Baryo/Leptogenesis

Baryo/leptogenesis

Bhupal Dev Washington University in St. Louis

15th Workshop on High Energy Physics Phenomenology

IISER Bhopal

December 15, 2017 One number −→ BSM Physics

Matter-Antimatter Asymmetry

nB − nB¯ −10 ηB ≡ ' 6.1 × 10 nγ Matter-Antimatter Asymmetry

nB − nB¯ −10 ηB ≡ ' 6.1 × 10 nγ

One number −→ BSM Physics Baryogenesis Ingredients [Sakharov ’67]

Ingredients are not enough.

+ = 6

Baryogenesis

Dynamical generation of baryon asymmetry.

Basic ingredients: [Sakharov ’67] B violation, C & CP violation, departure from thermal equilibrium Necessary but not sufﬁcient. The Standard Model has all the basic ingredients, but CKM CP violation is too small (by ∼ 10 orders of magnitude). Observed Higgs boson mass is too large for a strong ﬁrst-order phase transition. Requires New Physics!

Baryogenesis

DynamicalBaryogenesis generation of baryon Ingredients asymmetry. [Sakharov ’67] Basic ingredients: [Sakharov ’67] B violation,IngredientsC & CP violation, are not departure enough. from thermal equilibrium Necessary but not sufﬁcient.

+ = 6

A mechanism for baryogenesis is needed. No known mechanism works in the Standard Model. Baryogenesis

+ = 6

The Standard Model has all the basic ingredients, but CKMACP mechanismviolation is too for small baryogenesis (by ∼ 10 orders of is magnitude). needed. Observed Higgs boson mass is too large for a strong ﬁrst-order phase transition. No known mechanism works in the Standard Model. Requires New Physics! EW or TeV-scale (e.g. EW baryogenesis, resonant leptogenesis, ARS leptogenesis, Higgs decay leptogenesis, cogenesis, WIMPy baryogenesis, soft leptogenesis) Sub-EW scale (e.g. Post-sphaleron baryogenesis)

This talk is mostly on Low-scale baryo/leptogenesis Testable effects in the form of collider signatures, gravitational waves, electric dipole moment, 0νββ, lepton ﬂavor violation, n − n¯ oscillation, ... Can be used to falsify these scenarios.

Baryogenesis Landscape

For review, see e.g. J. Cline, hep-ph/0609145. Many interesting ideas. Can broadly divide into 3 classes, based on the energy scale involved. High-scale (e.g. GUT baryogenesis, Afﬂeck-Dine baryogenesis, vanilla leptogenesis) Problems: Monopole, gravitino overproduction, testability. EW or TeV-scale (e.g. EW baryogenesis, resonant leptogenesis, ARS leptogenesis, Higgs decay leptogenesis, cogenesis, WIMPy baryogenesis, soft leptogenesis) This talk is mostly on Low-scale baryo/leptogenesis Testable effects in the form of collider signatures, gravitational waves, electric dipole moment, 0νββ, lepton ﬂavor violation, n − n¯ oscillation, ... Can be used to falsify these scenarios.

Baryogenesis Landscape

For review, see e.g. J. Cline, hep-ph/0609145. Many interesting ideas. Can broadly divide into 3 classes, based on the energy scale involved. High-scale (e.g. GUT baryogenesis, Afﬂeck-Dine baryogenesis, vanilla leptogenesis) Problems: Monopole, gravitino overproduction, testability. EW or TeV-scale (e.g. EW baryogenesis, resonant leptogenesis, ARS leptogenesis, Higgs decay leptogenesis, cogenesis, WIMPy baryogenesis, soft leptogenesis) Sub-EW scale (e.g. Post-sphaleron baryogenesis) Baryogenesis Landscape

[Fukugita, Yanagida ’86]

A cosmological consequence of the seesaw mechanism.

Provides a common link between neutrino mass and baryon asymmetry.

Naturally satisﬁes the Sakharov conditions. L violation due to the Majorana nature of heavy RH neutrinos. L/ → B/ through sphaleron interactions. New source of CP violation in the leptonic sector (through complex Dirac Yukawa couplings and/or PMNS CP phases). Departure from thermal equilibrium when ΓN . H. Popularity of Leptogenesis Popularity of Leptogenesis Leptogenesis for Pedestrians

[Buchmuller,¨ Di Bari, Plumacher¨ ’05]

Three basic steps:

1 Generation of L asymmetry by heavy Majorana neutrino decay:

2 Partial washout of the asymmetry due to inverse decay (and scatterings):

3 Conversion of the left-over L asymmetry to B asymmetry at T > Tsph. Boltzmann Equations

[Buchmuller,¨ Di Bari, Plumacher¨ ’02] dN N = −(D + S)(N − Neq), dz N N dN∆L eq = εD(N − N ) − N∆ W , dz N N L

(where z = mN1 /T and D, S, W = ΓD,S,W /Hz for decay, scattering and washout rates.) FInal baryon asymmetry:

η∆B = d · ε · κf ' 28 1 ' . / → / d 51 27 0 02 (L B conversion at Tc + entropy dilution from Tc to recombination epoch).

κf ≡ κ(zf ) is the ﬁnal efﬁciency factor, where

Z z R z 00 00 0 D dNN − dz W (z ) κ(z) = dz e z0 D + S dz0 zi Resonant Leptogenesis •

CP Asymmetry

Φ Φ† Φ† L Φ† Nα Nα Nα Nβ Nα × C L × C Nβ Ll Ll Φ × C Ll tree(a) self-energy(b) (c)vertex

c c 2 c 2 Γ(Nα → Ll Φ) − Γ(Nα → Ll Φ ) |bhlα| − |bhlα| εlα = ≡ P c c † † Γ(Nα → Lk Φ) + Γ(Nα → L Φ ) (h h) + (hc hc ) Importance of self-energyk eﬀects (when mk mb b αα mb b )αα | N1 − N2| ≪ N1,2 with the one-loop resummed Yukawa couplings [Pilaftsis, Underwood[J. Liu, ’03] G. Segr´e, PRD48 (1993) 4609; X M. Flanz, E. Paschos, U. Sarkar, PLB345 (1995) 248; bhlα = bhlα − i |αβγ |bhlβ L. Covi, E. Roulet, F. Vissani, PLB384 (1996) 169; . β,γ . mα(mαAαβ + mβ Aβα) − iRαγ [mαAγβ (mαAαγ + mγ Aγα) + mβ Aβγ (mαAγα + mγ Aαγ )] × J. R. Ellis, M. Raidal, T. Yanagida, PLB546 (2002), 228.] 2 − 2 + 2 + ( )[ 2 | |2 + ( 2 )] mα mβ 2imαAββ 2iIm Rαγ mα Aβγ mβ mγ Re Aβγ

2 Importance of the heavy-neutrinomα width eﬀects: Γ1 NXα ∗ Rαβ = ; Aαβ (h) = hlαh β . 2 − 2 + 2 b 16π b bl mα mβ 2imαAββ [A.P., PRD56 (1997) 5431; A.P. and T. Underwood,l NPB692 (2004) 303.]

