Leptogenesis via the Relaxation of Higgs and other Scalar Fields

Transcription

1 Leptogenesis via the Relaxation of Higgs and other Scalar Fields Louis Yang Department of Physics and Astronomy University of California, Los Angeles PACIFIC 2016 September 13th, 2016 Collaborators: Alex Kusenko and Lauren Pearce Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 1) PACIFIC 2016

2 Outline 1 Leptogenesis via scalar field relaxation 2 Isocurvature perturbations 3 Cosmic Infrared Background fluctuation excess Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 2) PACIFIC 2016

3 Leptogenesis via scalar field relaxation Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 3) PACIFIC 2016

4 Matter-antimatter asymmetry Our universe contains most baryon but no anti-baryon η B = n B /n γ = Ω B h 2 = from both CMB observation and BBN. Sakharov s conditions for Baryogenesis 1 B violation 2 C and CP violations 3 Deviation from thermal equilibrium Standard Model do satisfy all the conditions but the CP phase is too small to generate enough asymmetry. (And, the Higgs mass is too heavy) Leptogenesis: Make L first. Then, Sphaleron process turns L into B Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 4) PACIFIC 2016

5 Standard Thermal Leptogenesis Fukugita and Yanagida (1986) SM + Right Handed Majorana neutrino N R RH Majorana neutrino Violates L CP -violating phases in the neutrino Yukawa couplings Out of equilibrium decay of RH neutrino Requirements: The heavy RH neutrino have to be in thermal bath: T > M R Neutrino mass m ν < 0.2 ev We will look at an interesting alternative which works for T < M R. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 5) PACIFIC 2016

6 Higgs potential ( ) 2 V (Φ) = m 2 Φ Φ + λ Φ Φ LHC has discovered the standard model Higgs boson with m h = ± 0.21 ± 0.11 GeV. λ is smaller than was expected. Due to quantum correction, the λ can be very small or even be negative at scale φ GeV. With such small λ, Higgs field can obtain large VEV during inflation. The relaxation of such large VEV after inflation can lead to interesting consequence in cosmology. Leptogenesis Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 6) PACIFIC 2016

7 Leptogenesis via Scalar Field Relaxation Basic Ingredients: 1 Large initial VEV of a scalar field φ 0 = φ 2 2 Relaxation of the scalar field 3 Coupling between L current and derivative of φ O ( t φ 2) j 0 L 4 L-violating process V(ϕ) Scalar VEV Rolls Down Reheating Leads to l, q l, q ϕ Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 7) PACIFIC 2016

8 1. Quantum Fluctuations during Inflation During inflation, scalar fields can obtain vacuum expectation values (VEVs) through quantum fluctuation. The field can also roll down classically toward its equilibrium minimum φ + 3H φ dv (φ) = dφ with relaxation time scale [ d 2 ] 1/2 V (φ) τ roll dφ 2 = 1 m eff If m eff H I, there is insufficient time for the field to roll down. A large field value φ 0 = φ 2. Quantum fluctuation makes perturbation for all the wavelengths within the horizon: p = k/a > H I. Once those fluctuations are pushed outside the horizon, they become classical and are frozen. V(ϕ) ϕ min Quantum Jump ϕ Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 8) PACIFIC 2016

9 1. Quantum Fluctuations during Inflation During inflation, scalar fields can obtain vacuum expectation values (VEVs) through quantum fluctuation. The field can also roll down classically toward its equilibrium minimum φ + 3H φ dv (φ) = dφ with relaxation time scale [ d 2 ] 1/2 V (φ) τ roll dφ 2 = 1 m eff If m eff H I, there is insufficient time for the field to roll down. A large field value φ 0 = φ 2. Quantum fluctuation makes perturbation for all the wavelengths within the horizon: p = k/a > H I. Once those fluctuations are pushed outside the horizon, they become classical and are frozen. V(ϕ) ϕ min Quantum Jump ϕ Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 8) PACIFIC 2016

10 1. Quantum Fluctuations during Inflation During inflation, scalar fields can obtain vacuum expectation values (VEVs) through quantum fluctuation. The field can also roll down classically toward its equilibrium minimum φ + 3H φ dv (φ) = dφ with relaxation time scale [ d 2 ] 1/2 V (φ) τ roll dφ 2 = 1 m eff If m eff H I, there is insufficient time for the field to roll down. A large field value φ 0 = φ 2. Quantum fluctuation makes perturbation for all the wavelengths within the horizon: p = k/a > H I. Once those fluctuations are pushed outside the horizon, they become classical and are frozen. V(ϕ) ϕ min Quantum Jump ϕ Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 8) PACIFIC 2016

