lhc physics: higgs and beyond...“intermediate” bsm sector non-sm flavor probe physics at energy...

G. Isidori – LHC Physics: Higgs and beyond COURSE D'HIVER 2016 du LAL, 17-19 Feb 2016

Lecture I: What we learned from run-I[The SM as an effective theory & the “ghost” of the anthropic principle] Lecture II: What we can hope to learn from run-II (at high-pT)[Future prospects in Higgs physics and direct NP searches]

Lecture III: Indirect searches for NP[Flavor physics beyond the SM]

LHC Physics: Higgs and beyond

Gino Isidori[ University of Zürich ]

(a personal selection of topics in the wast domain of LHC physics)


IntroductionThe flavor sector of the SM

Present status of CKM fitsThe flavor structure of the SM viewed as EFT

The flavor problemThe MFV hypothesisVariations on the “MFV theme”

Speculations on the breaking of LFU in B decaysRecent anomalies in B physicsSpeculations on the breaking of LFU

Conclusions

Lecture III: Indirect searches for NP[Flavor physics beyond the SM]

Introduction

Twofold role of Flavor Physics[ = study of flavor-changing and CPV phenomena, of both quarks and leptons]

We need to search for New Physics [with a broad spectrum perspective given the lack of NP signal so far...]

Indirect probe of physics at energy scales not directly accessible at accelerators

Identify symmetries and symmetry-breaking patterns beyond those present in the SM

The SM is likely to be an effective theory, i.e. the limit(in the experimentally accessible range of energies and effective couplings)

of a more fundamental theory, with new degrees of freedom


Twofold role ofFlavor Physics

SM

flavor-violatinginteractions

High-scale[flavor-symmetric?]

theory


Higgssector

The observed pattern of fermion masses angles does not seem to be accidental !


Introduction

Twofold role ofFlavor Physics

SM +

flavor-violatinginteractions

High-scale[flavor-symmetric?]

theory

Higgssector

“intermediate”BSM sector

non-SMflavor

Probe physics at energy scales not directly accessible at accelerators



Introduction

With flavor physics we address the second set of key questions of particle physics:

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]

Introduction


The flavor sector of the SM

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 )


The flavor structure of the SM

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

Σ ψ = QL , uR ,dR ,LL ,eR Σi=1..3 ψi iD ψi

QL = uL

dL

LL = νL

eL

, uR , dR , , eR





U(1)L × U(1)B × U(1)Y × SU(3)Q × SU(3)U × SU(3)D ×...

Flavor mixingLepton numberBarion number

Hypercharge



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:

_

_

_

_






QLi YD


i MDik dR

k + ...

QLi YU


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




QLi YD


i MDik dR

k + ...

QLi YU


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:

YD = V × diag(yd ,ys ,yb)

YU = diag(yu ,yc ,yt)

V= unitary matrix

or

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 + ...




Jwμ = uL

γ μ dL → uL

V γμ dL

_ _



_

_

_

_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 masses

3+1 CKM parameters



Jwμ = uL

γ μ dL → uL

V γμ dL

_ _



_

_

_

_QL

i YDik dR

k ϕ → dL

i MDik dR

k + ...

QLi YU

ik uRk ϕc → uL

i MUik uR

k + ...



The SM quark flavor sector is described by 10 observable parameters:

6 quark masses

3+1 CKM parameters

1-λ2/2 λ Aλ3(ρ-iη)

- λ 1-λ2/2 Aλ2

Aλ3(1-ρ-iη) -Aλ2 1

≈VCKM


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.


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

Present status of CKM fits


Significant constraints on the flavor structure of possible

new degrees of freedom

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

The redundancy of CKM fits allow us to investigate the flavor structure of the new degrees of freedom

which hopefully will show up above the electroweak scale

Λ = effective scale of new physics

+ Σ On(d) (ϕ, Aa, ψi)

cn

Λd-4 ℒeff = ℒgauge (Aa, ψi) + ℒHiggs(ϕ, Aa, ψi )

The flavor structure of the SM viewed as EFT


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 + D]

CP-violating observables

Rare decays:FCNC modes (B→ll, BK* ll,...)Helicity-suppressed observables

Forbidden processes

Exclusive and inclusive semi-leptonic b→u decays ( |Vub| )

