Leptogenesis from GeV-Scale Sterile Neutrinos

Transcription

1 Leptogenesis from GeV-Scale Sterile Neutrinos Björn Garbrecht Physik-Department T70 Technische Universität München Lorentz Center Workshop Matter over Antimatter: The Sakharov conditions After 50 years Leiden, 08/05/17

2 Outline 1. Sakharov Conditions and Leptogenesis Non-Equilibrium CP Violation Baryon Number Violation 2. Closed-Time-Path Approach 3. Akhmedov Rubakov Smirnov (ARS)/GeV-Scale Leptogenesis 4. Conclusions

3 Table of Contents 1. Sakharov Conditions and Leptogenesis Non-Equilibrium CP Violation Baryon Number Violation 2. Closed-Time-Path Approach 3. Akhmedov Rubakov Smirnov (ARS)/GeV-Scale Leptogenesis 4. Conclusions

4 Dynamical Generation of the BAU: Sakharov Conditions What was known in : Dirac equation 1955: CP T theorem (Pauli) 1964: CP (Cronin & Fitch) 1932: positron 1956: parity violation (Wu) 1964: CMB (Penzias & Wilson) Today: Baryon-to-photon ratio η B = (6.16 ± 0.15) [Planck, 68% confidence level], i.e. in the early Universe, there was one extra quark per ten billion quark-antiquark pairs. Creating the baryon (B) asymmetry of the Universe (BAU) from symmetric initial conditions (baryogenesis) requires [Sakharov (1966)] 1 B violation, 2 charge (C) and charge-parity (CP ) violation, 3 departure from equilibrium % dark energy baryons 4.9 % 26.8 % dark matter [Planck (2013)] Remark on 3rd Condition CP T -invariance theorem is the QFT generalization of the time reversal invariance well-known from classical mechanics and electrodynamics. Need to break time-reversal (T ) invariance to allow for CP asymmetry. Realize this thermodynamically (2nd law, non-equilibrium irreversible processes).

5 Table of Contents 1. Sakharov Conditions and Leptogenesis Non-Equilibrium CP Violation Baryon Number Violation 2. Closed-Time-Path Approach 3. Akhmedov Rubakov Smirnov (ARS)/GeV-Scale Leptogenesis 4. Conclusions

6 Kinetic & Fluid Equations Set of equations describing a non-equilibrium system of a large number of particles Should be derivable from first principles classical: Liouville equations (with interaction potentials) quantum: Schwinger-Dyson equations in Closed-Time-Path (CTP) formalism Truncations/approximations Reduction to irreversible kinetic equations in the form of Boltzmann equations (or variants thereof taking e.g. account of flavour coherence, quantum statistics) Further reduction down to fluid equations (in terms of number densities and bulk flows instead of particle distributions) Allows for analytical/numerical treatment Liouville/Schwinger- Dyson equations (microscopic kinetic equations) Boltzmann-like kinetic equation for distribution functions fluid equations for number densities/ bulk flows

7 Kinetic Equations in Early Universe Cosmology Example: Inferring the Asymmetry from Observations Baryon-to-photon ratio η B = (6.16 ± 0.15) can be inferred from observations light elements produced during Big Bang Nucleosnynthesis (BBN), anisotropies of the cosmic microwave background (CMB), in particular baryon acoustic oscillations (BAOs). Theoretical predictions from Boltzmann/fluid equations that model network of nuclear reactions or scatterings of photons, electrons and nuclei/ons. µ j µ X = tnx jx + 3HnX = CX C X = 1 d 3 p i δ 4 (p 2E X (2π 3 X + p A1 + p B1 ) )2E i i { (1 ± f X)(1 ± f A1) f B1 M B1 B 2 XA 1 A 2 2 f Xf A1 (1 ± f B1) M XA1 A 2 B 1 B 2 2} n X: number density j X: current density j µ : four-current µ: cov. derivative H: Hubble rate C X: collision term f i: distribution fn. Agreement between BBN & and CMB values for BAU huge success aim to repeat this e.g. for baryogenesis or dark matter abundance

8 Non-Equilibrium and Neutrinos Neutrinos Masses & Mixings Mass Parameters for Active Neutrinos from Oscillation Experiments m 2 21 = ev 2, m 2 31 = ev 2 (NH), m i < 0.23eV [Gonzalez-Garcia, Maltoni, Schwetz (2014)], upper bound from 95% c.l. i ν n = Uai ν a, a a = e, µ, τ; n = 1, 2, 3 m m 2 0 = U mu 0 0 m 3 for Majorana neutrinos, for Dirac neutrinos just like CKM mechanism. U is the Pontecorvo-Maki- Nakagawa-Sakata (PMNS) matrix. m 3 2 m 2 2 m 1 2 Normal atmospheric: ev 2 solar: ev 2 Inverted solar: ev 2 atmospheric: ev 2 ν e ν µ ν τ Active neutrino mass differences & mixing [from JUNO physics paper (2015)] Why is the mass scale of neutrinos (several mev) much below that for other SM particles, e.g. electron (511 kev), or top quark (173 GeV)? m 2 2 m 1 2 m 3 2

9 Non-Equilibrium and Neutrinos Seesaw Mechanism This talk Type I seesaw: Introduce n N hypothetical right-handed neutrinos N (RHNs) with Majorana mass matrix M (can take it to be diagonal), couple these to to Standard Model lepton l = (ν, e L) and Higgs doublets φ, φ = v = 174 GeV: L SM L SM + 1 N c 2 i (i / M ij)n j Yia l aφ N i Y ia Niφl a; a = e, µ, τ ( ) ( ) 1 (3 + n N ) (3 + n N ) matrix: ( ν N 0 c md ν c ) 2 m T, m D M N D = Y v }{{} =:M Assume ( M ) m block-diagonalization ( ) m 0 1 θθ = 0 M ŨMŨ θ, Ũ = θ 1 θ + O(θ 3 ), θ = Y vm 1 θ Majorana mass matrix for light ( neutrinos: m = v 2 Y M 1 Y, diagonalised by U, for heavy neutrinos M N = M θ θm + Mθ T θ ) + O(θ 3 ), diagonalised by U N ν light = U ( (1 1 2 θθ )ν θn c) (, ν heavy = U N (1 1 2 θt θ )N θ T ν c) Comprehensive overview of leptogenesis in the type I seesaw mechanism throughout the parameter space, in particular for all mass scales M.

10 Non-Equilibrium and Neutrinos Out-of-Equilibrium Dynamics Simplest Meaningful Network of Fluid Equations Describing Leptogenesis : dn Ni + 3Hn Ni =Γ i(n Ni n eq Ni dt ) Γ i = Yi 2 8π Mi ( ) 3 dn L + 3Hn L =εγ i(n Ni n eq Ni dt ) W nl W = Γi M 2 e M T 4 T n Ni: number density of N i; n L: lepton charge density; W : washout rate; ε = (Γ Ni lh Γ Ni lh )/(Γ Ni lh + Γ Ni lh ): decay asymmetry; T : temperature Best compromise between large L violating rate (1st S. condition) and and large deviation from equilibrium (3rd S. condition): Γ H for T M (i.e. at freezeout, when the RHNs become Maxwell suppressed). Y 2 M/(8π) T 2 /m Pl M 2 m Y /m Pl 2 v 2 M m 8πv 2 /m Pl 0.1 mev Light Neutrino Mass Scale points to Role of RHNs in Baryogenesis Out-of-equilibrium property of the N independent of the mass scale. Tendency of being somewhat close to equilibrium, i.e. Γ H around T M strong washout. However, a lot of parametric freedom. Assume M M W for now, get back to case M GeV in section on ARS

11 Table of Contents 1. Sakharov Conditions and Leptogenesis Non-Equilibrium CP Violation Baryon Number Violation 2. Closed-Time-Path Approach 3. Akhmedov Rubakov Smirnov (ARS)/GeV-Scale Leptogenesis 4. Conclusions

12 CP Violation & Quantum Interference Brief Reminder of the Basics Squared amplitude for some CP violating process: a 1 a m A a e iϕa + b 1 b n A b e iϕ b 2 (a 1 a mb 1 b -term me i(ϕa ϕb) + c.c.) A aa b a i, b i: coupling constants A a,b : amplitudes stripped of coupling constants arg(a 1 a mb 1 b m): weak phase ϕ a,b : ( strong ) phases of A a,b Rate for CP conjugate process: a 1 a m A a e iϕa + b 1 b n A b e iϕ b 2 (a 1 a -term mb 1 b me i(ϕa ϕb) + c.c.) A aa b Difference: (a 1 a mb 1 b m a 1 a mb 1 b m)(e i(ϕa ϕ b) e i(ϕa ϕ b) ) =4Im[e i(ϕa ϕ b) ]Im[a 1 a mb 1 b n] A aa b

13 CP Violation & Quantum Interference Brief Reminder of the Basics Squared amplitude for some CP violating process: a 1 a m A a e iϕa + b 1 b n A b e iϕ b 2 (a 1 a mb 1 b -term me i(ϕa ϕb) + c.c.) A aa b a i, b i: coupling constants A a,b : amplitudes stripped of coupling constants arg(a 1 a mb 1 b m): weak phase ϕ a,b : ( strong ) phases of A a,b Rate for CP conjugate process: a 1 a m A a e iϕa + b 1 b n A b e iϕ b 2 (a 1 a -term mb 1 b me i(ϕa ϕb) + c.c.) A aa b Difference: (a 1 a mb 1 b m a 1 a mb 1 b m)(e i(ϕa ϕ b) e i(ϕa ϕ b) ) =4Im[e i(ϕa ϕ b) ]Im[a 1 a mb 1 b n] A aa b Im[e iϕ a,b ] comes from coherent superposition of different quantum states. For calculable problems, these often correspond to on-shell cuts in a Feynman diagram (typical view on standard leptogenesis) or to flavour mixing and oscillations (typical view on ARS leptogenesis). There are parametric regimes where calculations based on the cuts in wave-function diagrams lead to the same answer as those based on the time evolution of mixing and oscillating states.

14 Standard Approach to Standard Leptogenesis L SM L SM N c i (i / M ij)n j Y ia l aφ N i Y ia Niφl a; a = e, µ, τ; i = 1, 2,... decay asymmetry: ε Ni = Γ Ni lh Γ Ni lh Γ Ni lh +Γ Ni lh [Fukugita, Yanagida (1986); Covi, Roulet, Vissani (1996)] Wave Function & Vertex Contributions: ε wf Ni = 1 M i M j Im[(Y Y ) 2 ij ] 8π Mi 2 M j 2 (Y resonant enhancement for M Y ) i M j ii j i ε vertex Ni = 1 8π j i [ ( ) ( )] M j M M j 2 Im[(Y Y log 1 + M ) 2 2 ij ] i Mi 2 i Mj 2 (Y Y ) ii Understand situation when M 2 i M 2 j M i,jγ Ni,j does not hold.

15 Real Intermediate State (RIS) Problem Interference of tree & loop amplitudes CP violation. ( ) CP violating contributions ( strong phase ) from discontinuities loop momenta where cut particles are on shell. Is and? an extra process or is it already accounted for by Including ( ) only CP asymmetry is already generated in equilibrium. CP T theorem.

16 (Inverse) Decays & CP Asymmetry Consider the squared matrix elements, ε being the decay asymmetry. Naive multiplication suggests that an asymmetry is generated already in equilibrium: Γ lφ lφ 1 + 2ε, Γ lφ lφ 1 2ε Ad hoc fix: Subtract real intermediate states (RIS) from [Kolb, Wolfram (1980)]. Fix of the approach by a posteriori imposing CP T theorem Better Way Out Compute the real time (time dependent perturbation theory), non-equilibrium (statistical physics) evolution of the quantum field theory states of interest. Do not try this at home: The unstable N are not asymptotic states of a unitary S matrix conflict with the CP T theorem.

17 CP Phases in the Type I Seesaw Model Low-energy phases : one Dirac phase δ and two Majorana phases α 1,2 in the PMNS matrix The combination Y ia Y aj that enters the sum of asymmetries in all a flavours a = e, µ, τ is invariant under changes in PMNS matrix. n N(n N 1) high-energy phases 2 Only if the light neutrinos are Majorana, such as it is the case in the type I seesaw, of course

18 Casas-Ibarra Parametrization & Inverse Seesaw Y = U m diag R M diag 2 v R: complex orthogonal matrix ( complex angles) Large imaginary parts of complex angles lead to large R, Y. Cancellations in the light neutrinos mass, desirable to explain & to protext these with symmetry Approximate lepton number conservation Explains/requires approximate mass degeneracy such that two of the RHNs form a pseudo-dirac state Inverse seesaw (preferred setup for ARS?) ( ) ( ) 0 md 0 MN M with M = and µ m M N µ D M N m T D m = m D M 1 1 N µmn mt D

19 Table of Contents 1. Sakharov Conditions and Leptogenesis Non-Equilibrium CP Violation Baryon Number Violation 2. Closed-Time-Path Approach 3. Akhmedov Rubakov Smirnov (ARS)/GeV-Scale Leptogenesis 4. Conclusions

20 Lepton & Baryon Number Violation RHNs are their only antiparticles can decay either N i lφ or N i lφ and therefore violate lepton number L. In absence of lepton number violation (LNV) and lepton flavour violation (LFV) a = B 3 L a is conserved. B: baryon asymmetry L a : asymmetry in lepton flavour a, in total: L = a=e,µ,τ In absence of LNV but presence of LFV only B L is conserved. Sphaleron Conversion: B = a=e,µ,τ a = 28 (B L) 79 SM prefactor, differs (slightly) in other models. L a

21 Lepton Number Violating (LNV) and Lepton Number Conserving (LNC) Scenarios After initial creation of asymmetries = a=e,µ,τ { 0 (LNV) a = 0 (LNC) In the LNC case, flavour-dependent washout may lead to 0 after all (at least prior to sphaleron conversion). LNV source does not depend on low-energy phases. LNC source in general depends on both, high and low-energy phases.

22 Table of Contents 1. Sakharov Conditions and Leptogenesis Non-Equilibrium CP Violation Baryon Number Violation 2. Closed-Time-Path Approach 3. Akhmedov Rubakov Smirnov (ARS)/GeV-Scale Leptogenesis 4. Conclusions

23 Closed-Time-Path Approach In-in generating functional (in contrast to in-out for S matrix elements): [Schwinger (1961); Keldysh (1965); Calzetta & Hu (1988)] Z[J +, J ] = = The Closed Time Path: Dφ(τ)Dφ in Dφ+ in φ in φ(τ) φ(τ) φ+ in φ in ϱ φ+ in Dφ Dφ + e i d 4 x{l(φ + ) L(φ )+J + φ + J φ } Path-ordered Green functions: i ab δ (u, v) = 2 δj a(u)δj b (v) log Z[J +, J ] e.g. j µ (x) = tr[γ µ C[ψ (x 1 ) ψ + (x 2 )] ] x1 =x 2 =x Aim: Calculate in O(t) in J± =0 = i C[φa (u)φ b (v)] Wigner Transformation of Two-Point Functions (Green Function or Self Energy) A(k, x) = d 4 r e ik r A (x + r/2, x r/2) distribution function x: average coordinate macroscopic evolution r k: relative coordinate microscopic (quantum)

24 Path Ordered Green Tree Level Four propagators (two of which are linearly } independent): i < (u, v) = i + (u, v) = φ(v)φ(u) i > (u, v) = i + Wightman functions (u, v) = φ(u)φ(v) i T (u, v) = i ++ (u, v) = T [φ(u)φ(v)] Feynman propagator i T (u, v) = i (u, v) = T [φ(u)φ(v)] Dyson propagator Perturbation theory can be formulated in terms of tree-level Wigner-space propagators: i < (p, t) =2πδ(p 2 + m 2 ) [ ϑ(p 0 )f(p, t) + ϑ( p 0 )(1 + f( p, t)) ] i > (p, t) =2πδ(p 2 + m 2 ) [ ϑ(p 0 )(1 + f(p, t)) + ϑ( p 0 ) f( p, t) ] i T i (p, t) = p 2 m 2 + iε + 2πδ(p2 + m 2 ) [ ϑ(p 0 )f(p, t) + ϑ( p 0 ) f( p, t) ] i T i (p, t) = p 2 m 2 iε + 2πδ(p2 + m 2 ) [ ϑ(p 0 )f(p, t) + ϑ( p 0 ) f( p, t) ] f(p, t), f(p, t): Particle and antiparticle distribution functions. Carry flavour indices (relevant for leptogenesis: sterile & active flavour).

25 Schwinger-Dyson & Kadanoff-Baym Equations Feynman Rules Vertices either + or. Connect vertices a = ± and b = ± with i ab. Factor 1 for each vertex. Schwinger-Dyson equations These describe in principle the full time evolution. However, truncations, e.g. perturbation theory, are needed. The <, > +, + parts of the Schwinger-Dyson equations are the celebrated Kadanoff-Baym equation: ( 2 m 2 ) <,> Π H <,> Π <,> H = 1 ( Π > < Π < >) } 2 {{} collision term Remaining linear combination gives pole-mass equation: ( 2 m 2 )i R,A Π R,A i R,A = iδ 4, R, A: retarded, advanced, Π H, H = Re[Π R, R ] First principle derivation of Boltzmann-like kinetic equations. [Keldysh (1965); Calzetta & Hu (1988)]

26 Leptogenesis in the CTP Approach Schwinger-Dyson equations relevant for leptogenesis: [Buchmüller, Fredenhagen (2000); De Simone, Riotto (2007); Garny, Hohenegger, Kartatvtsev, Lindner (2009-); Beneke, BG, Herranen, Schwaller (2010-); Anisimov, Buchmüller, Drewes, Mendizabal (2010-)] Truncation that yields leading asymmetry in non-degenerate regime M i Γ i, M j Γ j M 2 i M 2 j : Non-minimal truncations e.g. systematic inclusion of thermal corrections.

27 Unitarity Restored (without RIS) CTP approach readily yields inclusive rates for the creation of the charge asymmetry. No need to separately remove unwanted/unphysical contribution a posteriori. Loop insertions in propagator for N must be resummed unless (typical p T ) { Y Mi 2 M j p 2 / 2 + Mi 2 Γ i 2 /(16π)M i for M i T Y 2 g 2 log g T for M i T.

28 Leptogenesis from Oscillations/Resonant Limit Evolution for Matrix-Valued RHN Distributions δf Nh (i.e. deviation from equilibrium form f eq N ) δf Nh + a2 (η) i[m 2, δf 2k 0 Nh ] + f eq N = 2{ Re[Y Y t ] k ˆΣ A N k 0 ihim[y Y t ] k ˆΣ A } N, δf k 0 Nh ˆΣ A N : spectral (cut part) self energy, a(η), η : scale factor and conformal time, d/dη, h: helicity, k = ( k, k 0 k/ k ) i[m 2, δf Nh ] ij = i(m 2 i M 2 j )δf Nhij for diagonal M 2 RHN flavour oscillations Off-diagonal entries of δf Nh ij correspond to interference between the different N i that give rise to CP violation ( strong phases ) Note: If δf Nh and off diagonal elements of the collision term can be neglected, recover result from standard resonant leptogenesis next slide Evolution equations are well behaved for M 2 0. Solutions δf Nh enter into the resummed RHN propagators. [BG, Herranen (2010); Iso, Shimada (2014); BG, Gautier, Klaric (2014)]

29 Regulator for Resonant Leptogenesis in Strong Washout Wave-function contribution: ε wf Ni = 1 8π j i M i M j (M 2 i +M 2 j ) (M 2 i M 2 j )2 +R Im[(Y Y ) 2 ij ] (Y Y ) ii In the degenerate limit, this will dominate over the vertex contribution. Proposed forms for regulator R ( M = (M i + M j )/2): R = M 4 64π (Y Y ) 2 2 jj = M 2 Γ 2 j [Pilaftsis (1997); Pilaftsis, Underwood (2003)] R = M ( ) 4 64π [Y Y ] 2 ii [Y Y 2 ] jj [Anisimov, Broncano, Plümacher (2005)] R = M ( ) 4 64π [Y Y ] 2 ii + [Y Y 2 ] jj [Garny, Hohenegger, Kartavtsev (2011)] R = M 4 ([Y Y ] 11 + [Y Y ] 22 ) 2 ( (Im[Y Y 64π 2 [Y Y ] 11 [Y Y ] 12 ) 2 + det Y Y ) ] 22 Obtained by algebraic solution to oscillation equation, neglecting δf N [BG, Gautier, Klaric (2014); Iso, Shimada (2014)]

30 Resonant Leptogenesis in the Strong Washout Regime Quasistatic Approximation Neglect derivative term provided the eigenvalues (that originate from the mass and the damping terms) in the kinetic equation for are larger than the Hubble rate H obtain linear system of equations for δf Nh. [BG, Gautier, Klaric (2014); Iso, Shimada (2014)]. Regulator: R= M 4 64π 2 ([Y Y ] 11 +[Y Y ] 22 ) 2 [Y Y ] 11 [Y Y ] 22 ((Im[Y Y ] 12 ) 2 +det Y Y ) Applies in strong washout regime, i.e. a large portion of parameter space. blue: full result; red: result using effective decay asymmetry ε; Y aa = n Laa/s. Here, MΓ M 2. Yττ εττ Yµµ εµµ Yee εee z= M/T

31 Table of Contents 1. Sakharov Conditions and Leptogenesis Non-Equilibrium CP Violation Baryon Number Violation 2. Closed-Time-Path Approach 3. Akhmedov Rubakov Smirnov (ARS)/GeV-Scale Leptogenesis 4. Conclusions

32 Leptogenesis from Oscillations RHNs perform first oscillation at temperature T osc ( M 2 i M 2 j m Pl ) 1/3 Off-diagonal correlations for the RHNs yield strong phase Sizeable asymmetries generated around T osc (see plots on next slide) In standard leptogenesis, early asymmetries are washed out by the time T M. Only asymmetry produced around T M survives (strong washout). Loopholes to Preserve Early Asymmetries GeV-scale RHNs ( T osc 10 5 GeV) typically do not equilibrate prior to the electroweak phase transition where B settles to final value (sphaleron freezeout). [Akhmedov, Rubakov, Smirnov (1998); Asaka, Shaposhnikov (2005)]. Early asymmetry preserved until baryon number B freezes in. One individual active flavour (typically (ν e, e L)) is only weakly washed out, such that early asymmetries survive [BG (2014)].

33 Leptogenesis from Oscillation Dynamics Generation of the BAU Re[δn12 odd ]/s Δa/s YB T Γ M z RHNs perform first oscillation at T osc ( M 2 i M 2 j m Pl ) 1/3. Off-diagonal correlations lead to CP violating source for lepton flavour asymmetries (purely flavoured). Contributions from subsequent oscillations average out. Transfer of asymmetries into helicity asymmetries of RHNs leads to Y L 0. Large active-sterile mixing possible if one active flavour is more weakly washed out than the other two. Asymmetry frozen in at T EW, where sphalerons are quenched by the developing Higgs vev. δn = d 3 k/(2π) 3 δf N momentum averaging z = T EW /T ; a: lepton asymmetry in flavour a = e, µ, τ; δn: number density of RHNs; Y B : entropy-normalized baryon asymmetry. [Marco Drewes, BG, Dario Gueter, Juraj Klarić, ]

34 Leptogenesis from Oscillation Dynamics Oscillatory vs Overdamped Regime Re[δn12 odd ]/s Δa/s YB T Γ M z Re[δn12 odd ]/s Δa/s YB T Γ M z z = T EW /T ; a: lepton asymmetry in flavour a = e, µ, τ; δn: number density of RHNs; Y B : entropy-normalized baryon asymmetry.

35 Leptogenesis from Oscillation of GeV-scale RHNs Why it works at mass scales much smaller than for standard leptogenesis Source term for flavoured early asymmetries in oscillatory regime around T osc:[drewes, BG (2012)] S ab = 32i M c,i,j ii 2 M2 jj i j { (Y ai Y icy cj Y jb) (2π) 3 2 d 3 k k 2 +M 2 ii [ (M 2 ii +2k 2 )(ˆΣ A0 N 2 +ˆΣ Ai N 2 ) 4 k k 2 +Mii 2 +(Y ai Y ic Y t cj Y jb)m ii M jj ˆΣA Nµ ˆΣAµ N } δf Nhii (k). ˆΣ A0 N ] ˆk i ˆΣ Ai N ˆΣ A N = [Besak, Bödeker (2012); BG, Glowna, Schwaller (2013)] RHNs relativistic ˆΣ A N dominated by thermal effects Lepton number violating contribution M 2 / M 2 (Majorana mass insertion) requires M 2 /M 2 0 for resonant enhancement. Lepton flavour violating (lepton number conserving) contribution T 2 / M 2 large enhancement for M 2 T 2 no/less pronounced mass degeneracy needed. Leptogenesis is viable with n N = 3 non-degenerate (in mass) RHNs of the GeV scale [Drewes, BG (2012)] and for masses GeV [BG (2014)].

36 Leptogenesis from Oscillation of GeV-scale RHNs Why it works at mass scales much smaller than for standard leptogenesis Source term for flavoured early asymmetries in oscillatory regime around T osc:[drewes, BG (2012)] S ab = 32i M c,i,j ii 2 d 3 k M2 jj (2π) 3 2 k 2 +M ii 2 i j { [ ] (Y ai Y icy cj Y jb) (M 2 ii +2k 2 )(ˆΣ A0 N 2 +ˆΣ Ai N 2 ) 4 k k 2 +Mii 2 ˆΣ A0 N ˆk i ˆΣ Ai t-channel divergence that is regulated by N +(Y ai Y ic Y cj t Y Landau} damping/debye screening logarithmically N δf enhanced, Nhii (k). dominant contribution jb)m ii M jj ˆΣA ˆΣAµ Nµ to production of ultrarelativisc RHNs ˆΣ A N = [Besak, Bödeker (2012); BG, Glowna, Schwaller (2013)] RHNs relativistic ˆΣ A N dominated by thermal effects Lepton number violating contribution M 2 / M 2 (Majorana mass insertion) requires M 2 /M 2 0 for resonant enhancement. Lepton flavour violating (lepton number conserving) contribution T 2 / M 2 large enhancement for M 2 T 2 no/less pronounced mass degeneracy needed. Leptogenesis is viable with n N = 3 non-degenerate (in mass) RHNs of the GeV scale [Drewes, BG (2012)] and for masses GeV [BG (2014)].

37 Direct & Indirect Searches for GeV-scale RHNs Direct searches: Mixing between active neutrinos and RHNs: U ai θ ai = vy ai /Mi GeV-scale RHNs can be produced in heavy meson (D, B) decays in B factories or beam dump experiments. Sensitivity of B factories is limited because RHNs can decay outside of the detector. SHiP Search for Hidden Particles: Proposed beam dump CERN: Indirect signals: Rate for 0νββ decay in type I seesaw mechanism can be enhanced for GeV-scale RHNs compared to other mass regions. Lepton universality in meson decays. Charged lepton flavour violation.

38 Experimental Prospects Normal Hierarchy 10-5 BAU (upper bound) 10-7 ILC LBNE CEPC U SHiP FCC-ee(Z) BAU (lower bound) disfavoured by global constraints M [GeV] Active-sterile mixing: U ai θ ai = vy ai /M i; U 2 = trθ θ; n N = 2

39 GeV-Scale Leptogenesis & Approximate LNC Normal Hierarchy M = 1 GeV U Maximal U 2 = a U 2 a for viable leptogenesis shows particular flavour patterns Uμ U 2 µ 2 /U /U Larger U 2 require smaller U 2 e /U 2 in order for the asymmetry stored in l e to survive washout prior to sphaleron freezeout [Drewes, BG, Gueter, Klarić, ] Ue 2 Ue /U2 /U 22

40 Table of Contents 1. Sakharov Conditions and Leptogenesis Non-Equilibrium CP Violation Baryon Number Violation 2. Closed-Time-Path Approach 3. Akhmedov Rubakov Smirnov (ARS)/GeV-Scale Leptogenesis 4. Conclusions

41 Conclusions The observed neutrino mass scale suggests that the coupling strengths of RHNs in the type I seesaw mechanism are favourable for leptogenesis independent of the scale of the seesaw. In addition, seesaw implements CP violation and and effective B violation via L violation & sphalerons. In case we are lucky enough to discover GeV-scale RHNs soon, ARS leptogenesis predicts particular flavour patterns that allow to test this mechanism (so far discussions for n N = 2). Would be interesting to use what we have learnt for reaction rates and flavour (de)coherence to revisit Electroweak Baryogenesis.

42 50 Years of Sakharov s Puzzle A challenge to experiment & theory, QFT (QCD, EFT, lattice,...), hadrons & nuclear theory, atoms & molecules, BSM, non-equilibrium physics

43 50 Years of Sakharov s Puzzle A challenge to experiment & theory, QFT (QCD, EFT, lattice,...), hadrons & nuclear theory, atoms & molecules, BSM, non-equilibrium physics When will we know the answer (if ever)?

44 50 Years of Sakharov s Puzzle A challenge to experiment & theory, QFT (QCD, EFT, lattice,...), hadrons & nuclear theory, atoms & molecules, BSM, non-equilibrium physics When will we know the answer (if ever)? * Probably before the Netherlands win the World Cup. Thanks for trying. We do appreciate your effort!