Leptogenesis via Higgs Condensate Relaxation

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1 The Motivation Quantum Fluctuations Higgs Relaxation Leptogenesis Summary Leptogenesis via Higgs Condensate Relaxation Louis Yang Department of Physics and Astronomy University of California, Los Angeles TASC 2015 November 14th, 2015 Collaborator: Alexander Kusenko and Lauren Pearce Leptogenesis via Higgs Condensate Relaxation (slide 1) TASC 2015

The Motivation Quantum Fluctuations Higgs Relaxation Leptogenesis Summary The Motivation The recent discovery of the Higgs boson with mass M h = 125.7 ± 0.

2 The Motivation Quantum Fluctuations Higgs Relaxation Leptogenesis Summary The Motivation The recent discovery of the Higgs boson with mass M h = ± 0.4 GeV [Particle Data Group 2014] The Higgs potential V (φ) = 1 2 m2 φ λφ4 Very small or negative quartic coupling λ at high scale when consider renormalization group equation (RGE) a meta-stable electroweak vacuum Higgs potential is very shallow at high scale Scalar fields with shallow potentials can obtain large vacuum expectation values (VEVs) during inflation. Post-inflationary Higgs field relaxation possibility to account for the matter-antimatter asymmetry of the Universe. [Dario Buttazzo et al. JHEP 1312 (2013) 089] Leptogenesis via Higgs Condensate Relaxation (slide 2) TASC 2015

3 The Motivation Quantum Fluctuations Higgs Relaxation Leptogenesis Summary Quantum Fluctuations during Inflation During de Sitter expansion, a scalar field can jump quantum mechanically to a nonzero field value due to quantum fluctuation. The field can also roll down classically toward its equilibrium minimum. φ + 3H φ dv (φ) = dφ Classical relaxation time: τ roll 1 [ d 2 ] 1/2 V (φ) = m eff dφ 2 If τ roll H 1 I the Hubble time scale, insufficient time for the field to roll down. Develop a large field value φ 0 during inflation. The VEV is such that V H (φ 0 ) H 4 I For the Higgs field, it obtains a VEV φ 0 λ 1/4 H I V(ϕ) ϕ min Quantum Jump Roll Down Classically ϕ Leptogenesis via Higgs Condensate Relaxation (slide 3) TASC 2015

4 The Motivation Quantum Fluctuations Higgs Relaxation Leptogenesis Summary Relaxation of the Higgs Condensate during Reheating As inflation ends, the Higgs field is no longer frozen. The generated Higgs VEV then rolls down and oscillates around φ = 0 with decreasing amplitude within τ roll H 1. Φ t Φ Φ I GeV I 10 3 GeV T max GeV Λ eff Φ GeV H I GeV T Λ Φ 0 t End of Inflation at t 0 Leptogenesis via Higgs Condensate Relaxation (slide 4) TASC 2015

5 The Motivation Quantum Fluctuations Higgs Relaxation Leptogenesis Summary Leptogenesis The relaxation of the Higgs condensate across the entire Universe after inflation can leads to many interesting physics. One possibility is to explain the matter-antimatter asymmetry (Baryogenesis or Leptogenesis). A. Kusenko, L. Pearce, L. Yang, Phys. Rev. Lett. 114 (2015) 6, L. Pearce, L. Yang, A. Kusenko, M. Peloso, Phys. Rev. D 92 (2015) 2, L. Yang, L. Pearce, A. Kusenko, Phys. Rev. D 92 (2015) Sakharov conditions for Baryogenesis/Leptogenesis: Out of thermal equilibrium: Time-dependent Higgs VEV CP-violation: Higher dimensional operators,... Baryon/Lepton number violation: Right-handed Majorana neutrinos Leptogenesis via Higgs Condensate Relaxation (slide 5) TASC 2015