Selected non-leptonic B decays sensitive to γ



The flavor problem

The “chain” mentioned before has already been closed, with quite good accuracy, in the case of down-type ΔF=2 observables (K0 and Bd,s mixing):

Highly suppressed amplitude potentially very sensitive

to New Physics

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


The ΔF=2 bounds

b d

bd Vqd Vq'b*

Vqb* Vq'd

B B_

q'

q

b d

bd Vqd Vq'b*

Vqb* Vq'd

B B_

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) ]

[CKM unitarity]


The ΔF=2 bounds


Vub*Vud = - Vtb

*Vtd - Vcb*Vcd

b d

bd Vqd Vq'b*

Vqb* Vq'd

B B_

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) ]

[CKM unitarity]

Aqq' ~

mq mq'

mW2

AΔF=2 ~ (Vtb*Vtd)2 + ...

g4mt2

16π2mW4

[expansion of the loop amplitude for small

(internal) quark masses]g4

16π2mW2

Const. + + ... ⟨ B| (bL γμ dL )

2 |B ⟩_ _


The ΔF=2 bounds


Vub*Vud = - Vtb

*Vtd - Vcb*Vcd

bL dL

bLdL Yqd Yq'b*

Yqb* Yq'd

B B_

q'R

qR

The origin of this behavior can be better understood if we

switch-off gauge interactions (“gauge-less limit”)ϕ+

dLi YU

ik uRk ℒYukawa →

_ϕ- + h.c.

YU = V+ × diag(yu, yc, yt)

≈ V+ × diag(0, 0, yt)


The ΔF=2 bounds


bL dL

bLdL Yqd Yq'b*

Yqb* Yq'd

B B_

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 origin of this behavior can be better understood if we

switch-off gauge interactions (“gauge-less limit”)


The ΔF=2 bounds


ℒeff = ℒSM

(yt2 Vtb

*Vtd)2

16π2mt2

M(Bd−Bd) ~ + cNP

1

Λ2

_

+ Σ On(d) cn

Λd-4The list of dimension 6 ops. includes (bL

γμ dL )2 that contributes

to Bd mixing at the tree-level

bL dLρ'bd

dL bL

Possible dynamical origin of this d=6 operator:

The flavor problem


The “chain” mentioned before has already been closed, with quite good accuracy, in the case of down-type ΔF=2 observables (K0 and Bd,s mixing), showing no significant deviations from the SM (at the 5%-30% level):

ℒeff = ℒSM

(yt2 Vtb

*Vtd)2

16π2mt2

M(Bd−Bd) ~ + cNP

1

Λ2

_

+ Σ On(d) cn

Λd-4

N.B.: In Kaon physics the CKM suppression is even stronger:

Bs-mix.: Vtb*Vts ~ λ2 Bd-mix.: Vtb

*Vtd ~ λ3 K-mix: Vts*Vtd ~ λ5

The list of dimension 6 ops. includes (bL

γμ dL )2 that contributes

to Bd mixing at the tree-level

The flavor problem



cNP

Serious conflict with the expectation of new physics around the TeV scale, to stabilize the electroweak sector of the SM [ The flavour problem ]

~ 1

~ 1(16π2)

Λ 2×104 TeV [K]

Λ 2×103 TeV [K]

treestrong + generic flavor

loop + generic flavor>~

>~

(yt2 Vtb

*Vtd)2

16π2mt2

M(Bd−Bd) ~ + cNP

1

Λ2

_

The flavor problem



~ 1

~ 1(16π2)


loop + generic flavor

~ (yt Vti*Vtj)2

~ (yt Vti*Vtj)2(16π2)

Λ 5 TeV [K & B]

Λ 0.5 TeV [K & B]

treestrong + “alignment”

loop + “alignment”>~

>~cNP

Λ 2×104 TeV [K]

Λ 2×103 TeV [K]>~

>~

(yt2 Vtb

*Vtd)2

16π2mt2

M(Bd−Bd) ~ + cNP

1

Λ2

_

The flavor problem



~ 1

~ 1(16π2)


loop + generic flavor

~ (yt Vti*Vtj)2

~ (yt Vti*Vtj)2(16π2)

Λ 5 TeV [K & B]

Λ 0.5 TeV [K & B]

treestrong + “alignment”

loop + “alignment”>~

>~cNP

Λ 2×104 TeV [K]

Λ 2×103 TeV [K]>~

>~

(yt2 Vtb

*Vtd)2

16π2mt2

M(Bd−Bd) ~ + cNP

1

Λ2

_

Comparable to the scales directly probed at the LHCand/or indirectly probed in precision Higgs physics

The flavor problem



Can we build NP models where the alignment with the CKM is “natural”?

