Higgs Vacuum Stability with Vector-like Fermions Shrihari - - PowerPoint PPT Presentation

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Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Higgs Vacuum Stability with Vector-like Fermions Shrihari Gopalakrishna Institute of Mathematical Sciences (IMSc), Chennai IMHEP IOP Bhubaneswar Jan 20 19 Vector-like

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Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability

Higgs Vacuum Stability with Vector-like Fermions

Shrihari Gopalakrishna

Institute of Mathematical Sciences (IMSc), Chennai IMHEP IOP Bhubaneswar Jan 2019

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability

Talk Outline

Vector-like Fermions (VLF) general aspects Vacuum decay basics Bounce configuration Higgs Vacuum Stability in the Standard Model with VLFs present

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability VLF basics

BSM VLF

Vector-like fermions have both L and R chiralities charged under a gauge-group. This allows a bare mass term. VLFs appear in many BSM extensions they are sometimes the lightest BSM states We study VLF effects on Higgs vacuum stability constraint on parameter space but any other new states will alter conclusions!

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability VLF basics

Vector-like fermion (VLF) decoupling

VLF has independent source of mass M (not given by m = λv) Can make M arbitrarily large Yukawa coupling can be small; so perturbative Nice decoupling behavior : S,T, U, h → γγ, gg → h, ... For instance hγγ, ggh couplings

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability VLF basics

VLF signatures

Observables Precision Electroweak Probes LHC signals Direct: b′ → tW ,bZ; t′ → bW , tZ, th;

χ → tW

Indirect: Higgs coupling modifications FCNC probes Vacuum stability implications

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability LHC Search Limits

Vector-like fermion (t′,b′) search

[ATLAS: 1808.02343; PRL 2018]

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability EW Precision & Higgs coupling probes

EWPrecision + Higgs Observables

[S.Ellis, R.Godbole, SG, J.Wells; 1404.4398, JHEP 2014]

Precision electroweak observables (S, T, U) Modifications to hgg, hγγ couplings: σ(gg → h) Γ(h → γγ) We compute ratios

Γh→gg SM , Γh→γγ SM

using leading-order expressions

QCD corrections to ratios small: [Furlan ’11] [Gori, Low ’13]

µVBF

γγ

≈ Γγγ ΓSM

γγ

; µggh

ZZ ≈ Γgg

ΓSM

gg

; µggh

γγ ≈ Γgg

ΓSM

gg

Γγγ ΓSM

γγ

; µggh

γγ

µggh

ZZ

≈ Γγγ ΓSM

γγ

≈ µVBF

γγ

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability EW Precision & Higgs coupling probes

2¯ 2 + 1¯ 1 model

Q + U model (ST Model like) : MVQD Model with Yχ = −1/6 λD = 1, MD = MQ, YQ = (1/6, −1/6) (solid, dashed)

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability EW Precision & Higgs coupling probes

Q + U model

[Q+U model from MVQD model with Yχ = −1/6]

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability EW Precision & Higgs coupling probes

LHC constraints on Higgs couplings

[ATLAS-CONF-2018-31] [CMS-HIG-17-031]

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Higgs Effective Potential

HIGGS EFFECTIVE POTENTIAL

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Higgs Effective Potential

RG-Improved Higgs Effective Potential

Classical potential: V = m2

h

2 h2 + λ 4 h4

Quantum Effective Potential: Veff(h) = m2

h eff

2

h2 + λeff (h)

4

h4 →

λeff (h) 4

h4 Set h ≡ µ; λeff(h) ≡ λ(µ) obeys an RGE like evolution:

d λ(µ) d ln µ = βλ (λ(µ), yt(µ), g3(µ), g2(µ), g1(µ), ...)

