higgs vacuum stability & physics beyond the standard modelpacific-2014 moorea, sept 2014 a....

Higgs Vacuum Stability & Physics Beyond the Standard Model

Archil Kobakhidze

AK & A. Spencer-Smith, Phys Lett B 722 (2013) 130 [arXiv:1301.2846] AK & A. Spencer-Smith, JHEP 1308 (2013) 036 [arXiv:1305.7283] AK & A. Spencer-Smith, arXiv:1404.4709

PASIFIC 2014 A UCLA Symposium on Particle Astrophysics and Cosmology Including

Fundamental InteraCtions September 15 - 20, 2014, Moorea, French Polynesia

PACIFIC-2014 Moorea, Sept 2014

A. Kobakhidze (U. of Sydney)

Combined 2012-13 data: It is a Higgs boson, maybe even the Higgs boson

2

The SM Higgs with MH=125.9± 0.4 GeV !  Naturalness problem: somewhat heavy than typical

prediction of the supersymmetric models and somewhat light than typical prediction of technicolour models.

!  More notably, the Standard Model vacuum state

is a false (local) vacuum. The true vacuum state and it carries large negative energy density ~ - (MP)4.

!  How long does the electroweak vacuum live?

EW h0|h|0iEW = vEW ⇡ 246 GeV

|0iEW

h0|h|0i ⇠ MP ⇡ 1018GeV ,


A. Kobakhidze (U. of Sydney) 3



EW vacuum lifetime: effective Higgs potential !  Electroweak Higgs doublet (in the unitary gauge):

!  Effective (quantum-corrected) potential

4

H =

✓0

h(x)/p2

◆

�(h) = �(µ) + �� ln(h/µ)

(4⇡)2�� = �6y4t + 24�2 + . . .

V (0)H (h) =�

8

�h2 � vEW

�2

V (1�loop)H (h) =�(h)

8

�h2 � vEW

�2,

yt(mt) ⇡ 1 , �(mh) ⇡ 0.13 �! �� < 0

EW vacuum lifetime: RG extrapolation of SM parameters !  Previous calculations: F. Bezrukov, M. Y. .Kalmykov, B. A. Kniehl and M. Shaposhnikov, JHEP 1210, 140 (2012) [arXiv:1205.2893 [hep-ph]];

G. Degrassi, S. Di Vita, J. Elias-Miro, J. R. Espinosa, G. F. Giudice, G. Isidori and A. Strumia, JHEP 1208, 098 (2012) [arXiv:1205.6497 [hep-ph]]; D. Buttazzo, G. Degrassi, P. P. Giardino, G. F. Giudice, F. Sala, A. Salvio and A. Strumia, JHEP 1312, 089 (2013) [arXiv:1307.3536].

3-loop RGE’s in mass-independent MSbar scheme; full 2-loop matching condition !  Our calculations: AK & A. Spencer-Smith, arXiv:1404.4709; A. Spencer-Smith, arXiv:1405.1975 1-loop RGE in mass-dependent scheme, 2 – and 3 – loop RGE’s in MSbar + corresponding matching condition

PACIFIC-2014 Moorea, Sept 2014 A. Kobakhidze (U. of Sydney) 5



EW vacuum lifetime: RG running of λ in a mass- dependent scheme Instability scale:

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[�(µi) = 0] log10

⇣ µiGeV

⌘⇡ 9.19± 0.65Mt ± 0.19Mh ± 0.13↵3 ± 0.02th



EW vacuum lifetime: flat spacetime estimate !  Large field limit:

!  Using Coleman’s prescription, one can calculate that the decay of electroweak vacuum is dominated by small size Lee-Wick bounce solution,

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VH =�̄� ln(h/µi)

4h4 , �̄� = ��|µ=µi

h⇤ = µie�1/4

R ⇠ 1/µm ⇡ 10�17/GeV, ��|µ=µm = 0

SLW =8⇡2

3|�(µm)|, |�(µm)| ⇡ 0.01� 0.02

PEW = e�p ⇡ 1, p = (µm/H0)4 exp (�SLW)



