Flavor without symmetries Alex Pomarol, UAB (Barcelona) Flavor - - PowerPoint PPT Presentation

Flavor without symmetries

Alex Pomarol, UAB (Barcelona)

Flavor without symmetries

Alex Pomarol, UAB (Barcelona) Apologizes: I am not going to talk

• n glances at the energy frontier

Flavor without symmetries

Alex Pomarol, UAB (Barcelona) Apologizes: I am not going to talk

• n glances at the energy frontier

Interpreting other “null results”: the absence of new flavor sources beyond the SM

After many years, no clear progress on the origin of flavor in the SM: Many ideas, but without sharp predictions

… contrary to gauge couplings → predictions from GUTs Higgs quartic → predictions from SUSY or Composite Higgs

L

• c

a l i z a t i

• n

i n e x t r a d i m e n s i

• n

s gauge flavor symmetries Froggatt-Nielsen M a s s e s f r

• m

l

• p

s

After many years, no clear progress on the origin of flavor in the SM: Many ideas, but without sharp predictions

… contrary to gauge couplings → predictions from GUTs Higgs quartic → predictions from SUSY or Composite Higgs

L

• c

a l i z a t i

• n

i n e x t r a d i m e n s i

• n

s gauge flavor symmetries Froggatt-Nielsen M a s s e s f r

• m

l

• p

s

In BSMs for the hierarchy problem things are even worse (or more

interesting), as generically predict new sources of flavor…

( ¯ fiγµfj)( ¯ flγµfk)

not serious deviation seen! ϵK, ϵ’/ϵ, ΔMB, B→Xll, …

“Cheap” way to avoid them:

but global symmetries are accidental ☛ Demand similar BSM flavor-structure as in the SM: Flavor under control for new physics scale at ~TeV Minimal Flavor Violation (MFV) So, why/how they arise?

Symmetries from dynamics!

SUSY:

Gauge Mediated Susy Breaking (GMSB) soft-masses through gauge interactions (flavor blind) Beyond minimal models… EDMs are sizable! de ∼ 10−28cm e ✓ MS 10 TeV ◆2 tan β But only few examples known: Q Q

~ ~

x

but today minimal GMSB highly tuned to reproduce mh~125 GeV

Symmetries from dynamics!

Composite Higgs:

But only few examples known: More difficult, as we must address the origin of Yukawas: Higgs associated to a composite operator: OH ∼ ¯ ψψ As dimension of OH is larger than 1 (dH>1) Yukawas, ffOH, are irrelevant couplings! We cannot push their origin to Planck-physics!

Symmetries from dynamics!

Yukawas from linear mixing to operators of the strong sector:

Llin = ✏fi ¯ fi Ofi

⤷ depending on the dimension of Of, we can have relevant or irrelevant couplings

(portal of fi to the strong sector)

Most interesting possibility:

Composite Higgs:

But only few examples known:

Symmetries from dynamics!

☛ large or small mixings ϵf

Yf ⇠ g∗✏fi✏fj ,

fi fj ☛ The smaller mixing, the smaller the mass:

⤷ coupling of the strong sector

O(1) numbers (anomalous dimensions γi of Ofi) can lead to large hierarchies: ☛ small mixings at ΛIR ✏fi(ΛIR) ∼ ✓ΛIR MP ◆γi From the RGE:

γi = Dim[Ofi] − 5/2 > 1

Explicit example (for the top):

arXiv:1502.00390

dimension at weak coupling: 9/2 dimension needed at strong coupling: 5/2 (γ= 2)

Possible? lattice could tell us!

n Υ

b) five ∈ 6 (antisym. matrix)

ΨL,R

a) three ∈ 4 (fundamental)

SU(4) strong sector

Operator that can be coupled to the top

G = SU(5) × SU(3) × SU(3)′ × U(1)X × U(1)′

H = SO(5) × SU(3)color × U(1)X

Global sym. Fermions: = Otop

ΨΥΨ

}

x x x x

Higgs bL, bR

sL, sR

dL, dR

ΛIR

AdS/CFT perspective

☛ easier from string theory?