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Higgs Effective Potential

1-loop SM RGE

βλ =

1 16π2

  • 24λ2 + 4Ncy2

t λ − 2Ncy4 t − 9g2 2 λ − 9 5 g2 1 λ + 9 8

  • g4

2 + 2 5 g2 2 g2 1 + 3 25g4 1

  • βyt =

yt 16π2

(3+2Nc )

2

y2

t − 8g2 3 − 9 4 g2 2 − 17 20g2 1

  • βga = g3

a ba

16π2 [We include some significant 2-loop β-functions (not shown)]

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Higgs Effective Potential

Effective VLF model and 1-loop RGE

[SG, Arunprasath V: 1812.11303 [hep-ph]]

An effective model with one SU(2) doublet χ and one SU(2) singlet ξ L ⊃ −Mχ ¯ χχ − Mξ ¯ ξξ − (˜ y ¯ χ · H∗ξ + h.c.) Their contributions to the RGE is:

βg3 =

g3 3 16π2

  • 2

3 n3

  • βg2 =

g3 2 16π2

  • 2

3 N′ c n2

  • βg1 =

g3 1 16π2

  • 4

5 N′ c

  • 2n2Y 2

χ + n1Y 2 ξ

  • βλ =

2nF 16π2

  • 4N′

c ˜

y2λ − 2N′

c ˜

y4 βyt =

nF 16π2 yt

  • 2N′

c ˜

y2 β˜

y = ˜ y 16π2

  • (3˜

y2+2Nc y2 t +4nF N′ c ˜ y2) 2

− 8ˆ nVLQ

F

g2

3 − 9 4 g2 2 − 17 20 g2 1

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Higgs Effective Potential

3 TeV VLQuark (VLQ) family (χ + ξ)

5 10 15

  • 0.02

0.00 0.02 0.04 0.06 0.08 0.10 log10 μ (GeV) λ(μ) MVLQ = 3 TeV (0) (0.3) (0.4) (0.5) (0.75) (1.0) (SM) 5 10 15 0.2 0.4 0.6 0.8 1.0 1.2 1.4 log10 μ (GeV) yt (μ) MVLQ = 3 TeV (0.3) (0.75) (0.9) (1.0) (SM)

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Higgs Effective Potential

VLQ family

8 10 12 14 16 18

  • 0.02
  • 0.01

0.00 0.01 0.02 0.03 log10 μ (GeV) λ(μ) y ˜ ( MVL ) = 0.1 (1 E3) (1 E4) (1 E5) (1 E7) (SM) 4 6 8 10 12

  • 0.02

0.00 0.02 0.04 0.06 0.08 0.10 log10 μ (GeV) λ(μ) y ˜ ( MVL ) = 0.5 (1 E7) (1 E5) (1 E3) (SM) 3 4 5 6 7 8 9 10 0.6 0.7 0.8 0.9 1.0 1.1 log10 μ (GeV) g3 (μ) y ˜ ( MVL ) = 0.5 (1 E3) (1 E5) (1 E7) (SM) 5 10 15 0.1 0.2 0.3 0.4 0.5 0.6 log10 μ (GeV) y ˜(μ) y ˜ ( MVL ) = 0.5 (1 E3) (1 E5) (1 E7)

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability

VACUUM STABILITY

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability

Vacuum Stability

(Possible cases) The Higgs Electroweak (EW) Vacuum can be: Stable: EW vacuum is the global minium Metastable: EW vacuum is a false vacuum with τdecay > τuniverse Unstable: EW vacuum is a false vacuum with τdecay < τuniverse

Singlet VLQ, Doublet VLQ or a VLQ family (with small ˜ y) can render the Higgs EW vacuum stable for suitable parameters!

Eg: With a VLQ family with ˜ y = 0.1, MVL 105GeV (example we considered earlier) the EW vacuum is absolutely stable.

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Bounce configuration and Vacuum tunneling

Computing vacuum decay probability

[Coleman: Aspects of Symmetry] [M.Sher: Phys.Rep. 1989]

If Higgs EW vacuum is not the true vacuum, vacuum tunneling can occur via a

Bounce configuration

To compute the tunneling probability, start with the Euclidean action: SE [h] =

  • d4ρ

1

2(∂ih)2 + Veff(h)

  • Look for a stationary point of SE that is O(4) symmetric,

i.e. h(ρi) = hB(ρ), where ρ =

  • ρiρi

[Coleman, Glasser, Martin 1978]

Equation of motion (EOM):

d2h dρ2 + 3 ρ dh dρ = ∂Veff ∂h

B.C. (dh/dρ)(ρ=0) = 0; h(ρ→∞) = v; (starting value h0) EOM is that of a classical particle in a potential −Veff with friction Solve this EOM to get hB(ρ) Probability that we would have tunneled into true vacuum in our Hubble volume: Ptunl = (h0/mt)4 e(404−SB ) where SB ≡ SE [hB] If Ptunl ∼ O(1), EW vacuum unstable and parameter disfavored!

