Higgs Vacuum Stability and Physics Beyond the Standard Model Archil Kobakhidze

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1 Higgs Vacuum Stability and Physics Beyond the Standard Model Archil Kobakhidze AK & A. Spencer-Smith, Phys Lett B 722 (2013) 130 [arxiv: ] AK & A. Spencer-Smith, JHEP 1308 (2013) 036 [arxiv: ]

2 Combined data: It is a Higgs boson, maybe even the Higgs boson 2

3 The Standard Model Higgs with m h = 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 0i EW EWh0 h 0i EW = v EW 246 GeV is a false (local) vacuum. The true vacuum state h0 h 0i M P GeV, and it carries large negative energy density ~ - (M P ) 4. How long does the electroweak vacuum live? 3

4 EW vacuum lifetime: flat spacetime estimate Electroweak Higgs doublet (in the unitary gauge): H = 0 h(x)/ p 2 V (0) H (h) = 8 h2 v EW 2 Effective (quantum-corrected) potential V (1 loop) H (h) = (h) 8 h 2 v EW 2, (h) = (µ)+ ln(h/µ) (4 ) 2 = 6yt y t (m t ) 1, (m h ) 0.13! < 0 4

5 EW vacuum lifetime: flat spacetime estimate AK & A. Spencer-Smith, arxiv: Instability scale (µ i )=0, µ i GeV 5

6 EW vacuum lifetime: flat spacetime estimate Large field limit: V H = ln(h/µ i ) 4 h = µ i e 1/4 h 4, = µ=µi Using Coleman s prescription, one can calculate that the decay of electroweak vacuum is dominated by small size Lee-Wick bounce solution, R 1/µ m /GeV, µ=µm =0 S LW = (µ m ), (µ m) P EW = e p 1, p =(µ m /H 0 ) 4 exp ( S LW ) << 1 Electroweak vacuum in the Standard Model is metastable! 6

7 EW vacuum in flat spacetime For m h < 126 GeV, stability up to the Planck mass is excluded at 98% C.L. J. Elias-Miro, et al, JHEP 1206 (2012) 031 [arxiv:126497] 7

8 EW vacuum in inflationary universe Electroweak vacuum decay may qualitatively differ in cosmological spacetimes: (i) Thermal activation of a decay process, T r <µ i (ii) Production of large amplitude Higgs perturbations during inflation, H inf <µ i [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 m e h >H inf Actually, the dominant decay processes are due to instantons, (Hawking-Moss, or more generic CdL) [AK & A. Spencer-Smith, Phys Lett B 722 (2013) 130 [arxiv: ]] V (h, )=V H (h)+v inf ( )+V H inf V inf ( )=V inf + V ( 0 inf)+1/2v 00 ( inf) = M 2 P 2 V 0 V inf 2 << 1, 1 << = M 2 P V 00 V inf << 1 8

9 EW vacuum in inflationary universe Fixed background approximation: = inf, ds 2 = d ( )d 3, ( )=H 1 inf sin(h inf ), = t 2 + r 2, 2 [0, /H inf ], H 2 inf = V inf /3M 2 P EoM for Higgs field: ḧ +3H inf cot(h inf ḣ(0) = ḣ( /H inf) =0 h L (x )=h R (x ) )ḣ ( 9

10 EW vacuum in inflationary universe =0,h(x) =h, 8 2 p exp 3 V H (h )+V H inf ( inf,h ) H 4 inf V H inf ( inf,h ) << V(h ) For, HM transition generates a fast decay of the electroweak vacuum, unless H inf < 10 9 (10 12 )GeV m h = 126 GeV, m t = 174(172) GeV n s < 1 Together with, this implies that only small-field inflationary models are allowed with a negligible tensor/scalar:, r<10 11 (10 5 ) 10

11 EW vacuum in inflationary universe Consider, V H inf = 2 h2 2 ( >0), m e h = 1/2 inf >H inf [O. Lebedev & A. Westphal Phys.Lett. B719 (2013) 415] [similar consideration applies ] 2 R2 h 2 h =( / ) 1/2 inf >µ i, ( (h ) < 0) Large-field chaotic inflation, with Naturalness constraint: Tuning is needed! Vinf =1/2m 2 2, m = 10 5 M P >1.4 p (H inf / inf ) 2 > <64 2 (m /m h )

12 EW vacuum in inflationary universe h(x) = In the limit 8 >< >: m e h 8h R 8+ x h >> H inf h 00 +3h 0 ( [x = m e h ] h R h 2 x 2 1, 0 apple x<x x(j 1 (ix )+iy 1 ( ix )) (J 1(ix)+iY 1 ( ix)), x <x<1, B CdL = 2 2 I<0, I = Z 1 0 x 3 dx apple h 2 (x) 1 x = 2p 2h h R h 2 (x) 2h 2 1/2 hr 1. h < 0, (µ >µ i ) < 0. p _ exp{ B CdL } >> 1 EW vacuum is unstable! 12

13 EW vacuum in inflationary universe Fast decay of EW ceases inflation globally (no eternal inflation) e 3H inf e ( H inf ) 4 p stop (3/p) 1/3 H 1 inf < 1.4H 1 inf The above considerations applies to models with curvaton Conclusions: For the unperturbed SM potential the condition of vacuum metastability rules out all large scale models. All models with sizeable Higgs-inflaton interactions are ruled out. Observation of tensor perturbations in the CMB by the Planck satellite would provide a strong indication of new physics beyond the Standard Model. 13

14 Neutrino masses and vacuum stability AK & A. Spencer-Smith, JHEP 1308 (2013) 036 [arxiv: ] (1) = y 4 t g g2 1 + g g 2 2 3g y 2 t 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. 14

15 Neutrino masses and vacuum stability AK & A. Spencer-Smith, JHEP 1308 (2013) 036 [arxiv: ] 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 III see-saw: additional electroweak-triplet scalar Left-right symmetric models: additional gauge bosons, scalars and fermions 15

16 Type II see-saw models and vacuum stability Scalar potential: (tr( )) 2 tr( V (, ) = m 2 + ( ) 2 + m 2 tr( ) (tr( )) 2 ) 2 apple + 4 ( )tr( ) + 5 [ 6, ] + p T i 2 +h.c.. 2 Neutrino masses: 1 p 2 (y ) fg l Tf L Ci 2 l g L + h.c. 16

17 Type II see-saw models and vacuum stability 17

18 Type II see-saw models and vacuum stability 18

19 Alternating LR-symmetric model with universal seesaw for all fermion masses Scalar sector: L 2 (1, 1, 2, 1/2), R 2 (1, 2, 1, 1/2). V ( L, R) = m 2 L L + R R + 2 L L + R R 2 + L L R R. New fermions: N L,N R 2 (1, 1, 1, 0), E L,E R 2 (1, 1, 1, 1), U il,u ir 2 (3, 1, 1, 2/3), D il,d ir 2 (3, 1, 1, 1/3), 19

20 Alternating LR-symmetric model with universal seesaw for all fermion masses 20

21 Conclusions: Electroweak vacuum (in)stability may already provide a hint for physics beyond the Standard Model Interesting interplay with cosmological inflation: observation of gravitational waves will provide a strong hint for a new physics that is responsible for the stabilization of the vacuum The most promising models of neutrino masses in this regard are: type II see-saw and LR models. They may potentially tested at the LHC 21