Flavor & CP-violation constraints

g2

∗

Λ2

IR

✏fi✏fj✏fk✏fl ¯ fiµfj ¯ fkµfl ,

g2

∗

16⇡2 g∗v Λ2

IR

✏fi✏fj ¯ fiµνfj gF µν

⤷ scale of the strong sector: expected ~TeV

ϵK bound: ΛIR > 10 TeV EDM bound: ΛIR > 100 TeV ⇣g∗ 3 ⌘ μ→eγ bound: ΛIR > 60 TeV ⇣g∗ 3 ⌘

Other alternatives:

For example: QR uR, dR If arise from a strong sector with elementary fermions, it is not unconceivable to be flavor symmetric

g2

⇤

Λ2

IR

(¯ uRµuR)2 give deviation in dijets distributions, pp → jj: ΛIR & 20 TeV

⇣g∗ 3 ⌘ All flavor mixings from left-handed: QR uR ∝ Yu ☛ MFV

arXiv:1106.6357 arXiv:1203.4220

But also generated: Consider some SM fermion fully composite:

Towards suppressing EDMs:

Avoid linear mixing of light fermions to BSM: Bilinear mixing:

Lbil ⇠ ¯ fiOHfj Llin = ✏fi ¯ fi Ofi

BSM

BSM

EDM at most at two-loop! Not possible in the MSSM, but possible in composite Higgs models

Possibility considered here:

G.Panico, AP 1603.06609

Llin = ✏fi ¯ fi Ofi

bilinear mixing generated at Λf

Lbil ⇠ ¯ fiOHfj

The larger the scale of decoupling, the smaller the fermion mass! ⤷ Operator of the strong sector that at ΛIR projects into the Higgs:

OH h0|OH|Hi 6= 0,

E.g. if a constituent get a mass ~Λf e.g. ⤷ portal decouples at higher energies:

(also related work by Matsedonskyi 15, Cacciapaglia etal 15)

OH ∼ ¯ ψψ

Λd Λs ObR OsR

Decoupling energy scale Operator

Λb OdR, OQL1 ΛIR

R, OQL2 R, OQL3

Down-quark sector

n Υ

b) five ∈ 6 (antisym. matrix)

ΨL,R

a) three ∈ 4 (fundamental)

SU(4) strong sector

Fermions: = Otop

ΨΥΨ

}

Envisaging from explicit examples:

add more elementary fermions Ψ with explicit masses MΨd MΨs MΨb

ΨΥΨ

d d

ΨΥΨ

s s

ΨΥΨ

b b

x x x x

Higgs bL, bR

sL, sR

dL, dR

ΛIR

x x x

Λb Λs Λd

I I I I I I

ΛIR

x

Higgs

bL, bR

sL, sR

dL, dR

AdS/CFT perspective

x x x x

Higgs bL, bR

sL, sR

dL, dR

ΛIR

x x x

Λb Λs Λd

I I I I I I

ΛIR

x

Higgs

bL, bR

sL, sR

dL, dR

AdS/CFT perspective

CFT3 → CFT2 → CFT1→ CFT0

Arising flavor structure

Down-quark sector Λd Λs ObR OsR

Decoupling energy scale Operator

Λb OdR, OQL1 ΛIR

R, OQL2 R, OQL3

d bottom, bR: L(3)

lin = ✏(3) bL ¯

QL3 OQL3 + ✏(3)

bR ¯

bR ObR .

O L(3)

bil =

1 ΛdH−1

b

(✏(3)

bL ¯

QL3)OH(✏(3)

bR bR)

below Λb: below ΛIR:

C A + g∗ B @ 0 0 0 0 0 0 ✏(3)

bL ✏(3) bR

1 C A ✓ΛIR Λb ◆dH−1

Ydown =

Down-quark sector Λd Λs ObR OsR

Decoupling energy scale Operator

Λb OdR, OQL1 ΛIR

R, OQL2 R, OQL3

Arising flavor structure

Λd Λs ObR OsR

Decoupling energy scale Operator

Λb OdR, OQL1 ΛIR

R, OQL2 R, OQL3

below Λs: below ΛIR:

O O L(1)

bil =

1 ΛdH−1

d

(✏(1)

bL ¯

QL3 + ✏(1)

sL ¯

QL2 + ✏(1)

dL ¯

QL1)OH(✏(1)

bR bR + ✏(1) sR sR + ✏(1) dRdR)

L(2)

lin = (✏(2) bL ¯

QL3 + ✏(2)

sL ¯

QL2) OQL2

2 + (✏(2)

bR bR + ✏(2) sR sR) OsR

+ g∗ B @ 0 ✏(2)

sL ✏(2) sR

✏(2)

sL ✏(2) bR

0 ✏(2)

bL ✏(2) sR

1 C A ✓ΛIR Λs ◆dH−1 Ydown =

Down-quark sector

Arising flavor structure

Λd Λs ObR OsR

Decoupling energy scale Operator

Λb OdR, OQL1 ΛIR

R, OQL2 R, OQL3

below ΛIR:

= g∗ B B @ ✏(1)

dL ✏(1) dR

✏(1)

dL ✏(1) sR

✏(1)

dL ✏(1) bR

✏(1)

sL ✏(1) dR

✏(1)

bL ✏(1) dR

1 C C A ✓ΛIR Λd ◆dH−1 1

Ydown =

Down-quark sector

Arising flavor structure

“onion” structure:

Ydown ' B @ Yd ↵ds

R Yd ↵db R Yd

↵ds

L Yd

Ys ↵sb

R Ys

↵db

L Yd

↵sb

L Ys

Yb 1 C A

@ Yf ⌘ g∗✏(i)

fLi✏(i) fRi

✓ΛIR Λf ◆dH−1

• Smaller Yukawas for large decoupling scale!
• Mixing angles suppressed by Yukawas: 𝛊ij~Yi/Yj

CKM mostly the rotation in the down-quark sector!

Arising flavor structure

f ' mf/v. T

Similarly for the up-quark sector (and lepton sector) Λu Λd Λs Λc Λt ∼ ΛIR OuR ObR OsR Decoupling scale Operator Λb OcR, OQL2 OtR, OQL3 OdR, OQL1

• Λ

[]

Scales of decoupling:

dimension of the Higgs operator

( )

OH ∼ ¯ ΥΥ

• Λ

[]

Scales of decoupling:

dimension of the Higgs operator

( )

OH ∼ ¯ ΥΥ

dH~2 needed to pass FCNC

(“walking TC”: dH~2 instead of ~3)

Flavor and CP-violating effects

Different effects at different scales: Effects from the top

∆F = 2 transitions

2 t (QL3µQL3)2

Λu Λd Λs Λc Λt ∼ ΛIR Λb ∼ Y 2

t

Λ2

IR

physical basis ϵK, ΔMBd, ΔMBs rotation ~ VCKM correlated and all close to the experimental value for ΛIR~2-3 TeV

correlated and all close to the experimental value for ΛIR~2-3 TeV Different effects at different scales: Effects from the top

2 t (QL3µQL3)2

Λu Λd Λs Λc Λt ∼ ΛIR Λb ∼ Y 2

t

Λ2

IR

physical basis ϵK, ΔMBd, ΔMBs rotation ~ VCKM

∆MBd ∆MBs ' ∆MBd ∆MBs

• SM

Interesting predictions:

• Only CKM phase
• ∆F = 2 transitions

Different effects at different scales: Effects from the top Λu Λd Λs Λc Λt ∼ ΛIR Λb physical basis K→μμ, ϵ’/ϵ, B→Xll, Z→bb rotation ~ VCKM correlated and all close to the experimental value for ΛIR~4-5 TeV

