Spontaneous Leptogenesis in Continuum-Clockwork Axion Models

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1 Spontaneous Leptogenesis in Continuum-Clockwork Axion Models [IBS-CTPU] [arxiv:1805.xxxxx] collaborators on this work: Kyu Jung Bae [IBS-CTPU] Chang Sub Shin [IBS-CTPU] PHENO 2018 Tuesday, May 8 th, / 13

2 Outstanding Issues [PDG BBN Review] matter-antimatter asymmetry: need to explain baryon-to-photon ratio: η 0 B n0 b n0 b n 0 γ n0 b n 0 γ Typically need Sakharov conditions: B and/or L violation C and CP violation departure from thermal equilibrium 02 / 13

3 Outstanding Issues matter-antimatter asymmetry: need to explain baryon-to-photon ratio: [PDG BBN Review] η 0 B n0 b n0 b n 0 γ n0 b n 0 γ Typically need Sakharov conditions: B and/or L violation C and CP violation departure from thermal equilibrium hinges on conservation of CP T alternatives exist if CP T spontaneously, e.g., with homogeneous scalar field ϕ: lepton current L eff 1 f µϕj µ l ϕ ( ) nl n f l µeff n L NG boson 02 / 13

4 Outstanding Issues matter-antimatter asymmetry: need to explain baryon-to-photon ratio: [PDG BBN Review] η 0 B n0 b n0 b n 0 γ n0 b n 0 γ Typically need Sakharov conditions: B and/or L violation C and CP violation departure from thermal equilibrium hinges on conservation of CP T alternatives exist if CP T spontaneously, e.g., with homogeneous scalar field ϕ: L eff 1 f µϕj µ l ϕ ( ) nl n f l µeff n L lepton current NG boson effective chemical potential µ eff ϕ/f for lepton number density n L opportunity for asymmetry generation at equilibrium 02 / 13

5 The µ eff 0 shifts equilibrium n eq L value away from zero: n eq L d 3 [ ] p 1 (2π) 3 e (p µ eff)/t e (p+µ eff)/t µ efft 2 when L-violation occurs sufficiently fast Γ L H need to specify source of L-violation: Assume see-saw mechanism with heavy M i Λ GUT T right-handed neutrinos Γ L = 4n eq l σ eff O(10 8 GeV) ( T GeV ) 3 03 / 13

6 Spontaneous Leptogenesis via Axions An axion-like field is a natural candidate for ϕ(x): recast using U(1) L anomalies: ϕ f µj µ l L eff 1 f µϕj µ l ϕ f µj µ l = ϕ f ( Nf g2 2 8π 2 W µν µν W weak which can readily arise [e.g., string axion models] [Kusenko 18] N f g1 2 8π 2 B µν µν B hypercharge With typical V (ϕ) Λ 4 cos (ϕ/f) potential, successful leptogenesis requires heavy m ϕ 10 8 GeV axion decays and is not suitable DM candidate ) 2πf eff V eff (ϕ) ϕ 2πf 04 / 13

7 Spontaneous Leptogenesis via Axions An axion-like field is a natural candidate for ϕ(x): recast using U(1) L anomalies: ϕ f µj µ l L eff 1 f µϕj µ l ϕ f µj µ l = ϕ f ( Nf g2 2 8π 2 W µν µν W weak which can readily arise [e.g., string axion models] [Kusenko 18] N f g1 2 8π 2 B µν µν B hypercharge With typical V (ϕ) Λ 4 cos (ϕ/f) potential, successful leptogenesis requires heavy m ϕ 10 8 GeV axion decays and is not suitable DM candidate ) interesting route forward: consider physics that deforms effective potential such that V eff (ϕ) retains curvature at edges but mass m ϕ is suppressed ϕ 2πf eff V eff (ϕ) 2πf 04 / 13

