Lepton Number Violation and Leptogenesis

BHUPAL DEV

Consortium for Fundamental Physics, The University of Manchester, United Kingdom.

[1a] BD, P. Millington, A. Pilaftsis and D. Teresi, Nucl. Phys. B 886, 569 (2014). [1b] BD, P. Millington, A. Pilaftsis and D. Teresi, arXiv:1504.07640 [hep-ph]. [2] BD, P. Millington, A. Pilaftsis and D. Teresi, Nucl. Phys. B 891, 128 (2015). [3a] BD, C. H. Lee and R. N. Mohapatra, Phys. Rev. D 90, 095012 (2014). [3b] BD, C. H. Lee and R. N. Mohapatra, arXiv:1503.04970 [hep-ph]. [4] BD, arXiv:1506.00837 [hep-ph].

WIN 2015 MPIK, Heidelberg, Germany.

June 12, 2015 Outline

Motivation

Low-scale Leptogenesis

Flavor Effects

Phenomenology

Conclusions and Outlook

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 1 / 20 Matter-Antimatter Asymmetry

nB − n¯B +0.086 10 η∆B ≡ = 6.105 0.081 × 10− [Planck (2015)] nγ −

Baryogenesis: Dynamical generation of baryon asymmetry. Sakharov conditions: Need B violation, C and CP violation, departure from thermal equilibrium. [Sakharov ’67] Requires some New Physics beyond the Standard Model.

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 2 / 20 Leptogenesis

[Fukugita, Yanagida ’86] (talk by M. Garny)

Introduce at least two SM-singlet heavy Majorana neutrinos (Nα). L violation due to the Majorana nature. New source of CP violation through complex Yukawa couplings. Departure from equilibrium due to N decay in an expanding Universe. L asymmetry partially converted to B asymmetry through (B + L)-violating sphaleron effects. [Kuzmin, Rubakov, Shaposhnikov ’85]

Heavy neutrinos can also explain the observed non-zero neutrino masses and mixing: Seesaw mechanism. [Minkowski ’77; Mohapatra, Senjanovic´ ’79; Yanagida ’79; Gell-Mann, Ramond, Slansky ’79; Glashow ’79; Schechter and Valle ’80] Leptogenesis is a cosmological consequence of the seesaw mechanism.

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 3 / 20 Resonant Leptogenesis • Leptogenesis in 3 Basic Steps

1 Generation of lepton asymmetry by decay of a heavy Majorana neutrino. Basic Leptogenesis Φ Φ† Φ† L Φ† Nα Nα Nα Nβ Nα N • × C L × C β Generation of lepton asymmetry Ll Ll Φ × C • Generation of lepton asymmetry Ll (a) (b) (c) 2 Partial washout of the asymmetry due to inverse decays and scatterings.

• Washout of lepton asymmetry L Φ† L Φ† Ni Ni Importance of self-energy eﬀects (when mN1 mN2 mN1,2) C | − C | ≪Φ L Φ [J.L Liu, G. Segr´e, PRD48 (1993) 4609; • Temperature of the Universe drops below due to the expansion (a) (b) 3 Conversion of the residual lepton asymmetry to baryon asymmetry. → Suppression of the inverse decay by a factor M. Flanz, E. Paschos, U. Sarkar, PLB345 (1995) 248; L Φ L Φ → Lepton asymmetry is generated! L. Covi, E. Roulet,† F. Vissani, PLB384 (1996)† 169; . Ni N.i

L Φ† L Φ† • Conversion of the lepton asymmetry to the baryon asymmetry J. R. Ellis,(c) M. Raidal, T. Yanagida, PLB546(d) (2002) 228.] • Violation of B + L due to the non-trivial structure of non-abelian gauge theories, while B – L is conserved • Transitions from one vacuum structure to another with a change of B and LFigure by 3 8:units∆L =2interactions between lepton and Higgs doublets. (a) and (b) correspond Importance of the heavy-neutrino width eﬀC ects: ΓN • Energy barrier between two vacuum structures which is overcome throughto thermal the process excitationLΦ L Φ† ,-(c)sphaleronand (d) correspondα to the process LL Φ†Φ†. ↔ ↔

