Higgs mass implications on the stability of the

Introduction
SM vacuum stability
Conclusions
Higgs mass implications on the stability of the
electroweak vacuum
J. Elias-Miró
joint work with J.R. Espinosa, G.Degrassi, S. Di Vita,
G.F. Giudice, G. Isidori, A. Riotto, A. Strumia
.
Universitat Autònoma de Barcelona (UAB)
Institut de Fı́sica d’Altes Energies (IFAE)
Cargese, August 2012
J. Elias-Miró
Stability of the EW vacuum
Introduction
SM vacuum stability
Conclusions
The Higgs sector of the SM
It is the part of the theory from which we have less
experimental information.
Interestingly, most of the theoretical problems of the SM arise
from the Higgs sector.
J. Elias-Miró
Stability of the EW vacuum
95% CL limit on σ/σSM
Introduction
SM vacuum stability
Conclusions
10
CMS, s = 7 TeV
L = 4.6-4.8 fb-1
Observed
Expected (68%)
Expected (95%)
1
10-1
110 115 120 125 130 135 140 145
Higgs boson mass (GeV)
for Mh ≈ 125 GeV, λ =
J. Elias-Miró
Mh2
2v 2
≈ 0.129
Stability of the EW vacuum
Introduction
SM vacuum stability
Conclusions
SM effective potential
Assume the SM up to very high energies,
is it a consistent model?
J. Elias-Miró
Stability of the EW vacuum
Introduction
SM vacuum stability
Conclusions
SM effective potential
For large field values, Vef f ≈ 41 λef f (φ)φ4 .
If λef f ≈ λ < 0 at some high energy scale ΛI , the Electroweak
(EW) minimum at φ = v ≈ 246 GeV of the Higgs potential is
unstable.
0.6
Effective potential Veff
0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.2
0.4
J. Elias-Miró
0.6
0.8
Classical field Φc
1.0
1.2
Stability of the EW vacuum
Introduction
SM vacuum stability
Conclusions
SM effective potential
But, can λ become negative? Yes, two main competing effects:
µ
dλ(µ)
= ( # λ2
d log(µ)
+ ... −# h4t + ...) + ...
, makes λ grow
, makes λ decrease.
ht (v) =
√
2Mt /v and λ(v) = Mh2 /(2v 2 ).
J. Elias-Miró
Stability of the EW vacuum
Introduction
SM vacuum stability
Conclusions
SM effective potential
But, can λ become negative? Yes, two main competing effects:
µ
dλ(µ)
= ( # λ2
d log(µ)
+ ... −# h4t + ...) + ...
, makes λ grow
, makes λ decrease.
ht (v) =
√
2Mt /v and λ(v) = Mh2 /(2v 2 ).
J. Elias-Miró
Stability of the EW vacuum
Introduction
SM vacuum stability
Conclusions
SM effective potential
But, can λ become negative? Yes, two main competing effects:
µ
dλ(µ)
= ( # λ2
d log(µ)
+ ... −# h4t + ...) + ...
, makes λ grow
, makes λ decrease.
ht (v) =
√
2Mt /v and λ(v) = Mh2 /(2v 2 ).
J. Elias-Miró
Stability of the EW vacuum
Introduction
SM vacuum stability
Conclusions
SM effective potential
J.EM, J. Espinosa, G.F. Giudice, G. Isidori, A. Riotto, A. Strumia. [hep/1112.3022]
J. Elias-Miró
Stability of the EW vacuum
Introduction
SM vacuum stability
Conclusions
SM effective potential
A Higgs mass of ∼ 125 GeV is a very special value
180
ili
stab
taMe
150
100
ty
Stability
50
0
0
50
100
150
200
Pole top mass Mt in GeV
Instability
Non-perturbativity
Top mass Mt in GeV
200
107
1010
Instability
Instability
Meta-stability
175
1,2,3 Σ
170
109
1012
165
115
Stability
120
125
130
135
Higgs mass Mh in GeV
Higgs mass Mh in GeV
G.Degrassi, S. Di Vita, J.EM, J. Espinosa, G.F. Giudice, G. Isidori, A. Strumia. [hep-ph/1205.6497]
J. Elias-Miró
Stability of the EW vacuum
Introduction
SM vacuum stability
Conclusions
SM effective potential
G.Degrassi, S. Di Vita, J.EM, J. Espinosa, G.F. Giudice, G. Isidori, A. Strumia. [hep-ph/1205.6497]
J. Elias-Miró
Stability of the EW vacuum
Introduction
SM vacuum stability
Conclusions
Conclusions
- From metastabilty considerations, a SM Higgs with
Mh ∼ 125 GeV does not imply an strict upper bound on the
scale of new physics.
- The Higgs quartic coupling becomes very small. Very
unlikely becomes zero at the Planck scale. However
λ(MP lanck ) ≈ 0
J. Elias-Miró
Stability of the EW vacuum
Introduction
SM vacuum stability
Conclusions
The SM is such a good model that admits a theoretical
extrapolation up to MP lanck without any consistency problem.
I hope this analysis will be soon invalidated by nature, due to
new physics coming in close to the EW scale...
Thank you for your attention!
J. Elias-Miró
Stability of the EW vacuum
Introduction
SM vacuum stability
Conclusions
J. Elias-Miró
Stability of the EW vacuum
Introduction
SM vacuum stability
Conclusions
dλH
2
= 12yt2 − 3g 0 − 9g 2 λH − 6yt4
d ln µ
i
3h 4
2
+
2g + (g 0 + g 2 )2 + 24λ2H + 4λ2HS ,
8
1
dλ
2
HS
= λHS [ 12yt2 − 3g 0 − 9g 2
(4π)2
d ln µ
2
+ 4 (3λH + 2λS ) + 8λHS ] ,
dλS
(4π)2
= 8λ2HS + 20λ2S .
d ln µ
(4π)2
J. Elias-Miró
Stability of the EW vacuum
(1)
Introduction
SM vacuum stability
Conclusions
1018
1 Σ band in:
16
Instability sclae in GeV
10
Mt =173.1±0.7 GeV
Αs HMz L=0.1184±0.0007
1014
1012
1010
108
118
120
122
124
126
Higgs mass in GeV
J. Elias-Miró
128
Stability of the EW vacuum
130
Introduction
SM vacuum stability
Conclusions
G.Degrassi, S. Di Vita, J.EM, J. Espinosa, G.F. Giudice, G. Isidori, A. Strumia. [hep-ph/1205.6497]
J. Elias-Miró
Stability of the EW vacuum
Introduction
SM vacuum stability
Conclusions
J. Elias-Miró
Stability of the EW vacuum
Introduction
SM vacuum stability
Conclusions
J. Elias-Miró
Stability of the EW vacuum
Introduction
SM vacuum stability
Conclusions
126
Higgs mass in GeV
125
124
123
122
1.0
1.2
1.4
1.6
1.8
̐Mt
J. Elias-Miró
Stability of the EW vacuum
2.0