Origin of EWSB Landau Ginzburg Potential with its origin unexplained - - PowerPoint PPT Presentation

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Origin of EWSB Landau Ginzburg Potential with its origin unexplained - - PowerPoint PPT Presentation

Aug 05, 2023 263 likes •661 views

M inimal N eutral N aturalness M odel Ling - Xiao Xu ( ) Peking University hep-ph/1810.01882 with Jiang - Hao Y u and Shou - hua Zhu KEK-PH 2018 Winter @ Tsukuba, Japan 5 December, 2018 Origin of EWSB Landau Ginzburg Potential with

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Minimal Neutral Naturalness Model

Ling-Xiao Xu (徐凌霄) Peking University

hep-ph/1810.01882 with Jiang-Hao Y u and Shou-hua Zhu

KEK-PH 2018 Winter @ Tsukuba, Japan 5 December, 2018

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Origin of EWSB

  • Landau Ginzburg Potential with its origin unexplained
  • Other Possibilities?

V(H) = − μ2H†H + λ(H†H)2 1

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Origin of EWSB

  • Landau Ginzburg Potential with its origin unexplained

V(H) = − μ2H†H + λ(H†H)2

  • Other Possibilities?
  • Pseudo Nambu-Goldstone Higgs (coset G/H)
  • Naturalness problem solved
  • Radiative Higgs potential

mh ∼ a yt f 4π ∼ 3MT 4π

  • EWSB explained

π → π + c

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Shift Symmetry

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Explaining EWSB

misalignment:

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SLIDE 5

misalignment:

2

Explaining EWSB

|Σ| = f

EWSB direction β ≪ γ ( v2 f 2 ∼ 1) No EWSB

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SLIDE 6

misalignment:

2

Explaining EWSB

|Σ| = f

EWSB direction β = γ ( v2 f 2 = 0.5) β ≪ γ ( v2 f 2 ∼ 1) No EWSB

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SLIDE 7

misalignment:

2

Explaining EWSB

|Σ| = f

EWSB direction β = γ ( v2 f 2 = 0.5)

γ ≪ β ( v2 f 2 ∼ 0.1)

β ≪ γ ( v2 f 2 ∼ 1) No EWSB as required by Higgs data

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SLIDE 8

|Σ| = f

EWSB direction β = γ ( v2 f 2 = 0.5)

γ ≪ β ( v2 f 2 ∼ 0.1)

β ≪ γ ( v2 f 2 ∼ 1)

Can small misalignment angle be realized naturally? even only considering fermion contribution?

No EWSB misalignment:

2

Explaining EWSB

as required by Higgs data

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Neutral Naturalness Era

mh ∼ a yt f 4π ∼ 3MT 4π

sub-TeV top partner

Colorless top partners are highly motivated!

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Neutral Naturalness Era

mh ∼ a yt f 4π ∼ 3MT 4π

sub-TeV top partner

Colorless top partners are highly motivated!

3

  • Neutral Naturalness Models (apology if I miss your work)

Twin Higgs: Quirky Little Higgs: Orbifold Higgs: Neutral Naturalness in SO(6)/SO(5) (trigonometric parity within coset): … Chacko, Goh, Harnik, 0506256 Cai, Cheng, Terning, 0812.0843 Craig, Knapen, Longhi, 1410.6808 Composite Twin Higgs: Geller, Telem, 1411.2974; Barbieri, Greco, Rattazzi, Wulzer, 1501.07803; Low, Tesi, Wang 1501.07890 Serra, Torre, 1709.05399; Csaki, Ma, Shu, 1709.08636; Dillon, 1806.10702

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Twin Higgs as a benchmark of neutral naturalness:

  • Mirror copy of the SM

˜ v, ˜ γ Neff

  • Coset: SU(4)/SU(3) or SO(8)/SO(7)
  • Additional Z2-breaking sources needed for vacuum misalignment

4

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Twin Higgs as a benchmark of neutral naturalness: Our construction with minimal spectrum and coset:

  • Mirror copy of the SM

˜ v, ˜ γ Neff

  • Coset: SU(4)/SU(3) or SO(8)/SO(7)
  • Additional Z2-breaking sources needed for vacuum misalignment
  • V

ector-like top partners: one doublet and one singlet

4

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SLIDE 13

Twin Higgs as a benchmark of neutral naturalness: Our construction with minimal spectrum and coset:

  • Mirror copy of the SM

˜ v, ˜ γ Neff

  • Coset: SU(4)/SU(3) or SO(8)/SO(7)
  • Additional Z2-breaking sources needed for vacuum misalignment
  • V

ector-like top partners: one doublet and one singlet

  • Minimal coset SO(5)/SO(4), without compositeness at low energies

4

Agashe, Contino, Pomarol, 0412089

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Twin Higgs as a benchmark of neutral naturalness: Our construction with minimal spectrum and coset:

  • Mirror copy of the SM

˜ v, ˜ γ Neff

  • Coset: SU(4)/SU(3) or SO(8)/SO(7)
  • Additional Z2-breaking sources needed for vacuum misalignment
  • V

ector-like top partners: one doublet and one singlet

  • Minimal coset SO(5)/SO(4), without compositeness at low energies
  • Natural vacuum misalignment even with only fermions

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Agashe, Contino, Pomarol, 0412089

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Fermion Embeddings

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Fermion Embeddings

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  • Quadratic divergence cancellation from symmetry perspective

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SLIDE 18
  • Quadratic divergence cancellation from symmetry perspective
  • Logarithmic divergent Higgs Potential from Y

ukawa terms

EWSB is triggered!

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SLIDE 19
  • Quadratic divergence cancellation from symmetry perspective
  • Logarithmic divergent Higgs Potential from Y

ukawa terms

EWSB is triggered!

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  • So far, vacuum is not correctly misaligned
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SLIDE 20

V acuum Misalignment

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  • Logarithmic divergent Higgs Potential including the mass term
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SLIDE 21

V acuum Misalignment

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  • Logarithmic divergent Higgs Potential including the mass term
  • Total logarithmic divergent Higgs potential
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SLIDE 22

V acuum Misalignment

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  • Logarithmic divergent Higgs Potential including the mass term
  • Total logarithmic divergent Higgs potential
  • Further including the finite part will not change the result
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Spectrum of Minimal Setup

EW scale v global symmetry breaking scale f t, W , Z singlet and doublet T and t vacuum misalignment PNGB Higgs

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Composite/Holographic Extension

EW scale v global symmetry breaking scale f t, W , Z

strong dynamics

singlet and doublet T and t Composite top Composite W and Z PNGB Higgs Composite T and t partial compositeness vacuum misalignment partial compositeness

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Two-site Construction

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composite states

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Two-site Construction

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composite states collective breaking: explicit breaking SO(5)2

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Holographic Setup for SM Top

  • Fermions living in the bulk

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Holographic Setup for SM Top

  • Fermions living in the bulk
  • Zero modes as the low energy building blocks

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Holographic Setup for SM Top

  • Fermions living in the bulk
  • Zero modes as the low energy building blocks
  • Breaking SO(5) on the IR brane

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  • Otherwise Higgs is an exact Goldstone boson
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Holographic Setup for Neutral Tops

  • Fermions living in the bulk
  • Zero modes as the low energy building blocks
  • UV brane construction
  • Breaking SO(5) on the IR brane

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Phenomenology

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  • Only two free parameters at low energies
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Phenomenology

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  • Only two free parameters at low energies
  • Rich Phenomenology to be done in the future

dark hadron spectra, heavy composites phenomenology, dark matter candidate, collider signatures and cosmological implications…

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Concluding Remarks

  • W

e present a neutral naturalness model with the Higgs boson identified as a PNGB of SO(5)/SO(4)

  • V

acuum misalignment naturally obtained with only fermions

  • UV realization in the holographic/composite Higgs framework
  • Finite Higgs potential in holographic/composite framework

still many to explore in the future!

Thank you!

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Backup Slides

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Symmetry Breaking in 5D

UV (H0) bulk (G) IR (H1)

realistic model:

G: SO(5) H1: SO(4) H0: SU(2) U(1)

Strong Dynamics (bulk+IR)

×

AM ≡ (Aμ, A5)

1

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SLIDE 36

Aμ

The boundary condition (+,+) reflects the fact that W , Z are massless before EWSB

Boundary Conditions

G: SO(5) H1: SO(4) H0: SU(2) U(1)

×

5D perspective: the Goldstone matrix corresponds to the Wilson line of A5 along the fifth dimension

2

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Strong Dynamics at Low Energies

  • Information of heavy particles encoded in form factors
  • Identical to the spectrum of the minimal setup
  • Explicitly check: Higgs is an exact Goldstone if all the mixings vanish

3

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Higgs Potential in Composite Models

The contribution of the whole tower of Kaluza-Klein states has been resummed

tR tL

sh sh

top top top top

×

pole

∑

i

M(i)

KK

ΠtLtR ΠtLtR

4