Is there a unique form of alignment that allows Λ ~ 1 TeV?

Does this shed light on the origin of fermion masses and CKM hierarchies?

Can we see deviations from the SM with more precise measurements? Where?

Some partial answers in the rest of this lecture, hopefully more complete answers from future flavor-physics data...

New flavor-breaking sources at the TeV scale (if any) are highly tuned

The flavor problem


SU(3)Q×SU(3)U×SU(3)D

Quark Flavor

Group

YD

VCKM

YU

This specific symmetry + symmetry-breaking pattern is responsible for the GIM suppression of Flavor Changing Neutral Currents, the suppression of CPV,...

all the successful SM predictions in the quark flavor sector

Flavor symmetry: U(3)5 = SU(3)Q

×SU(3)U ×SU(3)D

×...

[global symmetry of the SM gauge sector]

Symmetry-breaking terms: YU & YD

[quark Yukawa couplings]

ℒSM = ℒgauge + ℒHiggs

QLi YU

ij UR

j ϕ + QL

i YD

ij DR

j ϕc

_ _

Minimal Flavor Violation


Since the global flavor symmetry is already broken within the SM, is not consistent to impose it as an exact symmetry beyond the SM (fine-tuning, not invariant under quantum corrections)

However, we can (formally) promote this symmetry to be an exact symmetry, assuming the Yukawa matrices are the vacuum expectation values of appropriate auxiliary fields:

_ _E.g.: YD ~ (3,1,3) & YU ~ (3,3,1) under SU(3)Q

L×SU(3)U

R×SU(3)D

R

(1,1,3) (3,1,1) _

(3,1,3) _

(1,1,1) = invariant

ℒYukawa = QL YD DR ϕ + QL YUUR ϕc + LL YL eR ϕ + h.c._ _ _



SU(3)Q×SU(3)U×SU(3)D

Quark Flavor

Group

YD

VCKM

YUFlavor symmetry: U(3)5 = SU(3)Q

×SU(3)U ×SU(3)D

×...

[global symmetry of the SM gauge sector]

Symmetry-breaking terms: YD ~ 3Q

×

3D

Y5YU ~ 3Q ×

3U

_ _

[quark Yukawa couplings]

A natural mechanism to reproduce the SM successes in flavor physics -without fine tuning- is the MFV hypothesis:

Yukawa couplings = unique sources of flavor symmetry breaking also beyond SM



General principle (RGE invariant) which can be applied to any TeV-scale new-physics model

unknown“flavor-blind”

dynamics

⟨Y ⟩ ⟨Y ⟩

ΛF

breaking of GF

by means of ⟨Y ⟩

Λ (~ TeV)

flavor-blind dynamics [non-SM degrees of freedom stabilizing the Higgs mass]

SM degreesof freedom

natural cut-off scale of the effectivetheory



YD = diag(yd ,ys ,yb) YU = V+ × diag(yu ,yc ,yt)

A low-energy EFT satisfies the criterion of MFV if all higher-dimensional operators, constructed from SM and Y fields, are (formally) invariant under the flavor group [ SU(3)Q×SU(3)U×SU(3)D ]

Typical FCNC dim.-6 operator: QLi (YUYU

+)ij QLj × LL LL

_ _

We can always choose a quark basis where:

(3,3,1) _

(1,1,1)

(3,3,1) _

yi = 2½ mqi

〈 ϕ〉

⟨Y ⟩ ⟨Y ⟩



YD = diag(yd ,ys ,yb) YU = V+ × diag(yu ,yc ,yt)

A low-energy EFT satisfies the criterion of MFV if all higher-dimensional operators, constructed from SM and Y fields, are (formally) invariant under the flavor group [ SU(3)Q×SU(3)U×SU(3)D ]

Typical FCNC dim.-6 operator:

We can always choose a quark basis where:

same CKM structure

of the dominant (top-induced or short-distance)

SM contribution !