11 1. Quantum Fluctuations during Inflation During inflation, scalar fields can obtain vacuum expectation values (VEVs) through quantum fluctuation. The field can also roll down classically toward its equilibrium minimum φ + 3H φ dv (φ) = dφ with relaxation time scale [ d 2 ] 1/2 V (φ) τ roll dφ 2 = 1 m eff If m eff H I, there is insufficient time for the field to roll down. A large field value φ 0 = φ 2. Quantum fluctuation makes perturbation for all the wavelengths within the horizon: p = k/a > H I. Once those fluctuations are pushed outside the horizon, they become classical and are frozen. V(ϕ) ϕ min Quantum Jump Roll Down Classically ϕ Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 8) PACIFIC 2016

12 1. Quantum Fluctuations during Inflation During inflation, scalar fields can obtain vacuum expectation values (VEVs) through quantum fluctuation. The field can also roll down classically toward its equilibrium minimum φ + 3H φ dv (φ) = dφ with relaxation time scale [ d 2 ] 1/2 V (φ) τ roll dφ 2 = 1 m eff If m eff H I, there is insufficient time for the field to roll down. A large field value φ 0 = φ 2. Quantum fluctuation makes perturbation for all the wavelengths within the horizon: p = k/a > H I. Once those fluctuations are pushed outside the horizon, they become classical and are frozen. V(ϕ) ϕ min Quantum Jump Roll Down Classically ϕ Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 8) PACIFIC 2016

13 1. Quantum Fluctuations during Inflation During inflation, scalar fields can obtain vacuum expectation values (VEVs) through quantum fluctuation. The field can also roll down classically toward its equilibrium minimum φ + 3H φ dv (φ) = dφ with relaxation time scale [ d 2 ] 1/2 V (φ) τ roll dφ 2 = 1 m eff If m eff H I, there is insufficient time for the field to roll down. A large field value φ 0 = φ 2. Quantum fluctuation makes perturbation for all the wavelengths within the horizon: p = k/a > H I. Once those fluctuations are pushed outside the horizon, they become classical and are frozen. V(ϕ) ϕ min Quantum Jump Roll Down Classically ϕ Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 8) PACIFIC 2016

14 1. Quantum Fluctuations during Inflation During inflation, scalar fields can obtain vacuum expectation values (VEVs) through quantum fluctuation. The field can also roll down classically toward its equilibrium minimum φ + 3H φ dv (φ) = dφ with relaxation time scale [ d 2 ] 1/2 V (φ) τ roll dφ 2 = 1 m eff If m eff H I, there is insufficient time for the field to roll down. A large field value φ 0 = φ 2. Quantum fluctuation makes perturbation for all the wavelengths within the horizon: p = k/a > H I. Once those fluctuations are pushed outside the horizon, they become classical and are frozen. V(ϕ) ϕ min Quantum Jump Roll Down Classically ϕ Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 8) PACIFIC 2016

15 1. Large Initial VEV for Scalar Fields The average equilibrium VEV φ 0 = φ 2 is such that V (φ 0 ) HI 4 This is φ HI 2 /m for V m 2 φ 2 /2 φ λ 1/4 H I for V λφ 4 /4 For inflation scale Λ I GeV, H I = Λ 2 I / 3M pl GeV,with λ 0.01, the VEV is φ GeV. For such a large VEV, the scalar field can be sensitive to higher dimensional operators. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 9) PACIFIC 2016

16 2. Scalar Field Relaxation after Inflation After inflation, H decreases. When H < m φ, the scalar field can relax. φ rolls down and oscillate with decreasing amplitude due to the Hubble friction H. For λφ 4 potential, the typical relaxation time is t rlx 7λ 1/2 φ 1 0. V(ϕ) Reheating Φ t Φ0 1.0 I GeV I 10 3 GeV 0.8 Tmax GeV Λ eff Roll Down Classically Φ Φ GeV HI GeV 0.2 T ϕ min ϕ Λ Φ0t End of Inflation at t 0 Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 10) PACIFIC 2016

17 3. Effective Chemical Potential Dine et. al. (1991) Cohen, Kaplan, Nelson (1991) During the relaxation, the scalar field can be sensitive to higher dimensional operators. We consider the couplings between the derivative of φ and j µ B+L like L 6 = 1 ( Mn 2 µ φ 2) j µ B+L or L 5 = 1 ( µ φ) j µ B+L M n j µ B+L : the B + L ferimion current M n : new energy scale when the operator is relevant. These operators are similar to those used in spontaneous baryogenesis scenarios. Break CP T spontaneouslly! So the Sakharov s conditions doesn t has to be satisfied exactly. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 11) PACIFIC 2016

