Higgs Vacuum Stability & Physics Beyond the Standard Model
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1 Higgs Vacuum Stability & 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: ] AK & A. Spencer-Smith, arxiv: PASIFIC 2014 A UCLA Symposium on Particle Astrophysics and Cosmology Including Fundamental InteraCtions September 15-20, 2014, Moorea, French Polynesia
2 Combined data: It is a Higgs boson, maybe even the Higgs boson 2
3 The SM Higgs with M H =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 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: effective Higgs potential! Electroweak Higgs doublet (in the unitary gauge): V (0) H (h) = 8 h2 v EW 2 H = 0 h(x)/ p 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: RG extrapolation of SM parameters! Previous calculations: F. Bezrukov, M. Y..Kalmykov, B. A. Kniehl and M. Shaposhnikov, JHEP 1210, 140 (2012) [arxiv: [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: [hep-ph]]; D. Buttazzo, G. Degrassi, P. P. Giardino, G. F. Giudice, F. Sala, A. Salvio and A. Strumia, JHEP 1312, 089 (2013) [arxiv: ]. 3-loop RGE s in mass-independent MSbar scheme; full 2- loop matching condition! Our calculations: AK & A. Spencer-Smith, arxiv: ; A. Spencer-Smith, arxiv: loop RGE in mass-dependent scheme, 2 and 3 loop RGE s in MSbar + corresponding matching condition 5
6 EW vacuum lifetime: RG running of λ in a massdependent scheme Instability scale: µi [ (µ i ) = 0] log ± 0.65 Mt ± 0.19 Mh ± ± 0.02 th GeV 6
7 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 7
8 EW vacuum in flat spacetime: stability bound Stability bound: M t < ± ± 0.13 Mh ± 0.06 th GeV M exp t = ± ± 0.3 QCD GeV Absolute stability of the electroweak vacuum is excluded now at 99.98% CL [AK & A. Spencer-Smith, arxiv: , A. Spencer-Smith, arxiv: ] 8
9 EW vacuum in an 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 CdL-type) [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 9
10 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 ( 10
11 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 dominates p = N 4 e exp 2 2e µ 4 i H 4 inf 11
12 EW vacuum in inflationary universe 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! Together with n s < 1, this implies that only small-field inflationary models are allowed with a negligible tensor/scalar: r<10 11 (10 5 )! This seems now is excluded by the BICEP2 results: r, =
13 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) Vinf =1/2m 2 2, m = 10 5 M P! Large-field chaotic inflation, with 10 6 > >1.4 p (H inf / inf ) 2 > ! Naturalness constraint: Tuning is needed! <64 2 (m /m h )
14 EW vacuum in inflationary universe h(x) =! In the limit 8 >< >: m e h h 00 +3h 0 8h R 8+ x h >> H inf ( [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! 14
15 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 A 0 s = s A 2 s + g2 (X)H 2 inf 8 2 M 2 P, r 0 = g 2 (X) In light of BICEP2 the electroweak vacuum within the Standard Model is unstable! New physics must enter at energies < 10 9 GeV. 15
16 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. 16
17 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 II see-saw: additional electroweak-triplet scalar! Left-right symmetric models: additional gauge bosons, scalars and fermions 17
18 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. 18
19 Type II see-saw models and vacuum stability Stability conditions: Avoiding tachyonic instabilities: Tree level matching condition: 19
20 Type II see-saw models and vacuum stability 20
21 Type II see-saw models and vacuum stability 21
22 Alternating LR-symmetric model with universal seesaw for all fermion masses Scalar sector: SU(2) L SU(2) R U(1) B L 2 (1, 1, 2, 1/2), R 2 (1, 2, 1, 1/2). V ( L, R) = m 2 L L + R R L + 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), 22
23 Alternating LR-symmetric model with universal seesaw for all fermion masses Tree-level matching: One-loop matching: 23
24 Alternating LR-symmetric model with universal seesaw for all fermion masses 24
25 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 < 10 9 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
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