[A.P., PRD56 (1997) 5431; A.P. and T. Underwood,C NPB692 (2004) 303.] Bhupal Dev (Manchester) presentedLNV in andFig Leptogenesis8, these processes are: LΦ L Φ† andMPIKLL (06/12/15)Φ†Φ†,andtheirCP- 4 / 20 ↔ ↔ conjugate counterparts. For the first process, particular care is needed to properly subtract LΦ the RIS’s from the reduced cross-section σ C .Tothisend,wefirstdefinetheBreit-Wigner L Φ† s-channel propagators as ! 1 1 Pi− (x)= . (B.14) x ai + i√aici − Warsaw, 22–27 June 2014 Flavour CovarianceThen, the modulusin Leptogenesis square of a RIS subtracted propagator may bedeterminedbyA. Pilaftsis 1 2 1 2 π Di− (x) = Pi− (x) δ(x ai) 0 . (B.15) | | | | − √aici − →

This subtraction method is in line with the pole-dominance approximation discussed in Section 3, where the last step of (B.15) may be obtained by means of (3.2) 8.Notethat 1 2 D− (x) only occurs in the squared amplitude pertaining to an s-channel diagram. With | i | the help of the newly-defined quantities in (B.14) and (B.15),theproperlyRIS-subtracted 8Even though our subtraction approach appears to be similar totheonesuggestedrecentlyin[76], 1 2 our subtracted RIS propagator squared D− (x) actually differs from [77] by the fact that we use the | i | physical spectral representation of (3.2) for the distribution function δ(x a ), instead of an arbitrary − i regulating function with the same mathematical features. Wehavecheckedthatthedifference of the two approaches is numerically insignificant. Therefore, in agreement with earlier remarks in [78] and the recent observation made in [76], we also find that the earlier RIS-subtraction approaches, see e.g. [11,17,20], tend N to approximately overestimate the CP-conserving wash-out term γLΦ in the BE (4.33) by a factor of 3/2.

44 Problems with ‘Vanilla’ Leptogenesis

For a hierarchical heavy neutrino spectrum (mN1 mN2 ), lower bound on mN1 : [Davidson, Ibarra ’02; Buchmuller,¨ Di Bari, Plumacher¨ ’02]

! 8 η∆B 0.05 eV mN1 & 6.4 × 10 GeV × 10 p 2 6 10− ∆matm

Experimentally inaccessible mass range!

Also leads to a potetial tension with the gravitino overproduction bound on the 6 9 reheat temperature: Trh . 10 − 10 GeV [Khlopov, Linde ’84; Ellis, Kim, Nanopoulos ’84; ...; Kawasaki, Kohri, Moroi, Yotsuyanagi ’08]

An attractive solution: Resonant Leptogenesis. [Pilaftsis, Underwood ’03]

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 5 / 20 Resonant Leptogenesis

Ni Nj ε ε′

For quasi-degenerate heavy Majorana neutrinos, self-energy effects on the leptonic CP-asymmetry (ε-type) become dominant. Figure 3: ε-andε -types of CP violation in the decays of heavy Majorana neutrinos. [Flanz, Paschos, Sarkar′ ’95; Covi, Roulet, Vissani ’96]

Resonantly enhanced, even up to order 1, when ∆m ∼ Γ /2 m . [Pilaftsis ’97] N N N1,2 ν In (3.33), a matrix notation for the resummed effective Yukawacouplings(h¯ )li should be The quasi-degeneracy can be naturally motivated as due to approximate breaking± understood,of some with symmetryl =1, 2 in, 3and the leptonici =1, sector.2. As is illustrated in Fig. 3, it is now interesting to discuss the two different types of CP violation contributing to δ ,theso-calledε -and Heavy neutrino mass scale can be as low as the EW scale. Ni ′ ε-typesofCPviolation.Ifweneglectallself-energycontributions to δ and [(hν)3] [Pilaftsis, Underwood ’05; Deppisch, Pilaftsis ’10; BD, Millington, Pilaftsis, Teresi ’14] Ni O CP-conservingProvides terms, a potentially we then testable find thescenario known of leptogenesis,result for the withε′-type implications CP violation at both [4]: Energy and Intensity Frontiers. [Deppisch, BD, Pilaftsisν ν ’15;2 BD ’15] 2 Im (h † h )ij mNj δ ε′ = f , (3.34) Ni Ni ν ν 2 Bhupal Dev (Manchester) LNV8π and(h Leptogenesish ) m MPIK (06/12/15) 6 / 20 ≈ † ii ! Ni " with i = j.Instead,ifallone-loopvertexcorrectionshavebeenneglected, we obtain a ̸ simple formula for the ε-type CP violation [14,32]:

ν ν 2 2 2 (0) Im (h h ) (m m ) mN Γ † ij Ni − Nj i Nj δNi εNi = ν ν ν ν (0) 2 , (3.35) ≈ (h † h )ii (h † h )jj (m2 m2 )2 + m2 Γ Ni − Nj Ni Nj where i, j =1, 2(i = j)andthetree-leveldecaywidthsΓ(0) of the heavy Majorana ̸ Ni neutrinos Ni are given in (2.11). In ﬁnite-order perturbation theory, theabsorptiveterm 2 (0) 2 mNi ΓNj that occurs in the last denominator on the RHS of (3.35) is absent, thereby leading to a singular behaviour for ε in the mass-degenerate limit m m .However, Ni Ni → Nj the appearance of this regulating absorptive term due to the ﬁnite width of the heavy Majorana neutrinos should be expected on physical grounds and emerges naturally within our resummation approach. Finally, it should be noted that (3.35) is valid for a mixing system with two heavy Majorana neutrinos only. The generalization of (3.35) for the case of a three-heavy-Majorana-neutrino mixing is more involvedandhencehasbeenrelegated to Appendix A. Anon-zeroleptonicasymmetrycanbecreated,ifandonlyifthe following CP-odd quantity does not vanish [14]:

νR νR νR T νR ∆CP Im Tr (h )† h MS† MS MS† (h ) (h )∗ MS =0, (3.36) ≡ # $ ̸ 20 Flavordynamics of Leptogenesis

Flavor effects could be important for the time-evolution of lepton asymmetry. In the minimal scenario, two potential sources of ﬂavor effects due to α [Pilaftsis ’05; Blanchet, Di Bari, Jones, Marzola ’11] Heavy neutrino Yukawa couplings hl Note: Can also generate lepton asymmetry from heavy neutrino oscillations [Akhmedov, Rubakov, Smirnov ’98; Asaka, Shaposhnikov ’05] (talk by T. Asaka)

k [Barbieri, Creminelli, Strumia, Tetradis ’00; Abada, Davidson, Charged lepton Yukawa couplings yl Ibarra, Josse-Michaux, Losada, Riotto ’06; Nardi, Nir, Roulet, Racker ’06; Blanchet, Di Bari ’07]

Need a fully ﬂavor-covariant formalism to consistently capture all ﬂavor effects, including the interplay between them.

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 7 / 20 Flavor-covariant Master Equation

In the semi-classical Boltzmann approach, promote the number densities (numbers) to matrices in ﬂavor space: ‘density matrix’ formalism [Sigl, Raffelt ’93]

X X h X i n (t) ≡ hˇn (˜t;˜ti)it = Tr ρ(˜t;˜ti) ˇn (˜t;˜ti)

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

X X dn (t) dˇn (˜t;˜ti) dρ(˜t;˜ti) X = Tr ρ(˜t;˜ti) + Tr ˇn (˜t;˜ti) dt d˜t d˜t | {z } | {z } i[HX ,ˇnX ] i [H (˜t;˜t ), ρ(˜t;˜t )] 0 − int i i (Heisenberg) (Liouville-von Neumann) In the Markovian limit,

Z + d X X X 1 ∞ X n (k, t) ' ih [H , ˇn (k, t)] it − dt0 h [H (t0), [H (t), ˇn (k, t)]] it dt 0 2 int int −∞ (oscillation terms) (collision terms)

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 8 / 20 Application to Resonant Leptogenesis

For charged-lepton and heavy-neutrino matrix number densities,

d L m L m L m [n (p, t)] = − i EL(p), n (p, t) + [C (p, t)] dt s1s2 l s1s2 l s1s2 l d N β N β N β N λ µβ [n (k, t)] = −i EN (k), n (k, t) + [C (k, t)] + Gαλ[C (k, t)] G dt r1r2 α r1r2 α r1r2 α r2r1 µ

Collision terms are of the form

L m 1 n β m α [C (p, t)] ⊃ − [Fs s r r (p, q, k, t)] [Γs s r r (p, q, k)] , s1s2 l 2 1 1 2 l α 2 2 1 n β

Statistical tensor F = nΦ nL ⊗ 1 − nN − 1 + nΦ 1 − nL ⊗ nN . Absorptive rate tensor Γ: rank-4 object describing heavy neutrino decays and inverse decays.