6 The Motivation Quantum Fluctuations Higgs Relaxation Leptogenesis Summary Effective Chemical Potential In the early Universe, the Higgs field might be sensitive to higher dimensional operator L 6 = 1 ( µφ 2) j µ Λ 2 B+L 1 ( tφ 2) j n Λ 2 B+L 0 n where Λ n could be temperature T or the mass scale of M n. It can be generated from loops of heavy fermions or thermal loops with the electroweak anomaly equation. As the Higgs VEV rolls down, this lowers the energy of particle and raises the energy of antiparticle. Effective chemical potential to leptons µ eff = 1 0φ 2 Λ 2 n V(ϕ) Higgs VEV Rolls Down Reheating Leads to l, q l, q ϕ Leptogenesis via Higgs Condensate Relaxation (slide 6) TASC 2015

7 The Motivation Quantum Fluctuations Higgs Relaxation Leptogenesis Summary Lepton Number Violation Processes Another ingredient: Right-handed neutrino with Majorana mass M R Lepton-number-violating processes: ν Lh 0 ν Lh 0 ν Lν L h 0 h 0 & ν Lν L h 0 h 0 h 0 h 0 h 0 h 0 ν L N R N c R ν c l ν L N R N c R ν c l ν L h 0 ν c L h 0 N R N c R N R N c R ν l h 0 ν c l h 0 Leptogenesis via Higgs Condensate Relaxation (slide 7) TASC 2015

8 The Motivation Quantum Fluctuations Higgs Relaxation Leptogenesis Summary Boltzmann Transport Equation If the system is in equilibrium, the lepton asymmetry will reach a value n L,eq = 2 π 2 µ efft 2. However, the interaction is not fast enough for the system to reach equilibrium asymmetry. One describes this by the Boltzmann transport equation d d n L + 3Hn L 2 = π 2 T 3 σ R (n L + 2π ) 2 µ efft 2 where n L is the lepton asymmetry. Leptogenesis via Higgs Condensate Relaxation (slide 8) TASC 2015

9 The Motivation Quantum Fluctuations Higgs Relaxation Leptogenesis Summary Resulting Lepton Asymmetry log Η T Tmax First Φ crossing Μ eff T 2 Μ eff M n 2 Radiation Domination log t GeV 1 Example: Λ I = GeV, Γ I = 10 8 GeV, and T max = GeV For the blue curve, M n = GeV. The final asymmetry η = 45 2π 2 g n L T is enough to account for the asymmetry we observe today. Leptogenesis via Higgs Condensate Relaxation (slide 9) TASC 2015

10 The Motivation Quantum Fluctuations Higgs Relaxation Leptogenesis Summary Summary During inflation, the Higgs field can obtain a large VEV through quantum fluctuation. The relaxation of the Higgs condensate after inflation could create an effective chemical potential for lepton number. In the present of of lepton-number-violating processes due to right-handed neutrino, this produces sufficient lepton number to explain the asymmetry we observe today. Most importantly, the relaxation of Higgs condensate can lead to interesting phenomena. Thank you for your listening! Leptogenesis via Higgs Condensate Relaxation (slide 10) TASC 2015

11 The Higgs Field φ Mh Mt Mh Mt sign V log V GeV Electroweak Vacuum log Φ GeV Planck scale vacuum In our model, we consider the case that the second minimum is not below our electroweak minimum. Note m GeV 2. So when φ 10 2 GeV, the potential is well approximated by V H (φ) = 1 4 λ effφ 4. The λ eff around Planck scale can be approximated by the form λ eff (φ) λ min + α ln (φ/φ 0) 2. An example of the set of parameters is: λ min = , φ 0 = GeV, and α = Leptogenesis via Higgs Condensate Relaxation (slide 11) TASC 2015

12 Inflation The Universe appears to be almost homogeneous and isotropic today Inflation In the early universe, the energy density was dominated by vacuum energy. Inflation from a real scalar field: Inflaton I (x) L I = 1 2 gµν µi νi V I (I) The equation of motion is Ï+3HI+Γ II+ dv I (I) = 0, with H 2 di ( ) 2 ȧ = 8π (ρ a 3m 2 I + ρ other ) pl where we assume a uniform field configuration and a FRW spacetime ds 2 = dt 2 a (t) 2 ( dr 2 + r 2 dω 2). Leptogenesis via Higgs Condensate Relaxation (slide 12) TASC 2015

