Leptogenesis from a First-Order Lepton- Number Breaking Phase Transition

Transcription

1 Leptogenesis from a First-Order Lepton- umber Breaking Phase Transition Andrew Long TeVPA 2017 at Ohio State University Aug 10, 2017 based on work with Andrea Tesi & Lian-Tao Wang ( & JHEP)

2 Bubbles! Andrew Long TeVPA 2017 at Ohio State University Aug 10, 2017

3 Executive Summary In this talk, I m going to assume that lepton-number is broken spontaneously by the VEV of a new scalar singlet field that induces a Majorana mass for new sterile neutrinos. (light neutrino masses arise from the seesaw mechanism) assume that there was a corresponding cosmological phase transition in the early universe, and that it was first order. show that the baryon asymmetry of the universe can arise at this phase transition via the CP-violating scattering of heavy Majorana fermions from the bubble wall (similar to Cohen, Kaplan, & elson s original implementation of EW baryogenesis) calculate the predicted baryon asymmetry and discuss the associated phenomenology (gravitational waves, 0νββ, dark radiation) Andrew PASCOS

4 The Model

5 Minimal generalization of the leptogenesis model Promote the Majorana mass parameter to a scalar field: L = 1 2 M LH +h.c. (type-i seesaw model; thermal leptogenesis) L = 1 2 apples LH +h.c. U(S) (somesmes called the singlet Majoron model) ow the theory has a U(1) L symmetry under which the charges are Q L (L) = +1, Q L () = -1, and Q L (S) = +2.

6 Spontaneous L-number breaking The scalar potential U(S) causes S to get a vev, which breaks lepton-number.! hsi = v S / p 2 Yukawa interaction induces a Majorana mass L = 1 2 apples! 1 2 M M = applehsi

7 Light neutrino masses Integrating out the heavy Majorana neutrinos induces a Majorana mass for the light neutrinos L = 1 2 M LH! 2 LHLH M! 2 v2 M Fiducial Parameters: apples! apple 1 LH! U(S)! v S GeV M applev S GeV m 2 v 2 /M 0.1 ev

8 Baryogenesis Overview

9 Overview of the Mechanism 1 Thermal U(1) L symmetry restoration 2 First order phase transition 3 Scattering on Wall (CP & L violation) 4 Transfer of L-number to SM 5 Washout Avoidance

10 Lepton-number unbroken hsi =0 m =0 (1) Initially <S> = 0 and the U(1) L symmetry is restored. = massless, left-handed anti-lepton = massless, right-handed lepton

11 Lepton-number unbroken Lepton-number broken hsi =0 hsi 6=0 m =0 m >T (2) The U(1) L - breaking phase transition is first order. Bubbles of broken phase nucleate and expand.

12 Lepton-number unbroken Lepton-number broken hsi =0 hsi 6=0 m =0 m >T CP L (3) & bar in the plasma scatter from the bubble wall. è Scattering converts into -bar and -bar into, because interaction with the wall violates lepton-number. è If the interaction additionally violates CP, then an excess of over -bar develops.

13 L int = LH L L L L (4) In front of the wall, lepton-number is transferred from to SM leptons L via the LH Yukawa interaction

14 L int = LH L L L L L L L L (4) In front of the wall, lepton-number is transferred from to SM leptons L via the LH Yukawa interaction (5) Behind the wall, the washout of leptonnumber is avoided as long as m >~ 10 T

15 Overview of the Mechanism 1 Thermal U(1) L symmetry restoration 2 First order phase transition 3 Scattering on Wall (CP & L violation) 4 Transfer of L-number to SM 5 Washout Avoidance Some similarity with an early implementation of EW baryogenesis: Cohen, Kaplan, & elson (1990, 91) Related work by: Shu, Tait, & Wagner (2007); Fornal, Shirman, Tait, & West (2017); Cline, Kainulainen, & Tucker-Smith (2017)

16 It s the best of both worlds As in thermal leptogenesis we have a framework that naturally accommodates the light neutrino masses and predicts that the light neutrinos are Majorana particles. As in electroweak baryogenesis we have a first order phase transition, which furnishes complementary cosmological observables (gravitational waves).

17 Estimate the baryon asymmetry

18 The resultant baryon asymmetry The baryon-to-entropy ratio can be expressed as number density of B-number -to-l conversion factor (via LH) -number source (rate per unit volume) at the wall n B s = f L!B " L$ L f!l " $ L w v w S /CP s entropy density of plasma L-to-B conversion factor (via sphaleron) asymmetry washout factors wall passage Sme

19 The resultant baryon asymmetry The baryon-to-entropy ratio can be expressed as number density of B-number -to-l conversion factor (via LH) -number source (rate per unit volume) at the wall n B s = f L!B " L$ L f!l " $ L w v w S /CP s entropy density of plasma L-to-B conversion factor (via sphaleron) asymmetry washout factors wall passage Sme

20 The resultant baryon asymmetry The baryon-to-entropy ratio can be expressed as number density of B-number -to-l conversion factor (via LH) -number source (rate per unit volume) at the wall n B s = f L!B " L$ L f!l " $ L w v w S /CP s entropy density of plasma L-to-B conversion factor (via sphaleron) asymmetry washout factors wall passage Sme

21 The resultant baryon asymmetry The baryon-to-entropy ratio can be expressed as number density of B-number -to-l conversion factor (via LH) -number source (rate per unit volume) at the wall n B s = f L!B " L$ L f!l " $ L w v w S /CP s entropy density of plasma L-to-B conversion factor (via sphaleron) asymmetry washout factors wall passage Sme

22 CP-violating source of -number S / CP At the wall, the Majorana mass acquires a non-trivial profile m (z) M (z) =m (z) e i (z) θ(z) z Due to the phase gradient, and -bar effectively see potential energy barriers of different heights. E! E z (z) Consequently, and -bar have different probabilities to be reflected. We denote the reflection probabilities as R and R-bar.

23 CP-violating source of -number When a reflection occurs, lepton-number is violated hsi S / CP hsi This formalism was developed by Huet & elson (1995). Can also calculate source w/ semiclassical force formalism (see: Joyce, Prokopec, Turok; Cline, Kainulainen; Konstandin) probability R probability R-bar Consequently, the wall becomes a source of -number: S /CP (z) = 2 Z 1 1 dp x 2 Z 1 1 dp y 2 Z 1 0 dp z 2 f (out) f (in) R R thermalizason Sme scale phase space distribuson funcsons (Fermi-Dirac) for parscles incident on the wall from the bubble exterior (out) and interior (in) differensal reflecson probability arising from CP-violaSng effects, which goes as dθ/dz

24 CP-violating source of -number CP S / The integral evaluates to S /CP (T ) w v w 2 m (T ) 3 (T ) L w min (T ) 3, 0.1(T ) 1 e m (T )/T Boltzmann suppression In the regime T << m, only particles in the tail of the most momentum distribution have enough energy to enter the bubble. When all particles are reflected, R = R-bar = 1, the CP-violating effects vanish. Hence, the Boltzmann suppression.

25 -number diffusion The sourced -number diffuses away from the bubble wall. v w x di = p D x wall = v w t t imagine that -number (stars) is produced like a pulse v w z become equal when z v w L d = D /v w d = D /v 2 w z

26 -number diffusion The sourced -number diffuses away from the bubble wall. We describe this process with a transport equation: v w n 0 D n 00 n + S /CP where v w is the wall speed D is the diffusion coefficient Γ is the washout rate due to <--> -bar flips (active at the wall, and inside the bubble) S is the CP-violating source (only active at the wall)

27 -number diffusion In front of the wall, the solution is n (z) min 1 1, p D /vw 2 L w v w S /CP ev wz/d The -number precedes the wall for a distance D /v w. The amplitude is suppressed due to washout.

28 Conversion into L-number f!l In front of the wall, the -number excess pushes the LH Yukawa interaction out of equilibrium. L H The excess of s becomes a deficit of L s a negative L-number. n L LH D vw 2 where Γ LH is the thermally-averaged LH interaction rate. m H (T ) 2 n LH 2 T 2 T 2 b/c of seesaw: neutrino mass suppression makes conversion inefficient unless m >> v m m m H (T ) 2 v 2

29 Lepton-number washout avoidance " L! L The L-number diffuses into the bubble where U(1) L is broken. Lepton-number is threatened to be washed out by processes like H H L L The lepton-number will be suppressed by a washout factor dt 0 w.o.(t) h Z 1 i " L$ L =exp t L w.o. 2 m 5/2 T 3/2 e m /T h =exp Z TL 0 dt T Boltzmann suppression w.o(t ) H(T ) i

30 Lepton-number washout avoidance " L! L We evaluate the washout factor h " L$ L exp 32.5 x 5/2 e xi x=m (T L )/T L - Γ / ε _ need m >> T inside bubbles to suppress L- violasng washout. This is easier in EW baryogenesis, because the sphaleron mass is nonperturbasvely large, ~v/g. - - = / = /

31 Conversion into baryon-number f L!B Just like in thermal leptogenesis, the lepton-number is converted into baryon-number by the SM electroweak sphaleron processes. n B = n lep Q 1 Harvey & Turner (1990) L L L τ e µ Q Q 3 2

32 Putting it all together The predicted baryon-to-entropy ratio is n h B s ±28 79 min 1, p 45 (T ) m (T ) g T 3 1 i D h D /vw 2 LH vw 2 exp h min (T ) 3, 0.1(T ) 1i e m (T )/T and in the parameter regime of interest, this reduces to Z TL 0 dt T w.o(t ) H(T ) i n B s ± LH D /vw 2 h T p exp D /vw 2 Z TL 0 dt T w.o(t ) i (T ) m (T ) 3 H(T ) g T 3 e m (T )/T umerically, n B s m (T L ) GeV! (TL ) vw 1 g 1 x 2 e x e 32.5 x5/2 e x

33 Final Baryon Asymmetry κ = θ( ) = π = ote that the dependence on κ (the S Yukawa coupling) has dropped out. - washout suppresses asymmetry source suppresses asymmetry Sitting at x ~ 9, we are bounded below by exponential washout suppression & bounded above by exponential source suppression. Lowering m lowers λ (through the seesaw relation). This makes the àl conversion less efficient & suppresses the baryon asymmetry. / m sets λ (efficiency of - to-l conversion) = = ~ = = = - - = /

34 Final Baryon Asymmetry ote that the dependence on κ (the S Yukawa coupling) has dropped out. = / = θ( ) = π = Sitting at x ~ 9, we are bounded below by exponential washout suppression & bounded above by exponential source suppression. Lowering m lowers λ (through the seesaw relation). This makes the àl conversion less efficient & suppresses the baryon asymmetry. κ - / = - / = - / = - / = - - [ ]

35 Phenomenology Highlights

36 Phenomenology Highlights eutrinoless Double Beta Decay since the light neutrinos are Majorana particles, this lepton-number-violating channel is open. Majoron the goldstone boson of spontaneously broken U(1) L, which couples to the light neutrinos. However, if the scale of lepton-violation is as large as v L ~ GeV, the coupling is very suppressed (roughly m ν / v L ), making the majoron difficult to probe. Cosmic String etwork the breaking of a U(1) symmetry produces a network of topological defects, which persist in the universe today. As the strings gravitate, they produce gravitational wave radiation, which may be detectable with pulsar timing arrays. Gravitational Waves the first order U(1) L -breaking phase transition creates GW s when the bubbles collide. The spectrum is expected to peak at, f >~ (10 5 Hz)(T L / GeV), on the high side of LIGO.

37 Gravitational Wave Signature f & 10 5 Hz T L GeV

38 Executive Summary In this talk, I m going to assume that lepton-number is broken spontaneously by the VEV of a new scalar singlet field that induces a Majorana mass for new sterile neutrinos. (light neutrino masses arise from the seesaw mechanism) assume that there was a corresponding cosmological phase transition in the early universe, and that it was first order. show that the baryon asymmetry of the universe can arise at this phase transition via the CP-violating scattering of heavy Majorana fermions from the bubble wall (similar to Cohen, Kaplan, & elson s original implementation of EW baryogenesis) calculate the predicted baryon asymmetry and discuss the associated phenomenology (gravitational waves, 0νββ, dark radiation) Andrew PASCOS