Warsaw, 22–27 June 2014 Flavour Covariance in Leptogenesis A. Pilaftsis Testability of Seesaw

[Drewes ’15]

Figure 4:InA a bottom-up schematic illustration approach, of no the deﬁnite relation prediction between ofrmtrF the seesaw†F and M scale.I imposed by neutrino oscillation data (plot taken from Ref. [22]). Individual elements of F can deviate considerably from F0 if there are cancellations in (6). Cosmological constraints allow to further restrict the mass range, see Fig. 5

Figure 5: The allowed mass ranges for n =3heavy neutrinos NI depend upon whether the 3 lightest active neutrino is heavier (left panel) or lighter (right panel) than 3.25 10− eV [24]. The difference between the two cases comes from a combination of neutrino oscillation× data and early universe constraints. If the lightest active neutrino is relatively heavy, then all three NI need to have sizable mixings with active neutrinos to generate the three neutrino masses mi (n sterile neutrinos that mix with the active neutrinos can generate n active neutrino masses via the seesaw mechanism). This means that all of them are produced in significant amounts in the early universe. In this case there exists a mass range 1eV ! MI ! 100 MeV that is excluded for all NI by cosmological considerations, in particular big bang nucleosynthesis and constraints on the number of effective neutrino species Neff . If the lightest active neutrino is massless or rather light, then one heavy neutrino (here chosen tobeN1)canhaverather 2 tiny mixings Uα1. This allows to circumvent the cosmological bounds, and N1 can essentially have any mass. In both cases the upper end of the plot is not an upper bound on the mass; indeed there exists no known upper bound for the MI . Plot taken from Ref. [24].

8 Testability of Leptogenesis

Three regions of interest:

9 14 High scale: 10 GeV . mN . 10 GeV. Can be falsiﬁed with an LNV signal at LHC.

Collider-friendly scale: 100 GeV . mN . few TeV. Can be tested in collider and/or low-energy (0νββ, LFV) searches.

Low-scale:1 GeV . mN . 5 GeV. Can be tested at the intensity frontier: SHiP, DUNE or B-factories (LHCb, Belle-II). Testability of Leptogenesis

Three regions of interest:

9 14 High scale: 10 GeV . mN . 10 GeV. Can be falsiﬁed with an LNV signal at LHC.

Collider-friendly scale: 100 GeV . mN . few TeV. Can be tested in collider and/or low-energy (0νββ, LFV) searches.

Low-scale:1 GeV . mN . 5 GeV. Can be tested at the intensity frontier: SHiP, DUNE or B-factories (LHCb, Belle-II). Testability of Leptogenesis

Three regions of interest:

9 14 High scale: 10 GeV . mN . 10 GeV. Can be falsiﬁed with an LNV signal at LHC.

Collider-friendly scale: 100 GeV . mN . few TeV. Can be tested in collider and/or low-energy (0νββ, LFV) searches.

Low-scale:1 GeV . mN . 5 GeV. Can be tested at the intensity frontier: SHiP, DUNE or B-factories (LHCb, Belle-II). For more details, see

Dedicated volume on Leptogenesis (to appear in Int. J. Mod. Phys. A) 1 P. S. B. Dev, P. Di Bari, B. Garbrecht, S. Lavignac, P. Millington and D. Teresi, “Flavor effects in leptogenesis,” arXiv:1711.02861 [hep-ph]. 2 M. Drewes et al., “ARS Leptogenesis,” arXiv:1711.02862 [hep-ph]. 3 P. S. B. Dev, M. Garny, J. Klaric, P. Millington and D. Teresi, “Resonant enhancement in leptogenesis,” arXiv:1711.02863 [hep-ph]. 4 S. Biondini et al., “Status of rates and rate equations for thermal leptogenesis,” arXiv:1711.02864 [hep-ph]. 5 E. J. Chun et al., “Probing Leptogenesis,” arXiv:1711.02865 [hep-ph]. 6 C. Hagedorn, R. N. Mohapatra, E. Molinaro, C. C. Nishi and S. T. Petcov, “CP Violation in the Lepton Sector and Implications for Leptogenesis,” arXiv:1711.02866 [hep-ph]. Experimentally inaccessible! 9 Also leads to a lower limit on the reheating temperature Trh & 10 GeV. 6 9 In supergravity models, need Trh . 10 − 10 GeV to avoid the gravitino problem. [Khlopov, Linde ’84; Ellis, Kim, Nanopoulos ’84; Cyburt, Ellis, Fields, Olive ’02; Kawasaki, Kohri, Moroi, Yotsuyanagi ’08] 7 Also in conﬂict with the Higgs naturalness bound mN . 10 GeV. [Vissani ’97; Clarke, Foot, Volkas ’15; Bambhaniya, BD, Goswami, Khan, Rodejohann ’16]

Vanilla Leptogenesis

Hierarchical heavy neutrino spectrum (mN1 mN2 < mN3 ). Both vertex correction and self-energy diagrams are relevant. For type-I seesaw, the maximal CP asymmetry is given by

3 mN p εmax = 1 ∆m2 1 16π v 2 atm

Lower bound on mN1 : [Davidson, Ibarra ’02; Buchmuller,¨ Di Bari, Plumacher¨ ’02] ! 8 ηB 0.05 eV −1 mN1 > 6.4 × 10 GeV κf 6 × 10−10 p 2 ∆matm Vanilla Leptogenesis

Hierarchical heavy neutrino spectrum (mN1 mN2 < mN3 ). Both vertex correction and self-energy diagrams are relevant. For type-I seesaw, the maximal CP asymmetry is given by

3 mN p εmax = 1 ∆m2 1 16π v 2 atm

Lower bound on mN1 : [Davidson, Ibarra ’02; Buchmuller,¨ Di Bari, Plumacher¨ ’02] ! 8 ηB 0.05 eV −1 mN1 > 6.4 × 10 GeV κf 6 × 10−10 p 2 ∆matm

Experimentally inaccessible! 9 Also leads to a lower limit on the reheating temperature Trh & 10 GeV. 6 9 In supergravity models, need Trh . 10 − 10 GeV to avoid the gravitino problem. [Khlopov, Linde ’84; Ellis, Kim, Nanopoulos ’84; Cyburt, Ellis, Fields, Olive ’02; Kawasaki, Kohri, Moroi, Yotsuyanagi ’08] 7 Also in conﬂict with the Higgs naturalness bound mN . 10 GeV. [Vissani ’97; Clarke, Foot, Volkas ’15; Bambhaniya, BD, Goswami, Khan, Rodejohann ’16] Resonant Leptogenesis

Ll(k, r)

α N (p,s) ε ε′

Φ(q)

Dominant self-energy effects on the CP-asymmetry (ε-type) [Flanz, Paschos, Sarkar ’95; Covi, Roulet, Vissani ’96].