18 3. Effective Chemical Potential L 6 = 1 ( Mn 2 µ φ 2) j µ B+L or L 5 = 1 ( µ φ) j µ B+L M n These give effective chemical potentials to baryons and leptons µ 6 = 1 Mn 2 t φ 2 or µ 5 = 1 t φ M n When φ rolls down, this shifts the energy levels between fermions and anti-fermions. V(ϕ) Scalar VEV Rolls Down Reheating Leads to l, q l, q ϕ Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 12) PACIFIC 2016

19 3. Derivative coupling? Integration by part L 6 = 1 M 2 n M. E. Shaposhnikov (1987), M. E. Shaposhnikov (1988) ( µ φ 2) j µ B+L 1 Mn 2 φ 2 µ j µ B+L The operator is equivalent to L 6 1 Mn 2 φ (g 2 2 W W 1 ) 2 g 2 B B through the electroweak anomaly equation, where W and B are SU(2) L and U(1) Y gauge fields. For the case that φ is the Higgs field, this can be generated by 1 Heavy fermion in the loops: M n = M f 2 Thermal loops: M n = T Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 13) PACIFIC 2016

20 3. More derivative couplings L 6 operators Higgs fields h [A. Kusenko, L. Pearce, LY, arxiv: ] Elementary Goldstone boson Higgs [H. Gertov, F. Sannino, L. Pearce, LY, arxiv: ] L 5 operators Axion a(t) [A. Kusenko, K. Schmitz, T.T. Yanagida, arxiv: ] L eff g2 2 a (t) F 32π F = a (t) ( 2 µ ψγ µ ψ ) N f f a f a Majoron χ (t) [M. Ibe, and K. Kaneta, arxiv: ] L eff µχ j µ L 2MR 750 GeV pseudoscalar S [A. Kusenko, L. Pearce, LY, arxiv: ] L λ α s g SG a µν µν G a + 12πv λ α µν γ SF µν F EW πv EW Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 14) PACIFIC 2016

21 4. Right-handed Majorana neutrino N R Even though the energy levels for leptons and anti-leptons are different, we still need a lepton-number-violating process to produce net lepton asymmetry. Last ingredient: Right-handed neutrino N R with Majorana mass term M R. The processes for L = 2 are ν Lh 0 ν Lh 0 ν Lν L h 0 h 0 & ν Lν L h 0 h 0 For m ν 0.1 ev, σ R m 2 ν/16πv 4 EW GeV 2. h 0 h 0 NR NR c νl νl c νl h 0 NR NR νl h 0 h 0 h 0 NR NR c νl νl c νl c h 0 NR c NR c νl c h 0 Different from thermal leptogenesis: N R don t need to be in thermal bath. T < M R Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 15) PACIFIC 2016

22 The Boltzmann transport equation If the system was in equilibrium, the lepton asymmetry would reach a value n L,eq = 2 π 2 µ efft 2. However, the interactions are not fast enough for the system to reach the equilibrium because T < M R. The system still make some L asymmetry. Describes by the Boltzmann transport equation d dt n L + 3Hn L 2 π 2 T 3 σ R (n L + 2π 2 µ efft 2 ) where n L is the lepton number density. Washout: To suppressed the washout, the lepton-number-violating interaction T 3 σ R turns off before the scalar field stop oscillating! Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 16) PACIFIC 2016

23 Sample plots of lepton asymmetry evolution log(y = n / s) End of inflation T = T max First ϕ crossing 0 μ eff T -2 μ eff M n -2 Radiation Domination log(t [GeV -1 ]) Λ I = GeV, Γ I = 10 8 GeV, and T RH = GeV. For µ eff Mn 2 case, choose M n = GeV. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 17) PACIFIC 2016

24 Resulting asymmetry Approximate analytical formula for final lepton asymmetry (lepton to entropy density ratio) ( ) ( ) n T Y 90σR rlx 3 t2 rlx φ0 exp σ R T T 2 T 3 π 6 RH t2 π RH 2 RH 3 Γ rlx ( I g S M n exp 15 π 2 ) σ R TRH 2 T rlx Γ I for t rlx < t RH for t rlx > t RH where n = 2 for µ eff t φ 2 /M 2 n, and n = 1 for µ eff t φ /M n. Accurate to within an order of magnitude. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 18) PACIFIC 2016

25 Isocurvature perturbations Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 19) PACIFIC 2016

26 Isocurvature perturbations One issue with the CMB observations φ 0 = φ 2 is the average over several Hubble volumes. Different patch of the universe has different initial VEV due to fluctuation δφ 0. The fluctuation for massless field is δφ 0 /φ 0 1/ N where N is the number of e-folds of inflation. Since the final asymmetry Y φ n 0 with n 1, 2 Different baryon asymmetry in each Hubble volume δy B /Y B n/ N. [Figure from Lauren Pearce] Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 20) PACIFIC 2016

27 Isocurvature perturbations One issue with the CMB observations φ 0 = φ 2 is the average over several Hubble volumes. Different patch of the universe has different initial VEV due to fluctuation δφ 0. The fluctuation for massless field is δφ 0 /φ 0 1/ N where N is the number of e-folds of inflation. Since the final asymmetry Y φ n 0 with n 1, 2 Different baryon asymmetry in each Hubble volume δy B /Y B n/ N. [Figure from Lauren Pearce] Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 20) PACIFIC 2016

28 Isocurvature perturbations One issue with the CMB observations φ 0 = φ 2 is the average over several Hubble volumes. Different patch of the universe has different initial VEV due to fluctuation δφ 0. The fluctuation for massless field is δφ 0 /φ 0 1/ N where N is the number of e-folds of inflation. Since the final asymmetry Y φ n 0 with n 1, 2 Different baryon asymmetry in each Hubble volume δy B /Y B n/ N. φ 0 φ 0 φ 0 [Figure from Lauren Pearce] Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 20) PACIFIC 2016

29 Isocurvature perturbations One issue with the CMB observations φ 0 = φ 2 is the average over several Hubble volumes. Different patch of the universe has different initial VEV due to fluctuation δφ 0. The fluctuation for massless field is δφ 0 /φ 0 1/ N where N is the number of e-folds of inflation. Since the final asymmetry Y φ n 0 with n 1, 2 Different baryon asymmetry in each Hubble volume δy B /Y B n/ N. φ 0 φ 0 φ 0 [Figure from Lauren Pearce] Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 20) PACIFIC 2016

30 Isocurvature perturbations One issue with the CMB observations φ 0 = φ 2 is the average over several Hubble volumes. Different patch of the universe has different initial VEV due to fluctuation δφ 0. The fluctuation for massless field is δφ 0 /φ 0 1/ N where N is the number of e-folds of inflation. Since the final asymmetry Y φ n 0 with n 1, 2 Different baryon asymmetry in each Hubble volume δy B /Y B n/ N. [Figure from Lauren Pearce] Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 20) PACIFIC 2016

31 Isocurvature perturbations Since φ is not inflaton, the fluctuation in Y B is independent from the curvature perturbation coming from inflation. For N last 50, this produces large isocurvature perturbations δy B Y B n Nlast with n = 1, or 2 This is constrainted by CMB observations. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 21) PACIFIC 2016

32 Isocurvature perturbations: Constraints from Planck CMB observation by Planck satellite (2015) constrains the isocurvature perturbation by β iso (k ) = P II (k ) < and 0.038, P RR (k ) + P II (k ) at comoving wavenumbers k = Mpc 1 and 0.1 Mpc 1. These can be translated into a limit on baryonic isocurvature perturbations δy B Y B k However, the constraint is only for large scales l 60 Mpc (k 0.1 Mpc 1 ). Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 22) PACIFIC 2016

33 Isocurvature perturbations only in small scales For small scales (k 0.1 Mpc 1 ), CMB is limited by Silk damping (photon diffusion damping). Isocurvature perturbation in small scales (k 0.1 Mpc 1 ) is allowed. If the scalar field φ is massive (m φ H I ) at the beginning of the inflation, but becomes light (m φ < H I ) later, then the quantum fluctuation can only grow in the late time. And, the produced perturbation will only be in small scales ( ) 4/3 k e N TRH g 1/3 last H I Λ I S (T CMB) g 1/3 S (T RH) T CMB T RH where N last is the number of e-folds of inflation that the fluctuation of φ has grow. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 23) PACIFIC 2016

34 Isocurvature perturbations only in small scales Λ I = GeV Λ I = GeV Λ I = GeV T RH = GeV Λ I = GeV Λ I = GeV Λ I = GeV T RH = GeV k s [Mpc -1 ] k s [Mpc -1 ] Isocurvature constraint from CMB 10-4 Isocurvature constraint from CMB N last of e-folds N last of e-folds The wavenumber of the produced perturbation vs. the number of e-folds that the fluctuation has grow at different inflation energy scales Λ I and reheat termperatures T RH. For Λ I = GeV, T RH = GeV, the fluctuation for N last 50 only appear in scale smaller than 0.1 Mpc 1. This affect the structure formation and help on resolving the excess found in CIB fluctuation. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 24) PACIFIC 2016

35 Cosmic Infrared Background fluctuation excess Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 25) PACIFIC 2016

36 Relaxation Leptogenesis Isocurvature Perturbations CIB Fluctuation Excess Cosmic Infrared Background (CIB) anisotropies CIB is the infrared part of extragalactic backgound, which contains radiation from galaxies at all redshifts through out the entire cosmic history. The absolute intensity of CIB is difficult to be determined due to the large uncertainty associated with the foreground signal, Galactic components, and zodiacal light. Therefore, recent measurements focus on the anisotropies (spatial fluctuation) of CIB. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 26) PACIFIC 2016

37 Excess in CIB fluctuation A. Kashlinsky, astro-ph/ A. Cooray et. al., K. Helgason et. al., Akari and Spitzer: Excess in fluctuation at few arcmin scale in the near-ir (2-5 µm). δf 2 5µm ( 5 ) 0.09 nwm 2 sr 1 Not from known galaxy populations. Might come from first star forming at z 10, but have difficulty with pure adiabatic spectrum from inflation. Due to the insufficient perturbation in the small scale at high redshift (z 8) for structure to form. [Helgason et. al. (2016) and Kashlinsky (2016)] [Figure from K. Helgason et. al., ] Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 27) PACIFIC 2016

38 Large perturbations in small scales A possible solution from Leptogenesis via scalar field relaxation: 1 Produces large baryon perturbation (δ B = δρ B /ρ B 0.1) in small scales at the early universe if the fluctuation in φ only grows in the late time of inflation. 2 The large fluctuation in baryon density induces the corresponding perturbation in CDM δ CDM after recombination. 3 Total matter perturbations δ m in small scale are much larger than that from standard adiabatic perturbation from inflation. 4 Small structures (M halo 10 6 M ) form eariler 5 Produce more CIB fluctuation at z > 10. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 28) PACIFIC 2016

39 Growth of the perturbation 2 0 Without isocurvature pert. k = 100 Mpc With isocurvature pert. k = 100 Mpc -1 log δ λ -2-4 log δ λ -2-4 δb δcdm δm -6-8 ρ r = ρm Decoupling log(τ/τeq) Only adiabatic perturbation from inflation with R = z = 10 now -6-8 ρ r = ρm Decoupling log(τ/τeq) With isocurvature perturbation from leptogenesis with δ B = 0.14 For N last = 45.7, Λ I = GeV, T RH = GeV, the isocurvature starts at k s = 100 Mpc 1. The matter density perturbation exceed linear regime before z = 10 for the isocurvature perturbation Structures form earlier. z = 10 now Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 29) PACIFIC 2016

40 Halo collapses before z = 10 5 δ c / 2 σ M z = 10 z = 20 z = 40 z = log(m/m ) The rms density constrast σ M = [ δ 2 M (k, z) W T H (kr M ) dk/k ] 1/2 over the halo mass M at various z assuming isocurvature perturbation for scale k > 100 Mpc 1. Solid line: With isocurvature perturbation. Dashed line: With only adiabatic perturbation from inflation. Halo collapses by z when σ M (z) > δ c = For k s = 100 Mpc 1 (N last = 45.7), M halo 10 6 M collapses by z 20, which won t happen if without isocurvature perturbation. Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 30) PACIFIC 2016

41 Summary During inflation, scalar fields can obtain large VEVs through quantum fluctuation. Relaxation of the large VEV generally happens during the reheating after inflation. Through the derivative coupling between the scalar field and lepton current, leptogenesis can be possible, explaining the matter-antimatter asymmetry in the universe. This can generate additional baryonic isocurvature perturbations, which is not constrainted in the small angular scale by CMB observation. Isocurvature perturbation in small scale can then lead to first star forming earlier than what is expected from ΛCDM. This can be the origin of the excess in CIB fluctuations. Thank you for your attention! Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 31) PACIFIC 2016

42 Backup slide: parameter space for pseudoscalar case 14 No inflation Isocurvature constraint log(t R [GeV]) Λ I = GeV Λ I = GeV Λ I = GeV Λ I = GeV Tensor mode constraint Λ I < GeV log(m S [GeV]) Leptogenesis via the Relaxation of Higgs and other Scalar Fields (slide 32) PACIFIC 2016