Looking for New Physics via the Flavor Window

(1)

Introduction [The Flavor Window]

SUSY & Flavor [The Usual Suspects]

The B → K

^(*)

ll anomalies [Charming Penguins strike back]

Flavor physics with the BEH boson [Contact]

On the observed pattern of quark & lepton masses [The Matrix]

Conclusions

Looking for New Physics via the Flavor Window

Gino Isidori

[

University of Zürich & INFN

]

(2)

The Flavor

Introduction

(3)

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

Despite all its successes, 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

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SM

What determines the

observed pattern of quark

& lepton mass matrices?

flavor-violating interactions

Introduction

High-scale

[flavor-symmetric?]

theory

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

Higgs sector

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

(5)

SM +

Introduction

Two key open questions:

High-scale

theory Higgs

sector

“intermediate”

BSM sector non-SM

flavor

Are there other sources of flavor symmetry

breaking?

Probe physics at energy scales not directly accessible at accelerators

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

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Are there other sources of flavor symmetry breaking (beside the SM Yukawa couplings)?

→ talks by Derkach Kamenik '13, G.I. '13, ...

[wide literature]

That's the question addressed by precision measurements (& searches) of flavor- changing processes of quarks & charged-leptons → So far everything seems to fit well with the SM→ Strong limits on NP

+ O

_ΔF=2

ℒ

_eff

= ℒ

_SM ¹

Λ²

(7)

That's the question addressed by precision measurements (& searches) of flavor- changing processes of quarks & charged-leptons → So far everything seems to fit well with the SM→ Strong limits on NP [not to be overestimated...]

M

_X

> 200 TeV

MEG '13

BR(μ→eγ)

^exp

< 5.7×10

^-13

E.g.: γ

μ e

X

y_μ θ₁₂

Either NP is very heavy... ort it has a non-trivial flavor-breaking pattern...

~

(8)

M

_X

> 10 GeV

MEG '13

BR(μ→eγ)

^exp

< 5.7×10

^-13

E.g.: γ

μ e

X

~

y_μV₂₃ y_eV₃₁

(9)

There is still a wide (possibly interesting...) region of NP parameter space

(both in masses and couplings) that is waiting to be explored yet...

(10)

SUSY & Flavor

B → X_sγ B_s,d → μμ

|V_ub| &

CKMfits

ε_K, ϕ_s,d Δm_B_s,d

(11)

Weakly coupled theory + light Higgs (125 is well the SUSY region...) + dark-matter & unification

Some tuning in m_his unavoidable: do we really care if the fine-tuning is ~1% ? Despite the absence of signals, SUSY remains our best candidate for a UV

completion of the SM not far from the TeV scale:

Dimopulos, Giudice, '95 Cohen, Kaplan, Nelson '96 + many others...

Most of the low-scale SUSY virtues are maintained if we assume a flavor non- trivial spectrum

0.5 TeV 1.0 TeV 1.5 TeV

t_R

~

g~

t^~_L

W~ B~ μ

other squarks

b_L

~

“Split-family” SUSY

3^rd gen. squarks + Higgsinos key ingredients in the m_htuning

splitting the 3^rd family can easily be motivated in flavor models

(12)

b(s)

s(d) b(s)

s(d) q₃

~ q~₃

Possible “visible” [~ 5-20%] effects in

● CPV in K mixing (ε_K)

● CPV in B_s,d mixing (ϕ_s,d) g (γ, Z)

q_i (l_i)

g (χ )

q_j (l_j)

~ ~

q~₃ (l~₃) Possible “visible” [~ 5-20%] effects in

● Rare B decays (B_s → μμ, B_s → X_sγ)

● LFV (μ → eγ) & EDMs g (χ )~ ~

g (χ )~ ~

LHC experiments have started to directly explore this scenario & possible variations (e.g: mini-spilt...).

In this context, flavor physics plays a key role [non-trivial flavor structure] → BSM effects mediated by 3^rd gen. squarks & leptons:

The Usual Suspects

Barbieri et al. '12-'14; Delgado et al. '13 Althmanshofer, Harnik, Zupan, '13

Katz, Reece, Sajjad '14 + ...

