On Gravitational Corrections to the Electroweak Vacuum Decay

On Gravitational Corrections to theElectroweak Vacuum Decay

Alberto Salvio

Supported by

The resonance at 750 GeV

Fitting the peak:

1) Widths

2) Models

3) Theories

4) What next?

Alessandro Strumia, talk at , March 20, 2016

Top 2017, Braga, Portugal.(21st of September 2017)

Mainly based on

I Buttazzo, Degrassi, Giardino, Giudice, Sala, Salvio, Strumia (JHEP) arXiv:1307.3536

I Giudice, Isidori, Salvio, Strumia (JHEP) arXiv:1412.2769

I Salvio, Strumia, Tetradis, Urbano (JHEP) arXiv:1608.02555

http://arxiv.org/abs/1307.3536

http://arxiv.org/abs/1412.2769

https://arxiv.org/abs/1608.02555

Testing the Standard Model (SM) at ultrahigh energies

Two important goals of the LHC:

I testing the SM

I discovering new physics (NP)

But one can also complementary test the SM at even higher energies:e.g. the stability bound

Precise “running” of λ and its β-function

(βλ ≡

dλ

d lnµ

)

102 104 106 108 1010 1012 1014 1016 1018 1020

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

RGE scale Μ in GeV

Hig

gs

qu

arti

cco

up

lin

gΛ

3Σ bands in

Mt = 173.3 ± 0.8 GeV HgrayLΑ3HMZL = 0.1184 ± 0.0007HredLMh = 125.1 ± 0.2 GeV HblueL

Mt = 171.1 GeV

ΑsHMZL = 0.1163

ΑsHMZL = 0.1205

Mt = 175.6 GeV

102 104 106 108 1010 1012 1014 1016 1018 1020-0.020

-0.015

-0.010

-0.005

0.000

RGE scale Μ in GeV

Bet

afu

nct

ion

of

the

Hig

gs

qu

arti

cΒ Λ

3Σ bands in


[Buttazzo, Degrassi, Giardino, Giudice, Sala, Salvio, Strumia (2014)]

http://arxiv.org/pdf/1307.3536v4.pdf

Testing the Standard Model (SM) at ultrahigh energies

Two important goals of the LHC:

I testing the SM

I discovering new physics (NP)

But one can also complementary test the SM at even higher energies:e.g. the stability bound

Precise “running” of λ and its β-function

(βλ ≡

dλ

d lnµ

)

102 104 106 108 1010 1012 1014 1016 1018 1020

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

RGE scale Μ in GeV

Hig

gs

qu

arti

cco

up

lin

gΛ

3Σ bands in


Mt = 171.1 GeV

ΑsHMZL = 0.1163

ΑsHMZL = 0.1205

Mt = 175.6 GeV

102 104 106 108 1010 1012 1014 1016 1018 1020-0.020

-0.015

-0.010

-0.005

0.000

RGE scale Μ in GeV

Bet

afu

nct

ion

of

the

Hig

gs

qu

arti

cΒ Λ

3Σ bands in




Result for the stability of the electroweak (EW) vacuum

Phase diagram of the SM:

6 8 10

0 50 100 150 200

0

50

100

150

200

Higgs pole mass Mh in GeV

Top

pole

mas

sM

tin

GeV

LI =104GeV5

67

8910

1214

1619

Instability

Non

-pertu

rbativ

ity

Stability

Meta-sta

bility

107 108

109

1010

1011

1012

1013

1014

1016

120 122 124 126 128 130 132168

170

172

174

176

178

180

Higgs pole mass Mh in GeVT

op

pole

mas

sM

tin

GeV

1017

1018

1019

1,2,3 Σ

Instability

Stability

Meta-stability

[Buttazzo, Degrassi, Giardino, Giudice, Sala, Salvio, Strumia (2014)]The stability of the electroweak vacuum is violated at the ∼ 3σ level

We see the main uncertainty is due to the top mass, Mt


Result for the stability bound

Mh > 129.6 GeV + 2.0(Mt − 173.34 GeV)− 0.5 GeVα3(MZ)− 0.1184

0.0007± 0.3th GeV

The stability bound is violated at the ∼ 3σ level

Since the experimental error on the Higgs mass is small it is better to express thebound in terms of the pole top mass:

Mt < (171.53± 0.15± 0.23α3 ± 0.15Mh) GeV = (171.53± 0.42) GeV.



