ]:
A great success for the SM... ...and a great challenge for many of its extensions !
[Misiak et al. '07] [present exp. W.A.]
B(B → Xs γ) = (3.15±0.23)×10-4
[ μ ~ mb ]
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
The accuracy on exclusive FCNC B decays of the type B H+(γ, l+l−) depends on the th. control of B H hadronic form factors :
Several progress in the last few years [Light-cone sum rules, Heavy-quark expansion, Lattice] but typical errors still > 30%
A B f = ∑iC i ⟨ f ∣Qi∣B ⟩ μ ~ mb
Exclusive rare B decays:
~
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
The most difficult exclusive observables are the total branching ratios; however, f.f. uncertainties can be considerably reduced in appropriate ratios (or differential distributions) or considering very peculiar final states.
The accuracy on exclusive FCNC B decays of the type B H+(γ, l+l−) depends on the th. control of B H hadronic form factors :
Several progress in the last few years [Light-cone sum rules, Heavy-quark expansion, Lattice] but typical errors still > 30%
I. BR(Bs,d → μ+μ−) (→ Exercise: try to evaluate it in the gauge-less limit)
II. LFU ratios in B → H l+l−
A B f = ∑iC i ⟨ f ∣Qi∣B ⟩ μ ~ mb
Exclusive rare B decays:
Notable examples:
~
G. Isidori – EFT tools for Flavor Physics JOINT FGZ-PH Summer School – Garching, July 2017
∫ dΓ(B → H μμ)
∫ dΓ(B → H ee)RH =
H = K, K*