Leptogenesis and Colliders

Transcription

1 Leptogenesis and Coiders Bhupa Dev Washington University in St. Louis ACFI Workshop on Neutrinos at the High Energy Frontier UMass Amherst Juy 19, 2017

2 Matter-Antimatter Asymmetry η B n B n B n γ One number BSM Physics Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 2 / 45

3 Leptogenesis [Fukugita, Yanagida 86] A cosmoogica consequence of the seesaw mechanism. Provides a common ink between neutrino mass and baryon asymmetry. Naturay satisfies a the Sakharov conditions. L vioation due to the Majorana nature of heavy RH neutrinos. New source of CP vioation in the eptonic sector (through compex Dirac Yukawa coupings and/or PMNS CP phases). Departure from therma equiibrium when Γ N H. Freey avaiabe: /L /B through EW sphaeron interactions. Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 3 / 45

4 Popuarity of Leptogenesis [INSPIRE Database] Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 4 / 45

5 Popuarity of Leptogenesis [INSPIRE Database] Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 5 / 45

6 Leptogenesis for Pedestrians [Buchmüer, Di Bari, Pümacher 05] Three basic steps: 1 Generation of L asymmetry by heavy Majorana neutrino decay: 2 Partia washout of the asymmetry due to inverse decay (and scatterings): 3 Conversion of the eft-over L asymmetry to B asymmetry at T > T sph. Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 6 / 45

7 Botzmann Equations [Buchmüer, Di Bari, Pümacher 02] dn N dz dn L dz = (D + S)(N N N eq N ), = εd(n N N eq N ) N LW, (where z = m N1 /T and D, S, W = Γ D,S,W /Hz for decay, scattering and washout rates.) FIna baryon asymmetry: d η B = d ε κ f 0.02 (/L /B conversion at Tc + entropy diution from Tc to Trecombination). κ f κ(z f ) is the fina efficiency factor, where κ(z) = z z i dz D D + S dn N dz e z z dz W (z ) Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 7 / 45

8 CP Asymmetry N N ε = Φ L C N Φ L N β tree (a) sef-energy (b) vertex (c) Φ L C N L Φ Φ N β L C Γ(N L Φ) Γ(N L c Φ c ) [ Γ(N L k Φ) + Γ(N L c k Φc ) ] ĥ 2 ĥ c 2 (ĥ ĥ) + (ĥc ĥ c ) k rtance of sef-energy effects (when m N1 m N2 m N1,2 ) with the one-oop resummed Yukawa coupings [Piaftsis, Underwood [J. Liu, 03] G. Segré, PRD48 (1993) 460 M. Fanz, E. Paschos, U. Sarkar, PLB345 (1995) 24 ĥ = ĥ i ɛ βγ ĥ β L. Covi, E. Rouet, F. Vissani, PLB384 (1996) 16 β,γ. J. R. Eis, M. Raida, T. Yanagida, PLB546 (2002) 228 m(ma β + m β A β ) ir γ [m A γβ (m A γ + m γ A γ) + m β A βγ (m A γ + m γ A γ )] m 2 m2 β + 2im2 A ββ + 2iIm(R γ )[m 2 A βγ 2 + m β m γ Re(A 2 βγ )], rtance of the heavy-neutrino width effects: Γ N R β = m 2 m 2 m2 β + 2im2 A ; A β (ĥ) = 1 ββ 16π [A.P., PRD56 (1997) 5431; A.P. and T. Underwood, NPB692 (2004) 303 ĥ ĥ β. Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 8 / 45

9 Testabiity of Seesaw [Drewes 15] Figure 4: In Aa bottom-up schematic iustration approach, of nothe definite reation prediction between of rmtrf the seesaw F and Mscae. I imposed by neutrino osciation data (pot taken from Ref. [22]). Individua eements of F can deviate consideraby from F 0 if there are canceations in (6). Cosmoogica constraints aow to Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 9 / 45

10 Testabiity of Leptogenesis Three regions of interest: High scae: 10 9 GeV m N GeV. Can be fasified with an LNV signa at LHC. see Juia s tak Coider-friendy scae: 100 GeV m N few TeV. Can be tested in coider and/or ow-energy (0νββ, LFV) searches. this tak Low-scae: 1 GeV m N 5 GeV. Can be tested at the intensity frontier: SHiP, DUNE or B-factories (LHCb, Bee-II). see Jacobo s tak Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 10 / 45

11 Testabiity of Leptogenesis Three regions of interest: GUT/high scae: 10 9 GeV m N GeV. Can be fasified with an LNV signa at LHC. [Deppisch, Harz, Hirsch 14] see Juia s tak Coider-friendy scae: 100 GeV m N few TeV. Can be tested in coider and/or ow-energy (0νββ, LFV) searches. this tak Low-scae: 1 GeV m N 5 GeV. Can be tested at the intensity frontier: SHiP, DUNE or B-factories (LHCb, Bee-II). see Jacobo s tak Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 11 / 45

12 Testabiity of Leptogenesis Three regions of interest: GUT/high scae: 10 9 GeV m N GeV. Can be fasified with an LNV signa at LHC. [Deppisch, Harz, Hirsch 14] see Juia s tak Coider-friendy scae: 100 GeV m N few TeV. Can be tested in coider and/or ow-energy (0νββ, LFV) searches. this tak Low-scae: 1 GeV m N 5 GeV. Can be tested at the intensity frontier: SHiP, DUNE or B-factories (LHCb, Bee-II). see Jacobo s tak Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 12 / 45

13 Vania Leptogenesis Hierarchica heavy neutrino spectrum (m N1 m N2 < m N3 ). Both vertex correction and sef-energy diagrams are reevant. For type-i seesaw, the maxima CP asymmetry is given by matm 2 ε max 1 = 3 16π m N1 v 2 Lower bound on m N1 : [Davidson, Ibarra 02; Buchmüer, Di Bari, Pümacher 02] ( ) ( ) m N1 > η B 0.05 ev GeV κ f m 2 atm Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 13 / 45

14 Vania Leptogenesis Hierarchica heavy neutrino spectrum (m N1 m N2 < m N3 ). Both vertex correction and sef-energy diagrams are reevant. For type-i seesaw, the maxima CP asymmetry is given by matm 2 ε max 1 = 3 16π m N1 v 2 Lower bound on m N1 : [Davidson, Ibarra 02; Buchmüer, Di Bari, Pümacher 02] ( ) ( ) m N1 > η B 0.05 ev GeV κ f m 2 atm Experimentay inaccessibe! Aso eads to a ower imit on the reheating temperature T rh 10 9 GeV. In supergravity modes, need T rh GeV to avoid the gravitino probem. [Khopov, Linde 84; Eis, Kim, Nanopouos 84; Cyburt, Eis, Fieds, Oive 02; Kawasaki, Kohri, Moroi, Yotsuyanagi 08] Aso in confict with the Higgs naturaness bound m N 10 7 GeV. [Vissani 97; Carke, Foot, Vokas 15; Bambhaniya, BD, Goswami, Khan, Rodejohann 16] Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 13 / 45

15 Resonant Leptogenesis L (k, r) N (p, s) ε ε Φ(q) Dominant sef-energy effects on the CP-asymmetry (ε-type) [Fanz, Paschos, Sarkar 95; Covi, Rouet, Vissani 96]. Resonanty enhanced, even up to order 1, when m N Γ N /2 m N1,2. [Piaftsis 97; Piaftsis, Underwood 03] The quasi-degeneracy can be naturay motivated as due to approximate breaking of some symmetry in the eptonic sector. Heavy neutrino mass scae can be as ow as the EW scae. [Piaftsis, Underwood 05; Deppisch, Piaftsis 10; BD, Miington, Piaftsis, Teresi 14] A testabe eptogenesis scenario at both Energy and Intensity Frontiers. Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 14 / 45

16 Favor-diagona Rate Equations n γ H N z n γ H N z dη N dz dδη L dz ( ) = 1 ηn η N eq γ N L Φ ( ) η N = 1 ε 2 3 δηl L k (k,r) η N eq k L k(k,r) [ γ L Φ L c k Φc + γ L Φ L n (k2,r2) Lk(k1,r1) L (k1,r1) γ N L k bh Φ n [ h c b ] k n (q1)[n L (k1)] k r1 [ h c b ] k bn (p) L k Φ + ( δηl L k γ k ) ] (q2) (q1) Φ γ L L c k Φ Φc L Φ L [L c (k,r) (k2,r2)]m L (k,r) (a) (q1) L = 0 scattering, n [n L ] k n [ (L! L )] km. [L c (k1,r1)] [L c (k1,r1)]k bn (p) bn (p,s) [ h c b ] m bh n (q1)[ n L (k1)] r1 k bn (p,s) n (q)[n L n (q)[n L [ h c b r (k)] k bn (p,s) [ h c b r (k)] k bn (p) bn (p,s) ] ] (q2) k [ h c b ] k [ h c b ] (q1) c (q1) bh k bn (q) (q) (q) (q) (b) L = 0 scattering, n [ n L ] k [ (L c c! L c c )] n km. L n (k2,r2) Lk(k1,r1) (a) Inverse heavy-neutrino decay, L n [n L (k1,r1) ] k [ (L! N)] k (a) Inverse heavy-neutrino decay, n [n L ] k. Lm(k2,r2) (k2,r2)]m [ (L! N)] Lk(k1,r1) k. bh n [ h c b ] k n (q1)[n L (k1)] k r1 bh (q2) bn (p) [L c (k,r)] [L c (k,r)] (q1) [ h c b ][ h c b ] m [ h c b ] k m n (q1)[n L (k1)] k r1 [L c bn (p) bn (p) (k,r)] k [L c (q1) (k,r)] c (q2) k (q1) (q2) L (k1,r1) (q1) [ b h c ] bn ( bn (p,s) (a) L = 0 scattering, n (q)[ n n [n bh r L (k)] ] k k n [ (L! L )] km. (c) L = 2 scattering, bn (p,s) n [n L ] k bh k bn [ (L! L c c )] n km. (p,s) n (q)[ n L bh r (k)] k bn (p,s) c (q) c (q) bh [L c k (k2,r2)]m [L c (k1,r1)] L n (k2,r2) [L c (k1,r1)]k [L c (k1,r1)] [L c (k2,r2)] n [L c (k1,r1)]k Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 15 / 45

17 Anaytic Soution L ðzþ ¼ 3 2 K eff z : (4.38) to be B ¼ 2 5 [Deppisch, Piaftsis 11] N 1 3 L, N L z 1 z 2 z c z FIG. 1 (coor onine). Numerica soutions to BEs (4.32) and (4.35) for η N1 ¼ N1 = eq N 1 and L (z) 3 ε L,(z respectivey, in a RL 2z K mode with m N ¼ 220 GeV, eff 2 < z < z 3 ) 1 ¼ 10 6, K eff ¼ 10 2, ¼ 10 6 and z c ¼ m N =T c ¼ 1:6. z We note t estimate of regime of a right-hande weak scae given in (4. In the next 2 The onse the reative 2=3ðz 3 Þ3 K 1 ð anayticay which z 3 i approximati Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 16 / 45

18 Favordynamics Mi 1012 GeV 109 GeV Mi 1012 GeV 109 GeV Figure 1: The ten di erent three RH neutrino mass patterns requiring 10 di erent sets of Botzmann equations for the cacuation of the asymmetry [17]. component, escapes the washout from a ighter RH neutrino species [6]. Second, parts of the favour asymmetries (phantom terms) produced in the one or two favour regimes do not contribute to the tota asymmetry at the production but can contribute to the fina asymmetry [18]. Therefore, it is necessary to extend the density matrix formaism beyond the traditiona N1 -dominated scenario [6, 11, 19] and account for heavy neutrino favours e ects in Bhupa Dev order (Washington U.) Leptogenesis andarbitrary Coiders Workshop to cacuate the fina asymmetry for an choice of the RH neutrinoacfi masses. 17 / 45

19 Favordynamics Mi 1012 GeV 109 GeV Mi 1012 GeV 109 GeV Favor Figure effects at ow [Abada, mass Davidson, Ibarra,requiring Josse-Michaux, Losada, Riotto 1: important The ten di erent threescae RH neutrino patterns 10 di erent sets of 06; Nardi, Nir, Rouet,Botzmann Racker 06; equations De Simone,for Riotto Banchet, of Di the Bari,asymmetry Jones, Marzoa 12; BD, Miington, Piaftsis, Teresi 14] the 06; cacuation [17]. Two sources of favor effects: Heavy neutrino Yukawa coupings h [Piaftsis 04; Endoh, Morozumi, Xiong 04] component, escapes the washout from a ighter RH neutrino species [6]. Second, parts of Charged epton Yukawa coupings y k [Barbieri, Creminei, Strumia, Tetradis 00] the favour asymmetries (phantom terms) produced in the one or two favour regimes do Three distinct physica osciation and decoherence. not contribute to the phenomena: tota asymmetry mixing, at the production but can contribute to the fina asymmetry [18]. Captured consistenty in the Botzmann approach by the fuy favor-covariant Therefore, it is necessary to extend the density matrix formaism beyond the tradiformaism. [BD, Miington, Piaftsis, Teresi 14; 15] tiona N1 -dominated scenario [6, 11, 19] and account for heavy neutrino favours e ects in Leptogenesis andarbitrary Coiders Workshop the fina asymmetry for an choice of the RH neutrinoacfi masses. Bhupa Dev order (Washington U.) to cacuate 17 / 45

20 Master Equation for Transport Phenomena In quantum statistica mechanics, n X (t) ň X ( t; t i ) t { } = Tr ρ( t; t i ) ň X ( t; t i ). Differentiate w.r.t. the macroscopic time t = t t i : { } { } dn X (t) = Tr ρ( t; t i ) dňx ( t; t i ) dρ( t; t i ) + Tr ň X ( t; t i ) dt d t d t I 1 + I 2.. Use the Heisenberg EoM for I 1 and Liouvie-von Neumann equation for I 2. Markovian master equation for the number density matrix: d dt nx (k, t) i [H X 0, ň X (k, t)] t dt [H int(t ), [H int(t), ň X (k, t)]] t. Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 18 / 45

21 Master Equation for Transport Phenomena In quantum statistica mechanics, n X (t) ň X ( t; t i ) t { } = Tr ρ( t; t i ) ň X ( t; t i ). Differentiate w.r.t. the macroscopic time t = t t i : { } { } dn X (t) = Tr ρ( t; t i ) dňx ( t; t i ) dρ( t; t i ) + Tr ň X ( t; t i ) dt d t d t I 1 + I 2.. Use the Heisenberg EoM for I 1 and Liouvie-von Neumann equation for I 2. Markovian master equation for the number density matrix: d dt nx (k, t) i [H X 0, ň X (k, t)] t dt [H int(t ), [H int(t), ň X (k, t)]] t. (Osciation) (Mixing) Generaization of the density matrix formaism. [Sig, Raffet 93] Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 18 / 45

22 Coision Rates for Decay and Inverse Decay n Φ [n L ] k [γ(lφ N)] β k L N β [ĥ c ] β k [ĥ c ] N Φ L k (k, r) L (k, r) N β (p, s) [ĥ c ] β k n Φ (q)[n L r (k)] k [ĥ c ] N (p, s) Φ(q) Φ(q) Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 19 / 45

23 Coision Rates for 2 2 Scattering n Φ [n L ] k [γ(lφ LΦ)] n k m [ĥ c ] β k N β L [ĥ c ] N L n ĥ n β Φ ĥ m L m Φ L n (k 2, r 2 ) L k (k 1, r 1 ) L (k 1, r 1 ) L m (k 2, r 2 ) ĥ n β N β (p) [ĥ c ] β k n Φ (q 1 )[n L r 1 (k 1 )] k [ĥ c ] N (p) ĥ m Φ(q 2 ) Φ(q 1 ) Φ(q 1 ) Φ(q 2 ) Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 20 / 45

24 Fina Rate Equations H N n γ z H N n γ z d[η N ] β dz d[δη N ] β dz = i nγ 2 [E N, δη N ] β = 2 i n γ [ E N, η N ] β 1 { δη N N, Re(γ 2 ηeq N LΦ ) + [ N Re(γLΦ ) ] β 1 { } β η N N, Re(γ 2 ηeq N LΦ ) + 2 i [ Im(δγ N LΦ ) ] β } β η N eq i { } β η N, Im(δγ N LΦ ) H N n γ z d[δη L ] m dz = [δγlφ] N m { [ηn ] β ηeq N δη L, γ LΦ + L c Φ c γ LΦ LΦ [δγlφ] N m β + [δηn ] β 2 ηeq N } m 2 3 [δηl ] n k [γlφ] N m β ( [γ LΦ ] k m [γ LΦ L c Φ c n LΦ] k m n ) 2 3 {δη L, γ dec } m + [δγ back dec ] m Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 21 / 45

25 Fina Rate Equations: Mixing H N n γ z H N n γ z d[η N ] β dz d[δη N ] β dz = i nγ 2 [E N, δη N ] β = 2 i n γ [ E N, η N ] β 1 { δη N N, Re(γ 2 ηeq N LΦ ) + [ N Re(γLΦ ) ] β 1 { } β η N N, Re(γ 2 ηeq N LΦ ) + 2 i [ Im(δγ N LΦ ) ] β } β η N eq i { } β η N, Im(δγ N LΦ ) H N n γ z d[δη L ] m dz = [δγlφ] N m { [ηn ] β ηeq N δη L, γ LΦ + L c Φ c γ LΦ LΦ [δγlφ] N m β + [δηn ] β 2 ηeq N } m 2 3 [δηl ] n k [γlφ] N m β ( [γ LΦ ] k m [γ LΦ L c Φ c n LΦ] k m n ) 2 3 {δη L, γ dec } m + [δγ back dec ] m Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 21 / 45

26 Fina Rate Equations: Osciation H N n γ z H N n γ z d[η N ] β dz d[δη N ] β dz = i nγ 2 [E N, δη N ] β = 2 i n γ [ E N, η N ] β 1 { δη N N, Re(γ 2 ηeq N LΦ ) + [ N Re(γLΦ ) ] β 1 { } β η N N, Re(γ 2 ηeq N LΦ ) + 2 i [ Im(δγ N LΦ ) ] β } β η N eq i { } β η N, Im(δγ N LΦ ) H N n γ z d[δη L ] m dz = [δγlφ] N m { [ηn ] β ηeq N δη L, γ LΦ + L c Φ c γ LΦ LΦ [δγlφ] N m β + [δηn ] β 2 ηeq N } m 2 3 [δηl ] n k [γlφ] N m β ( [γ LΦ ] k m [γ LΦ L c Φ c n LΦ] k m n ) 2 3 {δη L, γ dec } m + [δγ back dec ] m Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 21 / 45

27 Fina Rate Equations: Charged Lepton Decoherence H N n γ z H N n γ z d[η N ] β dz d[δη N ] β dz = i nγ 2 [E N, δη N ] β = 2 i n γ [ E N, η N ] β 1 { δη N N, Re(γ 2 ηeq N LΦ ) + [ N Re(γLΦ ) ] β 1 { } β η N N, Re(γ 2 ηeq N LΦ ) + 2 i [ Im(δγ N LΦ ) ] β } β η N eq i { } β η N, Im(δγ N LΦ ) H N n γ z d[δη L ] m dz = [δγlφ] N m { [ηn ] β ηeq N δη L, γ LΦ + L c Φ c γ LΦ LΦ [δγlφ] N m β + [δηn ] β 2 ηeq N } m 2 3 [δηl ] n k [γlφ] N m β ( [γ LΦ ] k m [γ LΦ L c Φ c n LΦ] k m n ) 2 3 {δη L, γ dec } m + [δγ back dec ] m Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 21 / 45

28 Fied-Theoretic Transport Phenomena KeyMixing Resut and Osciations 10-6 dh L L dh mix L dh osc dh L 10-7 δη L mix δη L osc z = mnêt Combination g N 3 L I ( ( ĥ ĥ) = osc L 2 β M + mix L 2 yieds N, MN, a factor β) 2 MN Γ(0) ββ of 2 enhancement 2 2Kz compared β to the (ĥ ĥ)(ĥ ĥ) ( isoated contributions ββ M 2 N, Mfor 2 2 ( ) 2, N, weaky-resonant β) + MN Γ(0) ββ RL. g N 3 I ( ( ĥ ĥ) 2 β M 2 N, MN, β) 2 ( Γ(0) MN 2 2Kz (ĥ ĥ)(ĥ ĥ) ββ β + Γ(0) ββ ( M 2 N, M 2 N, β) 2 + M 2 N ( Γ(0) + Γ(0) ββ )2 I[(ĥ ĥ) β ] 2 (ĥ ĥ) (ĥ ĥ) β Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 22 / 45 )

29 Testabe Modes Need m N O(TeV). Naive type-i seesaw requires mixing with ight neutrinos to be Coider signa suppressed in the minima set-up (SM+RH neutrinos). Two ways out: Construct a TeV seesaw mode with arge mixing (specia textures of m D and m N ). Go beyond the minima SM seesaw (e.g. U(1) B L, Left-Right). Observabe ow-energy signatures (LFV, 0νββ) possibe in any case. Compementarity between high-energy and high-intensity frontiers. Leptogenesis brings in additiona powerfu constraints in each case. Can be used to test/fasify eptogenesis. Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 23 / 45

30 A Minima Mode of RL O(N)-symmetric heavy neutrino sector at a high scae µ X. Radiative RL: Sma mass spitting at ow scae from RG effects. [Branco, Gonzaez Feipe, Joaquim, Masina, Rebeo, Savoy 03] M N = m N 1 + M RG N, with M RG N = m N 8π 2 n ( µx m N ) Re [ h (µ X )h(µ X ) ]. A specific reaization: Resonant -genesis (RL ). [Piaftsis 04; Deppisch, Piaftsis 11] An exampe of RL τ with U(1) Le+L µ U(1) Lτ favor symmetry: 0 ae iπ/4 ae iπ/4 h = 0 be iπ/4 be iπ/4 + δh, ɛ e 0 0 δh = ɛ µ 0 0, ɛ τ κ 1 e i(π/4 γ 1) κ 2 e i(π/4 γ 2) But CP asymmetry vanishes up to O(h 4 ). [BD, Miington, Piaftsis, Teresi 15] Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 24 / 45

31 A Next-to-minima Mode [BD, Miington, Piaftsis, Teresi 15] Add an additiona favor-breaking M N : M N = m N 1 + M N + M RG N, with M N = M /2 M 2 0, 0 0 M 2 /2 h = 0 a e iπ/4 a e iπ/4 0 b e iπ/4 b e iπ/4 0 c e iπ/4 c e iπ/4 + ɛ e 0 0 ɛ µ 0 0 ɛ τ 0 0. Light neutrino mass constraint: M ν v 2 2 hm 1 N ht v 2 2m N m N m N a 2 ɛ 2 e m N ab ɛ m N eɛ µ ɛ eɛ τ m N ab ɛ m N eɛ µ m N b 2 ɛ 2 m µ N ɛ µɛ τ ɛ eɛ τ ɛ µɛ τ ɛ 2 τ, where m N 2 [ M N ] 23 + i ( [ M N ] 33 [ M N ] 22 ) = i M2. Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 25 / 45