13 The Brief History of the Early Universe 1 Slow-roll (inflation) regime: Ï dv di Γ I is not active. and I 2 V. 3HI = dv di, and H2 8π = 3m 2 V I (I) pl V(I) Slow-Roll Inflaton acts like vacuum energy. a(t) e Ht Coherent Oscillations 2 Coherent oscillations regime: a (t) (t t i ) 2/3 Inflaton acts like non-relativistic particle. The Universe is matter-dominated. Inflaton then decays into relativistic particles ρ R. Tmax ΡI Λ I I Radiation- Dominated ρ I + 3Hρ I + Γ I ρ I = 0 ρ I (t) = Λ4 I a (t) 3 e Γ I t TRH Coherent Oscillations (matter like) ΡR log t End of Inflation t ' t 1 I 3 Radiation-dominated regime: a (t) (t t i ) 1/2 At t = 1/Γ I, most of the inflatons decay into ρ R, Leptogenesis via Higgs and Condensate the reheating Relaxation is complete. (slide 13) TASC 2015

14 The Hawking-Moss Tunneling If V (φ f ) V (φ i ) V (φ i ), we have S E (φ i) S E (φ f ) = 3m4 pl 8 The transition rate is then ( Γ V exp 3m4 pl 8 [ 1 V (φ 1 ] i) V (φ f ) 3m4 pl 8 ) V (φ f ) V (φ i) V (φ i) 2 Thus, the transition is not suppressed as long as V (φ f ) V (φ i) < 8 V (φ i) 2 3m 4 pl V (φ f ) V (φ i) V (φ i) 2 Leptogenesis via Higgs Condensate Relaxation (slide 14) TASC 2015

15 Isocurvature perturbations One issue for applying to Leptogenesis φ 0 = φ 2 is the average over several Hubble volumes. Each Hubble volume has different initial φ 0 value. When inflation end, each patch of the observable universe began with different value of φ 0. If L 0 φ 2 Different asymmetry in each Hubble volume Large isocurvature perturbations, which are constrained by current CMB observation. [Figure from Lauren Pearce] Leptogenesis via Higgs Condensate Relaxation (slide 15) TASC 2015

16 Isocurvature perturbations One issue for applying to Leptogenesis φ 0 = φ 2 is the average over several Hubble volumes. Each Hubble volume has different initial φ 0 value. When inflation end, each patch of the observable universe began with different value of φ 0. If L 0 φ 2 Different asymmetry in each Hubble volume Large isocurvature perturbations, which are constrained by current CMB observation. [Figure from Lauren Pearce] Leptogenesis via Higgs Condensate Relaxation (slide 15) TASC 2015

17 Isocurvature perturbations One issue for applying to Leptogenesis φ 0 = φ 2 is the average over several Hubble volumes. Each Hubble volume has different initial φ 0 value. When inflation end, each patch of the observable universe began with different value of φ 0. If L 0 φ 2 Different asymmetry in each Hubble volume Large isocurvature perturbations, which are constrained by current CMB observation. φ 0 φ 0 φ 0 [Figure from Lauren Pearce] Leptogenesis via Higgs Condensate Relaxation (slide 15) TASC 2015

18 Isocurvature perturbations One issue for applying to Leptogenesis φ 0 = φ 2 is the average over several Hubble volumes. Each Hubble volume has different initial φ 0 value. When inflation end, each patch of the observable universe began with different value of φ 0. If L 0 φ 2 Different asymmetry in each Hubble volume Large isocurvature perturbations, which are constrained by current CMB observation. [Figure from Lauren Pearce] Leptogenesis via Higgs Condensate Relaxation (slide 15) TASC 2015