EW vacuum in flat spacetime: stability bound Stability bound:

Absolute stability of the electroweak vacuum is excluded now at 99.98% CL [AK & A. Spencer-Smith, arXiv:1404.4709, A. Spencer-Smith, arXiv:1405.1975]

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Mt < 170.16± 0.22↵3 ± 0.13Mh ± 0.06th GeVM expt = 173.34± 0.76↵3 ± 0.3QCD GeV



EW vacuum in an inflationary universe !  Electroweak vacuum decay may qualitatively differ in cosmological

spacetimes:

(i) Thermal activation of a decay process,

(ii) Production of large amplitude Higgs perturbations during inflation,

[J.R. Espinosa, G.F. Giudice, A. Riotto, JCAP 0805 (2008) 002] The bound that follows from the above consideration can be avoided, e.g., in curvaton models, or when

!  Actually, the dominant decay processes are due to instantons, (Hawking-Moss, or CdL-type) [AK & A. Spencer-Smith, Phys Lett B 722 (2013) 130 [arXiv:1301.2846]]

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Hinf < µi

Tr < µi

me↵h > Hinf

V (h,�) = VH(h) + Vinf(�) + VH�inf

Vinf(�) = Vinf + V 0⇤(�� inf) + 1/2V 00⇤ (�� inf)2 + ...

✏ =M2P2

✓V 0⇤Vinf

◆2



EW vacuum in inflationary universe !  Fixed background approximation:

!  EoM for Higgs field:

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� = �inf , ds2 = d�2 + ⇢2(�)d⌦3,

⇢(�) = H�1inf sin(Hinf�), � = t2 + r2, � 2 [0,⇡/Hinf ], H2inf = Vinf/3M2P

ḣ(0) = ḣ(⇡/Hinf) = 0

hL(x⇤) = hR(x⇤)

¨h+ 3Hinf cot(Hinf�) ˙h =@V (�inf , h)

@h



EW vacuum in inflationary universe !  Hawking-Moss instanton:

!  For ,

HM transition dominates

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@V

@h

= 0 , h(x) = h⇤,

VH�inf(�inf , h⇤)



EW vacuum in inflationary universe HM transition generates a fast decay of the electroweak vacuum, unless

!  Together with , this implies that only small-field inflationary models are allowed with a negligible tensor/scalar:

!  This seems now is excluded by the BICEP2 results:

,

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Hinf < 109(1012) GeV

mh = 126 GeV, mt = 174(172) GeV

ns < 1

r < 10�11(10�5)

r = 0.2+0.07�0.05



EW vacuum in inflationary universe

!  Consider, [O. Lebedev & A. Westphal Phys.Lett. B719 (2013) 415]

[similar consideration applies ]

!  Large-field chaotic inflation , with

!  Naturalness constraint:

Tuning is needed!

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VH�inf =↵

2h2�2 (↵ > 0), me↵h = ↵

1/2�inf > Hinf

h⇤ = (�↵/�)1/2�inf > µi, (�(h⇤) < 0)

⇥Vinf = 1/2m

2��

2, m� = 10�5MP

⇤

↵ < 64⇡2 (m�/mh)2 ⇡ 2 · 10�20

⇠

2R2h2

10�6 > ↵ > 1.4p|�| (Hinf/�inf)2 > 6 · 10�12 .



EW vacuum in inflationary universe

!  In the limit

EW vacuum is unstable!

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h(x) =

8><

>:8hR

✓8 +

⇣hRh⇤

⌘2x

2

◆�1, 0 x < x⇤

x⇤h⇤x(J1(ix⇤)+iY1(�ix⇤)) (J1(ix) + iY1(�ix)) , x⇤ < x < 1

,

x⇤ =2p2h⇤

hR

✓hR

h⇤� 1

◆1/2.

me↵h >> Hinf

h

00 + 3h0� =@V (�inf , h)

@h

, [x = me↵h �]

BCdL = �2⇡2

�

I < 0, I =

Z 1

0x

3dx

h

2(x)

✓1� h

2(x)

2h2⇤

◆�< 0, �(µ > µi) < 0.

p _ exp{�BCdL} >> 1



EW vacuum in inflationary universe !  Fast decay of EW ceases inflation globally (no eternal inflation)

!  The above considerations applies to models with curvaton

In light of BICEP2 the electroweak vacuum within the Standard Model is unstable! New physics must enter at energies < 109 GeV.