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 9 / 20 Collision Rates for Decay and Inverse Decay

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

N β Φ L k l β [C ]α ∝ n [n ]l [γ(LΦ → N)]k α

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 10 / 20 Collision Rates for 2 2 Scattering ↔

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)

L n Φ L k l n [C ]m ∝ n [n ]l [γ(LΦ → LΦ)]k m

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 11 / 20 Final Rate Equations

γ N β γ H n d[η ]α n h i β β 1 n o β N = − E , δηN + (γN ) − ηN , (γN ) i N Ref LΦ α N Ref LΦ z dz 2 α 2 ηeq α

γ N β H n d[δη ] h i β β i n o β N α = − γ E , ηN + (δγN ) − ηN , (δγN ) 2 i n N 2 i Imf LΦ α N Imf LΦ z dz α ηeq α β 1 n N N o − N δη , Ref(γLΦ) 2 ηeq α

γ L m [ηN ] α [δηN ] α HN n d[δη ]l N m β N m β β N m β = − [δγLΦ]l + N [δγLΦ]l α + N [γLΦ]l α z dz ηeq 2 ηeq m 1 n L LΦ LΦo 2 L n LΦ k m LΦ k m − δη , γL˜cΦ˜c + γLΦ − [δη ]k [γL˜cΦ˜c ]n l − [γLΦ ]n l 3 l 3

m 2 n L o back m − δη , γdec + [δγdec ]l 3 l

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 12 / 20 Final Rate Equations: Mixing

γ N β γ H n d[η ]α n h i β β 1 n o β N = − E , δηN + (γN ) − ηN , (γN ) i N Ref LΦ α N Ref LΦ z dz 2 α 2 ηeq α

γ N β H n d[δη ] h i β β i n o β N α = − γ E , ηN + (δγN ) − ηN , (δγN ) 2 i n N 2 i Imf LΦ α N Imf LΦ z dz α ηeq α β 1 n N N o − N δη , Ref(γLΦ) 2 ηeq α

γ L m [ηN ] α [δηN ] α HN n d[δη ]l N m β N m β β N m β = − [δγLΦ]l + N [δγLΦ]l α + N [γLΦ]l α z dz ηeq 2 ηeq

m 1 n L LΦ LΦo 2 L n LΦ k m LΦ k m − δη , γL˜cΦ˜c + γLΦ − [δη ]k [γL˜cΦ˜c ]n l − [γLΦ ]n l 3 l 3

m 2 n L o back m − δη , γdec + [δγdec ]l 3 l

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 12 / 20 Final Rate Equations: Oscillation

γ N β γ H n d[η ]α n h i β β 1 n o β N = − E , δηN + (γN ) − ηN , (γN ) i N Ref LΦ α N Ref LΦ z dz 2 α 2 ηeq α

γ N β H n d[δη ] h i β β i n o β N α = − γ E , ηN + (δγN ) − ηN , (δγN ) 2 i n N 2 i Imf LΦ α N Imf LΦ z dz α ηeq α β 1 n N N o − N δη , Ref(γLΦ) 2 ηeq α

γ L m [ηN ] α [δηN ] α HN n d[δη ]l N m β N m β β N m β = − [δγLΦ]l + N [δγLΦ]l α + N [γLΦ]l α z dz ηeq 2 ηeq

m 1 n L LΦ LΦo 2 L n LΦ k m LΦ k m − δη , γL˜cΦ˜c + γLΦ − [δη ]k [γL˜cΦ˜c ]n l − [γLΦ ]n l 3 l 3

m 2 n L o back m − δη , γdec + [δγdec ]l 3 l

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 12 / 20 Final Rate Equations: Charged Lepton Decoherence