(13)

Barbieri, Buttazzo, Sala, Straub, '14

Example I: ΔF=2 observables in Split-family” (or “Natural”) SUSY with

U(2)³ flavor symmetry

ΔM_Bs/ΔM_Bs^SM ΔM_Bd

ΔM_Bd^SM

Δϕ_s

|ε_K|/|ε_K^SM|

Points allowed by present CMS/ATLAS data:

(14)

Example I: ΔF=2 observables in Split-family” (or “Natural”) SUSY with

ΔM_Bs/ΔM_Bs^SM ΔM_Bd

ΔM_Bd^SM

Δϕ_s

|ε_K|/|ε_K^SM|

Points allowed by present CMS/ATLAS data + present flavor data

(15)

SUSY relative shift (x100)

M_H+ [TeV]

Example I: ΔF=2 observables in Split-family” (or “Natural”) SUSY with

ΔM_Bd ΔM_Bd^SM

|ε_K|/|ε_K^SM|

Points allowed by present CMS/ATLAS data + present flavor data

tanβ

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|ε_K|/|ε_K^SM|

SM fit, no ε_K N.B.: There is a (weak) evidence of a

(positive) non-standard contribution to ε_K

|V_ub|

Complementary role of

Belle-II [→ |V_ub| from B → πlν and B → τν ]

and LHCb [ → γ]

Example I: ΔF=2 observables in Split-family” (or “Natural”) SUSY with

In order to clarify the picture we need a more clean determination of |V_ub| & γ

ΔM_Bd ΔM_Bd^SM

N.B.: a positive contribution to ε_K is a general feature

of MFV-like SUSY models [light stops and/or charged H]

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b s

μ

B

^t μ ^b

s

μ

B

^t μ

Leading SM diagrams (unitary gauge):

b s

B

t μ

μ

χ b

s

B

t μ_R

μ_L A⁰, H⁰

Z χ Possible non-SM

contributions:

Relevant for BR = O(SM) Possible large enhancement (e.g. SUSY @ large tanβ)

These modes are a unique source of information about flavor physics beyond the SM:

theoretically very clean (virtually no long-distance contributions)

particularly sensitive to FCNC scalar currents and FCNC Z penguins

Example II: B

_s,d

→ μμ & SUSY

~ ~

~~

~ ~

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Recent developments both on the theory and on the experimental side:

BR_s,SM= (3.65 ± 0.23)×10^-9

(time-integrated average)

BR_s^(exp)= (2.9 ± 0.7)×10^-9

At this stage there is perfect compatibility, but we are only at the beginning...

BR_d,SM= (1.06 ± 0.09)×10^-10 BR_d^(exp)= (3.6 ± 1.5)×10^-10

LHCb + CMS '13 Bobeth, Gorbahn, Hermann, Misiak,

Stamou, Steinhauser '13 +

progress from Lattice QCD

An overall th. error below 5% is definitely within the reach in the next few years

Example II: B

_s,d

→ μμ & SUSY

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BR_s,SM= (3.65 ± 0.23)×10^-9 BR_s^(exp)= (2.9 ± 0.7)×10^-9

Example II: B

_s,d

→ μμ & SUSY

Buchmueller et al. [Mastercode]

Mahmoudi et al. [SuperIso]

Roszkowski et al. '12 Haisch & Mahmoudi '12 Althmanshofer et al. '13

…

The possible large effects occurring in the MSSM at

large tanβ are ruled out...

...but more precision on this mode can still provide

very valuable infos Constrained

MSSM

“Mastercode”

→ talk by de Vries

(20)

The B → K

^(*)

ll anomalies

Charming penguins

Strike back

penguin

(21)

The B → K

^(*)

ll anomalies

B → K*μμ signals from the 3 LHC experiments:

→ talk by Albrecht

(22)

Similarly to B_s,d → ll, also B → K^(*)ll are FCNC amplitudes and, as such, are useful probes of flavor dynamics beyond the SM

No SM tree-level contribution

Strong suppression within the SM because of CKM hierarchy

Key point to be addressed: th. control of QCD effects, larger and potentially more dangerous than in B_s,d → ll.

General considerations:

(23)

Similarly to B_s,d → ll, also B → K^(*)ll are FCNC amplitudes and, as such, are useful probes of flavor dynamics beyond the SM

No SM tree-level contribution

Strong suppression within the SM because of CKM hierarchy

Key point to be addressed: th. control of QCD effects, larger and potentially more dangerous than in B_s,d → ll.

General considerations:

1^st step: Construction of a local eff. Hamiltonian at the electroweak scale Three-step procedure to deal with the various scales of the problem:

H

_eff

= Σ

_i

C

_i

(M

_W

) Q

_i

b s

Heavy NP encoded in the C_i(M_W)

No difference among the various b → s ll decays

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

g

Q

₂ _{c, u}

p ~ μ b

s

eff

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

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

H

_eff

= Σ

_i

C

_i

(M

_W

) Q

_i

H

_eff

= Σ

_i

C

_i

(μ ~ m

_b

) Q

_i

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=(b c)_V₋_A(c s)_V₋_A

⋮

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non- perturbative

effects...

eff

Four-quark (tree-level) ops.:

Q1=(b s)_V₋_A(c c)_V₋_A Q₂=(b c)_V₋_A(c s)_V₋_A

⋮

H

_eff

= Σ

_i

C

_i

(M

_W

) Q

_i

H

_eff

= Σ

_i

C

_i

(μ ~ m

_b

) Q

_i

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

⋮

3^rd step: Evaluation of the hadronic matrix elements

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

inclusive (OPE + 1^m_b,cexpansion) exclusive modes (hadronic form factors → Lattice or LCSR)

A(B → f ) = Σ

_i

C

_i

(μ) 〈 f | Q

_i

|B 〉 (μ)

(26)

The anomalies:

I. The P₅' anomaly in B → K^*0μμ 3.7σ local discrepancy

vs. SM [Descotes-Genon et al. '13] II. Overall smallness of the four

BR(B → Hμμ), H=K^*0, K^*+, K⁺, K⁰ Pro NP:

Reduced tension with data in both cases with a unique fit of modified Wilson coefficients (mainly C₉)

The corresponding effective NP scale is high (~10 TeV), not in contradiction with other data

Descotes-Genon, Matias, Virto '13 Altmannshofer & Straub '13

Beaujean, Bobeth, van Dyk '13 Horgan et al. '13

(27)

The anomalies:

I. The P₅' anomaly in B → K^*0μμ

II. Overall smallness of the four

BR(B → Hμμ), H=K^*0, K^*+, K⁺, K⁰ 3.7σ local discrepancy

vs. SM [Descotes-Genon et al. '13]

Against NP:

Main effect in P₅' not far from cc threshold

Significance reduced with conservative estimates of non- factorizable corrections

Pro NP:

Jaeger et al. '12 Hambrock et al. '13 Hiller & Zwicky '13

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The anomalies:

I. The P₅' anomaly in B → K^*0μμ

II. Overall smallness of the four

BR(B → Hμμ), H=K^*0, K^*+, K⁺, K⁰ 3.7σ local discrepancy

vs. SM [Descotes-Genon et al. '13]

Against NP:

Main effect in P₅' not far from cc threshold

Significance reduced with conservative estimates of non- factoriz. corr. [but not everybody agree → talk by Hofer]

NP in photon-penguins only is “suspicious” [personal opinion] Pro NP:

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

(29)

The anomalies:

III. High-q²(resonance) region in B⁺ → K⁺μμ

Key features:

Clear failure of the factorization approach

[ → hint we have a poor control of QCD in such modes?]

Cannot be explained with the NP in bsll ops. (C₉) as in I. & II.

Maybe due to NP in b → scc ops? → possible to improve also in I. & II.

[Lyon & Zwicky '14], but very contrived from the model-building point of view.

Lyon & Zwicky '14

Future data could help to clarify the picture:

Data closer to the psi(1S) and psi (2S) region + fine q2-binning also from other exclusive modes [K vs. K* ?]

Data from inclusive modes → BELLE-II

TH = factorization ⊗ σ(e+e- → hadr)

(30)

The anomalies:

IV. The lepton universality ratio

dΓ(B⁺ → K⁺μμ)/dΓ(B⁺ → K⁺ee)

2.6σ from SM

Intriguing BSM hints in b → sll transitions, but no clear evidence yet (exp. fluctuations + theory errors may explain all the effects)

More data (on both exclusive & inclusive modes) can help to clarify the picture Key features:

Th. prediction very solid (QCD cannot affect lepton universality...)

NP in b → see? → does not fit in a trivial way with any of the previous anomalies...

Final considerations:

(31)

Flavor physics with the BEH boson

SM

High-scale

theory Higgs

sector

(32)

Higgs-mediated FCNCs are extremely suppressed in the SM, but can be very large in models with an extended Higgs sector.

Even assuming a single Higgs doublet, but allowing non-vanishing higher- dimensional operators → h-mediated FCNC are unavoidable:

Y

^ij

ψ

_Lⁱ

ψ

_R^j

ϕ + ε

^ij

ψ

_Lⁱ

ψ

_R^j

ϕ

³

+... 

(vY

^ij

+ v

³

ε

^ij

) ψ

_Lⁱ

ψ

_R^j

+ (Y

^ij

+ 3v

²

ε

^ij

) ψ

_Lⁱ

ψ

_R^j

h + ...  ε

^ij

= c

^ij

Λ

²

h FCNC couplings if Y^ij≠ c ε^ij

vY

_eff

IFlavor-violating Higgs decays

Azatov, Toharia, Zhu '09 Agashe & Contino '09

Interplay between:

Indirect constraints [from h-mediated amplitudes @ low-energies]

Direct FCNC h decays [enhanced sensitivity of h(125) → suppressed width]

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Strongly bounded by ΔF=2

(except for terms involving the top)

IFlavor-violating Higgs decays

Bounds less severe in the lepton sector, especially for the

τμ and τe modes

Indirect bounds imply BR(h → τμ, τe) < 10%~

Blankenburg, Ellis, G.I. '12 Harnik, Kopp, Zupan, '12 Davidson, Verdier, '12

Celis, Cirigliano, Passemar, '13 Kopp & Nardecchia '14

q_i q_j

q_j q_i

h

γ

l_i

h l_j l_k

(34)

IFlavor-violating Higgs decays

(35)

What determines the observed pattern of quark & lepton masses?

(36)

It works well for m_u,d

Maybe good also for ν masses

& mixing [anarchy]

But what about CKM and the other masses?

Natural hint from the pattern of Yukawa couplings.

Less evident, but not excluded, in the neutrino case

“large” flavor symmetry + “small”

breaking is the best way to explain the absence of NP signals so far in FCNCs

What determines the observed pattern of quark & lepton masses?

Two main roads:

The symmetric way Anarchy

Anthropic selection+

(37)

“Large” (non-Abelian) flavor groups + “small” breaking terms

U(3)³ = U(3)_Q×U(3)_U×U(3)_D

Largest flavor symmetry group compatible with the SM gauge symmetry MFV = minimal breaking of U(3)³ by (3,3) terms [SM Yukawa couplings]

Chivukula & Georgi, '89 D'Ambrosio, Giudice, G.I., Strumia, '02

Naturally small effects in FCNC observables

(assuming TeV-scale NP)

No explanation for Y hierarchies

(masses and mixing angles) & large symmetry breaking due to y_t

main virtue main problems

U(2)³= U(2)_Q×U(2)_U×U(2)_Dflavor symmetry Barbieri, G.I., Jones-Perez,

Lodone, Straub, '11

acting on 1^st& 2^nd generations

The exact symmetry limit is good starting point for the SM quark spectrum (m_u=m_d=m_s=m_c=0, V_CKM=1) → we only need small breakings terms

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I. A problem of both these approaches -attributing a special role to the

hierarchies of the Yukawa couplings- is the problem of neutrino masses:

Why neutrino mixing angles are not as small as in the quark sector?

Why the mass hierarchies in the neutrino sector are not as large?

II. A second common drawback is that the ansatz for the symmetry breaking pattern is put in “by hand” (non-dynamical spurion analysis)

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I. A problem of both these approaches -attributing a special role to the

hierarchies of the Yukawa couplings- is the problem of neutrino masses:

Why neutrino mixing angles are not as small as in the quark sector?

Why the mass hierarchies in the neutrino sector are not as large?

II. A second common drawback is that the ansatz for the symmetry breaking pattern is put in “by hand” (non-dynamical spurion analysis)

Yukawas from V(Y) U(3)³ invariant potentials

Gauging of U(3)³ & U(2)³

Feldmann et al. '09

Alonso, Gavela, et al. '11-'13

Nardi '11; Espinosa, Fong, Nardi '12

Albrecht, Feldmann, Mannel, '09 Grinstein, Redi, Villadoro, '09 D'Agnolo & Straub, '11

Recent th. progress

(40)

U(3)

⁵

LR LL

Let's assume the Yukawa couplings and the (Majorana) neutrino mass matrix are dynamical fields of the the MFV flavor group [ = U(3)⁵ ], and that their values are determined by a minimization principle (e.g. the potential minimum)

Y ∝ (0,0,1) [

unbroken U(2)_LxU(2)_R

] |M

_ν

| ∝ (1,1,1) [

unbroken O(3)_L

]

Michel & Radicati, '69 Cabibbo & Maiani, '69

The “natural solutions” [i.e. solution requiring no tuning in the parameters of the potential] are the configurations preserving maximally unbroken subgroups.

