POST-INFLATIONARY HIGGS RELAXATION AND THE ORIGIN OF MATTER- ANTIMATTER ASYMMETRY

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1 POST-INFLATIONARY HIGGS RELAXATION AND THE ORIGIN OF MATTER- ANTIMATTER ASYMMETRY LOUIS YANG ( 楊智軒 ) UNIVERSITY OF CALIFORNIA, LOS ANGELES (UCLA) DEC 30, TH INTERNATIONAL WORKSHOP ON DARK MATTER, DARK ENERGY AND MATTER-ANTIMATTER ASYMMETRY

2 OUTLINE The Higgs Potential Quantum Fluctuation During Inflation Higgs Relaxation After Inflation Leptogenesis via Higgs Field Relaxation Summary Based on: A. Kusenko, L. Pearce, LY, Phys.Rev.Lett. 114 (2015) 6, L. Pearce, LY, A. Kusenko, M. Peloso, Phys.Rev. D92 (2015) 2, LY, L. Pearce, A. Kusenko, Phys.Rev. D92 (2015)

3 THE HIGGS POTENTIAL 3

4 THE HIGGS BOSON In 2012, LHC has found the Higgs boson. V Φ = m 2 Φ + Φ + λ Φ + Φ, where Φ = v + h. Higgs boson mass: M h = ± ± GeV. A mass smaller than expected! A small quartic coupling λ μ = M t M h 2 2v V(φ) v h Electroweak Vacuum φ C. Patrignani et al.(particle Data Group), Chin. Phys. C, 40, (2016). 4

RUNNING OF λ J. Elias-Miro et al., Phys. Lett. B709, 222 (2012) G. Degrassi et al., JHEP 1208, 098 (2012) D. Buttazzo et al., arxiv:1307.

5 RUNNING OF λ J. Elias-Miro et al., Phys. Lett. B709, 222 (2012) G. Degrassi et al., JHEP 1208, 098 (2012) D. Buttazzo et al., arxiv: [hep-ph] QFT: Coupling constants changes with energy scale μ β λ = y t 4 + Due to large top mass m t = 1 2 y tv If no new physics, λ h becomes very small and turns negative at μ GeV. Figure from D. Buttazzo et al., arxiv: [hep-ph] 5

6 THE HIGGS EFFECTIVE POTENTIAL Another minimum in the potential: Planckain vacuum!! Much lower than the electroweak vacuum. Our universe can tunnel into the Planckain vacuum and end in a big crunch! ssss V lll V φ Planckian Vacuum h lll φ Our Electroweak Vacuum ~ GeV h 6

, JHEP 1208, 098 (2012) D. Buttazzo et al., arxiv:1307.

7 META-STABILITY OF OUR VACUUM J. Elias-Miro et al., Phys. Lett. B709, 222 (2012) G. Degrassi et al., JHEP 1208, 098 (2012) D. Buttazzo et al., arxiv: [hep-ph] Our universe seems to be right on the meta-stable region. 7

8 THE HIGGS EFFECTIVE POTENTIAL What does it imply? A shallow Higgs potential at large scale A large Higgs VEV during inflation ssss V lll V φ Planckian Vacuum h lll φ Our Electroweak Vacuum ~ GeV 8

9 QUANTUM FLUCTUATION DURING INFLATION 9

10 QUANTUM FLUCTUATION DURING INFLATION During inflation, quantum fluctuations get amplified. They becomes classical when the wavelength exits the horizon. φ(t) jumps randomly like Brownian motion. Horizon Horizon φ(x) Quantum fluctuation Inflation φ 0 0 Becomes classical 10

11 QUANTUM FLUCTUATION DURING INFLATION Quantum fluctuation brings the field to non-zero value. Classical rolling down follows φ + 3H I φ = V φ, which requires t rrr ~ d2 V φ dφ = 1 m φ If m φ H I, insufficient time to relax (slow-rolling). A non-zero VEV of the scalar field is building up. V(ϕ) ϕ min Quantum Jump Bunch, Davies (1978); Linde (1982); Hawking, Moss (1982); Starobinsky (1982); Vilenkin, Ford (1982); Starobinsky, Yokoyama (1994). Can t Roll Down Classically ϕ 11

12 LARGE INITIAL VEV OF SCALAR FIELDS A. A. Starobinsky (1982) A. Vilenkin (1982) Fokker-Planck equation: P c φ,t = j c where j c = P c φ, t : probability distribution of φ H 3 P c 8π 2 + P c H Massless scalar, the field undergoes random walks φ 0 φ 2 H I t = H I 22 Massive case V φ = 1 2 m2 φ 2 : φ 0 3 H I 8π 2 m For V(φ) = λ 4 φ4 : φ H I /λ 1/4 In general, V φ 0 ~ H I 4 dd dd N, N: number of e-folds 2 12

13 LARGE HIGGS VEV DURING INFLATION Higgs has a shallow potential at large scale (small λ). Large Higgs vacuum expectation value (VEV) during inflation. For inflationary scale Λ I = GeV, the Hubble rate Λ I 2 H I = ~10 11 GeV, and λ~0. 00, the Higgs VEV after 3M pp inflation is φ H I /λ 1/4 ~ GeV. For such a large VEV, the Higgs field can be sensitive to higher dimensional operators. 13