Is the meta-stability worrisome?

Flat space analysis:

171 172 173 174 175 17610-2000

10-1500

10-1000

10-500

1

Pole top mass Mt in GeV

Pro

bab

ilit

yof

vac

uum

dec

ay

1Σ bands in

Mh=125.1±0.2 GeV

Hred dottedLΑ3=0.1184±0.0007

Hgray dashedL

173.3±0.8

171 172 173 174 175 1761

10200

10400

10600

10800

101000


Lif

e-ti

me

inyr

LCDM

CDM

1Σ bands in

Mh=125.1±0.2 GeV


Hgray dashedL

Left: Probability of EW vacuum decay.

Right: The life-time of the EW vacuum, with 2

different assumptions for future cosmology: universes

dominated by the cosmological constant (ΛCDM) or

by the dark matter (CDM).



Is the meta-stability worrisome?

Flat space analysis:

171 172 173 174 175 17610-2000

10-1500

10-1000

10-500

1


Pro

bab

ilit

yof

vac

uum

dec

ay

1Σ bands in

Mh=125.1±0.2 GeV


Hgray dashedL

173.3±0.8

171 172 173 174 175 1761

10200

10400

10600

10800

101000


Lif

e-ti

me

inyr

LCDM

CDM

1Σ bands in

Mh=125.1±0.2 GeV


Hgray dashedL

Left: Probability of EW vacuum decay.

Right: The life-time of the EW vacuum, with 2

different assumptions for future cosmology: universes

dominated by the cosmological constant (ΛCDM) or

by the dark matter (CDM).



Details on the calculation of the probability of vacuum decay

The probability dP/dV dt per unit time and volume of creating a bubble of truevacuum within a space volume dV and time interval dt is

dP = dt dV Λ4B e−SB

SB is the action of the bounce of size R ≡ Λ−1B : the bounce h is an SO(4) symmetric

Euclidean solution

h′′ +3

rh′ =

dV

dh, with boundary conditions h′(0) = 0, h(∞) = hEW

[Coleman (1977); Coleman, Callan (1977)]

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.16.1248


Gravitational corrections

We are looking at extremely high energies, sometimes reaching the Planck mass, MPl.Does gravity play a role?

One can address this question in Einstein gravity (compatible with all experiments)

L = LEinstein + LSM − ξ|H|2R

However, Einstein gravity is an effective theory with a cutoff ∼ MPl

→ consider an expansion in E/MPl (it is not restrictive: for E > MPl the theorybreaks down)

Some details on the inclusion of gravity(First down in [Coleman, de Luccia (1980)])

The bounce equation becomes a Higgs-gravity system of equations

h′′ + 3ρ′

ρh′ =

dV

dh− ξhR, ρ′2 = 1 +

ρ2/M2Pl

3(1 + ξh2/M2Pl)

(h′2

2− V − 6

ρ′

ρξhh′

)where R is the Ricci scalar for the metric

ds2 = dr2 + ρ(r)2dΩ2

(dΩ is the volume element of the unit 3-sphere)

We developed a perturbation theory in 1/RMPl

(weak gravity expansion)

which is adequate to describe the gravitational corrections within Einstein gravity.

[Salvio, Strumia, Tetradis, Urbano (2016)]


https://arxiv.org/pdf/1608.02555.pdf



h′′ + 3ρ′

ρh′ =

dV

dh− ξhR, ρ′2 = 1 +

ρ2/M2Pl

3(1 + ξh2/M2Pl)

(h′2

2− V − 6

ρ′

ρξhh′




We developed a perturbation theory in 1/RMPl

(weak gravity expansion)

which is adequate to describe the gravitational corrections within Einstein gravity.






h′′ + 3ρ′

ρh′ =

dV

dh− ξhR, ρ′2 = 1 +

ρ2/M2Pl

3(1 + ξh2/M2Pl)

(h′2

2− V − 6

ρ′

ρξhh′




We developed a perturbation theory in 1/RMPl (weak gravity expansion)which is adequate to describe the gravitational corrections within Einstein gravity.




