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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 ,
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney) 3
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney)
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
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney)
EW vacuum lifetime: RG running of λ in a mass- dependent scheme Instability scale:
6
[�(µi) = 0] log10
⇣ µiGeV
⌘⇡ 9.19± 0.65Mt ± 0.19Mh ± 0.13↵3 ± 0.02th
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney)
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,
7
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)
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney)
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
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney)
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]]
9
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
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney)
EW vacuum in inflationary universe ! Fixed background approximation:
! EoM for Higgs field:
10
� = �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
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney)
EW vacuum in inflationary universe ! Hawking-Moss instanton:
! For ,
HM transition dominates
11
@V
@h
= 0 , h(x) = h⇤,
VH�inf(�inf , h⇤)
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney)
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:
,
12
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
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney)
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!
13
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 .
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney)
EW vacuum in inflationary universe
! In the limit
EW vacuum is unstable!
14
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
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney)
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.
15
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)
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney)
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.
16
�(1)� = 24�2 � 6y4t +
3
4g42 +
3
8
�g21 + g
22
�2+ �
��9g22 � 3g21 + 12y2t
�
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney)
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
17
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney)
Type II see-saw models and vacuum stability Scalar potential:
Neutrino masses:
18
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.
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney)
Type II see-saw models and vacuum stability Stability conditions:
Avoiding tachyonic instabilities:
Tree level matching condition:
19
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney)
Type II see-saw models and vacuum stability
20
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney)
Type II see-saw models and vacuum stability
21
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney)
Alternating LR-symmetric model with universal see- saw for all fermion masses Scalar sector: New fermions:
22
�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
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney)
Alternating LR-symmetric model with universal see- saw for all fermion masses Tree-level matching: One-loop matching:
23
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney)
Alternating LR-symmetric model with universal see- saw for all fermion masses
24
PACIFIC-2014 Moorea, Sept 2014
A. Kobakhidze (U. of Sydney)
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.
25