19 Solutions to the isocurvature perturbation issue Solutions: 1 IC-1: Second Minimum at Large VEVs (φ v EW ) E.g. V(ϕ) L lift = φ10 Λ 6 lift Second Min. ϕ 2 IC-2: Inflaton-Higgs coupling E.g. V(ϕ) L ΦI = 1 2 M I 2n 2n 2 φ2 Very Steep Potential due to Inflaton ϕ Leptogenesis via Higgs Condensate Relaxation (slide 16) TASC 2015

20 IC-1: Second minimum at large VEV Motivations: 1 At large VEVs, Higgs potential is sensitive to higher-dimensional operators. L lift = φ10 Λ 6 lift 2 There seems to be a planckian minimum below our electroweak (EW) vacuum. Our EW vacuum is not stable. 3 A higher-dimensional operator can lift the possible planckian minimum and stablize our EW vacuum. The second minimum becomes metastable and higher than the EW vacuum. Leptogenesis via Higgs Condensate Relaxation (slide 17) TASC 2015

21 IC-1: Second minimum at large VEV The scenario: 1 Large VEV at early stage of inflation 2 The initial Higgs VEV is trapped in this second minimum (quasi-stable vacuum) at the end of inflation. 3 Reheating destablize the quasi-stable vacuum. 4 Higgs field rolls down from the second minimum. V(ϕ) H 4 Early stage of inflation Second Min. ϕ Leptogenesis via Higgs Condensate Relaxation (slide 18) TASC 2015

22 IC-1: Second minimum at large VEV The scenario: V(ϕ) 1 Large VEV at early stage of inflation 2 The initial Higgs VEV is trapped in this second minimum (quasi-stable vacuum) at the end of inflation. 3 Reheating destablize the quasi-stable vacuum. 4 Higgs field rolls down from the second minimum. H 4 Trapped Second Min. ϕ Leptogenesis via Higgs Condensate Relaxation (slide 18) TASC 2015

23 IC-1: Second minimum at large VEV The scenario: 1 Large VEV at early stage of inflation 2 The initial Higgs VEV is trapped in this second minimum (quasi-stable vacuum) at the end of inflation. 3 Reheating destablize the quasi-stable vacuum. 4 Higgs field rolls down from the second minimum. V(ϕ) Reheating Thermal correction ϕ Leptogenesis via Higgs Condensate Relaxation (slide 18) TASC 2015

24 IC-1: Second minimum at large VEV The scenario: 1 Large VEV at early stage of inflation 2 The initial Higgs VEV is trapped in this second minimum (quasi-stable vacuum) at the end of inflation. 3 Reheating destablize the quasi-stable vacuum. 4 Higgs field rolls down from the second minimum. V(ϕ) Higgs VEV Rolls Down Reheating ϕ Leptogenesis via Higgs Condensate Relaxation (slide 18) TASC 2015

25 IC-1: Second minimum at large VEV < IC1 > Λ I = GeV Γ I = 10 9 GeV ϕ 0 = GeV ϕ/ϕ T(t) ϕ 0 t Leptogenesis via Higgs Condensate Relaxation (slide 19) TASC 2015

26 IC-2: Inflaton-Higgs coupling Introduce coupling between the Higgs and inflaton field. E.g. I 2n L ΦI = 1 2 M 2n 2 φ2. Motivations: This could be obtained by integrating out heavy states in loops. Induces an large effective mass m eff,φ ( I ) = I n /M n 1 for the Higgs field when I is large. If m eff,φ ( I ) H in the early stage of inflation, the slow roll condition is not satisfied. Leptogenesis via Higgs Condensate Relaxation (slide 20) TASC 2015