Resonantly enhanced, even up to order 1, when ∆mN ∼ ΓN /2 mN1,2 . [Pilaftsis ’97; Pilaftsis, Underwood ’03] The quasi-degeneracy can be naturally motivated as due to approximate breaking of some symmetry in the leptonic sector. Heavy neutrino mass scale can be as low as the EW scale. [Pilaftsis, Underwood ’05; Deppisch, Pilaftsis ’10; BD, Millington, Pilaftsis, Teresi ’14] A testable scenario at both Energy and Intensity Frontiers. Flavor effects important at low scale [Abada, Davidson, Ibarra, Josse-Michaux, Losada, Riotto ’06; Nardi, Nir, Roulet, Racker ’06; De Simone, Riotto ’06; Blanchet, Di Bari, Jones, Marzola ’12; BD, Millington, Pilaftsis, Teresi ’14] Two sources of ﬂavor effects: α [Pilaftsis ’04; Endoh, Morozumi, Xiong ’04] Heavy neutrino Yukawa couplings hl k [Barbieri, Creminelli, Strumia, Tetradis ’00] Charged lepton Yukawa couplings yl Three distinct physical phenomena: mixing, oscillation and decoherence. Captured consistently in the Boltzmann approach by the fully ﬂavor-covariant formalism. [BD, Millington, Pilaftsis, Teresi ’14; ’15]

Flavordynamics Flavordynamics

1012 GeV

109 GeV

1012 GeV

109 GeV

FlavorFigure effects 1:important The ten dierent at low three scale RH neutrino[Abada, mass Davidson, patterns Ibarra, requiring Josse-Michaux, 10 di Losada,erent sets Riotto of ’06; Nardi, Nir, Roulet,Boltzmann Racker ’06;equations De Simone, for Riotto the ’06; calculation Blanchet, ofDi theBari, asymmetry Jones, Marzola [17]. ’12; BD, Millington, Pilaftsis, Teresi ’14] Two sources of flavor effects: – Heavy neutrino Yukawa couplings h [Pilaftsis ’04; Endoh, Morozumi, Xiong ’04] component, escapes the washout from al lighter RH neutrino species [6]. Second, parts of Charged lepton Yukawa couplings y k [Barbieri, Creminelli, Strumia, Tetradis ’00] the flavour asymmetries (phantom terms)l produced in the one or two flavour regimes do Three distinctnot contribute physical to the phenomena: total asymmetrymixing at the production, oscillation but canand contributedecoherence to the final. Capturedasymmetry consistently [18]. in the Boltzmann approach by the fully flavor-covariant Therefore, it is necessary to extend the density matrix formalism beyond the tradi- formalism. [BD, Millington, Pilaftsis, Teresi ’14; ’15] tional N1-dominated scenario [6, 11, 19] and account for heavy neutrino flavours eects in Bhupal Devorder (Washington to calculate U.) the final asymmetryLeptogenesis for an and arbitrary Colliders choice of the RH neutrinoACFI masses. Workshop 17 / 45 This is the main objective of this paper. At the same time we want to show how Boltz- mann equations can be recovered from the density matrix equations for the hierarchical RH neutrino mass patterns shown in Fig. 1 allowing an explicit analytic calculation of the final asymmetry. In this way we will confirm and extend results that were obtained within asimplequantumstatecollapsedescription.Forillustrativepurposes,wewillproceedin a modular way, first discussing the specific eects in isolation within simplified cases and then discussing the most general case that includes all eects. The paper is organised in the following way.

In Section 2 we discuss the derivation of the kinetic equations for the N1-dominated scenario in the absence of heavy neutrino ﬂavours. This is useful both to show the extension from classical Boltzmann to density matrix equations and to highlight some

3 Flavordynamics Flavordynamics

1012 GeV

109 GeV

1012 GeV

109 GeV

FlavorFigure effects 1:important The ten dierent at low three scale RH neutrino[Abada, mass Davidson, patterns Ibarra, requiring Josse-Michaux, 10 di Losada,erent sets Riotto of ’06; Nardi, FlavorNir, effects Roulet,Boltzmann Racker important ’06;equations De Simone, at for Riotto low the ’06; calculationscale Blanchet,[Abada, ofDi theBari, asymmetry Davidson,Jones, Marzola[17]. Ibarra, ’12; BD, Josse-Michaux, Millington, Pilaftsis, Losada, Teresi ’14] Riotto ’06; Nardi, Nir, Roulet,Two Racker sources ’06; De of Simone, flavor Riotto effects: ’06; Blanchet, Di Bari, Jones, Marzola ’12; BD, Millington, Pilaftsis, Teresi ’14] – Heavy neutrino Yukawa couplings h [Pilaftsis ’04; Endoh, Morozumi, Xiong ’04] Two sourcescomponent, of flavor escapes effects: the washout from al lighter RH neutrino species [6]. Second, parts of Charged lepton Yukawa couplings y k [Barbieri, Creminelli, Strumia, Tetradis ’00] the flavour asymmetries (phantom terms)lα produced in the one or two flavour regimes do Heavy neutrino Yukawa couplings h [Pilaftsis ’04; Endoh, Morozumi, Xiong ’04] Three distinctnot contribute physical to the phenomena: total asymmetrylmixing at the production, oscillation but canand contributedecoherence to the final. Charged lepton Yukawa couplings y k [Barbieri, Creminelli, Strumia, Tetradis ’00] Capturedasymmetry consistently [18]. in the Boltzmannl approach by the fully flavor-covariant Therefore, it is necessary to extend the density matrix formalism beyond the tradi- Three distinctformalism physical. [BD, Millington, phenomena: Pilaftsis, Teresi ’14; ’15] mixing, oscillation and decoherence. tional N1-dominated scenario [6, 11, 19] and account for heavy neutrino flavours eects in CapturedBhupal consistently Devorder (Washington to calculate U.) in the the final Boltzmann asymmetryLeptogenesis for an and approach arbitrary Colliders choice by of the the RHfully neutrinoflavor-covariantACFI masses. Workshop 17 / 45 This is the main objective of this paper. At the same time we want to show how Boltz- formalism. [BD,mann Millington, equations Pilaftsis, can be recovered Teresi ’14; from ’15] the density matrix equations for the hierarchical RH neutrino mass patterns shown in Fig. 1 allowing an explicit analytic calculation of the final asymmetry. In this way we will confirm and extend results that were obtained within asimplequantumstatecollapsedescription.Forillustrativepurposes,wewillproceedin a modular way, first discussing the specific eects in isolation within simplified cases and then discussing the most general case that includes all eects. The paper is organised in the following way.

3 (Oscillation) (Mixing)

Generalization of the density matrix formalism. [Sigl, Raffelt ’93]

Master Equation for Transport Phenomena

In quantum statistical mechanics, n o X X ˜ ˜ ˜ ˜ X ˜ ˜ n (t) ≡ hnˇ (t; ti )it = Tr ρ(t; ti ) nˇ (t; ti ) .

˜ ˜ Differentiate w.r.t. the macroscopic time t = t − ti :

X ˇX ˜ ˜ ˜ ˜ dn (t) ˜ ˜ dn (t; ti ) dρ(t; ti ) X ˜ ˜ = Tr ρ(t; ti ) + Tr nˇ (t; ti ) ≡ I1 + I2.. dt d˜t d˜t

Use the Heisenberg EoM for I1 and Liouville-von Neumann equation for I2. Markovian master equation for the number density matrix:

Z +∞ d X X X 1 0 0 X n (k, t) ' ih [H0 , nˇ (k, t)] it − dt h [Hint(t ), [Hint(t), nˇ (k, t)]] it . dt 2 −∞ Master Equation for Transport Phenomena

In quantum statistical mechanics, n o X X ˜ ˜ ˜ ˜ X ˜ ˜ n (t) ≡ hnˇ (t; ti )it = Tr ρ(t; ti ) nˇ (t; ti ) .