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Bounce configuration and Vacuum tunneling

SM Veff, Bounce and Ptunl

5 10 15 10-4 1021 1046 1071 log10 μ (GeV) Veff (μ) (GeV)4 10-15 10-13 10-11 10-9 10-7 10-5 104 107 1010 1013 1016 ρ  h (GeV)

For the SM: SB = 2866 = ⇒ Ptunl ∼ 10−1013 SM EW vacuum is metastable, with τdecay ≫ τuniverse

[compare with Buttazzo et al, 2013]

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Bounce configuration and Vacuum tunneling

VLQ Veff, Bounce and Ptunl

[SG, Arunprasath V: 1812.11303 [hep-ph]]

2 4 6 8 10 12 10-2 108 1018 1028 1038 1048 log10 μ (GeV) Veff (μ) (GeV)4 10-7 10-6 10-5 10-4 0.001 0.010 0.100 100 104 106 108 ρ  h (GeV)

For VLQ family, MVL = 3 TeV, ˜ y = 0.57: SB = 469 = ⇒ Ptunl ∼ 10−4 If ˜ y > 0.57, Ptunl ∼ O(1), i.e. Higgs vacuum is unstable; such values are disfavored

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Bounce configuration and Vacuum tunneling

An approximation

Sapprox

B

=

8π2 3(−λ(t)) [Lee, Weinberg: NPB267, 1986]

4 6 8 10 12 14 16

  • 0.05

0.00 0.05 0.10 log10 μ (GeV) λ(μ) 4 6 8 10 12 14 16

  • 0.015
  • 0.010
  • 0.005

0.000 0.005 log10 μ (GeV) βλ (μ)

  • 0.05

0.00 0.05 0.10 10-13 10-8 0.001 100.000 107 1012 λ ( ρ ) I (ρ  )

Sapprox

B

works well for the SM

2 4 6 8 10 12

  • 0.15
  • 0.10
  • 0.05

0.00 0.05 0.10 log10 μ (GeV) λ(μ) 4 6 8 10 12

  • 0.016
  • 0.014
  • 0.012
  • 0.010
  • 0.008
  • 0.006
  • 0.004
  • 0.002

log10 μ (GeV) βλ (μ)

  • 0.10
  • 0.05

0.00 0.05 0.10 10-4 0.1 100 105 λ ( ρ ) I (ρ  )

Sapprox

B

cannot be used for VLF

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Bounce configuration and Vacuum tunneling

Aside: Application to Higgs Portal DM (VLL)

Can also apply to Higgs portal DM case:

[SG, T.Mukherjee: AHEP 2017]

10 49 cm 2 10 48 10 47 0.1 0.25 0.3

425 450 500 600 0.01 0.1 0.5 1 2 3 5 M Ψ GeV yΨ

10 45 cm 2 10 46 10 47 10 48 10 49 0.1 0.25 0.3 hh

0.0025 0.05 0.1 0.25 0.5 0.01 0.1 0.5 1 2 3 5 sh yΨ

Constraint requires sh ≪ 1, so vacuum stability constraint is with VLL (DM) effectively coupling with ˜ y ≡ yψsh ≪ 1

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nulogo.png Vector-like Fermions (VLF) Higgs Effective Potential Vacuum Stability Bounce configuration and Vacuum tunneling

Conclusions

Higgs vacuum is metastable in the SM life-time is much much larger than the age of the universe Many BSM theories include VLFs fermions can destabilize the vacuum we computed the renormalization group improved 1-loop Higgs effective potential with VLFs present and analyzed their effects on Higgs vacuum stability

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BACKUP SLIDES

BACKUP SLIDES

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Precision Electroweak Constraints

Precision Electroweak Constraints (S, T, Zb¯ b) (perturbatively calculable on the warped side) Bulk gauge symm - SU(2)L × U(1) (SM ψ, H on TeV Brane)

T parameter ∼ (

v MKK )2(kπR) [Csaki, Erlich, Terning 02]

S parameter also (kπR) enhanced

AdS bulk gauge symm SU(2)R ⇔ CFT Custodial Symm

[Agashe, Delgado, May, Sundrum 03]

T parameter - Protected; S parameter -

1 kπR for light bulk fermions

Implies heavy vector bosons: W ′

µ, Z ′ µ, ...