γ N β γ H n d[η ]α n h i β β 1 n o β N = − E , δηN + (γN ) − ηN , (γN ) i N Ref LΦ α N Ref LΦ z dz 2 α 2 ηeq α

γ N β H n d[δη ] h i β β i n o β N α = − γ E , ηN + (δγN ) − ηN , (δγN ) 2 i n N 2 i Imf LΦ α N Imf LΦ z dz α ηeq α β 1 n N N o − N δη , Ref(γLΦ) 2 ηeq α

m 2 n L o back m − δη , γdec + [δγdec ]l 3 l

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 12 / 20 A Uniﬁed Framework

Our flavor-covariant formalism provides a unified framework to consistently decribe all pertinent flavor effects: mixing, oscillation and decoherence. Mixing and Oscillation are distinct physical phenomena, analogous to neutral meson systems. ConfirmedField-Theoretic in a more rigorous Transport ‘first Phenomenaprinciples’ approach using Kadanoff-Baym Mixing and Oscillations formalism. [BD, Millington, Pilaftsis, Teresi ’14]

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

10-8 0.2 0.5 1

z = mN T Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 13 / 20

L L L Combination ”÷ = ”÷osc + ”÷mix yieldsê a factor of 2 enhancement compared to the isolated contributions for weakly-resonant RL. Testing Leptogenesis at Energy Frontier

Same sign dilepton plus two jets with no missing ET . [Keung, Senjanovic ’83]

q ℓ+ W + ℓ+ N

q¯′ W − j

Collinear enhancement effects could improve the LHC sensitivity by up to a factor of 10. [BD, Pilaftsis, Yang ’14; Das, BD, Okada ’14] (see talk by U. K. Yang)

q γ q j ℓ+ q γ j ℓ+ + ℓ j γ ℓ+ + q j N + N W q′′ ℓ + + γ W W + W q′ q′ W − N q′ q′ q′ j N j j

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 14 / 20 Testing Leptogenesis at Intensity Frontier

Low-energy Benchmark Point Experimental

observables in a Mminimal RLτ Model Limit 13 13 BR(µ → eγ) 1.9 × 10− < 5.7 × 10− 18 8 BR(τ → µγ) 1.6 × 10− < 4.4 × 10− 19 8 BR(τ → eγ) 5.9 × 10− < 3.3 × 10− 15 12 BR(µ → 3e) 9.3 × 10− < 1.0 × 10− Ti 13 13 Rµ e 2.9 × 10− < 6.1 × 10− Au→ 13 13 Rµ e 3.2 × 10− < 7.0 × 10− Pb→ 13 11 Rµ e 2.2 × 10− < 4.6 × 10− → 5 5 |Ω|eµ 1.8 × 10− < 7.0 × 10− 3 hmi [eV] 3.8 × 10− < (0.11–0.25)

[BD, Millington, Pilaftsis, Teresi ’14]

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 15 / 20 Testing Leptogenesis at Intensity Frontier

1 CHARM

ATLAS LHCb

0.01 Belle - NA3 II EWPD CMS

ΜΜΠ L3 -4 PS191 FMMF 10 ® LHC14 BEBC DELPHI K

2 K ®ΜΝ

N -6 CHARM Μ 10

V NuTeV

10-8 E949 SHiP LBNE FCC-ee 10-10 BBN Seesaw 10-12 0.1 1 10 100

MN GeV

[Deppisch, BD, Pilaftsis ’15]

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 16 / 20 H L Falsifying Leptogenesis Dominant Decay and Scattering Processes Observation of LNV could falsify leptogenesis (barring exceptions). [Deppisch, Harz, Hirsch ’14] (talks by M. Hirsch and J. Harz) • 2-body decay Generation of lepton asymmetryA concrete example: TeV-scale Leptogenesis in Left-Right Seesaw Large washout effects due to gauge scattering.

• 3-body decay Dilution of the lepton asymmetry

• -mediated scattering Dilution and washout of the lepton asymmetry

→ Which values of Yukawa couplings and are compatible with leptogenesis? = 18 TeV?