27 IC-2: Inflaton-Higgs coupling 1 In the early stage of inflation, I is large. Higgs potential is steep. Slow-roll condition is not satisfied. The Higgs VEV stay at φ = 0. 2 At the last N last e-folds of inflation, I, m eff,φ ( I ) < H I, Higgs VEV starts to develop. 3 At the end of inflation, the Higgs field has obtained a VEV φ 0 = φ 2 = H I Nlast. 2π V(ϕ) φ 2 ~0 Quantum jumps Rolls down classically Early stage of inflation H 4 ϕ 4 The Higgs VEV then rolls down from φ 0. Leptogenesis via Higgs Condensate Relaxation (slide 21) TASC 2015

28 IC-2: Inflaton-Higgs coupling 1 In the early stage of inflation, I is large. Higgs potential is steep. Slow-roll condition is not satisfied. The Higgs VEV stay at φ = 0. 2 At the last N last e-folds of inflation, I, m eff,φ ( I ) < H I, Higgs VEV starts to develop. 3 At the end of inflation, the Higgs field has obtained a VEV φ 0 = φ 2 = H I Nlast. 2π V(ϕ) Last N e-folds of inflation H 4 ϕ φ 2 starts to grow 4 The Higgs VEV then rolls down from φ 0. Leptogenesis via Higgs Condensate Relaxation (slide 21) TASC 2015

29 IC-2: Inflaton-Higgs coupling 1 In the early stage of inflation, I is large. Higgs potential is steep. Slow-roll condition is not satisfied. The Higgs VEV stay at φ = 0. 2 At the last N last e-folds of inflation, I, m eff,φ ( I ) < H I, Higgs VEV starts to develop. 3 At the end of inflation, the Higgs field has obtained a VEV φ 0 = φ 2 = H I Nlast. 2π 4 The Higgs VEV then rolls down from φ 0. V(ϕ) φ 2 = H I 2 N/4π 2 End of inflation ϕ Leptogenesis via Higgs Condensate Relaxation (slide 21) TASC 2015

30 IC-2: Inflaton-Higgs coupling 1 In the early stage of inflation, I is large. Higgs potential is steep. Slow-roll condition is not satisfied. The Higgs VEV stay at φ = 0. 2 At the last N last e-folds of inflation, I, m eff,φ ( I ) < H I, Higgs VEV starts to develop. 3 At the end of inflation, the Higgs field has obtained a VEV φ 0 = φ 2 = H I Nlast. 2π 4 The Higgs VEV then rolls down from φ 0. V(ϕ) After inflation Rolls down classically ϕ Leptogenesis via Higgs Condensate Relaxation (slide 21) TASC 2015

31 IC-2: Inflaton-Higgs coupling For N last = 5 8, the isocurvature perturbation only develops on the small angular scales which are not yet constrained. ϕ/ϕ < IC2 > Λ I = GeV Γ I = 10 8 GeV N last = 8 ϕ 0 = GeV ϕ 0 t Leptogenesis via Higgs Condensate Relaxation (slide 22) TASC 2015

32 Relaxation of the Higgs field after inflation During the oscillation of the Higgs field, the Higgs condensate can decay into several product particles: Non-perturbative decay: W and Z bonsons Φ0 WT k 0,Τ log n k Λ I = GeV and Γ I = 10 9 GeV for IC-1 Perturbative decay (thermalization): top quark. Those decay channels do affect the oscillation of the Higgs field but they becomes important only after several oscillations. Leptogenesis via Higgs Condensate Relaxation (slide 23) TASC 2015

33 Perturbative decay (thermalization) to top quark Thermalization rate is comparable to the Hubble parameter only after the maximum reheating has been reached H(t) H(t) GeV t GeV 1 H(t) vs Γ H(t) through top quark for IC-1, with the parameters Λ I = GeV and Γ I = 10 9 GeV. The vertical lines: the first time the Higgs VEV crosses zero, and the time of maximum reheating, from left to right. Leptogenesis via Higgs Condensate Relaxation (slide 24) TASC 2015

Evolution of Scalar Fields in the Early Universe

Evolution of Scalar Fields in the Early Universe Louis Yang Department of Physics and Astronomy University of California, Los Angeles PACIFIC 2015 September 17th, 2015 Advisor: Alexander Kusenko Collaborator: