Testing Higgs Relaxation Leptogenesis: Why Isocurvature Is More - PowerPoint PPT Presentation

Dine et. al., Phys.Lett. B257 (1991) 351-356 Spontaneous Baryogenesis Cohen, Kaplan, Nelson Phys.Lett. B263 (1991) 86-92 Spontaneous Baryogenesis L ⊇ ( ∂ t � a � / f ) n B + L If scatterings in plasma are rapid on the VEV evolution timescale: ◮ Treat VEV as a classical background when constructing Hamiltonian ◮ Effective chemical potential µ ∼ ∂ t � a � / f for B + L charge ◮ Scatterings with B - or L -number violation lead to asymmetry Lauren Pearce (UIUC) 8 / 23

Dolgov & Freese Spontaneous Baryogenesis Phys.Rev. D51 (1995) 2693-2702 hep-ph/9410346 Spontaneous Baryogenesis L ⊇ ( ∂ t � a � / f ) n B + L If scatterings in plasma are rapid on the VEV evolution timescale: ◮ Treat VEV as a classical background when constructing Hamiltonian ◮ Effective chemical potential µ ∼ ∂ t � a � / f for B + L charge ◮ Scatterings with B - or L -number violation lead to asymmetry If not, analyze asymmetric particle production using Bogoliubov analysis Lauren Pearce (UIUC) 8 / 23

Higgs Relaxation Leptogenesis Higgs Relaxation Leptogenesis Consider instead the operator: L ⊇ ϕ 2 W ˜ W , ϕ : Higgs field Λ 2 n Lauren Pearce (UIUC) 9 / 23

Higgs Relaxation Leptogenesis Higgs Relaxation Leptogenesis Consider instead the operator: L ⊇ ϕ 2 W ˜ W , ϕ : Higgs field Λ 2 n Following same steps as above gives: L ⊇ ∂ µ ϕ 2 j µ B + L Λ 2 n Lauren Pearce (UIUC) 9 / 23

Higgs Relaxation Leptogenesis Higgs Relaxation Leptogenesis Consider instead the operator: L ⊇ ϕ 2 W ˜ W , ϕ : Higgs field Λ 2 n Following same steps as above gives: L ⊇ ∂ µ ϕ 2 j µ B + L Λ 2 n � � ϕ 2 � gives: Higgs VEV φ = L ⊇ ∂ t φ 2 n B + L Λ 2 n Lauren Pearce (UIUC) 9 / 23

Higgs Relaxation Leptogenesis Higgs Relaxation Leptogenesis Consider instead the operator: L ⊇ ϕ 2 W ˜ W , ϕ : Higgs field Λ 2 n Following same steps as above gives: L ⊇ ∂ µ ϕ 2 j µ B + L Λ 2 n � � ϕ 2 � gives: Higgs VEV φ = L ⊇ ∂ t φ 2 n B + L Λ 2 n If have B - or L -violating processes, produces a matter/antimatter asymmetry Lauren Pearce (UIUC) 9 / 23

Higgs Relaxation Leptogenesis Advantages The Higgs field exists & naturally acquires a large VEV during inflation Lauren Pearce (UIUC) 10 / 23

Higgs Relaxation Leptogenesis Advantages The Higgs field exists & naturally acquires a large VEV during inflation ∂ t φ 2 decreases during relaxation in every Hubble patch Lauren Pearce (UIUC) 10 / 23

Higgs Relaxation Leptogenesis Advantages The Higgs field exists & naturally acquires a large VEV during inflation ∂ t φ 2 decreases during relaxation in every Hubble patch Therefore same sign asymmetry in each Hubble patch Lauren Pearce (UIUC) 10 / 23

Higgs Relaxation Leptogenesis Advantages The Higgs field exists & naturally acquires a large VEV during inflation ∂ t φ 2 decreases during relaxation in every Hubble patch Therefore same sign asymmetry in each Hubble patch (Unlike ∂ t � a � ) Lauren Pearce (UIUC) 10 / 23

CP Violation & Higgs Relaxation Leptogenesis CPT & CP Note that ( ∂ t φ 2 / Λ n ) n B + L breaks CPT Lauren Pearce (UIUC) 11 / 23

CP Violation & Higgs Relaxation Leptogenesis CPT & CP Note that ( ∂ t φ 2 / Λ n ) n B + L breaks CPT (as does ( ∂ t � a � / f ) n B + L ) Lauren Pearce (UIUC) 11 / 23

CP Violation & Higgs Relaxation Leptogenesis CPT & CP Note that ( ∂ t φ 2 / Λ n ) n B + L breaks CPT (as does ( ∂ t � a � / f ) n B + L ) However, this is dynamical CPT breaking, due to the evolving VEV Lauren Pearce (UIUC) 11 / 23

CP Violation & Higgs Relaxation Leptogenesis CPT & CP Note that ( ∂ t φ 2 / Λ n ) n B + L breaks CPT (as does ( ∂ t � a � / f ) n B + L ) However, this is dynamical CPT breaking, due to the evolving VEV Both aW ˜ W / f and ϕ 2 W ˜ W / Λ 2 n conserve CPT : C P T Psuedoscalar ( a ) 1 − 1 − 1 Scalar ( ϕ ) 1 1 1 Gauge fields ( F ˜ F ) 1 − 1 − 1 Lauren Pearce (UIUC) 11 / 23

CP Violation & Higgs Relaxation Leptogenesis CPT & CP Note that ( ∂ t φ 2 / Λ n ) n B + L breaks CPT (as does ( ∂ t � a � / f ) n B + L ) However, this is dynamical CPT breaking, due to the evolving VEV Both aW ˜ W / f and ϕ 2 W ˜ W / Λ 2 n conserve CPT : C P T Psuedoscalar ( a ) 1 − 1 − 1 Scalar ( ϕ ) 1 1 1 Gauge fields ( F ˜ F ) 1 − 1 − 1 However, the effective operator ϕ 2 W ˜ W / Λ 2 n does break CP ... Lauren Pearce (UIUC) 11 / 23

CP Violation & Higgs Relaxation Leptogenesis CPT & CP Note that ( ∂ t φ 2 / Λ n ) n B + L breaks CPT (as does ( ∂ t � a � / f ) n B + L ) However, this is dynamical CPT breaking, due to the evolving VEV Both aW ˜ W / f and ϕ 2 W ˜ W / Λ 2 n conserve CPT : C P T Psuedoscalar ( a ) 1 − 1 − 1 Scalar ( ϕ ) 1 1 1 Gauge fields ( F ˜ F ) 1 − 1 − 1 However, the effective operator ϕ 2 W ˜ W / Λ 2 n does break CP ... → Λ n involves both the scale of new physics and the CP violation in this new sector Lauren Pearce (UIUC) 11 / 23

CP Violation & Higgs Relaxation Leptogenesis Building the ϕ 2 W ˜ W / Λ 2 n Operator I generally don’t discuss model building much: Lauren Pearce (UIUC) 12 / 23

CP Violation & Higgs Relaxation Leptogenesis Building the ϕ 2 W ˜ W / Λ 2 n Operator I generally don’t discuss model building much: ◮ All of our constraints & parameter space results depend only on Λ n Lauren Pearce (UIUC) 12 / 23

CP Violation & Higgs Relaxation Leptogenesis Building the ϕ 2 W ˜ W / Λ 2 n Operator I generally don’t discuss model building much: ◮ All of our constraints & parameter space results depend only on Λ n But since this is a workshop on CP violation, I will discuss model building... Lauren Pearce (UIUC) 12 / 23

M. E. Shaposhnikov (1987) CP Violation & Model Building M. E. Shaposhnikov (1988) Standard Model As Shaposhnikov pointed out, this operator exists in the Standard Model: Lauren Pearce (UIUC) 13 / 23

M. E. Shaposhnikov (1987) CP Violation & Model Building M. E. Shaposhnikov (1988) Standard Model As Shaposhnikov pointed out, this operator exists in the Standard Model: (Works in basis in which diagonalizes SU (2) eigenstates, so Higgs couplings are not diagonal) Lauren Pearce (UIUC) 13 / 23

M. E. Shaposhnikov (1987) CP Violation & Model Building M. E. Shaposhnikov (1988) Standard Model As Shaposhnikov pointed out, this operator exists in the Standard Model: (Works in basis in which diagonalizes SU (2) eigenstates, so Higgs couplings are not diagonal) To pick up the CP -violating CKM phase, need to use all three generations of quarks: Lauren Pearce (UIUC) 13 / 23

M. E. Shaposhnikov (1987) CP Violation & Model Building M. E. Shaposhnikov (1988) Standard Model As Shaposhnikov pointed out, this operator exists in the Standard Model: (Works in basis in which diagonalizes SU (2) eigenstates, so Higgs couplings are not diagonal) To pick up the CP -violating CKM phase, need to use all three generations of quarks: L R L Lauren Pearce (UIUC) 13 / 23

M. E. Shaposhnikov (1987) CP Violation & Model Building M. E. Shaposhnikov (1988) Standard Model As Shaposhnikov pointed out, this operator exists in the Standard Model: (Works in basis in which diagonalizes SU (2) eigenstates, so Higgs couplings are not diagonal) To pick up the CP -violating CKM phase, need to use all three generations of quarks: L R L But this operator is extremely tiny: Lauren Pearce (UIUC) 13 / 23

M. E. Shaposhnikov (1987) CP Violation & Model Building M. E. Shaposhnikov (1988) Standard Model As Shaposhnikov pointed out, this operator exists in the Standard Model: (Works in basis in which diagonalizes SU (2) eigenstates, so Higgs couplings are not diagonal) To pick up the CP -violating CKM phase, need to use all three generations of quarks: L R L But this operator is extremely tiny: ◮ Small CP -violating phase Lauren Pearce (UIUC) 13 / 23

M. E. Shaposhnikov (1987) CP Violation & Model Building M. E. Shaposhnikov (1988) Standard Model As Shaposhnikov pointed out, this operator exists in the Standard Model: (Works in basis in which diagonalizes SU (2) eigenstates, so Higgs couplings are not diagonal) To pick up the CP -violating CKM phase, need to use all three generations of quarks: L R L But this operator is extremely tiny: ◮ Small CP -violating phase ◮ Small quark Yukawa couplings Lauren Pearce (UIUC) 13 / 23

CP Violation & Model Building L R L Model Building But there’s a more serious problem as well: Lauren Pearce (UIUC) 14 / 23

CP Violation & Model Building L R L Model Building But there’s a more serious problem as well: Quark masses ∝ Higgs VEV φ Lauren Pearce (UIUC) 14 / 23

CP Violation & Model Building L R L Model Building But there’s a more serious problem as well: Quark masses ∝ Higgs VEV φ So Λ n ∝ φ Lauren Pearce (UIUC) 14 / 23

CP Violation & Model Building L R L Model Building But there’s a more serious problem as well: Quark masses ∝ Higgs VEV φ So Λ n ∝ φ So the coefficient of the j µ B + L term is: � φ 2 � φ 2 � � ∂ µ ∝ ∂ µ = 0 Λ 2 φ 2 n Lauren Pearce (UIUC) 14 / 23

CP Violation & Model Building L R L Model Building A similar operator can be constructed using leptons: Lauren Pearce (UIUC) 14 / 23

CP Violation & Model Building L R L Model Building A similar operator can be constructed using leptons: (Even smaller Yukawas) Lauren Pearce (UIUC) 14 / 23

CP Violation & Model Building L R L Model Building A similar operator can be constructed using leptons: (Even smaller Yukawas) But scale Λ n ∝ M RH if RH neutrinos have a Majorana mass Lauren Pearce (UIUC) 14 / 23

CP Violation & Model Building L R L Model Building A similar operator can be constructed using leptons: (Even smaller Yukawas) But scale Λ n ∝ M RH if RH neutrinos have a Majorana mass Easiest solution: Copy the lepton sector, with larger Yukawa couplings and smaller Majorana masses Lauren Pearce (UIUC) 14 / 23

CP Violation & Model Building L R L Model Building A similar operator can be constructed using leptons: (Even smaller Yukawas) But scale Λ n ∝ M RH if RH neutrinos have a Majorana mass Easiest solution: Copy the lepton sector, with larger Yukawa couplings and smaller Majorana masses (Make sure Yukawa couplings are large enough that you don’t disturb Higgs decays) Lauren Pearce (UIUC) 14 / 23