In minimal LRSM, MWR > 18 TeV for successfulJ.-M. Frere, leptogenesis. T. Hambye, and G. Vertongen[Frere,, Hambye, 2009 Vertongen ’09]

In a class of TeV-scale LRSM with large MD elements [BD, Lee, Mohapatra ’14], including

ﬂavor effects could lower the leptogenesis bound to MWR & 10 TeV. [BD, Lee, Mohapatra ’14, ’15]

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 17 / 20 Lower Bound of RH Gauge Boson Mass Lower Bound on MWR from Leptogenesis

[BD, Lee, Mohapatra ’15]

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 18 / 20 Plots Lepton Number Violation and Electric Dipole Moment of electron Correlation with LFV Observables • Lepton Number Violation and Electric Dipole Moment of electron

• • EDM of

• EDM of

[BD, Lee, Mohapatra ’15]

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 19 / 20 Conclusions and Outlook

Leptogenesis provides an attractive link between two seemingly disparate pieces of evidence for BSM physics, namely, neutrino mass and baryon asymmetry.

Resonant Leptogenesis provides a way to test this idea in laboratory experiments.

Flavor effects play a crucial role in the calculation of the lepton asymmetry.

We have developed a fully ﬂavor-covariant formalism, which provides a complete and uniﬁed description of Resonant Leptogenesis.

TeV-scale leptogenesis has potential testable effects at both Energy and Intensity frontiers.

Could be falsiﬁed at the LHC and other low-energy experiments.

Other possible low-scale baryogenesis mechanisms?

NEW: A Simple Model for TeV-scale B/ and L/ and Resonant Baryogenesis [BD and R. N. Mohapatra, arXiv:1504.07196 [hep-ph]]

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 20 / 20 A Numerical Example

10-5 N L -3 total, Ηin=0, ∆Ηin=10 I mN = 400 GeV L N L +∆Η total, Ηin=0, ∆Ηin=0

L ΗN ΗN ∆ΗL +∆Η total, in= eq, in=0 -6 10 N N L N diag., Ηin=Ηeq, ∆Ηin=0 N diag., analytic

N N L L diag., Ηin=Ηeq, ∆Ηin=0 L - N N L 7 N, L diag., Ηin=Ηeq, ∆Ηin=0 ∆Η 10 ±

L -∆Ηobs

10-8 -∆ΗL

10-9 0.2 1 zc 10 20

z = mN T

[BD, P. Millington, A. Pilaftsis and D. Teresi, arXiv:1504.07640 [hep-ph]] Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 16 / 20 Testing L-R Leptogenesis at Energy Frontier

q ℓ+ q ℓ+ q ℓ+ q ℓ+ W + W + W + W + ℓ+ R ℓ+ R ℓ+ ℓ+ N N N N

q¯′ W − j q¯′ WR− j q¯′ W − j q¯′ WR− j

j j j j (a) LL (b) RR (c) RL (d) LR

0.1 MN = 100 GeV EWPD

10-4 LL 2 N { -7 V

È 10 RL

10-10 RR

Seesaw 10-13 3 4 5 6 7 8 9 10

MWR TeV

[Chen, BD, Mohapatra ’13] H L Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 17 / 20 Heavy Neutrino Searches: Current Status and Future Prospects

1 Π

ee ATLAS Ν ® Belle

0.01 e

K EWPD LEP2 ® NA3 K

Ν L3 LHC14 10-4 e ® DELPHI ILC Π 2 JINR -6 CHARM

eN 10

V GERDA LBNE - 10 8 PS191 SHiP FCC-ee 10-10 BBN Seesaw 10-12 0.1 1 10 100

MN GeV

[Deppisch, BD, Pilaftsis ’15]

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 18 / 20 H L Heavy Neutrino Searches: Current Status and Future Prospects

0.01 EWPD factory NOMAD - B CHARM -4 10 DELPHI 2

N -6 Τ 10

V LBNE 10-8 SHiP

FCC-ee 10-10 BBN Seesaw 10-12 0.1 1 10 100

MN GeV

[Deppisch, BD, Pilaftsis ’15]

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 19 / 20 H L Lower Bound ofLower RH Bound Gauge on M fromBoson Leptogenesis Mass WR

[BD, Lee, Mohapatra ’15]

Bhupal Dev (Manchester) LNV and Leptogenesis MPIK (06/12/15) 20 / 20