∆F = 1 transitions

)2 ¯ QL3µQL3iH† ! D µH

∼ g∗Yt Λ2

IR

Different effects at different scales: Effects from the top Λu Λd Λs Λc Λt ∼ ΛIR Λb physical basis K→μμ, ϵ’/ϵ, B→Xll, Z→bb rotation ~ VCKM correlated and all close to the experimental value for ΛIR~4-5 TeV

∆F = 1 transitions

)2 ¯ QL3µQL3iH† ! D µH

∼ g∗Yt Λ2

IR

Suppressed if left↔right symmetry

Different effects at different scales: Effects from the strange scale Λu Λd Λs Λc Λt ∼ ΛIR Λb physical basis

ϵK

rotation ~ VCKM

∆F = 2 transitions

)2 (QL2sR)(sRQL2)

∼ g2

∗

Λ2

s

close to the experimental value for Λs~105 TeV

Different effects at different scales: Effects from the strange scale Λu Λd Λs Λc Λt ∼ ΛIR Λb physical basis

ϵK

rotation ~ VCKM close to the experimental value for Λs~105 TeV

∆F = 2 transitions

)2 (QL2sR)(sRQL2)

∼ g2

∗

Λ2

s

• Λ

[]

dH~2 needed

Like in “walking” TC, we need large anomalous dimension for OH:

dH~2

(γ=1)

OH ∼ ¯ ψψ If so, theory close to an unstable point in the CFT: For dH<2, relevant singlet in the theory: dim[ ]<4 (large N)

|OH|2

|OH|2

Like in “walking” TC, we need large anomalous dimension for OH:

dH~2

(γ=1)

μ

near conformal

α | | OH ∼ ¯ ψψ dim[ ]<4 (large N)

|OH|2

dH~2 ☛ dim[ ]~4 marginal deformation useful to generate ΛIR ≪MP:

|OH|2

If so, theory close to an unstable point in the CFT: For dH<2, relevant singlet in the theory: |OH|2

Like in “walking” TC, we need large anomalous dimension for OH:

dH~2

(γ=1)

μ

near conformal

α | | OH ∼ ¯ ψψ dim[ ]<4 (large N)

|OH|2

dH~2 ☛ dim[ ]~4 marginal deformation useful to generate ΛIR ≪MP:

|OH|2

From AdS/CFT: dim of CFT operator ⬌ mass in AdS 5D Higgs mass slightly below the BF-bound: m2 = −4 − ✏

e−1/√✏

If so, theory close to an unstable point in the CFT: For dH<2, relevant singlet in the theory: |OH|2

EDMs

• Largest constraint from the top EDM:
• EDM of u,d,e suppressed by Λd,u,e>109 GeV

Weinberg operator

dN

top top

γ γ h e e tL hhi

• Two-loop Barr-Zee-like diagrams to de:

☛ dN & de around the present bound for ΛIR ~ TeV Always EDM!

If only one scale for each family:

OuR ObR OsR Decoupling scale Operator OcR, OQL2 OtR, OQL3 OdR, OQL1 Λu ∼ Λd ∼ Λe Λc ∼ Λs ∼ Λµ Λt ∼ Λb ∼ Λτ Only main difference: μ→eγ gets close to the exp. bound Splittings within a given family must be explained by different mixings (ϵfi) at the respective scales

Other issues:

• Neutrino masses:

1 Λ2dH−1

ν

¯ LcOHOHL ,

• Modifications to Higgs couplings:

Similar effects as with linear mixing

mν ' g2

∗v2

ΛIR ✓ΛIR Λν ◆2dH−1

⇠ mν ⇠ 0.1 0.01 eV for Λν ⇠ 0.8 1.5 ⇥ 108 GeV .

Majorana: Dirac:

1 ΛdH−1

ν

OH ¯ LνR

for dH~2, dimension-5 operator as in the SM for dH~2, dimension-7 operator

Λ ()

• Δ

ϵ → μ+μ- μ → γ

• Summary

many observables around the corner! Buys you more time to dream… Flavor from dynamical scales (bilinear mixing) consistent with BSM TeV physics