˜ ˜ Differentiate w.r.t. the macroscopic time t = t − ti :

X ˇX ˜ ˜ ˜ ˜ dn (t) ˜ ˜ dn (t; ti ) dρ(t; ti ) X ˜ ˜ = Tr ρ(t; ti ) + Tr nˇ (t; ti ) ≡ I1 + I2.. dt d˜t d˜t

Use the Heisenberg EoM for I1 and Liouville-von Neumann equation for I2. Markovian master equation for the number density matrix:

Z +∞ d X X X 1 0 0 X n (k, t) ' ih [H0 , nˇ (k, t)] it − dt h [Hint(t ), [Hint(t), nˇ (k, t)]] it . dt 2 −∞

(Oscillation) (Mixing)

Generalization of the density matrix formalism. [Sigl, Raffelt ’93] Collision Rates for Decay and Inverse Decay

β Φ L k l −→ n [n ]l [γ(LΦ → N)]k α rank-4 tensor

β N Nα c˜ β [hc˜]l [h ]k α b b b b Φ ↓

l Lk(k, r) L (k, r)

β Φ L k N (p,s) n (q)[nr (k)]l Nα(p,s) c˜ β c˜ l [h ]k [h ] α b b b Φ(q) Φ(q) b Collision Rates for 2 ↔ 2 Scattering

Φ L k l n n [n ]l [γ(LΦ → LΦ)]k m −→ rank-4 tensor

L c˜ β c˜ l [h ]k [h ] α N β Nα b b

n b b L Φ Lm n α h β hm

b b Φ ↓

n l L (k2, r2) Lk(k1, r1) L (k1, r1) Lm(k2, r2)

n c˜ β Φ L k c˜ l α h β [h ]k n (q1)[nr1 (k1)]l [h ] α hm N β(p) N (p) b b b α b Φ(q2) b Φ(q1) Φ(q1) b Φ(q2) Field-Theoretic Transport Phenomena KeyMixing Result and Oscillations

dhL -6 10 L dhmix L dhosc L dh 10-7

10-8 0.2 0.5 1

z = mN T

= † )2 2 − 2 Γ(0) L gN 3 X L bh bhLαβ L MN, α MN, β MNbββ δηmix ' Combination ”÷ = ”÷osc + ”÷mix yieldsê a factor of 2 enhancement, 2 2Kz ( † ) ( † ) 2 2 2 (0) 2 comparedα6= toβ thebh bh isolatedαα bh bh contributionsββ MN, α − M forN, weakly-resonant β + MNbΓββ RL.

= † )2 2 − 2 Γ(0) + Γ(0) L gN 3 X bh bh αβ MN, α MN, β MN bαα bββ δηosc ' . † † † 2 2 2Kz 2 2 2 2 (0) (0) =[(h h)αβ ] α6=β (bh bh)αα(bh bh)ββ − + (Γ + Γ )2 b b MN, α MN, β MN bαα bββ † † (bh bh)αα(bh bh)ββ ARS 3

time

coherent oscillations L↵ NI NJ L L↵ NI

H H H

YL1 =0 YL1 > 0 YL1 > 0

YL2 ,YL3 =0 YL2 ,YL3 < 0 YL2 ,YL3 < 0

YL =0 YL =0 YL =0 ↵ ↵ ↵ ↵ ↵ ↵ 6 P P P FIG. 1. The basic stages leading to the creation of a total lepton asymmetry from left to right: out-of-equilibrium scattering 2 of LH[Akhmedov, leptons begin Rubakov, to populate Smirnov ’98] the sterile neutrino abundance at order ( F ); after some time of coherent oscillation, a small fraction of the sterile neutrinos scatter back into LH leptons to createO | an| asymmetry in individual lepton flavours at order ( F 4); finally, at order ( F 6), a total lepton asymmetry is generated due to a di↵erence in scattering rate into sterile neutrinosO | among| the di↵erent activeO | | flavours. lowing inflation, there is no abundance of sterile neutri- states1 and remain coherent as long as the active-sterile nos, and out-of-equilibrium scatterings mediated by the Yukawa coupling remains out of equilibrium, since in the Yukawa couplings begin to populate the sterile sector, as minimal model there are no other interactions involving shown on the left side of Fig. 1. The sterile neutrinos the sterile neutrinos. are produced in a coherent superposition of mass eigen-

Some time later, a subset of the sterile neutrinos scat- In the absence of ecient washout interactions, which is ter back into LH leptons, mediating L↵ L transi- ensured by the out-of-equilibrium condition, this di↵er- tions as shown in the centre of Fig. 1. Since! the sterile ence in rates creates asymmetries in the individual LH neutrinos remain in a coherent superposition in the in- lepton flavours L↵. termediate time between scatterings, the transition rate Denoting the individual LH flavour abundances (nor- L↵ L includes an interference between propagation malized by the entropy density, s)byYL nL /s and mediated! by the di↵erent sterile neutrino mass eigen- ↵ ⌘ ↵ the asymmetries by YL YL Y , we note that the states. The di↵erent mass eigenstates have di↵erent ↵ ⌘ ↵ L↵† processes at order ( F 4) discussed thus far only convert phases resulting from time evolution; for sterile neutri- O | | L↵ into L, conserving total SM lepton number, nos NI and NJ , the relative phase accumulated during a i(! ! ) dt small time dt is e I J ,where (M )2 (M )2 (M )2 Y = Y = 0 at ( F 4). (5) ! ! N I N J N IJ . (3) Ltot L↵ O | | I J ↵ ⇡ 2T ⌘ 2T X In the interaction basis, this CP-even phase results from an oscillation between di↵erent sterile neutrino flavours, Since sphalerons couple to the total SM lepton number, and explains the moniker of leptogenesis through neu- it follows that no baryon asymmetry is generated at this trino oscillations. order as well, YBtot = 0. Total lepton asymmetry is, When combined with the CP-odd phases from the however, generated at order ( F 6): the excess in each Yukawa matrix, neutrino oscillations lead to a di↵erence individual LH lepton flavourO due| to| the asymmetry from between the L↵ L rate and its complex conjugate, ! Eq. (4) leads to a slight increase of the rate of L↵ N † t 2 ! MIJ vs. L↵† N. The result is that active-sterile lepton scat- (L↵ L ) (L† L† ) Im exp i dt0 ! ! ↵ ! / 2T (t ) terings can convert individual lepton flavour asymmetries I=J  ✓ Z0 0 ◆ X6 into asymmetries in the sterile neutrinos. But, since the Im F F ⇤ F ⇤ F . (4) ↵I I ↵J J rates of conversion, (L N †), are generically di↵erent ⇥ ↵ ! ⇥ ⇤ for each lepton flavour ↵, this leads to a depletion of some of the individual lepton asymmetries at a faster rate than 1 This is true assuming generic parameters with no special align- others, leading to an overall SM lepton asymmetry and ment of the sterile-neutrino interaction and mass eigenstates. an overall sterile neutrino asymmetry. Because L N tot Higgs Decay

