variations on minimal flavour violation - uni-siegen.de on minimal flavour violation (quarks and ......

Variations on Minimal Flavour Violation(Quarks and Leptons)

Thorsten Feldmann

Particle Theory Seminar,RWTH Aachen, 12. January 2012

Th. Feldmann (Uni Siegen) Variations on MFV Aachen, January 2012 1 / 29

SM works astonishingly well, but . . .

Hierarchy Problem in the Higgs Sector: Why MW � MPlanck ?

Dark Matter in the Universe: New weakly-interacting stable Particles ?

Origin of Neutrino Masses ?

Baryon-Antibaryon–Asymmetry in the Universe: New Sources of CP Violation ?

? Origin of Hierarchies in Fermion Masses and Mixings ?

. . .

New Particles, Forces, Conceptsat Higher Energies?

Grand Unification

Supersymmetry

Extra Dimensions

. . .


Lessons from Flavour Physics

Quark Sector:CKM-Mechanism for flavour transitions in the SM experimentally confirmed.

√

7→ Flavour Sector of New Physics@TeV must be highly non-generic. (!)

7→ Precision Flavour Observables constrain Parameter Space of NP Models. (!)

Lepton Sector:Neutrino Oscillations:

I Neutrinos have (tiny) mass 7→ New Physics around the GUT scale. (?)I Large mixing angles (in contrast to quark sector). (!)

Flavour Violation in charged lepton transitions (LFV):I Tiny (unmeasurable) in minimally extended SM. (

√)

I Drastically enhanced in generic NP Models. (!?)

Postulate Symmetry Principle: Minimal Flavour Violation

— “Flavour– and CP–Violation from NP still governed by SM Parameters, only” —


Outline: Variations on MFV

1 Introduction√

2 Flavour Symmetries and Minimal Flavour ViolationMFV (Andante)Beyond MFV (Presto)— Intermezzo : A sequential 4th generation —Dynamical FS Breaking (Allegro Moderato)Inverted MFV (Vivace)

3 Summary

based on work together with:Michaela Albrecht, Andras Joseph, Martin Jung, Thomas Mannelalso: Andrzej Buras, Björn Duling, Tillmann Heidsieck, Christoph Promberger, Stefan Recksiegel


Flavour Symmetries and Minimal Flavour Violation


1. Minimal Flavour Violation (MFV – Quark Sector)

Idea: [Buras et al., Ciuchini et al., . . . ]

Flavour Coefficients of NP Operators related to SM Yukawa Matrices from:

− Lqyuk = (Q

iLH) Y ij

U (UR)j + (QiLH) Y ij

D (DR)j + h.c.

Formalism: [D’Ambrosio, Cirigliano, Isidori et al., . . . ]

SM Yukawa Matrices as VEVs of auxiliary “Spurion“ Fields (in some effective theory)

YU = 〈SU (x)Λ〉 ∼ (3, 3, 1)

YD = 〈SD(x)Λ〉 ∼ (3, 1, 3)

⇔ break SU(3)QL× SU(3)UR × SU(3)DR × U(1)2

I Book-Keeping Device for NP Flavour EffectsI Dynamical Interpretation (?)I Systematical Extensions (?)


Example: MFV in the MSSM [see e.g. Colangelo/Nikolidakis/Smith 2008]

Consider soft SUSY breaking terms in the Lagrangiansquark masses:

M2QL

= a0 1 + a1 YUY †U + a2 YDY †D + . . .

M2UR

= b0 1 + b1 Y †UYU + b2 Y †UYDY †DYU + . . .

M2DR

= c0 1 + c1 Y †DYD + c2 Y †DYUY †UYD + . . .︸︷︷︸9 independent structures = 3x9 real coefficients

squark trilinear couplings: (mix QL and UR , DR )

AU ={

y0 1 + y1 YUY †U + y2 Y †UYDY †DYU + . . .}

YU

AD ={

z0 1 + z1 YUY †U + z2 Y †UYDY †DYU + . . .}

︸︷︷︸YD

9 independent structures = 2x9 complex coefficients

MFV hypothesis: All coefficients O(1) or smaller

(Expansion of a generic flavour matrix would lead to coefficients enhanced by mtmu

, 1sin θC

, . . . )


Example: Model-independent MFV – NP as Effective TheoryAllow for New Effective Operators (dim> 4) in terms of SM Fields.

Construct Invariants under Gauge and Flavour Group, using YU and YD .

