Decay of the Higgs condensate after inflation

Transcription

1 Decay of the Higgs condensate after inflation Stanislav Rusak K. Enqvist, S. Nurmi Kosmologietag - May 9th

2 Outline Why Higgs decay? Higgs during inflation Decay of the Higgs after inflation Non-perturbative production of weak gauge bosons Role of non-abelian interactions Conclusions Introduction Overview 2 / 14

3 Why Higgs decay? Higgs: exists. Decay dynamics only depend on Standard Model couplings. Relevant for other models involving the Higgs (e.g. Higgs-modulated inflaton decay). Introduction Motivation 3 / 14

4 Higgs sector S = { 1 d 4 x 4 ηµα η νβ( ) FµνF a αβ a + G µν G αβ [ ]} +a 4 (D µ Φ) D µ Φ + λ(φ Φ) (Φ Φ) 2 4 Fµν a = µ A a ν ν A a µ + gɛ abc A b µa c ν, G µν = µ B ν ν B µ, D µ Φ = ( µ iga aµτ a i2 ) g B µ Φ Introduction Motivation 4 / 14

5 Higgs during inflation Higgs is a light spectator field during inflation. Stochastic formalism (Starobinsky & Yokoyama 94): h h 2 = 0.36λ 1/4 H Scale of inflation from BICEP: H GeV. Introduction Motivation 5 / 14

6 Stability of the vacuum Higgs effective potential V eff λ(h) 4 h4 Instability: for SM best fit parameters self-coupling λ < 0 at scale GeV. Λ SM best fit M t BF±1Σ M t BF±2Σ Energy scale GeV For top mass 2σ below best fit, stable up to inflationary scale. Effective potential exhibits a maximum V max near the instability scale. Inflationary perturbations must not push over the hill: H 4 < V max. K. Enqvist, T. Meriniemi, S. Nurmi 14 Introduction Vacuum stability 6 / 14

7 Stability of the vacuum Higgs effective potential V eff λ(h) 4 h4 V eff Instability: for SM best fit parameters self-coupling λ < 0 at scale GeV Energy scale GeV For top mass 2σ below best fit, stable up to inflationary scale. Effective potential exhibits a maximum V max near the instability scale. Inflationary perturbations must not push over the hill: H 4 < V max. K. Enqvist, T. Meriniemi, S. Nurmi 14 Introduction Vacuum stability 6 / 14

8 Higgs after inflation EOM: After a while solution: [ χ + λχ 2 ä ] χ = 0, χ = 1 a Φ a 2 χ = χ osc cn [ λχosc (τ τ osc ), ] 1. 2 The Higgs starts to oscillate and to decay. Dominant decay channel: non-perturbative production of weak gauge bosons W ± and Z. K. Enqvist, T. Meriniemi, S. Nurmi 13 Introduction After inflation 7 / 14

9 Non-perturbative decay Transverse modes of W and Z bosons obey the Lame equation ( g2 d2 AT 1 qw = 4λ T 2 2 A = 0 with + κ + q cn z, 2 +g 02 dz 2 2 qz = g 4λ q W SM Best fit q Z SM Best fit 1.5 Strength of resonance h * H GeVL Κ Solutions are resonantly amplified within specific bands. The running of the couplings will determine in which band resonance happens. For the Standard Model broad resonance regime q > q Non-perturbative decay Linear dynamics 8 / 14

10 Onset of non-abelian dynamics When do non-abelian interactions come into play? Hartree approximation : estimate non-abelian contribution as a vacuum expectation of the linear solutions g 2 η [ ] µν A b µa b ν A a i A b ia b µ A a ν b a Non-Abelian terms induce effectve masses for the gauge bosons: m 2 W = 2g2 λχ 2 osc 3π 2 m 2 Z = 4g2 λχ 2 osc cos θ W 3π 2 0 dκκ 2( X W 2 + cos θ 2 W X Z 2), 0 dκκ 2 X W 2, Non-perturbative decay Linear dynamics 9 / 14

11 Non-Abelian corrections The induced masses shut down the resonance Abelian n k Non Abelian n k n k := ω k 2 H [ A 2 ω 2 k + A 2 ] 1 2 Non-perturbative decay Non-linear dynamics 10 / 14

12 Onset of backreaction When will produced particles backreact on the Higgs dynamics? Weak gauge bosons induce an effective mass for the Higgs m 2 χ = g2 [ ] 2 W µ + W µ + (cos θ W ) 2 Z µ Z µ 4 (1) The initial effective mass of the higgs m 2 χ0 q 1 m 2 W,Z0. For broad resonance (q > 0) produced particles backreact on the Higgs before they significantly affect their own dynamics. m m osc 1000 m Wind m W0 100 m Zind m Z0 m Hind m osc z Non-perturbative decay Non-linear dynamics 11 / 14

13 Narrow resonance What about narrow resonance? Could be relevant if 1) physics beyond the Standard Model changes the running of couplings 2) the decaying field is something other than the Higgs In the narrow resonance regime the dynamics of the gauge fields are affected before the onset of backreaction on the Higgs. Non-Abelian corrections must be taken into account m m osc n k m ind m osc 10 Abelian n k 0.05 m 0 1 Non Abelian n k Non-perturbative decay Narrow resonance 12 / 14

14 Summary Higgs condensate is generated during inflation and decays mainly through non-perturbative production of the weak gauge bosons W ± and Z. Non-Abelian interactions induce effective masses for the fields which shut down particle production. In the broad resonance (SM) regime the non-abelian terms come into play after backreaction on the Higgs so the linear stage can be described by an Abelian model. For narrow resonance (beyond SM) non-abelian interactions affect already the linear stage and must be taken into account. Conclusions Summary 13 / 14

15 Outlook Beyond the Hartree approximation : lattice simulations needed for a detailed understanding of the system (in progress). Thermal effects: the buildup of a thermal bath resulting from the decay of the inflaton will will modify the dynamics: typically the effect is to shut down the resonance. Implications for other physics, e.g., generation of curvature perturbations from Higgs-modulated inflaton decay, Higgs inflation etc. Conclusions Outlook 14 / 14