CP Violation & Model Building Basic Conditions Need to involve states that: Lauren Pearce (UIUC) 15 / 23

CP Violation & Model Building Basic Conditions Need to involve states that: Couple to the Higgs Lauren Pearce (UIUC) 15 / 23

CP Violation & Model Building Basic Conditions Need to involve states that: Couple to the Higgs Couple to the SU (2) gauge bosons Lauren Pearce (UIUC) 15 / 23

CP Violation & Model Building Basic Conditions Need to involve states that: Couple to the Higgs Couple to the SU (2) gauge bosons Do not (all) get their masses from the Higgs mechanism Lauren Pearce (UIUC) 15 / 23

CP Violation & Model Building Basic Conditions Need to involve states that: Couple to the Higgs Couple to the SU (2) gauge bosons Do not (all) get their masses from the Higgs mechanism Allow for additional CP violation Lauren Pearce (UIUC) 15 / 23

CP Violation & Model Building Basic Conditions Need to involve states that: Couple to the Higgs Couple to the SU (2) gauge bosons Do not (all) get their masses from the Higgs mechanism Allow for additional CP violation Several other options as well Lauren Pearce (UIUC) 15 / 23

CP Violation & Model Building Basic Conditions Need to involve states that: Couple to the Higgs Couple to the SU (2) gauge bosons Do not (all) get their masses from the Higgs mechanism Allow for additional CP violation Several other options as well Main Point We don’t particularly care about the source of CP violation in the UV-complete theory, once the effective operator is constructed and the “effective scale” Λ n is known Lauren Pearce (UIUC) 15 / 23

Γ Λ Λ ϕ Λ Having Said That... In the Standard Model, the relevant parameter space is in the regime in which the use of effective field theory is questionable: Lauren Pearce (UIUC) 16 / 23

Having Said That... In the Standard Model, the relevant parameter space is in the regime in which the use of effective field theory is questionable: - 24 - 22 - 26 16 Inflaton scale: Λ I = 10 15 GeV - 18 x -axis: Inflaton decay scale Γ I , 14 - 20 controls reheating → creation of Λ n < T Max - 14 log ( Λ n [ GeV ]) plasma in which / L interactions 12 - 16 occur Λ n < ϕ 0 - 10 (Used RH neutrino for / 10 L - 12 violation, masses set high - 6 enough to suppress thermal 8 - 4 - 8 leptogenesis) 5 6 7 8 9 log ( Γ I [ GeV ]) Lauren Pearce (UIUC) 16 / 23

Having Said That... In the Standard Model, the relevant parameter space is in the regime in which the use of effective field theory is questionable: - 24 - 22 - 26 16 Models with extended Higgs - 18 sector: 14 ◮ Can protect flat direction - 20 Λ n < T Max ◮ Regime in which EFT is - 14 log ( Λ n [ GeV ]) 12 valid - 16 Λ n < ϕ 0 - 10 H. Gertov et. al., Phys.Rev. D93 10 - 12 (2016) no.11, 115042 - 6 8 - 4 - 8 5 6 7 8 9 log ( Γ I [ GeV ]) Lauren Pearce (UIUC) 16 / 23

Having Said That... In the Standard Model, the relevant parameter space is in the regime in which the use of effective field theory is questionable: - 24 - 22 - 26 Relevant scales: Λ n ∼ 10 8 to 16 10 10 GeV - 18 14 - 20 Λ n < T Max - 14 log ( Λ n [ GeV ]) 12 - 16 Λ n < ϕ 0 - 10 10 - 12 - 6 8 - 4 - 8 5 6 7 8 9 log ( Γ I [ GeV ]) Lauren Pearce (UIUC) 16 / 23

Having Said That... In the Standard Model, the relevant parameter space is in the regime in which the use of effective field theory is questionable: - 24 - 22 - 26 Relevant scales: Λ n ∼ 10 8 to 16 10 10 GeV - 18 14 - 20 (Not likely to be probed any Λ n < T Max - 14 log ( Λ n [ GeV ]) time soon) 12 - 16 Λ n < ϕ 0 - 10 10 - 12 - 6 8 - 4 - 8 5 6 7 8 9 log ( Γ I [ GeV ]) Lauren Pearce (UIUC) 16 / 23