7→ non-trivial Flavour Structures: (again withO(1) coefficients)

QLYUY †UQL , DRH†Y †DYUY †UQL , DRY †DYUY †UYDDR , etc.

→ Flavour-Changing Neutral Currents require at least two CKM Elements.Dominance of m2

t V∗tDVtD′ , (can be singled out by non-linear version of MFV [TF/Mannel])

→ Transitions with Right-Handed Quarks acquire Mass Suppression mq .

New contributions to flavour transitions suppressedby same factors of VCKM and mquark as in the SM.

⇒ NP Scales in the (few) TeV Range still allowed.

For a detailed phenomenological analysis, see [D’Ambrosio et al., hep-ph/0207036].


Example: Model-independent MFV – NP as Effective TheoryAllow for New Effective Operators (dim> 4) in terms of SM Fields.

Construct Invariants under Gauge and Flavour Group, using YU and YD .for instance, with b → d Transitions:

dL

(V∗td m2

t Vtb + . . .)

bL , dRh0md

(V∗td m2

t Vtb + . . .)

bL , dRmd

(V∗td m2

t Vtb + . . .)

mbbR

→ Flavour-Changing Neutral Currents require at least two CKM Elements.Dominance of m2

t V∗tDVtD′ , (can be singled out by non-linear version of MFV [TF/Mannel])

→ Transitions with Right-Handed Quarks acquire Mass Suppression mq .

New contributions to flavour transitions suppressedby same factors of VCKM and mquark as in the SM.

⇒ NP Scales in the (few) TeV Range still allowed.

For a detailed phenomenological analysis, see [D’Ambrosio et al., hep-ph/0207036].


MFV in the Lepton Sector (MLFV) [Cirigliano et al, hep-ph/0507001, hep-ph/0601111]

Requires additional assumptions about Origin of Neutrino Masses:SM as Effective Theory

Leff = LSM +1

ΛLNVOdim−5 +

1Λ2

LFVOdim−6 + . . .

I Unique dim-5 operator: breaks lepton number, generates neutrino massesI Various dim≥ 6 operators: induce lepton-flavour violating transitionsI Assumption: ΛLFV � ΛLNV

Flavour Structures associated with Lepton Masses:

Lmass 3 (LiH) (YE )ij (ER)j +1

ΛLNV(Li H) g ij

ν (H†Lj )c + h.c.

MLFV: Expand flavour coefficients of dim≥ 6 operators in terms of

YE ∼ (3, 3)gν ∼ (6, 1)

}of SU(3)L ⊗ SU(3)ER

Leading LFV effect proportional to∆m2

atmv2

ΛLNVΛLFV

can be singled out by using a non-linear representation of MLFV. [TF/Mannel, arXiv:0806.0717]


MLFV Phenomenology (minimal field content)

LFV decay rates are sizable, only if ΛLNV � ΛLFV ,

Example: Br(µ→ eγ) > 10−13 requires ΛLNV > 109 · ΛLFV .

ΛLNV drops out in ratios of LFV decays, e.g. Br(µ→ eγ)/Br(τ → µγ)

using ΛLNV = 1010 · ΛLFV

[from Isidori, arXiv:0908.0404]

⇒ Better experimental prospects to observe µ→ eγ than τ → µγ.

Alternative realizations of MLFV within see-saw constructions possible,see e.g. [Alonso et al. 11, Gavela et al. 09, Branco et al. 07, Davidson et al. 06]


2. Beyond Minimal Flavour Violation

Ad hoc: Allow some NP parameters to be of O(1)←→ some coefficients in the MFV expansion have to be� 1

Systematical approach (model-independent): [TF/Mannel 07]

Stick to effective-theory picture.

Introduce additional spurion fields (with different transformation under FS).(for instance, YR ∼ (1, 3, 3) or ZL ∼ (8, 1, 1) )

Find constraints on magnitude of new spurions:• Self-consistency constraints from SM Yukawa terms,

+ Model-dependent assumptions.

→ alternative book-keeping device . . .

”Next-to-minimal Flavour Violation“ (nMFV)


Example: Extending the SM by a 4th Generation

Add another (sequential) Quark-Family: (t ′L, b′L), t ′R , b′R

Quark mixing matrix contains 3 new mixing angles and 2 new CP-phases

MFV perspectiveNew source of flavour violation: Complex vector under SU(3)QL :

Generic O(1) Entries: Violation of Flavour Precision Observables

Consistency Conditions in nMFV

θi4θj4 . θij (i, j = 1..3 for SM quarks)

MFV is recovered only for θi4 ≡ 0.