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e3Hinf⌧e�(⌧Hinf )4p

⌧stop

⇡ (3/p)1/3H�1inf

< 1.4H�1inf

A0s =

s

A2s +g2(X)H2inf8⇡2M2P

, r0 =16✏

1 + ✏g2(X)



Neutrino masses and vacuum stability AK & A. Spencer-Smith, JHEP 1308 (2013) 036 [arXiv:1305.7283]

①  Extension of the electroweak gauge sector ②  Extension of a scalar sector ③  Extension of the fermionic sector

!  Working with MS-bar couplings: ①  Modification of beta-functions above the particle mass threshold ②  Finite threshold correction due to the matching of low and high

energy theories

!  Neutrino oscillations (= masses) provide the most compelling evidence for the physics beyond the Standard Model.

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�(1)� = 24�2 � 6y4t +

3

4g42 +

3

8

�g21 + g

22

�2+ �

��9g22 � 3g21 + 12y2t

�



Neutrino masses and vacuum stability AK & A. Spencer-Smith, JHEP 1308 (2013) 036 [arXiv:1305.7283]

!  Type I see-saw models: additional massive sterile neutrinos – not capable to solve the vacuum stability problem

!  Type III see-saw models: additional electroweak-triplet fermions – may solve the problem for very specific range of parameters

More promising candidates:

!  Type II see-saw: additional electroweak-triplet scalar

!  Left-right symmetric models: additional gauge bosons, scalars and fermions

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Type II see-saw models and vacuum stability Scalar potential:

Neutrino masses:

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V (�,�) = �m2��†�+ �(�†�)2 +m2�tr(�†�) +�12(tr(�†�))2

+�22

⇥(tr(�†�))2 � tr(�†�)2

⇤+ �4(�

†�)tr(�†�) + �5�†[�†,�]�+

�6p2�T i�2�

†�+ h.c.

�.

1p2(y�)fgl

TfL Ci�2�l

gL + h.c.



Type II see-saw models and vacuum stability Stability conditions:

Avoiding tachyonic instabilities:

Tree level matching condition:

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Type II see-saw models and vacuum stability

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Type II see-saw models and vacuum stability

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Alternating LR-symmetric model with universal see- saw for all fermion masses Scalar sector: New fermions:

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�L 2 (1,1,2, 1/2), �R 2 (1,2,1, 1/2).

V (�L,�R) = �m2⇣�†L�L + �

†R�R

⌘+

�

2

⇣�†L�L + �

†R�R

⌘2+ ��†L�L�

†R�R.

NL, NR 2 (1,1,1, 0),EL, ER 2 (1,1,1,�1),

UiL, UiR 2 (3,1,1, 2/3),DiL, DiR 2 (3,1,1,�1/3),

SU(2)L ⇥ SU(2)R ⇥ U(1)B�L



Alternating LR-symmetric model with universal see- saw for all fermion masses Tree-level matching: One-loop matching:

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Alternating LR-symmetric model with universal see- saw for all fermion masses

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Conclusions: !  The absolute stability of the electroweak vacuum is

excluded at 99.98% CL

!  In light of BICEP2 discovery of B-modes the electroweak vacuum within the Standard model is unstable. New physics, stabilizing the electroweak vacuum, must enter the game at scales < 109 GeV.

!  The most promising models of neutrino masses with a stable electroweak vacuum are: type II see-saw and LR models. They may potentially be tested at LHC.

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higgs vacuum stability & physics beyond the standard modelpacific-2014 moorea, sept 2014 a....

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