8 Spontaneous Leptogenesis via Axions An axion-like field is a natural candidate for ϕ(x): recast using U(1) L anomalies: ϕ f µj µ l L eff 1 f µϕj µ l ϕ f µj µ l = ϕ f ( Nf g2 2 8π 2 W µν µν W weak which can readily arise [e.g., string axion models] [Kusenko 18] N f g1 2 8π 2 B µν µν B hypercharge With typical V (ϕ) Λ 4 cos (ϕ/f) potential, successful leptogenesis requires heavy m ϕ 10 8 GeV axion decays and is not suitable DM candidate ) interesting route forward: consider physics that deforms effective potential such that V eff (ϕ) retains curvature at edges but mass m ϕ is suppressed example: this appears in continuum-clockwork potentials ϕ 2πf eff V eff (ϕ) 2πf 04 / 13

9 discrete clockwork mechanism: [Choi et al. 14] [Kaplan, Rattazzi 15] [Choi, Im 15] N + 1 scalars θ j with nearest-neighbor interactions (q Z): L µ 2 f 2 cos (θ j+1 qθ j ) N 1 j=0 U(1) N+1 broken down to U(1) CW : θ j θ j + αq j remaining massless field ϕ has an overlap with each θ j : ϕ θ j q j N for N 1 overlap ϕ θj SM θ 0 θ 1 θ 2 θ 3 θ 4 θ 5 θ 6 θ N any couplings q N ϕo SM exponentially suppressed 05 / 13

10 overlap ϕ θj SM θ 0 θ 1 θ 2 θ 3 θ 4 θ 5 θ 6 θ N any couplings q N ϕo SM exponentially suppressed 05 / 13

11 consider N continuum limit: identify y jϵ with extra spatial coordinate ϵ = πr N 0 size = πr overlap ϕ θj SM θ 0 θ 1 θ 2 θ 3 θ 4 θ 5 θ 6 θ N any couplings q N ϕo SM exponentially suppressed 05 / 13

12 Continuum-Clockwork Axion In continuum limit, find action for resulting bulk field θ(x, y): S = f 5 3 d 5 x [( µ θ) 2 + ( y θ m sin θ) 2] 2 massless 4D mode ϕ(x) realized as: [ ] θ(x, y) tan = e my u [ϕ(x)] 2 [ ie πmr sn ϕ(x) 2if e 2πmR ] any small deviation in boundary masses generates a potential: V eff (ϕ) = Λ 4 {1 cos [θ(x, 0)]} = 2Λ4 [u(ϕ)] [u(ϕ)] 2 m 2 eff 2 V eff ϕ 2 = e ϕ=0 so curvature as ϕ 0 is suppressed 2πmR Λ4 f 2 Veff(φ)/(2Λ 4 ) [Giudice et al. 16] [Craig et al. 17] [Choi et al. 17] extended range 2πf eff 1.0 mr =0 mr = mr =2 mr =5 mr =7 mr = quadratic φ/(πf eff ) 06 / 13

13 Continuum-Clockwork Axion In continuum limit, find action for resulting bulk field θ(x, y): S = f 5 3 d 5 x [( µ θ) 2 + ( y θ m sin θ) 2] 2 massless 4D mode ϕ(x) realized as: [ ] θ(x, y) tan = e my u [ϕ(x)] 2 [ ie πmr sn ϕ(x) 2if e 2πmR ] any small deviation in boundary masses generates a potential: V eff (ϕ) = Λ 4 {1 cos [θ(x, 0)]} = 2Λ4 [u(ϕ)] [u(ϕ)] 2 m 2 eff 2 V eff ϕ 2 = e ϕ=0 so curvature as ϕ 0 is suppressed 2πmR Λ4 f 2 Veff(φ)/(2Λ 4 ) [Giudice et al. 16] [Craig et al. 17] [Choi et al. 17] large curvature drives leptogenesis more efficiently quadratic small curvature suppresses decays, allows for Ω ϕ Ω DM φ/(πf eff ) 06 / 13

14 Some Interesting Early Dynamics fields [mr =0] fields [mr =10] reheating reheating θ/π φ/(πf eff ) w w φ log [a/a RH ] m eff = 1eV tracking phase θ/π φ/(πf eff ) w w φ f eff = GeV taking mr 0 shows substantial differences: prior to undergoing coherent oscillations, axion field enters tracking phase : [ ] meff t ϕ(t) 2f log + constant 2 for many e-foldings that drives w ϕ w = 1 3 tracking prevents µ eff = θ oscillations that would wash out asymmetry and triggers these dynamics at higher temperatures deformation of mr > 0 potential triggers leptogenesis at higher temperatures 07 / 13

15 Some Interesting Early Dynamics nl generation fields [mr =10] Γ L/H = 0.1 reheating Γ L/H = 10 3 Γ L/H = 10 5 n L/s n eq L /s log [a/a RH ] m eff = 1eV tracking phase n obs L /s θ/π φ/(πf eff ) w w φ f eff = GeV taking mr 0 shows substantial differences: prior to undergoing coherent oscillations, axion field enters tracking phase : [ ] meff t ϕ(t) 2f log + constant 2 for many e-foldings that drives w ϕ w = 1 3 tracking prevents µ eff = θ oscillations that would wash out asymmetry and triggers these dynamics at higher temperatures deformation of mr > 0 potential triggers leptogenesis at higher temperatures 07 / 13

16 Viable Regions from Numerical Simulations mr the baryon asymmetry η B and axion abundance Ω ϕ can be achieved simultaneously in observed amounts: η B η B obs f eff =10 13 GeV Ω φ Ω obs DM V eff (φ I) > 3H I m eff [ev] excluded from decays decays suppressed not only by small effective mass m eff = Λ 2 e πmr /f, but also by suppressed couplings Γ ϕ m3 eff f 2 e πmr abundance at large mr only weakly depends on clockwork factor e πmr : Ω ϕ Ω obs DM [ feff /log ( 4e πmr) GeV ] 2 meff 3.7meV constraints from isocurvature? at first glance, presents a major concern for this type of scenario 08 / 13

17 Isocurvature Perturbations The axion is subject to de-sitter quantum fluctuations during inflation δϕ = H I 2π In our model, ultimately manifested in isocurvature mode two ways: 1 axion-photon isocurvature S ϕγ δ ϕ 1 + w ϕ 3 4 δ γ 2 baryon-photon isocurvature S Bγ δn B n B 3 4 δ γ both show significant departures from standard (mr = 0) case 09 / 13

18 Isocurvature Perturbations Baryon Component 10 using H I = 10 8 GeV When ϕ is slowly rolling most of baryon number density n B is produced: n B θt 2 [V eff (ϕ)]2 [1 V eff 2Λ 4 ] Veff 2Λ 4 perturbation at the end of slow roll: { [ ]} δn B 2 V eff (ϕ) n B V eff (ϕ) 1 V eff (ϕ) 1 V eff Λ 4 2 V eff (ϕ) 1 V δϕ eff 2Λ 4 inflection points/cancelations in terms can drive 0 Numerical simulations show additional suppression by up to O(10) factor P CDMγ eff /Peff[obs] CDMγ mr=15 mr=5 mr= φ I πf eff cancelation in δn B terms mr=1 mr=0 10 / 13

19 Isocurvature Perturbations Axion Component The tracking behavior in axion field implies a non-trivial evolution in S ϕγ 10 3 (1 + w φ ) S φγ 1 d [(1 + w ϕ )S ϕγ ] = Γ 2 d log a 2 [(1 + w ϕ )S ϕγ ] Γ = dγ d log a where it is coupled to the intrinstic entropy perturbation: pressure perturbation Γ δp ϕ /ρ ϕ c 2 ϕ δ ϕ 1 c 2 ϕ adiabatic sound speed reheating tracking phase log [a/a RH ] mr =10 can be solved analytically to show amplitude of S ϕγ 1/ a falls while axion follows tracking trjaectory 11 / 13