(YU YU+)ij ≈ yt

2 V3iV3j *

V+ × diag( yu

2, yc2, yt

2 ) × V

≈ V+ × diag(0, 0, yt

2) × V

yi = 2½ mqi

〈 ϕ〉

QLi (YUYU

+)ij QLj × LL LL

_ _



Flavor symmetry: U(3)5 = U(3)Q

×U(3)U ×U(3)D

×...

Symmetry-breaking terms: YD ~ 3Q

×3D YU ~ 3Q×3U

o_ _

General principle that can be implemented independently of the specific high-energy completion of the theory

Within the generic effective theory approach, the bounds on the scale of New Physics are reduced to few TeV (at most)

It leads to a very predictive framework:

Main virtues:

All flavor-changing loop-induced amplitudes have the same CKM/Yukawa structure as in the SM. Only the flavor-independent magnitude of the transition amplitudes can be modified.

U(3)Q×U(3)U×U(3)D

Quark Flavor

Group

YU

YD

VCKM

Basic assumptions:


All flavor-changing loop-induced amplitudes have the same CKM/Yukawa structure as in the SM [e.g.: A(sdZ) ~ Vts

*Vtd, A(bsZ) ~ Vtb*Vts, …].

Only the flavor-independent magnitude can be modified

Z

dLsL newd.o.f.

Yst + Ytd

A(sdZ)

A(bsZ)

Vtd

Vtb= as in the SM...

As a result, the most the tight experimental constraints on rare processes are naturally satisfied:


A few important comments:

I) MFV is not a theory of flavor

It does not allow us to compute the Yukawa couplings in terms of some more fundamental parameters

It is a useful predictive (hence falsifiable) construction that allow us to identify which are the irreducible sources of flavor-symmetry breaking




To prove MFV from data we would need to

observe some deviation form the SM in rare processes

observe the CKM pattern predicted by MFV [within same type of amplitudes]

In most of the processes measured so far we cannot go beyond the 10%-20% level of precision (even if the exp. precision is much better) because of irreducible theoretical uncertainties on evaluating the overall strength of the SM amplitude (non-perturbative effects of strong interactions)

Some more rare decays not observed so far could provide more useful infos.Very interesting candidates: Bd,s l

+l- (currently under investigation @ LHC)

1

Λ2 A[b→d(s)] ∼ Vtd(s) cSM + cNP

1

MW2

(0) (0)

II) Despite its phenomenological success, MFV is far from being “verified”


Typical examples: Bd,s l

+l-

... and, hopefully, spectacular NP effects in the charged lepton sector:

B(μ→eγ) could reach values in the 10-12 - 10-13 range (within the reach of MEG)

Sizable enhancements still possible in models with an extended Higgs sector



III) Even within the “pessimistic” MFV hypothesis, we can still expect sizable deviations from the SM in various B physics observables...

II) Despite its phenomenological success, MFV is far from being “verified”

µ eTeV-scale

new physics


U(3)3 = U(3)Q×U(3)U×U(3)D

Largest flavor symmetry group compatible with the SM gauge symmetry

MFV hypothesis: the Yukawa couplings are the only breaking terms of this large flavor symmetry group

U(3)Q×U(3)U×U(3)D

Quark Flavor

Group

YD

VCKM

YUSmall deviations from the SM in flavor-violating observables (in agreement with data)

virtue main problemNo explanation for Y hierarchies (non-dynamical spurion analysis)


Variations on the “MFV theme”

U(3)3 = U(3)Q×U(3)U×U(3)D

U(2)3 = U(2)Q×U(2)U×U(2)D

Barbieri, G.I., Jones-Perez,Lodone, Straub, '11


MFV = minimal breaking of U(3)3 by (3,3) terms [SM Yukawa couplings]

acting on 1st& 2nd generations

Same protection of FCNCs+

Additional virtue:

The exact symmetry limit is good starting point for the SM spectrum (mu=md=ms=mc=0, VCKM=1) → small breakings terms needed

An interesting variation of MFV is obtained considering the following subgroup:

Yu = yt 0

0 1

V

0 1

0 0 Δ

|V| ~ 0.04 |Δ| ~ 0.006

Unbrokensymmetry



U(3)3 = U(3)Q×U(3)U×U(3)D

U(2)3 = U(2)Q×U(2)U×U(2)D

Barbieri, G.I., Jones-Perez,Lodone, Straub, '11


MFV = minimal breaking of U(3)3 by (3,3) terms [SM Yukawa couplings]

acting on 1st& 2nd generations

An interesting variation of MFV is obtained considering the following subgroup:



Large mass gap (several TeV) not controlled by flavor symmetries (as opposite to MFV)and fine-tuning considerations

This flavor symmetry is particularly interesting in the SUSY context, since it allow to realize the“split-family” scenario discussed yesterday:

Speculations on the breaking of LFU in B physics



Recent anomalies in B physics

A series of recent (and less recent) anomalies in B physics have received a lot of attention recently:

Beside the significance of each anomaly, what makes them particularly (at least in my opinion) is the fact they all seem to be connected to a possible violation of Lepton Flavor Universality

I. Anomalies in B → D(*) τν [LHCb, Belle, Babar]

II. Anomalies in B → K(*) μμ / ee [LHCb]


Test of LFU in charged currents [τ vs. light leptons (μ, e) ]:

SM prediction quite solid: f.f. uncertainty cancel (to a good extent...) in the ratio Consistent exp. results by 3 (very) different experiments

NEW → NEW →

~1.8σ ~3.2σ


Test of LFU in charged currents [τ vs. light leptons (μ, e) ]:

SM prediction quite solid: f.f. uncertainty cancel (to a good extent...) in the ratio Consistent exp. results by 3 (very) different experiments

4σ excess over SM (if D and D* combined)The two channels are well consistent with a universal enhancement (~30%) of the SM bL → cL τL νL amplitude (RH or scalar amplitudes disfavored)

M. Rotondo

bL cL

WτL νL




The largest anomaly is the one [obs. in 2013 and confirmed with higher stat. in 2015] in the P5' [B → K*μμ] angular distribution.But less significant anomalies present also in other B → K*μμ observables and also in other b→sμμ channels [overall smallness of all BR(B → Hadron + μμ)]




B → K(*) ll are FCNC amplitudes (“natural” probes of physics beyond the SM):

No SM tree-level contributionStrong suppression within the SM because of CKM hierarchy

Key point to be addressed: th. control of QCD effects

I. Construction of a local eff. Hamiltonian at the electroweak scale

Three-step procedure to deal with the various scales of the problem:

Heff = Σi Ci(MW) Qi b s

Heavy NP encoded in the Ci(MW) No difference among all b → s ll decays


Mixing of the four-quark Qi into the FCNC Qi [“dilution” of the potentially interesting NP]:

g

Q2 c, u

p ~ μ

b

s

II. Evolution of Heff down to low scales using RGE

Negligible for Q10 [Bs,d → ll & B → K(*)ll ]

Large for “photon penguins” Q9 [ B → K(*)ll only]

Heff = Σi Ci(MW) Qi

Heff = Σi Ci(μ ~ mb) Qi

FCNC operators (E.W. penguins)

Q9= Q

f(b s)

V −A(l l)

V

Q10=Q

f(b s)

V−A(l l)

A

⋮

Four-quark (tree-level) ops.:

Q1=(b s)

V−A(c c)

V −A

Q2=(bc)

V−A(c s)

V−A

⋮


II. Evolution of Heff down to low scales using RGE

Heff = Σi Ci(MW) Qi

Heff = Σi Ci(μ ~ mb) Qi

FCNC operators (E.W. penguins)

Q9= Q

f(b s)

V −A(l l)

V

Q10=Q

f(b s)

V−A(l l)

A

⋮

Four-quark (tree-level) ops.:

Q1=(b s)

V−A(c c)

V −A

Q2=(bc)

V−A(c s)

V−A

⋮

III. Evaluation of the hadronic matrix elements

sensitivity to long-distances (cc threshold...)

distinction between different modes

A(B → f ) = Σi Ci(μ) ⟨ f | Qi |B ⟩ (μ)

non-perturbative effects...




observables designed to cancel f.f. dependence in the HQ limit




Against NP: Main effect in P5' not far from cc threshold“NP” mainly in C9 (↔ charm)

