SO(3) family symmetry and axions Mario Reig Phys. Rev. D 98, - - PowerPoint PPT Presentation

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SO(3) family symmetry and axions Mario Reig Phys. Rev. D 98, - - PowerPoint PPT Presentation

Feb 20, 2024 250 likes •443 views

SO(3) family symmetry and axions Mario Reig Phys. Rev. D 98, 095008; [arXiv: 1805.08048] MR , J.W.F. Valle, F. Wilczek Moriond EW 2019 SO(3) as a gauge family symmetry: The threefold way The famous question of " Who ordered the muon?

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SLIDE 1

SO(3) family symmetry and axions

Mario Reig

  • Phys. Rev. D 98, 095008; [arXiv: 1805.08048]

MR, J.W.F. Valle, F. Wilczek

Moriond EW 2019

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SLIDE 2

SO(3) as a gauge family symmetry: The threefold way

The famous question of "Who ordered the muon?" has now been escalated to "Why does Nature repeat herself?" (Wilczek & Zee, 1978)

  • The model:
  • PREDICTIONS: CKM & MASS RELATIONS

Moriond EW 2019

3rd

2nd

1st

2nd 2nd

3rd 3rd 1st 1st

Mario Reig

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SLIDE 3

SO(3) as a gauge family symmetry: The threefold way

The famous question of "Who ordered the muon?" has now been escalated to "Why does Nature repeat herself?" (Wilczek & Zee, 1978)

  • The model:
  • PREDICTIONS: CKM & MASS RELATIONS

Vcb=0 Mtop=15 GeV

Moriond EW 2019

3rd

2nd

1st

2nd 2nd

3rd 3rd 1st 1st

Mario Reig

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SLIDE 4

Problems of the original threefold way

  • A very light top quark:
  • Bottom decaying mainly to up through charged current:
  • SO(3) broken at EW scale: unacceptable FCNC

Mtop=15 GeV Vcb=0

FCNC coupling Mario Reig Moriond EW 2019

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SLIDE 5

Opportunities of the original threefold way

  • A very light top quark:
  • Bottom decaying mainly to up through charged current:
  • SO(3) broken at EW scale: unacceptable FCNC

Mtop=15 GeV Vcb=0

up-type and down-type Higgses: PQ symmetry!

Break SO(3) with a SM singlet: PQ & seesaw mechanism!

Mario Reig Moriond EW 2019

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SLIDE 6

The threefold way, revamped

  • Extend the SM with a gauged, horizontal SO(3) symmetry.
  • Use the PQ mechanism to solve strong CP problem, avoiding

the wrong top quark mass prediction.

  • Link flavor, PQ and lepton number symmetry breaking through

the vev of a SM singlet.

arXiv: 1805.08048

MR, J.W.F. Valle, F. Wilczek

Mario Reig Moriond EW 2019

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SLIDE 7

Mass hierarchies

  • Let fermions be in SO(3) triplets, f

3. ∼

  • Because of product rules, 3x3=1+3+5, we can use a singlet,

triplet or five-plet scalar to generate fermion masses.

  • 3 and 5 are particularly interesting:

In this limit the 1st generation fermions are massless and the CKM is the identity

Moriond EW 2019

arXiv: 1805.08048

Mario Reig

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SLIDE 8

Emergence of the CKM matrix

  • To generate 1st generation fermion mass and CKM we take

perturbations around the minimum.

  • Perturbations change the mass matrix:
  • Generate 1st gen. Mass & quark mixing:

Seesaw-like formula for 1st generation Mixing angles as function of q masses

Moriond EW 2019

arXiv: 1805.08048

Mario Reig

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SLIDE 9

Duplicated Higgs sector: mass relations and the axion

  • In the absence of vector-like quarks, the U(1)PQ can only be anomalous

if there is a duplicated Higgs sector:

  • A relation between down-type quarks and charged leptons appear due

to SO(3) symmetry.

  • The relation with up-type quarks is avoided thanks to the duplicated

Higgs sector.

Non-trivial flavor-axion connection

(also in: Morisi, Peinado, Shimizu, Valle, ‘11)

Moriond EW 2019

arXiv: 1805.08048

Mario Reig

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SLIDE 10

Flavor protection and the PQ scale

  • Pseudo-Goldstone bosons or axions coupled to flavor lead to

strong constraints, mainly coming from .

  • This constraints the PQ breaking scale to be
  • SO(3) symmetry ensures universal PQ charges for all families.
  • SO(3) gauge familons contribute to and

however, this processes are suppressed by . This constraints the PQ scale to be

Moriond EW 2019

arXiv: 1805.08048

Mario Reig

(See F. Goertz talk)

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SLIDE 11

CONCLUSIONS

  • PQ symmetry and the axion offer attractive

possibilities for flavor model building

  • SO(3)F turns out to be a very compelling and

predictive symmetry to describe flavor.

  • Interesting flavor-axion-neutrino connection

appears in the SO(3)F theory.

Moriond EW 2019

arXiv: 1805.08048

Mario Reig

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SLIDE 12

Back-up slides

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How to derive the mass relation

Assumption: (exp. input) Moriond EW 2019

arXiv: 1805.08048

Mario Reig

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SU(3)F as a family symmetry

  • If SU(3)F is vector-like (LH and RH in triplets). Because of

product rules, 3x3*=1+8, we can use a singlet or octet scalar to generate fermion masses: BAD SCENARIO FOR FERMION MASS HIERARCHIES.

  • If SU(3)F is chiral (LH in triplet, RH in anti-triplet). Because of

product rules, 3x3=3*+6, we can use a triplet or sextet scalar to generate fermion masses: [SU(3)F]3 ANOMALY UNLESS ADDING EXTRA FERMIONS.

Moriond EW 2019

arXiv: 1805.08048

Mario Reig

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SLIDE 15

CP violation in the quark sector

  • CP violation observables are proportional to the Jarlskog

invariant, J.

  • CP violation arises from perturbations around minimum

Moriond EW 2019

arXiv: 1805.08048

Mario Reig

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SLIDE 16

Particle content of the model

  • Fermions come in triplets.
  • A duplicated Higgs, up and down-type, sector is introduced.
  • An SM singlet, σ, breaks SO(3) and PQ at high E.

Moriond EW 2019

arXiv: 1805.08048

Mario Reig

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SLIDE 17

Flavor symmetries and unification

  • Constraints to flavor symmetries arise if we require

compatibility with unification.

  • (chiral) Family SU(3) symmetry is quantumly inconsistent

with minimal content of GUTs.

  • Example: SO(10)xSU(3) with fermions in the (16,3)

representation suffers the triangle [SU(3)]3 anomaly.

  • This leave us with only
  • ne possibility:

SO(3) symmetry

Moriond EW 2019

arXiv: 1805.08048

Mario Reig