¯l ¯l N 41 N

m˜ m˜ log10 /eV Fig. 7. Thermal cut in the `¯N decay,log which10 gives/eV rise to its purely-thermal L-violating ! -1 0 1 2 3 CP-violation. -1 0 1 2 3 1.0 1.0 FCC-ee FCC-ee -7 treated as approximately conserved. However, as originally103 argued in [63], and later YB<0 -1 Y B>0 conﬁrmed in the Ra↵elt-Sigl formalism0 in [64], leptogenesis102 can occur also via L- 0.5 violating Higgs decays0.5 , i.e. the decays of the Higgs doublet into a RH neutrino and -9 a SM lepton that do involve-2 a Majorana mass insertion10 and violate L, analogously -8 SHiP to leptogenesis from N decays. This LNVSHiP e↵ect can become important, or even

GeV GeV 2 / / 5 N -9 dominant with respectN to the LNC one discussed in detail in the previous sections, 0.0 YB>0 0.0 -5 m m in some regions of the parameter space in0.8 the resonant regime MNi MNj n MNi. 10 -10 10 -10 2 | | In Ref. [63] this phenomenon was studied in the (quantum) Boltzmann equations log log -11 formalism, with CP-violating rates accounting for the CP violation in the decays -0.5 `¯N. This process-0.5 is depicted in Fig. 7. Naively, one would1.2 not expect any CP PS191 $ BBN PS191 -13 violation in this decay: in order to be kinematically accessible, this decay requires BBN M + M

Need mN . O(TeV). −5 Naive type-I seesaw requires mixing with light neutrinos to be . 10 . Collider signal suppressed in the minimal set-up (SM+RH neutrinos). Two ways out:

Construct a TeV seesaw model with large mixing (special textures of mD and mN ). Go beyond the minimal SM seesaw (e.g. U(1)B−L, Left-Right). Observable low-energy signatures (LFV, 0νββ) possible in any case. Complementarity between high-energy and high-intensity frontiers. Leptogenesis brings in additional powerful constraints in each case. Can be used to test/falsify leptogenesis. Dirac neutrino Yukawa matrix must be invariant under Z2 and CP, i.e. under the

generator Z of Z2 and X(s). [BD, Hagedorn, Molinaro (in prep)]

A Predictive RL Model

2 2 Based on residual leptonic ﬂavor Gf = ∆(3n ) or ∆(6n ) (with n even, 3 - n, 4 - n) and CP symmetries. [Luhn, Nasri, Ramond ’07; Escobar, Luhn ’08; Feruglio, Hagedorn, Zieglar ’12] CP symmetry is given by the transformation X(s)(r) in the representation r and depends on the integer parameter s, 0 ≤ s ≤ n − 1. [Hagedorn, Meroni, Molinaro ’14] A Predictive RL Model

Dirac neutrino Yukawa matrix must be invariant under Z2 and CP, i.e. under the

generator Z of Z2 and X(s). [BD, Hagedorn, Molinaro (in prep)]

† 0 ? 0 ? Z (3) YD Z(3 ) = YD and X (3) YD X(3 ) = YD .   y1 0 0 0 † YD = Ω(s)(3) R13(θL)  0 y2 0  R13(−θR ) Ω(s)(3 ) . 0 0 y3 The unitary matrices Ω(s)(r) are determined by the CP transformation X(s)(r). Form of the RH neutrino mass matrix invariant under ﬂavor and CP symmetries:   1 0 0 MR = MN  0 0 1  0 1 0 For y1 = 0 (y3 = 0), we get strong normal (inverted) ordering, with mlightest = 0. q q √ p ∆m2 M ∆m2 atm N sol MN | cos 2 θ | NO : y = 0, y = ± , y = ± R 1 2 v 3 v r p q (|∆m2 |−∆m2 ) p 2 atm sol MN |∆matm| MN | cos 2 θ | IO : y = 0, y = ± , y = ± R 3 2 v 1 v

Only free parameters: MN and θR .

Fixing Model Parameters

Six real parameters: yi , θL,R , MN . 2 2 θL ≈ 0.18(2.96) gives sin θ23 ≈ 0.605(0.395), sin θ12 ≈ 0.341 and 2 sin θ13 ≈ 0.0219 (within 3σ of current global-ﬁt results). Light neutrino masses given by the type-I seesaw:   2 θ θ   y1 cos 2 R 0 y1y3 sin 2 R  2   0 y2 0  (s even),  v 2  y y sin 2θ 0 −y 2 cos 2θ M2 = 1 3 R 3 R ν  − 2 θ − θ  MN  y1 cos 2 R 0 y1y3 sin 2 R  2 ( ) .   0 y2 0  s odd  2 −y1y3 sin 2θR 0 y3 cos 2θR Fixing Model Parameters

Only free parameters: MN and θR . Low Energy CP Phases and 0νββ

Dirac phase is trivial: δ = 0.

For mlightest = 0, only one Majorana phase α, which depends on the chosen CP transformation: π s sin α = (−1)k+r+s sin 6 φ and cos α = (−1)k+r+s+1 cos 6 φ with φ = , s s s n

where k = 0 (k = 1) for cos 2 θR > 0 (cos 2 θR < 0) and r = 0 (r = 1) for NO (IO). Restricts the light neutrino contribution to 0νββ:

 p + + p ∆ 2 + (− )s k 1 2 θ 6 i φs ∆ 2 . 1  msol 2 1 sin L e matm (NO) mββ ≈ q 3 s+k 6 i φs 2 2  1 + 2 (−1) e cos θL ∆matm (IO) .

2 2 For n = 26, θL ≈ 0.18 and best-ﬁt values of ∆msol and ∆matm, we get

0.0019 eV . mββ . 0.0040 eV (NO) 0.016 eV . mββ . 0.048 eV (IO). High Energy CP Phases and Leptogenesis

At leading order, three degenerate RH neutrinos. Higher-order corrections can break the residual symmetries, giving rise to a quasi-degenerate spectrum:

M1 = MN (1 + 2 κ) and M2 = M3 = MN (1 − κ) .

CP asymmetries in the decays of Ni are given by X ˆ ? ˆ ˆ † ˆ εiα ≈ Im Y YD,αj Re Y YD Fij D,αi D ij j6=i

Fij are related to the regulator in RL and are proportional to the mass splitting of Ni .

We ﬁnd ε3α = 0 and

y2 y3 2 2 ε α ≈ (−2 y + y (1 − cos 2 θ )) sin 3 φ sin θ sin θ F (NO) 1 9 2 3 R s R L,α 12 y1 y2 2 2 ε α ≈ (−2 y + y (1 + cos 2 θ )) sin 3 φ cos θ cos θ F (IO) 1 9 2 1 R s R L,α 12

with θL,α = θL + ρα 4π/3 and ρe = 0, ρµ = 1, ρτ = −1.