Significance reduced with conservative estimates of non-factorizable corrections

Pro NP: Reduced tension in all the observables with a unique fit of non-standard Ci(MW)

Jaeger et al. '12 Hambrock et al. '13, Hiller & Zwicky '13, Lyon & Zwicky '14



Pro NP: Reduced tension in all the observables with a unique fit of non-standard short-distance Wilson coefficients Descotes-Genon, Matias, Virto '13, '15

Altmannshofer & Straub '13, '15Beaujean, Bobeth, van Dyk '13Horgan et al. '13

Altmannshofer & Straub '15



Last but not least, the most interesting effect in b → sll transitions the 2.6σ deviation from the SM observed in the LFU ratio

∫ dΓ(B+ → K+μμ)

∫ dΓ(B+ → K+ee)

[1-6] GeV2

RK =

Negligible th. error → clean test of LFU (in neutral currents)

Bordone et al. work in prog.

RK = 1 ± O(1%)

This anomaly is perfectly described assuming NP only in b→sμμ [and not in b→see] consistently with the various b→sμμ anomalies


Speculations on the breaking of LFU

(Some of) these recent results have stimulated a lot of theoretical activity.

Most interesting aspect: possible breaking of LFU, both in charged currents (b → cτν vs. b → cμν) and in neutral currents (b → sμμ vs. b → see)

A few general messages:

LFU is not a fundamental symmetry of the SM Lagrangian (accidental symmetry in the gauge sector, broken by Yukawas)

LFU tests at the Z peak are not too stringent (→ gauge sector)

Most stringent tests of LFU involve only 1st-2nd gen. quarks & leptons

→ Natural to conceive NP models where LFU is violated more in processes with 3rd gen. quarks (↔ hierarchy in Yukawa coupl.)


+ many others...

(Some of) these recent results have stimulated a lot of theoretical activity:

...but till last summer most attempts focused only on one set of anomalies (either charged or neutral currents)

What I will discuss next are some general considerations in trying to describe both these effect within simplified (rather general) semi-dynamical models.

Speculations on the breaking of LFU


Anomalies are seen only in semi-leptonic (quark×lepton) operators

RR and scalar currents disfavored → LL current-current operators

Necessity of at least one SU(2)L-triplet effective operator ( + maybe a singlet one):

Bhattacharya et al. '14Alonso, Grinstein, Camalich '15Greljo, GI, Marzocca '15

EFT-type considerations:

Large coupling (competing with SM tree-level ) in bc (=33CKM) → l3 ν3 Small non-vanishing coupling (competing with SM FCNC) in bs → l2 l2






QL

QL

LL

LL

LQ current

LL currentQQ current

Two natural classes of mediators, giving rise to different correlations among quark×lepton, (evidence) and quark×quark + lepton×lepton (bounds)







Large coupling (competing with SM tree-level ) in bc (=33CKM) → l3 ν3 Small non-vanishing coupling (competing with SM FCNC) in bs → l2 l2Two natural classes of mediators, giving rise to different correlations among quark×lepton, (evidence) and quark×quark + lepton×lepton (bounds)

+ small corrections for 2nd (& 1st) generations



→ fits well with the idea of approximate U(2)n flavor symmetry

I. From R(D*) & R(D) data [Γ(b → cτν)/Γ(b → cμν)] →

Λ2

General consequences in charged currents:


II. In principle, it should be possible to get a strong bound on the sub-leading leptonic coupling (λμμ) from Γ(b → cμν)/Γ(b → ceν), but surprisingly it is not so stringent (|λμμ| < 0.1) → no dedicated studies @ B-facotries ! ~


Λ2



II. In principle, it should be possible to get a strong bound on the sub-leading leptonic coupling (λμμ) from Γ(b → cμν)/Γ(b → ceν), but surprisingly it is not so stringent (|λμμ| < 0.1) → no dedicated studies @ B-facotries ! ~


III. Even if it is hard to quantify, this breaking of LFU in c.c could decrease the (old) tension between exclusive & inclusive determinations of |Vub| & |Vcb|:

B → Xc,u τuν

μνν

Irreducible bkg. for the inclusive meas. subtracted (at present) assuming SM-like Γ(B → Xc,uτν)

if Γ(B → Xc,uτν) is enhanced

over the SM → |Vc(u)b|incl. are over estimated

Λ2



Main assumptions:

Non-Universal flavor structure of the currents → mainly 3rd generations

We assume the effective triplet operator is the result of integrating-out a heavy triplet of vector bosons (W', Z') coupled to a single current:

Greljo, GI, Marzocca '15

A simplified dynamical model:

→ Coupling to 3rd generations not suppressed [dynamical assumption]

→ Coupling to light generations controlled by small U(2)q × U(2)l breaking spurions related to sub-leading terms in the Yukawa couplings

down-typemass basis


+

several constraints:

R(D*)R(D)RK P5'(B → K*μμ)

B(B → Kνν) ΔMBs , ΔMBd

CPV(D-D)Γ(B → Xμν)/Γ(B → Xeν)τ → 3μ Γ(τ → μνν)/Γ(τ → eνν)

Overall good fit of low-energy data (non-trivial given tight constraints from ΔF=2 & LFV)

5 free parameters:

Best fit point:

(flavor structure of the sub-leading terms not really probed)

A simplified dynamical model → low-energy global fit:


A simplified dynamical model → low-energy global fit:


… and gives several clear predictions for future low-energy data:

b → c(u) lν

ℒeff works well...

b → s μμ

b → s ττ

b → s νν

, but overall size of the anom. should decrease

|NP| ~ |SM| → large enhancement (~ BR×4) or strong suppr.

~ ± 50% deviation from SM in the rate

Meson mixing

τ decays

~ 10% deviations from SM both in ΔMBs & ΔMBd

τ → 3μ not far from present exp. bound

BR(B→D*τν)/BRSM = BR(B→Dτν)/BRSM = BR(Λb → Λcτν)/BRSM

= … = BR(Bu → τν)/BRSM Rμ/e(X) ~ 10% Rτ/μ(X)

A simplified dynamical model → further low-energy tests:


The dynamical model

W' and Z' resonances in the mass range:

Strong constraint on gH from e.w. precisions tests:

The “heavy vector triplet” eff. Lagrangian [Pappadopulo, Tham, Torre, Wulzer, '14]in a rather peculiar parameter range:

≈ 0.3 < 0.01~

A simplified dynamical model → high-energy constraints:


The heavy vectors are produced mainly from 3rd gen. quarks (bb → Z', bc → W' ) and decay mainly in 3rd generations quarks or leptons (Z' → ττ,bb,tt, W' →tb, τν)

The only really stringent constraint comes from Z' → ττ

Not a very easy signature...



The heavy vectors are produced mainly from 3rd gen. quarks (bb → Z', bc → W' ) and decay mainly in 3rd generations quarks or leptons (Z' → ττ,bb,tt, W' →tb, τν)

The only really stringent constraint comes from Z' → ττ

Minimal version of the model(no exotic decay channels)

ruled out by direct searches

Not a very easy signature...


Greljo, GI, Marzocca '15


N.B.: while the low-energy consequences are almost independent from the structure of the underlying dynamical model, the high-energy consequences can be very different.

For instance, choosing the LQ mediator, we have a perfect candidate also for the mediator of the “S(750)”→γγ,gg effective couplings...



QL

QL

LL

LL

LQ current

LL currentQQ current

Conclusions


Conclusions

We entered in a very special era in particle physics: the SM is a successful theory that has no intrinsic energy limitations.

While waiting for possible clear clues for physics beyond the SM from high-energy experiments, the key (and difficult) question we face is: what determines the precise values of SM parameters?[“anarchy + anthropic selection” vs. “new symmetries”]


Conclusions

We entered in a very special era in particle physics: the SM is a successful theory that has no intrinsic energy limitations.

While waiting for possible clear clues for physics beyond the SM from high-energy experiments, the key (and difficult) question we face is: what determines the precise values of SM parameters?[“anarchy + anthropic selection” vs. “new symmetries”]

In this perspective, (some of) the anomalies that are emerging both at high-pT and in flavor physics could be the first hints of new symmetries...

We cannot exclude the anthropic principle is the right explanation for some of these couplings (e.g. for the cosmological constant), but it is definitely premature to give-up the attempt of finding dynamical explanations for most of them.


lhc physics: higgs and beyond...“intermediate” bsm sector non-sm flavor probe physics at energy...

Documents