14 HIGGS FIELD RELAXATION 14

15 POST-INFLATIONARY HIGGS RELAXATION As the inflation end, the H drops. When H < m φ,eff, the Higgs field can relax classically φ t + 33 t φ t + V eff φ, T t = 0 φ V eff (φ, T) is the finite temperature effective potential. Higgs field oscillates with decreasing amplitude due to the Hubble friction. Relaxation time /3 1 t rrr = t RR if thermal mass dominates V a T T RR t α RR 2 T 2 T 2 φ 2 t rrr = 6. 99/ λφ 0 if the zero T dominates V λφ 4 /4 Typically during reheating or right after reheating. 15

16 POST-INFLATIONARY HIGGS RELAXATION Thermal mass dominated Zero T potential dominated What can this do for us? Breaks time reversal symmetry, and provides the out of thermal equilibrium condition. An important epoch for the matter-antimatter asymmetry! 16

17 POST-INFLATIONARY HIGGS RELAXATION If the thermal mass dominates, V φ, T 1 2 α T 2 T 2 φ 2 where α T λ g g y t at μ = GeV. The equation of motion is approximately A solution: φ t + 2 t φ t + α T 2 T RR φ t = φ 0 Γ J 2 3 where β = T RR t RR and x = t/t RR. 2 t t RR 4α T β 3 φ t = 0 4 x3 1 α T β 2 3 x 17

18 LEPTOGENESIS VIA THE RELAXATION OF THE HIGGS FIELD 18

19 SAKHAROV CONDITIONS Andrei D. Sakharov (1967) Successfully Leptogenesis requires: 1. Deviation from thermal equilibrium Post-inflationary Higgs relaxation 2. C and CC violations CC phase in the quark sector (not enough), higher dimensional operator, 3. Lepton number violation Right-handed Majorana neutrino, others 19

20 EFFECTIVE OPERATOR M. E. Shaposhnikov (1987), M. E. Shaposhnikov (1988) Consider the effective operator: O 6 = 1 Λ n 2 φ2 g 2 WW g 2 BB, W and B: SS 2 L and U 1 Y gauge fields W : dual tensor of W Λ n : energy scale when the operator is relevant In standard model, integrating out a loop with all 6 quarks: But suppressed by small Yukawa and small CC phase 20

21 EFFECTIVE OPERATOR O 6 = 1 Λ n 2 φ2 g 2 WW g 2 BB Replace the SM fermions by heavy states that carry SS 2 charge. Scale: Λ n = M n mass (must not from the SM Higgs) or Λ n = T temperature 21

22 EFFECTIVE CHEMICAL POTENTIAL Dine et. al. (1991) Cohen, Kaplan, Nelson (1991) O 6 = 1 Λ n 2 φ2 g 2 WW g 2 BB Using electroweak anomaly equation, we have O 6 = 1 2 Λ φ 2 μ μ j B+L, n μ where j B+L is the B + L fermion current. Integration by part: O 6 = 1 Λ n 2 μ φ 2 μ j B+L Similar to the one use by spontaneous baryogenesis. Breaks CPT spontaneously while φ is changing! Sakharov conditions doesn t have to be satisfied explicitly in this form. 22

23 EFFECTIVE CHEMICAL POTENTIAL O 6 = 1 Λ n 2 μ φ 2 μ j B+L Effective chemical potential for baryon and lepton number: μ eff = 1 Λ n 2 t φ 2 Shifts the energy levels between fermions and anti-fermions while Higgs is rolling down (φ 0). V(ϕ) Scalar VEV Rolls Down Reheating Leads to l, q l, q ϕ 23

24 LEPTON NUMBER VIOLATION Last ingredient: Right-handed neutrino N R with Majorana mass term M R. The processes for ΔΔ = 2: ν L h 0 ν L h 0 ν L ν L h 0 h 0 ν L ν L h 0 h 0 For m ν ~0. 1 ev, σ R ~ Σ 2 im ν,i ~10 33 GeV v EE 24

25 EVOLUTION OF LEPTON ASYMMETRY LY, Pearce, Kusenko Phys. Rev. D92 (2015) Boltzman equation: n L + 33n L 2 π 2 T3 σ R n L 2 π 2 μ eeet 2 Λ I = GeV, Γ I = 10 8 GeV, T RR = GeV, and φ 0 = GeV. For μ eff M n 2 case, choose M n = GeV. Could be the origin of matter-antimatter asymmetry! 25

26 SUMMARY Our universe seems to be right on the meta-stable region. The quartic coupling of the Higgs potential turns negative giving a shallow potential. Higgs can obtain large vacuum expectation during inflation. The relaxation of the Higgs VEV happens during reheating. Higgs relaxation provides the out of thermal equilibrium condition and breaks T invariant. Leptogenesis via the Higgs relaxation is possible. Higgs relaxation is an important epoch in the early universe. Thanks for your listening! 26

POST-INFLATIONARY HIGGS RELAXATION AND THE ORIGIN OF MATTER- ANTIMATTER ASYMMETRY

POST-INFLATIONARY HIGGS RELAXATION AND THE ORIGIN OF MATTER- ANTIMATTER ASYMMETRY LOUIS YANG ( 楊智軒 ) UNIVERSITY OF CALIFORNIA, LOS ANGELES (UCLA) DEC 27, 2016 NATIONAL TSING HUA UNIVERSITY OUTLINE Big