ε2α are the negative of 1α with F12 being replaced by F21. Correlation between BAU and 0νββ

60 4,9,22 25 40 ■ ■ 6,7,20 ■■■ 2,11,24 ■ 23 20 ■ 5,8,18

10 ■

10 0 0,13■

B ■ η 21 -20 ■ ■ 3,10,16 ■ 15 -40 ■ ■ 19 17 1,12,14 NO -60 0.0020 0.0025 0.0030 0.0035

mββ [eV] Correlation between BAU and 0νββ

20 ■ ■ 4,9,22 25 ■■■ 6,7,20 ■ 2,11,24 23 10 ■ ■ 10 5,8,18

10 0 0,13■ B

η ■ 21 ■ -10 15 3,10,16 19 ■ 1,12,14 17 ■ IO ■ ■ -20 0.020 0.025 0.030 0.035 0.040 0.045

mββ [eV] Correlation between BAU and 0νββ

20 4,9,22 25 ■ ■ 6,7,20 ■■■ 2,11,24 ■ 23 10 ■ 5,8,18

10 ■

10 0 0,13■

B ■ η ■ 21 -10 nEXO ■ 3,10,16 ■ 15 ■ 19 -20 ■ 1,12,14

17 LEGEND 1k IO LEGEND 200 -30 0.020 0.025 0.030 0.035 0.040 0.045

mββ [eV] Decay Length

ˆ † ˆ For RH Majorana neutrinos, Γα = Mα (YD YD)αα/(8 π). We get M Γ ≈ N 2 y 2 cos2 θ + y 2 + 2 y 2 sin2 θ , 1 24 π 1 R 2 3 R M Γ ≈ N y 2 cos2 θ + 2 y 2 + y 2 sin2 θ , 2 24 π 1 R 2 3 R M Γ ≈ N y 2 sin2 θ + y 2 cos2 θ . 3 8 π 1 R 3 R

For y1 = 0 (NO), Γ3 = 0 for θR = (2j + 1)π/2 with integer j. For y3 = 0 (IO), Γ3 = 0 for jπ with integer j. Long Lived Particle Searches at LHC

In either case, N3 is an ultra long-lived particle. Suitable for MATHUSLA (MAssive Timing Hodoscope for Ultra-Stable NeutraL PArticles) [Coccaro, Curtin, Lubatti, Russell, Shelton ’16; Chou, Curtin, Lubati ’16]

In addition, N1,2 can have displaced vertex signals at the LHC. MATHUSLA Surface Detector

SHiP experiment Decay Length

1000 MATHUSLA NO 1 LHC displaced ( m )

L 0.001

10-6 0.0 0.5 1.0 1.5 2.0

θR/π

N1 (red), N2 (blue), N3 (green).

MN =150 GeV (dashed), 250 GeV (solid). Decay Length

1000 MATHUSLA IO 1 LHC displaced ( m )

L 0.001

10-6 0.0 0.5 1.0 1.5 2.0

θR/π

N1 (red), N2 (blue), N3 (green).

MN =150 GeV (dashed), 250 GeV (solid). We consider a minimal U(1)B−L extension. Production cross section is no longer Yukawa-suppressed, while the decay is, 2 giving rise to displaced vertex. [Deppisch, Desai, Valle ’13] within the standard minimal seesaw sector by choosing q specific flavour textures in the mass matrix of the type-I q seesaw, see for example [12–14]. − u W d l  For definiteness here we focus on LFV in the electron- Z' N  muon sector induced by the mixing between isodoublet and isosinglet neutrinos, via the corresponding Yukawa N l − couplings. As a result, the heavy neutrinos couple to u β charged leptons via their small isodoublet components d W − q ✓e,µ, which we treat as free parameters. It is convenient to write these couplings in terms of an overall mixing q strength, ✓ p✓e✓µ and the ratio of mixing strengths, r ✓e/✓⌘µ. These parameters are unrestricted by eµ FIG. 1: Feynman diagram for heavy Majorana neutrino pro- the smallness⌘ of neutrino masses; however they are con- duction through the Z0 portal at the LHC. strained by weak universality precision measurements to e,µ 2 be ✓ . 10 [15]. We do not take into account possible constraints on ✓ from neutrinoless double beta decay LOW ENERGY LEPTON FLAVOUR VIOLATION searches. Although highly stringent for a heavy Majo- rana neutrino, they are avoided in the presence of can- In the scenario considered here, the LFV branching cellations, such as in the quasi-Dirac neutrino case. ratio for the process µ e can be expressed as [18] ! 2 3 2 mN 4 Br(µ e)=3.6 10 G ✓ , (3) ! ⇥ m2 ⇥ ✓ W ◆ 2x3 +5x2 x 3x3 with G = log(x), 4(1 x)3 2(1 x)4

where the loop function G (x) is of order one with the limits G 1/8 for mN mW and G 1/2 for Z0 MODELS ! ! ! mN mW . This prediction should be compared with the current experimental limit [1],

13 Various physics scenarios beyond the Standard Model Br (µ e) < 5.7 10 (90% C.L.), (4) MEG ! ⇥ predict di↵erent types of TeV-scale Z0 gauge bosons as- sociated with an extra U(1) that could arise, say, from from the MEG experiment which aims at a final sensitiv- 13 unified SO(10) or E(6) extensions. An introduction and ity of Br(µ e) 10 . The expression (3) therefore ! ⇡ extensive list of references can be found in Ref. [16]. Elec- results in a current upper limit on the mixing parame- 2 troweak precision measurements restrict the mass and ter ✓ . 0.5 10 for mN = 1 TeV. In contrast, the ⇥ 7 couplings of a Z boson. For example, lepton universal- mixing strength ✓ 10 expected in the standard high- 0 ⇡ ity at the Z peak places lower limits on the Z0 boson scale type-I seesaw mechanism Eq. (1) would lead to an 31 mass of the order (1) TeV [17] depending on hyper- unobservable LFV rate with Br(µ e) 10 . ! ⇡ charge assignments.O From the same data, the mixing If the photonic dipole operator responsible for µ e ! angle between Z0 and the SM Z is constrained to be and also contributing to µ eee and µ e conversion in 4 ! ⇣Z < (10 ). For a discussion of direct limits on Z0 nuclei is dominant, searches for the latter two processes massesO see [15]. Recent limits from searches at the LHC do not provide competitive bounds on the LFV scenario will be discussed in more detail below. at the moment. Depending on the breaking of the additional U(1)0 symmetry, non-decoupling e↵ects may appear which can boost the e↵ective Z eµ vertex contribut- In the following we work in a simplified U(1)0 scenario 0 ing to µ eee and µ e conversion in nuclei [19]. with only a Z0 and N present beyond the SM. For the ! mechanism described here to work, it is crucial that there are no other particles present through which the heavy neutrino can decay unsuppressed. For definiteness we HEAVY NEUTRINOS FROM THE Z0 PORTAL assume two reference model cases: the SO(10) derived U(1)0 coupling strength with the charge assignments of The process under consideration is depicted in Fig- the model described in [6], and a leptophobic variant ure 1. As shown, we will focus on the channel where the where the U(1)0 charges of SM leptons are set to zero. heavy neutrinos decay into SM W bosons which in turn

Collider Signal

Need an efﬁcient production mechanism. −6 In our scenario, yi . 10 suppresses the Drell-Yan production (∗) pp → W → Ni `α ,

and its variants. [Han, Zhang ’06; del Aguila, Aguilar-Saavedra, Pittau ’07; BD, Pilaftsis, Yang ’14; Han, Ruiz, Alva ’14; Deppisch, BD, Pilaftsis ’15; Das, Okada ’15] Even if one assumes large Yukawa, the LNV signal will be generally suppressed by the quasi-degeneracy of the RH neutrinos [Kersten, Smirnov ’07; Ibarra, Molinaro, Petcov ’10; BD ’15]. Need to go beyond the minimal type-I seesaw to realize a sizable LNV signal. Collider Signal

Need an efﬁcient production mechanism. −6 In our scenario, yi . 10 suppresses the Drell-Yan production (∗) pp → W → Ni `α ,

We consider a minimal U(1)B−L extension. Production cross section is no longer Yukawa-suppressed, while the decay is, 2 giving rise to displaced vertex. [Deppisch, Desai, Valle ’13] within the standard minimal seesaw sector by choosing q specific flavour textures in the mass matrix of the type-I q seesaw, see for example [12–14]. − u W d l  For definiteness here we focus on LFV in the electron- Z' N  muon sector induced by the mixing between isodoublet and isosinglet neutrinos, via the corresponding Yukawa N l − couplings. As a result, the heavy neutrinos couple to u β charged leptons via their small isodoublet components d W − q ✓e,µ, which we treat as free parameters. It is convenient to write these couplings in terms of an overall mixing q strength, ✓ p✓e✓µ and the ratio of mixing strengths, r ✓e/✓⌘µ. These parameters are unrestricted by eµ FIG. 1: Feynman diagram for heavy Majorana neutrino pro- the smallness⌘ of neutrino masses; however they are con- duction through the Z0 portal at the LHC. strained by weak universality precision measurements to e,µ 2 be ✓ . 10 [15]. We do not take into account possible constraints on ✓ from neutrinoless double beta decay LOW ENERGY LEPTON FLAVOUR VIOLATION searches. Although highly stringent for a heavy Majo- rana neutrino, they are avoided in the presence of can- In the scenario considered here, the LFV branching cellations, such as in the quasi-Dirac neutrino case. ratio for the process µ e can be expressed as [18] ! 2 3 2 mN 4 Br(µ e)=3.6 10 G ✓ , (3) ! ⇥ m2 ⇥ ✓ W ◆ 2x3 +5x2 x 3x3 with G = log(x), 4(1 x)3 2(1 x)4

where the loop function G (x) is of order one with the limits G 1/8 for mN mW and G 1/2 for Z0 MODELS ! ! ! mN mW . This prediction should be compared with the current experimental limit [1],

0.100 NO ee eμ 0.010 μμ ττ ( fb ) 0.001 LNV σ 10-4

10-5 200 400 600 800 1000 1200 1400 1600

MN (GeV) √ At s = 14 TeV LHC and for MZ 0 = 3.5 TeV. Collider Signal

0.100 IO ee eμ 0.010 μμ ττ ( fb ) 0.001 LNV σ 10-4

10-5 200 400 600 800 1000 1200 1400 1600

MN (GeV) √ At s = 14 TeV LHC and for MZ 0 = 3.5 TeV. Bound on Z 0 Mass

Z 0 interactions induce additional dilution effects, e.g. NN → Z 0 → jj.

Successful leptogenesis requires a lower bound on MZ 0 . [Blanchet, Chacko, Granor, Mohapatra ’09; Heeck, Teresi ’17; BD, Hagedorn, Molinaro (in prep)] Bound on Z 0 Mass

Z 0 interactions induce additional dilution effects, e.g. NN → Z 0 → jj.

Successful leptogenesis requires a lower bound on MZ 0 . [Blanchet, Chacko, Granor, Mohapatra ’09; Heeck, Teresi ’17; BD, Hagedorn, Molinaro (in prep)]

5000 ■ □□□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ ■ □□■ ■ □□■ □□■ ■ □□■ □□■ □□■ □□■ □□■ □□■ □■ ■ ■ ■ ■ ■ ■ □□□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ ■ □□■ ■ □□■ □□■ ■ □□■ □□■ □□■ □□■ ■ ■ □■ ■ ■ ■ ■ ■ ■ ■ □□□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ ■ □□■ □□■ □□■ □□■ ■ □□■ □□■ □□■ □□■ ■ ■ □□■ ■ ■ ■ □■ ■ ■ ■ ■ □□□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ ■ □□■ ■ ■ ■0.01□■ ■ ■ ■ ■ 4500 ■ ■ ■ □□□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ □□■ ■ □□■ ■ ■ ■ □■ ■ ■ ■ ■ ■ ■ ■ ■□□□■□□■□□■□□■□□■□□■□□■□□■□□■□□■□□■□□■□□■ ■ ■□□■ ■ ■□■ ■ ■ ■ ■ ■ ■ ■ log (|η |/ηobs) ■■■■□□□■□□■□□■□□■□□■□□■□□■□□■□□■□□■□□■■□□■■■□■■■■0.02■■■■■■■ 10 B B ■■■■■□□□■□□■□□■□□■□□■□□■□□■□□■■□□■■□■■■■■■■■■■■■■■ 1.6 ■■■■■□□□■□□■□□■□□■□□■□□■■□□■■□■■■■■■■■■■■■■■■■ 4000 ■■■■■□□□■■■□□■■□□■■□■■■■■■■■■■■■■■■■■■ 1. ■■■■■■■■□□□■■□□■■□■■■■■■■■■■0.05■■■■■■■■ ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ 0.44 ] ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ -0.16 3500 ■■■■■■■■■■■■■■■■■■■■■■■0.1■■■■■■■ GeV ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ [ -0.75

′ ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ Z ■■■■■■■■■■■■■■■■■■■■■■■0.2■■■■■■■ -1.4

M ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ 3000 ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ -1.9 ■■■■■■■■■■■■■■■■■■■■■■■0.5■■■■■■■ ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ -2.5 ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ 2500 ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ -3.1 ■■■■■■■■■■■■■■■■■■■■■■■■1■■■■■■ ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ -3.7 ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ -4.3 2000 ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■

500 1000 1500 2000 2500

MN [GeV] Presented a predictive RL model based on residual ﬂavor and CP symmetries. Correlation between BAU and 0νββ. Correlation between BAU and LNV signals (involving displaced vertex) at the LHC. Can probe neutrino mass hierarchy (complementary to oscillation experiments). Leptogenesis can be falsiﬁed at the LHC.

Conclusion

Leptogenesis provides an attractive link between neutrino mass and observed baryon asymmetry of the universe. Resonant Leptogenesis provides a way to test this idea in laboratory experiments. Flavor effects play a crucial role in the calculation of lepton asymmetry. Developed a fully ﬂavor-covariant formalism to consistently capture all ﬂavor effects in the semi-classical Boltzmann approach. Approximate analytic solutions are available for a quick pheno analysis. Conclusion

Presented a predictive RL model based on residual ﬂavor and CP symmetries. Correlation between BAU and 0νββ. Correlation between BAU and LNV signals (involving displaced vertex) at the LHC. Can probe neutrino mass hierarchy (complementary to oscillation experiments). Leptogenesis can be falsiﬁed at the LHC. Conclusion

Resonant `-genesis (RL`). [Pilaftsis (PRL ’04); Deppisch, Pilaftsis ’10]

Minimal model: O(N)-symmetric heavy neutrino sector at a high scale µX . Small mass splitting at low scale from RG effects. m µ M = 1 + ∆MRG , ∆MRG = − N X h†(µ )h(µ ) . N mN N with N 2 ln Re X X 8π mN

An example of RLτ with U(1)Le+Lµ × U(1)Lτ ﬂavor symmetry:

 −iπ/4 iπ/4  0 ae ae h =  0 be−iπ/4 beiπ/4  + δh , 0 0 0   e 0 0 δh =  µ 0 0  , −i(π/4−γ1) i(π/4−γ2) τ κ1e κ2e A Next-to-minimal RL` Model

[BD, Millington, Pilaftsis, Teresi ’15] 4 Asymmetry vanishes at O(h ) in minimal RL`.

Add an additional ﬂavor-breaking ∆MN :   ∆M1 0 0 RG MN = mN 1 + ∆MN + ∆MN , with ∆MN =  0 ∆M2/2 0  , 0 0 −∆M2/2

 −iπ/4 iπ/4    0 a e a e e 0 0 −iπ/4 iπ/4 h =  0 b e b e  +  µ 0 0  . −iπ/4 iπ/4 0 c e c e τ 0 0 Light neutrino mass constraint:

 ∆mN 2 2 ∆mN  a − e ab − eµ −eτ 2 2 mN mN v −1 T v ∆mN ∆mN 2 2 Mν ' − hM h ' ab − eµ b − µ −µτ , N  mN mN  2 2mN 2 −eτ −µτ −τ where ∆mN ≡ 2 [∆MN ]23 + i [∆MN ]33 − [∆MN ]22 = − i ∆M2 . Benchmark Points

Parameters BP1 BP2 BP3

mN 120 GeV 400 GeV 5 TeV c 2 × 10−6 2 × 10−7 2 × 10−6 −6 −5 −5 ∆M1/mN − 5 × 10 − 3 × 10 − 4 × 10 −8 −9 −8 ∆M2/mN (−1.59 − 0.47 i) × 10 (−1.21 + 0.10 i) × 10 (−1.46 + 0.11 i) × 10 a (5.54 − 7.41 i) × 10−4 (4.93 − 2.32 i) × 10−3 (4.67 − 4.33 i) × 10−3 b (0.89 − 1.19 i) × 10−3 (8.04 − 3.79 i) × 10−3 (7.53 − 6.97 i) × 10−3 −8 −8 −7 e 3.31 i × 10 5.73 i × 10 2.14 i × 10 −7 −7 −6 µ 2.33 i × 10 4.30 i × 10 1.50 i × 10 −7 −7 −6 τ 3.50 i × 10 6.39 i × 10 2.26 i × 10

Observables BP1 BP2 BP3 Current Limit BR(µ → eγ) 4.5 × 10−15 1.9 × 10−13 2.3 × 10−17 < 4.2 × 10−13 BR(τ → µγ) 1.2 × 10−17 1.6 × 10−18 8.1 × 10−22 < 4.4 × 10−8 BR(τ → eγ) 4.6 × 10−18 5.9 × 10−19 3.1 × 10−22 < 3.3 × 10−8 BR(µ → 3e) 1.5 × 10−16 9.3 × 10−15 4.9 × 10−18 < 1.0 × 10−12 Ti −14 −13 −20 −13 Rµ→e 2.4 × 10 2.9 × 10 2.3 × 10 < 6.1 × 10 Au −14 −13 −18 −13 Rµ→e 3.1 × 10 3.2 × 10 5.0 × 10 < 7.0 × 10 Pb −14 −13 −18 −11 Rµ→e 2.3 × 10 2.2 × 10 4.3 × 10 < 4.6 × 10 −6 −5 −7 −5 |Ω|eµ 5.8 × 10 1.8 × 10 1.6 × 10 < 7.0 × 10 Falsifying (High-scale) Leptogenesis at the LHC

102 1010 u u

100 u d 108 qi f 1 -2 D 10 X -106 fb 10 6 f @ 10 g g 2 d d 1 2 Ψ LHC

Σ 10-4 q j g 10-10000 3 Y 104 f 3 g f 1 q 4 i g 10-6 4 EW X -100 2 f f ΗL ΗL =10 10 X Y' 2 4 -2 10 G H=1 g1 g 2 W Y 10-8 f 3 q 0 1 2 3 4 5 j g 3 f 4 MX TeV

[Deppisch, Harz, Hirsch (PRL ’14)] @ D Falsifying (Low-scale) Leptogenesis?

One example: Left-Right Symmetric Model. [Pati, Salam ’74; Mohapatra, Pati ’75; Senjanovic,´ Mohapatra 75]

Common lore: MWR > 18 TeV for leptogenesis. [Frere, Hambye, Vertongen ’09] Mainly due to additional ∆L = 1 washout effects induced by WR .

−11/2 True only with generic YN 10 . . 30 Somewhat weaker in a class of low-scale LRSM with larger Y . N 25 Y [BD, Lee, Mohapatra ’13] tot =1

A lower limit of MWR & 10 TeV. ) 20 TeV A Discovery of MWR at the LHC rules ( R

out leptogenesis in LRSM. W

m 15 [BD, Lee, Mohapatra ’14, ’15; Weak Washout Dhuria, Hati, Rangarajan, Sarkar ’15] Strong 10 Y Washout tot =3

m N > mW 5 R -1.0 -0.5 0.0 0.5 1.0 m Log10 [ N /TeV]

L 8 3.8 3.5 Figure 4: Contour plots of ⌘ (zc) =2.47 10 for h = 10 (dashed lines) and h = 10 Y | | Y ⇥ (solid lines) with "tot = 1 (red lines) and "tot = 3 (blue lines). The green dot corresponds to the example ﬁt value presented in Section 3.

5. Summary In this proceedings, we address two issues related to seesaw models for neutrino masses. The first one deals with whether the TeV scale can be naturally in the TeV range without fine-tuning of parameters. We present a natural TeV scale left-right model which achieves this goal and therefore provides a counterexample to the common lore that either the seesaw scale must be superheavy or the active-sterile neutrino mixing must be tiny in a UV-complete seesaw model. The second issue addresses the important question: Whether in such low scale models, one can have successful leptogenesis, and if so, what constraints are implied by this on the mass of the RH gauge boson. In an explicit TeV-scale LR model, with an explicit fermion mass fit, we find the lower bound to be 13.1 TeV and for generic models in this class of L-R seesaw with enhanced neutrino Yukawa couplings compared to the canonical seesaw case and with maximal possible CP asymmetry for each flavor, this bounds becomes 9.9 TeV.

Acknowledgement The work of P. S. B. D. is supported by the Lancaster-Manchester-Sheeld Consortium for Fundamental Physics under STFC grant ST/L000520/1. The work of C. H. L. and R. N. M. is supported by the NSF grant No. PHY-1315155.