Having Said That... In the Standard Model, the relevant parameter space is in the regime in which the use of effective field theory is questionable: - 24 - 22 - 26 Relevant scales: Λ n ∼ 10 8 to 16 10 10 GeV - 18 14 - 20 (Not likely to be probed any Λ n < T Max - 14 log ( Λ n [ GeV ]) time soon) 12 - 16 Other observational Λ n < ϕ 0 - 10 consequences? 10 - 12 - 6 8 - 4 - 8 5 6 7 8 9 log ( Γ I [ GeV ]) Lauren Pearce (UIUC) 16 / 23

Isocurvature Perturbations VEV Variation The Fokker-Planck equation gives us the Higgs VEV averaged over many Hubble volumes Lauren Pearce (UIUC) 17 / 23

Isocurvature Perturbations VEV Variation The Fokker-Planck equation gives us the Higgs VEV averaged over many Hubble volumes Lauren Pearce (UIUC) 17 / 23

Isocurvature Perturbations VEV Variation The Fokker-Planck equation gives us the Higgs VEV averaged over many Hubble volumes The VEVs in individual Hubble volumes will vary φ ′′ 0 φ ′ φ 0 0 Lauren Pearce (UIUC) 17 / 23

Isocurvature Perturbations VEV Variation The Fokker-Planck equation gives us the Higgs VEV averaged over many Hubble volumes The VEVs in individual Hubble volumes will vary Therefore, the final φ ′′ 0 φ ′ φ 0 partial-antiparticle 0 asymmetry also varies Lauren Pearce (UIUC) 17 / 23

Isocurvature Perturbations VEV Variation The Fokker-Planck equation gives us the Higgs VEV averaged over many Hubble volumes The VEVs in individual Hubble volumes will vary Therefore, the final partial-antiparticle asymmetry also varies Lauren Pearce (UIUC) 17 / 23

Isocurvature Perturbations Isocurvature Perturbations Because the Higgs VEV does not dominate the energy density of the universe, these are isocurvature perturbations Lauren Pearce (UIUC) 18 / 23

S. Weinberg Isocurvature Perturbations Phys.Rev. D70 (2004) 083522 astro-ph/0405397 Isocurvature Perturbations Because the Higgs VEV does not dominate the energy density of the universe, these are isocurvature perturbations Weinberg has a famous theorem that isocurvature perturbations must decay when as the universe thermalizes... Lauren Pearce (UIUC) 18 / 23

S. Weinberg Isocurvature Perturbations Phys.Rev. D70 (2004) 083522 astro-ph/0405397 Isocurvature Perturbations Because the Higgs VEV does not dominate the energy density of the universe, these are isocurvature perturbations Weinberg has a famous theorem that isocurvature perturbations must decay when as the universe thermalizes... ...“become adiabatic if the universe after inflation enters an era of local thermal equilibrium, with no non-zero conserved quantities ” Lauren Pearce (UIUC) 18 / 23

Isocurvature Perturbations Isocurvature Perturbations Because the Higgs VEV does not dominate the energy density of the universe, these are isocurvature perturbations Weinberg has a famous theorem that isocurvature perturbations must decay when as the universe thermalizes... ...“become adiabatic if the universe after inflation enters an era of local thermal equilibrium, with no non-zero conserved quantities ” In our scenario: isocurvature perturbations survive because they are carried along with nonzero lepton/baryon number Lauren Pearce (UIUC) 18 / 23

Isocurvature Perturbations Isocurvature Perturbations Because the Higgs VEV does not dominate the energy density of the universe, these are isocurvature perturbations Weinberg has a famous theorem that isocurvature perturbations must decay when as the universe thermalizes... ...“become adiabatic if the universe after inflation enters an era of local thermal equilibrium, with no non-zero conserved quantities ” In our scenario: isocurvature perturbations survive because they are carried along with nonzero lepton/baryon number Why Isocurvature? Few theories produce isocurvature perturbations Lauren Pearce (UIUC) 18 / 23

