Vacuum decay rate in the standard model and beyond Yutaro Shoji - - PowerPoint PPT Presentation

Vacuum decay rate in the standard model and beyond

Yutaro Shoji (KMI, Nagoya U.)

KEK-PH 2018 Winter, Dec 4-7 2018 https://github.com/YShoji-HEP/ELVAS

• Phys. Lett. B771(2017)281; M. Endo, T. Moroi, M. M. Nojiri, YS

JHEP11(2017)074; M. Endo, T. Moroi, M. M. Nojiri, YS

• Phys. Rev. Lett. 119 (2017) no.21, 211801; S. Chigusa, T. Moroi, YS
• Phys. Rev. D97 (2018) no.11, 116012; S. Chigusa, T. Moroi, YS

Work in progress with S. Oda, D. Takahashi

Introduction

Vacuum decay in the standard model

Vacuum Energy Field value

V (Φ) = λ(Φ†Φ)2 − M 2(Φ†Φ)

102 GeV

• [ / ]

λ

Standard Model Planck EW

[see Espinosa’s talk today]

Vacuum decay in the standard model

Vacuum Energy Field value

V (Φ) = λ(Φ†Φ)2 − M 2(Φ†Φ)

102 GeV

1010 GeV

1017 GeV

Standard Model EW vacuum of the SM is meta-stable

Decay

Bubble nucleation rate

γ = Ae−B

B = SE(¯ φ)

Bounce solution (Fubini-Lipatov instanton)

B = 8π2 3|λ|

¯ φ(r) = s 8 |λ| R R2 + r2

R :

Size of the instanton

Independent of R (classical scale invariance)

A rate to have a bubble in unit volume for a negative λ

Bubble nucleation rate

γ = Ae−B

A rate to have a bubble in unit volume

A ∼ ✓det S00

E|bounce

det S00

E|false

◆1/2

+ + + + · · · + +

Higgs Top NG boson Gauge Ghost Mixed [C. G. Callan, S. R. Coleman, ’77]

Quantum correction to B

exp(

)

Typical scale?

γ = Ae−B

A rate to have a bubble in unit volume

A ∼ M 4

A ∼ ✓det S00

E|bounce

det S00

E|false

◆1/2

Dimensional analysis Typical scale

What is the typical scale?

SM is classically scale invariant

Renormalization scale?

γ = Ae−B

B = SE(¯ φ)

B = 8π2 3|λ|

A rate to have a bubble in unit volume

What is the renormalization scale for λ?

• [ / ]

λ

Standard Model

The pre-factor is important!

γ = Ae−B

B = SE(¯ φ)

B = 8π2 3|λ|

A rate to have a bubble in unit volume

A ∼ ✓det S00

E|bounce

det S00

E|false

◆1/2

The renormalization scale uncertainty is canceled @1-loop

If we calculate A, we do not have such problems

We do not need “typical scale”

Standard Model @ one-loop

Instability 107 109 1010 1012 115 120 125 130 135 165 170 175 180 Higgs mass Mh in GeV Pole top mass Mt in GeV 1,2,3 s Instability Stability Meta-stability

• G. Ishidori, G. Ridolfi, A. Strumia; ‘01

However, There were no established ways to subtract dilatational and gauge zero modes They use an approx. for the gauge zero mode subtraction, which is gauge dependent

However, There were no established ways to subtract dilatational and gauge zero modes They use an approx. for the gauge zero mode subtraction, which is gauge dependent

Gauge zero mode

JHEP 1711 (2017) 074, M. Endo, T. Moroi, M. M. Nojiri, YS We have found the correct treatment of the gauge zero mode

Flat direction Bounce

det S00

E|bounce = 0

Higgs SU(2) [A. Kusenko, K. M. Lee, E. J. Weinberg; ’97]

Contents

• Introduction
• Gauge invariance and analytic formulas
• Models beyond the standard model
• Summary

Gauge invariance and analytic formulas

Gauge fixing

LGF = 1 ξ (∂µAµ)2

NG boson

LGF = (∂µAµ − g ¯ φχ)2

Numerical Evaluation Treatment of gauge zero modes Semi-analytical Evaluation

• Phys. Lett. B771(2017)281

JHEP11(2017)074 Bounce solution

Gauge fixing

LGF = 1 ξ (∂µAµ)2

NG boson

LGF = (∂µAµ − g ¯ φχ)2

Numerical Evaluation Treatment of gauge zero modes Semi-analytical Evaluation

• Phys. Lett. B771(2017)281

JHEP11(2017)074

Standard Model

• A. Andreassen, W. Frost, M. D. Schwartz; ‘17
• S. Chigusa, T. Moroi, YS; ‘ 17

Bounce solution

Standard Model

• !"#

!"" !"$ !"% !"& !'# !(# !(" !($ !(% !(& !&# !! / )*+ !! / !"#

• S. Chigusa, T. Moroi, YS; ‘ 18

cf.) A. Andreassen, W. Frost, M. D. Schwartz; ‘17

• S. Chigusa, T. Moroi, YS; ‘ 17

log10

• γPl × Gyr Gpc3

How about

• ther models?

Bubble nucleation rate (decay rate of a vacuum) [A. Andreassen, W. Frost, M. D. Schwartz; ’17, S. Chigusa, T. Moroi, YS; ’18]

B = 8π2 3|λ|

• ln A′(h)

MS = −3

4 − 6 ln AG + 5 2 ln π 3 − 5 2 ln |λ| 8 + 3 ln µR 2 ,

• ln A(σ)

MS = −1

2Sσ(zκ) + κ |λ| + κ2 3|λ|2

• 1 + γE + ln µR

2

• ,
• ln A(ψ)

MS = − y4

3|λ|2

• 1 + γE + ln µR

2

• − 2y2

3|λ| 25 4 + γE + ln µR 2

• + Sψ(zy),
• .

. .

γ =

• d ln R 1

R4

• A′(h)A(σ)A(ψ)A(Aµ,ϕ)e−B

MS, µ

Manifestly gauge invariant analytic formulas

Tree 1-loop

ELVAS

https://github.com/YShoji-HEP/ELVAS c++ package for ELectroweak VAcuum Stability

BSM fermions

!"#$ !"#% !&#$ !&#% !'#$ !'#% !%#$ $#$ $#" $#' $#( $#) !#$ *+,!"[ !! / -./ ] !! ! ! " #$ #% #& $'$ $'% $'& $'! $'" #'$ ()*!"[ !! / +,- ] !! ! " # $% $& $! %'% %'& %'! %'" %'# $'% ()*!"[ !! / +,- ] !!

Right handed neutrino Vector-like quarks Vector-like leptons

• S. Chigusa, T. Moroi, YS; ‘ 18

Fermions make our vacuum unstable

BSM scalars

Two Higgs Doublet Model (in the context of the DFSZ axion model)

* Charge breaking vacuum may appear * Bottom and Tau Yukawa couplings can become large * Bounce is multi-field working with S. Oda, D. Takahashi at OIST * Additional quartic couplings We need to include quantum corrections from photon as well Large bottom and tau couplings with a large tanβ Vacuum structure becomes more non-trivial First example of one-loop calculation for multi-field bounce solution (but it can be reduced to single-field) Scalars are more interesting!

Summary

• We found a way to treat the gauge zero modes gauge

invariantly and the final result is manifestly gauge invariant.

• We applied it to the standard model and confirmed that

the lifetime of the EW vacuum is much longer than the age of the Universe.

• We provide a c++ package that can calculate decay rates

for generic models with approximate scale invariance.