Impact of Einstein gravity on the phase diagram of the SM

114 116 118 120 122 124 126 128168

170

172

174

176

178

180

Higgs pole mass Mh in GeV

ToppolemassMtinGeV Gravity

for |ξ| =

10

Gravity

ignored

or for ξ =

-1/6

1,2,3 σ

Instability

Metastability

Stability

This updates the plot in [Salvio, Strumia, Tetradis, Urbano (2016)] by using morerecent measurements of Mt.


Unnaturalness of the SM + Einstein gravity

Recall naturalness:

δM2h ∼

g2M2NP

(4π)2

.M2h

this can occur

I when MNP ∼ TeV

I when g 1 and MNP TeV

A problem:

gravity introduces a large scale MPl TeV


Recall naturalness:

δM2h ∼

g2M2NP

(4π)2.M2

h

this can occur

I when MNP ∼ TeV


A problem:



Recall naturalness:

δM2h ∼

g2M2NP

(4π)2.M2

h

this can occur

I when MNP ∼ TeV


A problem:


Naturalness and gravity

We do not know if GN simply describes a coupling constantor signals the presence of new degrees of freedom with mass MPl = 1/

√8πGN

But (Einstein) gravitational interactions increase as energy increases

Idea (softened gravity): consider theories where the power-law increase of thegravitational coupling stops at ΛG MPl.

The gravitational contribution to the Higgs mass is then

δM2h ≈

GNΛ4G

(4π)2

Requiring naturalness → ΛG . 1011 GeV

[Giudice, Isidori, Salvio, Strumia (2014)]

http://arxiv.org/pdf/1412.2769.pdf

Naturalness and gravity

We do not know if GN simply describes a coupling constantor signals the presence of new degrees of freedom with mass MPl = 1/

√8πGN

But (Einstein) gravitational interactions increase as energy increases

Idea (softened gravity): consider theories where the power-law increase of thegravitational coupling stops at ΛG MPl.

The gravitational contribution to the Higgs mass is then

δM2h ≈

GNΛ4G

(4π)2

Requiring naturalness → ΛG . 1011 GeV

[Giudice, Isidori, Salvio, Strumia (2014)]

http://arxiv.org/pdf/1412.2769.pdf

Softened gravity and the stability of the EW vacuum

Given that gravity becomes soft at high energies it negligibly affect the stability issue

(checked in a concrete realization of softened gravity)

However, other UV completion of Einstein gravity, such as string theory can affectthese results

But, Planck-scale physics cannot suppress sub-Planckian contributions to SM vacuumdecay, which can only be affected by new physics at lower energies.

Conclusions

I In the pure SM the vacuum stability is excluded at roughly 3σ level

I These calculations involve the extrapolation of the SM potential up to Planckianenergies so one may wonder if gravity changes the result

I We included Einstein gravity within its regime of validity and found that thecorrections are small, even including ξ

I We assumed a desert between the EW and the Planck scale. What aboutnaturalness? We discussed that a modification of gravity which softened thestrength of gravity at high energy leads to negligible modifications

Disclaimer: New physics below MPl may or may not change completely the results.So these calculations are useful as tests of the SM hypothesis and are possible meansto find further evidences for new physics.

Conclusions

I In the pure SM the vacuum stability is excluded at roughly 3σ level

I These calculations involve the extrapolation of the SM potential up to Planckianenergies so one may wonder if gravity changes the result

I We included Einstein gravity within its regime of validity and found that thecorrections are small, even including ξ

I We assumed a desert between the EW and the Planck scale. What aboutnaturalness? We discussed that a modification of gravity which softened thestrength of gravity at high energy leads to negligible modifications

Disclaimer: New physics below MPl may or may not change completely the results.So these calculations are useful as tests of the SM hypothesis and are possible meansto find further evidences for new physics.

Thank you very much for your attention

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On Gravitational Corrections to the Electroweak Vacuum Decay