20 Isocurvature Perturbations Axion Component The tracking behavior in axion field implies a non-trivial evolution in S ϕγ 1 d [(1 + w ϕ )S ϕγ ] = Γ 2 d log a 2 [(1 + w ϕ )S ϕγ ] Γ = dγ d log a where it is coupled to the intrinstic entropy perturbation: pressure perturbation Γ δp ϕ /ρ ϕ c 2 ϕ δ ϕ 1 c 2 ϕ adiabatic sound speed can be solved analytically to show amplitude of S ϕγ 1/ a falls while axion follows tracking trjaectory δn B /n B can also be dynamically suppressed reheating tracking phase (1 + w φ ) S φγ δn L /n L log [a/a RH ] mr =0 mr =10 mr =10 axion tracking dynamics lead generically to a suppression of the axion S ϕγ and baryon S Bγ isocurvature modes 11 / 13

21 Revisiting the Viable Regions Including Isocurvature Constraints We cannot actually discriminate between S Bγ and S ϕγ contributions in CMB observations together these bound effective CDM isocurvature: P eff CDMγ(k ) η B η B obs 10 [ ΩB Ω CDM S Bγ + V eff (φ I) > 3H I 1 Ω ϕ Ω CDM S ϕγ ] mr Ω φ Ω obs DM excluded by isocurvature f eff =10 13 GeV m eff [ev] exclusion from decays 12 / 13

22 Revisiting the Viable Regions Including Isocurvature Constraints We cannot actually discriminate between S Bγ and S ϕγ contributions in CMB observations together these bound effective CDM isocurvature: mr P eff CDMγ(k ) η B η B obs Ω φ Ω obs DM [ ΩB Ω CDM S Bγ + V eff (φ I) > 3H I Ω ϕ Ω CDM S ϕγ ] isocurvature suppressed by tracking dynamics and cancelations in S Bγ : interesting regions remain viable excluded by isocurvature f eff =10 13 GeV m eff [ev] exclusion from decays 12 / 13

23 TAKE-AWAY MESSAGE: Taking advantage of deformations in the effective potential of continuum-clockwork axion, we can produce appropriate matter-antimatter asymmetry via spontaneous leptogenesis, with axion serving as dark matter candidate with proper abundance axion exhibits tracking behavior driven towards radiation-like equation of state prior to coherent oscillations suppression of isocurvature and more efficient asymmetry production due to these dynamics modifications to form of baryonic isocurvature THANK YOU FOR YOUR ATTENTION! 13 / 13

24 [BEGIN BACK-UP SLIDES] 13 / 13

25 The Discrete-Clockwork A Brief Review for Context In the discrete clockwork mechanism N + 1 axions θ j are coupled by nearest-neighbor interactions (with q Z): L = 1 N N 1 f 2 ( µ θ j ) 2 + µ 2 f 2 cos (θ j+1 qθ j ) 2 j=0 [Choi, Kim, Yun 14] [Choi, Im 15] [Kaplan, Rattazzi 15] symmetry U(1) N+1 broken down to a single U(1) CW : θ j θ j + αq j The massless field ϕ associated with U(1) CW has an overlap with each θ j : j=0 ϕ θ j q j N for N 1 that localizes ϕ toward end of θ j -chain with strength set by q As a result, couplings to other operators gθ j O give hierarchically different contributions to massless mode gq j N ϕo SM θ 0 θ 1 θ 2 θ 3 θ 4 θ 5 θ 6 θ N any couplings q N ϕo SM exponentially suppressed overlap ϕ θj 13 / 13

26 The Discrete-Clockwork A Brief Review for Context [Choi, Kim, Yun 14] [Choi, Im 15] [Kaplan, Rattazzi 15] overlap ϕ θj SM θ 0 θ 1 θ 2 θ 3 θ 4 θ 5 θ 6 θ N any couplings q N ϕo SM exponentially suppressed 13 / 13

27 The Discrete-Clockwork A Brief Review for Context [Choi, Kim, Yun 14] [Choi, Im 15] [Kaplan, Rattazzi 15] consider N continuum limit: identify y jϵ with extra spatial coordinate ϵ = πr N 0 size = πr overlap ϕ θj SM θ 0 θ 1 θ 2 θ 3 θ 4 θ 5 θ 6 θ N any couplings q N ϕo SM exponentially suppressed 13 / 13