Problem: Zb¯ b shifted

3rd gen quarks (2,2)

[Agashe, Contino, DaRold, Pomarol 06]

Zb¯ b coupling - Protected Precision EW constraints ⇒ MKK 1.5 − 2.5 TeV

Implies top partners: t′, b′, χ, ...

[Carena, Ponton, Santiago, Wagner 06,07]

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Warped Fermions

SM fermions : (+, +) BC → zero-mode “Exotic”fermions : (−, +) BC → No zero-mode

1st KK vectorlike fermion

Typical ctR , ctL : (−, +) top-partners “light” c : Fermion bulk mass parameter

[Choi, Kim, 2002] [Agashe, Delgado, May, Sundrum, 03] [Agashe, Perez, Soni, 04] [Agashe, Servant 04]

Look for it at the LHC

[Dennis et al, ‘07] [Carena et al, ‘07] [Contino, Servant, ‘08] [Atre et al, ‘09, ‘11] [Aguilar-Saavedra, ‘09] [Mrazek, Wulzer, ‘09] [SG, Moreau, Singh, ‘10] [SG, Mandal, Mitra, Tibrewala, ‘11] [SG, Mandal, Mitra, Moreau : ‘13]

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Fermion rep : Zb¯ b not protected (DT model)

[Agashe, Delgado, May, Sundrum ‘03]

Complete SU(2)R multiplet QL ≡ (2, 1)1/6 = (tL, bL) ψtR ≡ (1, 2)1/6 = (tR, b′) ψbR ≡ (1, 2)1/6 = (T, bR)

“Project-out” b′, T zero-modes by (−, +) B.C.

New ψVL : b′, T b ↔ b′ mixing Zb¯ b coupling shifted So LEP constraint quite severe

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Fermion rep : Zb¯ b protected (ST & TT models)

QL = (2, 2)2/3= tL χ bL T

  • [Agashe, Contino, DaRold, Pomarol ‘06]

ZbLbL protected by custodial SU(2)L+R ⊗ PLR invariance WtLbL, ZtLtL not protected, so shifts Two tR possibilities:

1

Singlet tR (ST Model) :

(1, 1)2/3 = tR New ψVL : χ, T

2

Triplet tR (TT Model) :

(1, 3)2/3 ⊕ (3, 1)2/3 = ψ

′

tR ⊕ ψ

′′

tR =  

tR √ 2

χ′ b′ − tR

√ 2

  ⊕   

t ′′ √ 2

χ′′ b′′ − t

′′ √ 2

  

New ψVL : χ, T, χ′, b′, χ′′, t′′, b′′

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Fermion rep : Zb¯ b protected (ST & TT models)

QL = (2, 2)2/3= tL χ bL T

  • [Agashe, Contino, DaRold, Pomarol ‘06]

ZbLbL protected by custodial SU(2)L+R ⊗ PLR invariance WtLbL, ZtLtL not protected, so shifts Two tR possibilities:

1

Singlet tR (ST Model) :

(1, 1)2/3 = tR New ψVL : χ, T

2

Triplet tR (TT Model) :

(1, 3)2/3 ⊕ (3, 1)2/3 = ψ

′

tR ⊕ ψ

′′

tR =  

tR √ 2

χ′ b′ − tR

√ 2

  ⊕   

t ′′ √ 2

χ′′ b′′ − t

′′ √ 2

  

New ψVL : χ, T, χ′, b′, χ′′, t′′, b′′

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Hidden sector DM ψ

[SG, Lee, Wells 2009] SM × U(1)X : U(1)X sector: Xµ, Φhid, ψ L ⊃ −α |H|2|Φhid|2 + η

2 XµνBµν − κφhid ¯

ψψ

Bµ Xµ φSM φH ψ SM

Higgs portal DM: Self-annihilation

ψ SM φH φSM ψ ψ ψ φH φSM φSM φH

Channels ψψ → b ¯ b , W +W − , ZZ , hh , t¯ t

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Hidden sector DM ψ

[SG, Lee, Wells 2009] SM × U(1)X : U(1)X sector: Xµ, Φhid, ψ L ⊃ −α |H|2|Φhid|2 + η

2 XµνBµν − κφhid ¯

ψψ

Bµ Xµ φSM φH ψ SM

Higgs portal DM: Self-annihilation

ψ SM φH φSM ψ ψ ψ φH φSM φSM φH

Channels ψψ → b ¯ b , W +W − , ZZ , hh , t¯ t