Examples for ”Allowed“ Patterns of 4G Mixing–Matrix

V 4G ∼

1 λ λ3 λ4

λ 1 λ2 λ3

λ3 λ2 1 λ

λ4 λ3 λ 1

∼

1 λ λ3 λ2

λ 1 λ2 λ

λ3 λ2 1 λ

λ2 λ λ 1

V 4G ∼

1 λ λ3 λ2

λ 1 λ2 λ3

λ3 λ2 1 λ

λ2 λ3 λ 1

∼

1 λ λ3 λ3

λ 1 λ2 λ2

λ3 λ2 1 λ

λ3 λ2 λ 1

Experimental Constraints:Tree-level decays: |Vud |, |Vus|, |Vub|, |Vcd |, |Vcs|Meson-mixing: εK , ∆MK , ∆MBd , ∆MBs , SψKs

Rare decays: B → Xsγ, Xs`+`−, Bs → µ+µ−, K± → π±νν

[Buras/Duling/TF/Heidsieck/Promberger/Recksiegel 10]

also: [Bobrowski/Lenz/Riedl/Rohrwild, Soni et al. . . . ]


Correlations between new CP-Phases δ24 vs. δ14 for different scalings

(4, 3, 1)(4, 3, 2)

(2, 1, 1)(2, 2, 1)

(2, 3, 1) (3, 2, 1)

larger 4G mixing angles ←→ stronger correlations between CP phases

each nMFV sub-scenario exhibits different correlations between flavour observables

Corollary: 4G Model cannot yield strong enhancement of AdirCP in D decays (!)


Example: Bs → µµ vs. Bd → µµ

MFV and SM4 vs. other NP models (courtesy of D. Straub)

MFV: Br[Bd → µµ] = |Vtd/Vts|2 Br[Bs → µµ]

SM4: Anti-Correlation between Bs → µµ and Bd → µµ


A sequential 4th Lepton Generation (Dirac neutrinos)

New heavy charged lepton τ ′ and (Dirac-)neutrino ντ ′ .

4× 4 mixing matrix in the lepton sector Uij

[Lacker/Menzel, arXiv:1003.4532]; [Buras et al, arXiv:1006.5356]

Radiative µ and τ decays:

+

γ

WW

νi

µ e +

γ

νi

Wµ e

Br(τ → µγ)

Br(µ→ eγ)'∣∣∣∣Uτ4

Ue4

∣∣∣∣2 Br(τ− → ντµ−νµ)

Br(τ → µγ)

Br(τ → eγ)'∣∣∣∣Uµ4

Ue4

∣∣∣∣2 Br(τ− → ντµ−νµ)

Br(τ− → ντe−νe)≈∣∣∣∣Uµ4

Ue4

∣∣∣∣2Br(τ → eγ)

Br(µ→ eγ)'∣∣∣∣Uτ4

Uµ4

∣∣∣∣2 Br(τ− → ντe−νe)

stringent constraints on |Ui4| elements, independent of heavy neutrino mass (!)

µ–e conversion in nuclei:

conversion rate directly proportional to |Ue4Uµ4|2


4G Correlations for Radiative Decays and µ-e Conversion

τ → µγ vs. τ → eγ

within experimental reach,but not simultaneously (!)

µ–e conversion vs. µ→ eγ

possible constraints on |Ue4Uµ4|even tighter

[from Buras/Duling/TF/Heidsieck/Promberger 2010]


3. Dynamical Flavour Symmetry Breaking (Quarks)

Yukawa Matrices as Dynamical Scalar Fields in an Effective Theory:

YU → SU(x)/Λ , YD → SD(x)/Λ

Scalar potential in terms of positive hermitian matrices (1⊕ 8 under SU(3)QL) :

SUS†U ≡u0√

3+ λaua , 0 ≤ u ≡

√uaua ≤ u0

SDS†D ≡d0√

3+ λada , 0 ≤ d ≡

√dada ≤ d0

takes the most general form (dim ≤ 4)

V = a1 u0 + a2 d0 + a3 u2 + a4 d2 +a5

2u2

0 +a6

2d2

0 + a7 u0d0 + a8 uada

option 1 (normal hierarchy) u0 = u 6= 0 d0 = d = 0 yt 6= 0option 2 (degenerate hierarchy) u0 6= 0 u = d0 = d = 0 yu = yc = yt 6= 0

. . . . . . . . . . . .

[A. Joseph, diploma work]


Dynamical Flavour Symmetry Breaking (Leptons)

Minimal Set-Up:For the first step of FSB, the situation is as for quarks, with

YUY †U → gcνgν , YDY †D → YE Y †E

→ Inverted Neutrino Hierarchy does not occur (for minimal set-up)(would correspond to 2 degenerate eigenvalues and 1 vanishing eigenvalue)

Difference between Quarks and Leptons in later steps of FSB,from dim-6 invariants in terms of matrix

〈X 〉 ≡ gcνY c

E Y TE gνYE Y †E

(also responsible for additional CP phases in lepton sector)


Flavour Hierarchies from Spurion Potential (Quarks)

Imagine potential, such that ”option 1” is realized, with yt = 〈SU〉33Λ

= O(1)

⇒ Original SM Flavour Symmetry spontaneously broken

SU(3)3 yt 6=0−→ SU(2)2 × SU(3)× U(1)

↓ . . . continue with smaller Yukawa entries . . . ↓

Hierarchies in Masses and Mixings ↔ Sequence of partially broken FS

yu,d Λ� ys θ12 Λ� ys Λ� yb θ13 Λ� yb θ23 Λ� yb Λ� Λ .

[TF/Jung/Mannel]

But what about the Goldstone Bosons of broken FS?

Longitudinal Modes for Massive Gauge Bosons of Gauged Flavour Symmetry

Hierarchies in Fermion Masses and Mixings→ Hierarchy of Gauge-Boson Masses

[Albrecht/TF/Mannel]


4. Inverted MFV from Gauged Flavour Symmetries with New Fermions

SM with gauged flavour symmetries suffers from Quantum Anomalies (!)I introduce new heavy fermionic partners for quarks and leptonsI construct low-energy effective theory by integrating out heavy particles

Simplest Option: Independent Yukawa sectors for SM and NP fermions

YX ∝ 〈SX 〉/Λ (“normal“ MFV)

Yukawa couplings in effective theory with cut-off Λ [Albrecht/TF/Mannel]

Alternative Option: ”See-Saw Coupling” of SM and NP fermions

YX ∝ MX 〈SX 〉−1 (”inverted” MFV)

From renormalizable theory with fundamental Dirac masses MX [Grinstein/Redi/Villadoro]

(. . . integrating out heavy fermions contributes to effective spurion potential . . . )


Example: See-Saw Masses for Down-Quarks

Renormalizable Lagrangian with 2 additional chiral singlets:

L 3 (QL H)ψdR + ψd SD ψdR + MD ψd DR + h.c.

Assumption: 〈H〉 � MD . 〈SD〉

ψdR ' −MD 〈SD〉−1DR ⇒ Leff 3 −QL 〈H〉 MD 〈SD〉−1︸︷︷︸ DR + h.c.

≡ YD


Phenomenological Consequences of Inverted MFV (schematically)

NP effects from integrating outI heavy flavour gauge bosons, new heavy fermions,I heavy Higgs modes (fluctuations around 〈SU,D〉)

Flavour effects in the Quark Sector:

Smallest entries in 〈SU,D〉 correspond to 3rd generation, e.g.:1yt

MU �θ23

ycMU �

1yb

MU �θ23

ysMU �

1yc

MU �1ys

MU �θ12

yu,dMU �

1yu,d

MU .

⇒ expect strongest constraints from transitions involving 3rd and 2nd generation

Since yt ' 1, one needs 〈SU〉33 ∼ MUI sizable mixing between tR and its heavy partner⇒ Constraints from EW precision data [numerical details in Grinstein/Redi/Villadoro]I Flavour phenomenology worked out in [Buras et al. 2011]

Lepton Sector:Different choices for new fermion representations (!)Guide line: embedding into GUT multiplets

I SU(4)× SU(2)L × SU(2)R models→ new lepton singletsI SU(5) models→ new lepton singlets and doublets [TF 2010]


See-Saw Masses for Leptons (guided by SU(5))

including right-handed Dirac neutrinos:

L` =(

ER H† + ψνR H†)ψ` + ψ`R SE ψ` + ψνR Sν ψν + ME ψ`R `L + Mν νR ψν + h.c.

Charged leptons: YE ∼ −ME〈SE〉−1(as for d-quarks)

Neutrinos: Yν ∼ −Mν〈Sν〉−1YE ∼ ME Mν〈SE Sν〉−1

I natural suppression of neutrino masses with respect to charged leptons√

I no Majorana masses allowed or requiredI modification of MFV construction in the lepton sector (→ to be explored)


Summary

Flavour Symmetry Breaking in the SM characterized byparticular Hierarchy of Fermion Masses and Mixings.

MFV Hypothesis translates these features to NP models,via Spurion Analysis in ET context.Also Systematical Deviations from MFV can be studied.

I e.g. sequential 4th generation.

Possible Dynamical Effects ?I Spontaneous FSB↔ Hierarchies in masses and mixings.I Goldstone modes as longitudinal modes of heavy flavour gauge bosons.I New fermions to cancel gauge anomalies for local flavour symmetries.I See-saw mechanism for SM quarks and leptons.

Open Questions:I Dynamical construction of effective potential for sequential FSB?I Natural realization of large mixing angles in Lepton Sector?I Phenomenology of inverted LFV?I . . .


Backup Slides


Flavour Hierarchies↔ Sequence of FSB

Assume (for instance) : yt > yb > yc > ybθ23 > ybθ13 > ys > ysθ12 > yu,d

Flavour Symmetry GBs Spur. VEVs Symm. Scale

SU(3)QL× SU(3)UR

× SU(3)DR× U(1)2 0 36 0 26

SU(2)QL× SU(2)UR

× SU(3)DR× U(1)3 9 26 1 17 Λ ∼ yt Λ

SU(2)QL× SU(2)UR

× SU(2)DR× U(1)3 14 20 2 12 Λ′ ∼ yb Λ

SU(2)DR× U(1)4 19 14 3 7 Λ(2) ∼ yc Λ

SU(2)DR× U(1)3 20 12 4 6 Λ(3) ∼ ybλ

2 Λ

SU(2)DR× U(1)2 21 10 5 5 Λ(4) ∼ ybλ

3 Λ

U(1)2 24 6 6 2 Λ(5) ∼ ys Λ

U(1)2 (CP broken) 24 4 7+1 2 Λ(6) ∼ ysλ Λ

– (CP broken) 26 0 9+1 0 Λ(7) ∼ yu,d Λ

Balance:# Spurions + # VEVs− # Symmetries = 10

# Goldstones + # Spurions + # VEVs = 36

Each subsequent VEV corresponds to a smaller cut-off Λ(n),setting the scale for the associated scalar and gauge boson masses.

Adjacent scales are separated by not more than 1 order of magnitude: Λ(n) ≈ λ(n+1) Λ .


(minimal) SU(5) Embedding

minimal scenario:I Higgs 5-plet for EWSB, triplet component

assumed heavyI Higgs 24-plet breaking SU(5)I only 10-plets, 5-plets and 1-plets for fermionic

matter

SU(5) gauge anomalies cancel

Assigning different transformations toindividual multiplet components withrespect to gauged flavour symmetriesexplicitly breaks SU(5) (!)

Only flavour sub-group(SU(3)QL=Uc

R× SU(3)DR

)× (SU(3)`L × SU(3)ER × SU(3)νR )

is anomaly-free.


See-Saw Masses for Quarks and Leptons (guided by SU(5))

Down-Quarks (as before):

L = QL H ψDR + ψd SD ψDR + MD ψd DR + h.c.

Down-quarks: YD ∼ −MD〈SD〉−1, only heavy coloured SU(2)L singlets



Leptons (including right-handed Dirac neutrinos):

L` =(

ER H† + ψνR H†)ψ` + ψ`R SE ψ` + ψνR Sν ψν + ME ψ`R `L + Mν νR ψν + h.c.

Charged leptons: YE ∼ −ME〈SE〉−1, new heavy doublets√

Neutrinos: Yν ∼ −Mν〈Sν〉−1YE ∼ ME Mν〈SE Sν〉−1

I natural suppression of neutrino masses with respect to charged leptons√

I no Majorana masses allowed or requiredI modification of MFV construction in the lepton sector (→ to be explored)



Up-Quarks:

LU =12

(X T

L H†QL + UR H† ψQ

)+ TU

(ψQR ψQ + X T

L X cR

)+ MU

(ψQR QL + UR X c

R)

+ h.c.

Flavour spurion matrix TU symmetric, complex 6-plet under SU(3)QL=UcR.

New heavy coloured doublets and singlets.

2 new CP-phases (relative orientation of heavy fermions) (→ to be explored).


variations on minimal flavour violation - uni-siegen.de on minimal flavour violation (quarks and ......

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