28 The Continuum-Clockwork Axion [Giudice et al. 16] [Craig et al. 17] [Choi et al. 17] Taking the number of clockwork fields N we can construct a continuum limit: S = f 5 3 d 5 x [( µ θ) 2 + ( y θ m sin θ) 2] 2 with y interpreted as coordinate of an S 1 /Z 2 flat extra dimension of size πr, and θ = θ(x, y) is now a bulk angular field with periodicity θ θ + 2π The bulk/boundary masses above furnish a massless 4D axion ϕ(x): [ ] θ(x, y) tan = e my u [ϕ(x)] 2 where [ ϕ(x) ] u [ϕ(x)] = ie πmr sn e 2πmR 2if Jacobi elliptic function f 5 f 3 2m (1 e 2πmR ) A mode expansion for δθ θ θ δθ(x, y) = f 0 (y)δϕ(x)+ f n (y)δϕ n (x) n=1 shows localization of the massless mode δϕ is retained: f 0 (y) sech [m (y y 0 )] y 0 log [ u(ϕ) ] localization dependent on 4D axion VEV ϕ 13 / 13

29 Effective 4D-Axion Potential While this axion ϕ is massless, a small deviation in boundary mass generates an effective potential: V eff (ϕ) = Λ 4 {1 cos [θ(x, 0)]} = 2Λ4 [u(ϕ)] [u(ϕ)] 2 m 2 eff 2 V eff ϕ 2 clockwork factor analogous to q 2N = ϕ=0 shape of potential V eff (ϕ) is contorted as mr deviates from zero, since position of localization set by ϕ 2πmR Λ4 e f 2 SM brane [Choi, Im, Shin 17] effective periodicity 2πf eff 1.0 mr =0 mr = mr =2 mr =5 mr =7 mr = Veff(φ)/(2Λ 4 ) ϕ πf eff θ(x, 0)O(x) quadratic φ/(πf eff ) ϕ 0 δϕ profile y =0 y =πr e mπr δϕ couplings suppressed O(x) f for ϕ 0 13 / 13

30 Effective 4D-Axion Potential While this axion ϕ is massless, a small deviation in boundary mass generates an effective potential: V eff (ϕ) = Λ 4 {1 cos [θ(x, 0)]} = 2Λ4 [u(ϕ)] [u(ϕ)] 2 m 2 eff 2 V eff ϕ 2 clockwork factor analogous to q 2N = ϕ=0 shape of potential V eff (ϕ) is contorted as mr deviates from zero, since position of localization set by ϕ 2πmR Λ4 e f 2 SM brane [Choi, Im, Shin 17] effective periodicity 2πf eff 1.0 large curvature drives leptogenesis 0.8 more efficiently Veff(φ)/(2Λ 4 ) ϕ πf eff θ(x, 0)O(x) quadratic small curvature suppresses decays, allows for Ω ϕ Ω DM φ/(πf eff ) ϕ 0 δϕ profile y =0 y =πr e mπr δϕ couplings suppressed O(x) f for ϕ 0 13 / 13

31 Summary of the Model The effective four-dimensional model then appears as S eff = d 4 x [ g 1 ] 2 gµν µ ϕ ν ϕ V eff (ϕ) µ eff n L + The leptons couple to θ θ(x, 0): sgn{ϕ} 2Λ V 4 µ eff θ eff = (ϕ) (1 V eff ) ϕ Veff 2Λ 4 2Λ 4 n eq L µ eff non-linear function of both {ϕ, ϕ} which significantly alters dynamics from the standard scenario: d(n L /s) d log T = T T L ( nl T L GeV ) s neq L s To model during/after reheating: inflaton ρ φ + 3Hρ φ = Γ φ ρ φ ρ R + 4Hρ R = +Γ φ ρ φ + Γ ϕ ρ ϕ radiation and the axion evolution goes as ϕ + ( 3H+Γ ϕ ) ϕ + V eff ϕ = µ eff ϕ Γ L(n L n eq L ) backreaction usually negligible 13 / 13

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