Alonso, Gavela, G.I., Maiani, '13

Under this hypothesis, we are naturally led to a hierarchical

spectrum for quarks & charged leptons and a degenerate spectrum for neutrinos The symmetric way [a possible option...]

(41)

Alonso, Gavela, G.I, Maiani, '13

O(3)_L U(2)_LxU(2)_R U(1)_L23xU(2)_R

A “natural orientation” of O(3)_L vs. U(2)_L preserving an unbroken U(1) symmetry implies a π/4 mixing angle in the PMNS matrix

.

U(3)

_E

×U(3)

_L

Y ∝ (0,0,1)

LR LL

[

] M

_ν

∝ 1 0 0 0 0 1 0 1 0

unbroken O(3)_L

same U(3)

_L

basis

The symmetric way [a possible option...]

(42)

LR LL

Sub-leading ^U(2)_L breaking resolving 1-2 degeneracy

|s₁₃| ~ O(ε), |s₁₂| ~ O(1)

Δm_atm²

m_ν² = O(ε) m_μ

m_τ = O(ε)

<

|s₁₃| ~ 0.2

~ 0.06 <

m_μ m_τ

Y ∝ (0,0,1) [

] M

_ν

∝ 1 0 0 0 0 1 0 1 0

unbroken O(3)_L

same U(3)

_L

basis

Alonso, Gavela, G.I, Maiani, '13

<m_ν> ≈ 0.1 eV

U(3)

_E

×U(3)

_L

(43)

LL

If all this is correct... 0ν2β decay experiments

should be very close to observe a positive signal...

present bounds near

future reach

M

_ν

∝ 1 0 0 0 0 1 0 1 0

unbroken O(3)_L

Δm_atm²

m_ν² = O(ε)

+

<m_ν> ≈ 0.1 eV

U(3)

_E

×U(3)

_L

(44)

Conclusions

Flavor-changing transitions represent a “unique window” on BSM physics.

There is still a lot to learn & explore, also in view of HL-LHC.

The “Usual Suspects” (ε_K, ϕ_s, B → μμ, ...) may hide NP signals @ 10% level in well-motivated models (e.g. “split-family SUSY”) → need combined th+exp precision at the few% level → essential to improve quality of CKM fits

Intriguing NP hints (of “exotic” nature) in B → K^(*)ll decays, but picture far form being clear → more data can help to clarify the situation

Worth to improve searches of exotic flavor-violating effects, such as H → τμ [many additional interesting searches not covered in this talk...]

We should not give-up on models trying to “explain” masses & mixing from symmetry principles → the overall scale of neutrino masses could be the key...

(45)

(46)

What's P₅' ?

(47)

Rare K decays

The unique features of

K → πνν

- Unique probes of possible deviations from MFV -

Smallness of the CKM suppression factor (V_ts^*V_td~ λ⁵) High th. cleanness (unique for loop-induced meson decays):

~2% for BR(K_L) & ~ 5% for BR(K⁺)

(48)

Other anomalies:

I. Direct CPV in charm decay: Δa_CP= a_CP(K⁺K-) - a_CP(π⁺π-)

W.A. 2012: (0.67 ± 0.16)% LHCb-2014: (0.14 ± 0.16_stat± 0.08_syst)%

Gone...!

II. Di-muon semileptonic asymmetry by D0

Not confirmed by other expts.

(if due to B-meson mixing) III. BR(B → D^(*)τν) by BABAR

[ → talk by Browder ] Still there...

TH warnings: Require low-scale NP (~ 100 GeV)

+ contrived ops. structure Fajfer et al. '12

(49)

Example of B-physics observable that will NOT be dominated by the TH error even in the long term:

BR(B_d → μμ) BR(B_s →μμ)

BR(B_u →τν) BR(B_u →μν)

N.B.: there are various clean ratios of this kind

BR(B_s → ττ) BR(B_s →μμ)

...

And future efforts in B physics could possibly address also

τ → 3μ, τ → μγ, ...

Future prospects in B physics @ hadron colliders