Isocurvature Perturbations Isocurvature Perturbations Because the Higgs VEV does not dominate the energy density of the universe, these are isocurvature perturbations Weinberg has a famous theorem that isocurvature perturbations must decay when as the universe thermalizes... ...“become adiabatic if the universe after inflation enters an era of local thermal equilibrium, with no non-zero conserved quantities ” In our scenario: isocurvature perturbations survive because they are carried along with nonzero lepton/baryon number Why Isocurvature? Few theories produce isocurvature perturbations Stringently constrained by CMB & Lyman α data Lauren Pearce (UIUC) 18 / 23

Isocurvature In fact, too strong... In fact, isocurvature constraints already rule out the naive version I’ve introduced here (details below)! Lauren Pearce (UIUC) 19 / 23

Isocurvature In fact, too strong... In fact, isocurvature constraints already rule out the naive version I’ve introduced here (details below)! Decrease amplitude of perturbations → suppresses asymmetry Lauren Pearce (UIUC) 19 / 23

Isocurvature In fact, too strong... In fact, isocurvature constraints already rule out the naive version I’ve introduced here (details below)! Decrease amplitude of perturbations → suppresses asymmetry Cannot eliminate isocurvature perturbations! Lauren Pearce (UIUC) 19 / 23

Isocurvature In fact, too strong... In fact, isocurvature constraints already rule out the naive version I’ve introduced here (details below)! Decrease amplitude of perturbations → suppresses asymmetry Cannot eliminate isocurvature perturbations! But can shift to smaller scales via a Higgs-inflaton coupling: Couplings ∼ I n φ m lead to � I n � φ m terms in the potential V ( φ ) φ Lauren Pearce (UIUC) 19 / 23

Isocurvature In fact, too strong... In fact, isocurvature constraints already rule out the naive version I’ve introduced here (details below)! Decrease amplitude of perturbations → suppresses asymmetry Cannot eliminate isocurvature perturbations! But can shift to smaller scales via a Higgs-inflaton coupling: Couplings ∼ I n φ m lead to � I n � φ m terms in the potential V ( φ ) Can destroy flatness φ Lauren Pearce (UIUC) 19 / 23

Isocurvature In fact, too strong... In fact, isocurvature constraints already rule out the naive version I’ve introduced here (details below)! Decrease amplitude of perturbations → suppresses asymmetry Cannot eliminate isocurvature perturbations! But can shift to smaller scales via a Higgs-inflaton coupling: Couplings ∼ I n φ m lead to � I n � φ m terms in the potential V ( φ ) Can destroy flatness These terms → 0 at the end of inflation φ Lauren Pearce (UIUC) 19 / 23

Isocurvature In fact, too strong... In fact, isocurvature constraints already rule out the naive version I’ve introduced here (details below)! Decrease amplitude of perturbations → suppresses asymmetry Cannot eliminate isocurvature perturbations! But can shift to smaller scales via a Higgs-inflaton coupling: Couplings ∼ I n φ m lead to � I n � φ m terms in the potential V ( φ ) Can destroy flatness These terms → 0 at the end of inflation VEV grows only at end of inflation φ Lauren Pearce (UIUC) 19 / 23

Isocurvature In fact, too strong... In fact, isocurvature constraints already rule out the naive version I’ve introduced here (details below)! Decrease amplitude of perturbations → suppresses asymmetry Cannot eliminate isocurvature perturbations! But can shift to smaller scales via a Higgs-inflaton coupling: Couplings ∼ I n φ m lead to � I n � φ m terms in the potential V ( φ ) Can destroy flatness These terms → 0 at the end of inflation VEV grows only at end of inflation φ Isocurvature only on small scales Lauren Pearce (UIUC) 19 / 23

Isocurvature Isocurvature & Small Structures Parameterize by N last , number of e-folds VEV grows through 10 6 T RH = 10 10 GeV Λ I = 10 16 GeV Λ I = 10 14 GeV 10 4 Λ I = 10 12 GeV k s [ Mpc - 1 ] 100 k s : Largest scale of isocurvature 1 Lyman - α Forest constraint perturbations 0.01 CMB constraint 10 - 4 35 40 45 50 55 N last of e - folds Lauren Pearce (UIUC) 20 / 23