32 Benchmark Points Parameters BP1 BP2 BP3 m N 120 GeV 400 GeV 5 TeV c M 1 /m N M 2 /m N ( i) 10 8 ( i) 10 9 ( i) 10 8 a ( i) 10 4 ( i) 10 3 ( i) 10 3 b ( i) 10 3 ( i) 10 3 ( i) 10 3 ɛ e 3.31 i i i 10 7 ɛ µ 2.33 i i i 10 6 ɛ τ 3.50 i i i 10 6 Observabes BP1 BP2 BP3 Current Limit BR(µ eγ) < BR(τ µγ) < BR(τ eγ) < BR(µ 3e) < R Ti µ e < R Au µ e < R Pb µ e < Ω eµ < Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 26 / 45

33 A Discrete Favor Mode for RL Based on residua eptonic favor G f = (3n 2 ) or (6n 2 ) (with n even, 3 n, 4 n) and CP symmetries. [Luhn, Nasri, Ramond 07; Escobar, Luhn 08; Ferugio, Hagedorn, Ziegar 12] LH epton doubets L transform in a faithfu compex irrep 3, RH neutrinos N in an unfaithfu rea irrep 3 and RH charged eptons R in a singet 1 of G f. 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, Moinaro 14] Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 27 / 45

34 A Discrete Favor Mode for RL Based on residua eptonic favor G f = (3n 2 ) or (6n 2 ) (with n even, 3 n, 4 n) and CP symmetries. [Luhn, Nasri, Ramond 07; Escobar, Luhn 08; Ferugio, Hagedorn, Ziegar 12] LH epton doubets L transform in a faithfu compex irrep 3, RH neutrinos N in an unfaithfu rea irrep 3 and RH charged eptons R in a singet 1 of G f. 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, Moinaro 14] Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 27 / 45

35 A Discrete Favor Mode for RL Based on residua eptonic favor G f = (3n 2 ) or (6n 2 ) (with n even, 3 n, 4 n) and CP symmetries. [Luhn, Nasri, Ramond 07; Escobar, Luhn 08; Ferugio, Hagedorn, Ziegar 12] LH epton doubets L transform in a faithfu compex irrep 3, RH neutrinos N in an unfaithfu rea irrep 3 and RH charged eptons R in a singet 1 of G f. 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, Moinaro 14] One exampe: [BD, Hagedorn, Moinaro (in prep)] y Y D = Ω(s)(3) R 13 (θ L ) 0 y 2 0 R13 ( θ R ) Ω(s)(3 ). 0 0 y M R = M N θ L 0.18(2.96) gives sin 2 θ (0.395), sin 2 θ and sin 2 θ (within 3σ of current goba-fit). [Hagedorn, Moinaro 16] Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 27 / 45

36 Fixing Mode Parameters Light neutrino masses given by the type-i seesaw: y1 2 cos 2θ R 0 y 1 y 3 sin 2θ R 0 y2 2 0 (s even), Mν 2 = v 2 y 1 y 3 sin 2θ R 0 y3 2 cos 2θ R M N y1 2 cos 2θ R 0 y 1 y 3 sin 2θ R 0 y2 2 0 (s odd). y 1 y 3 sin 2θ R 0 y3 2 cos 2θ R For y 1 = 0 (y 3 = 0), we get strong norma (inverted) ordering, with m ightest = 0. M N m 2 m atm so M 2 N cos 2 θ NO : y 1 = 0, y 2 = ±, y 3 = ± R IO : y 3 = 0, y 2 = ± Ony free parameters: M N and θ R. v M N m 2 atm v, y 1 = ± v M N ( m 2 atm m 2 so) cos 2 θ R v Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 28 / 45

37 Low Energy CP Phases and 0νββ Dirac phase is trivia: δ = 0. For m ightest = 0, ony one Majorana phase, which depends on the chosen CP transformation: sin = ( 1) k+r+s sin 6 φ s and cos = ( 1) k+r+s+1 cos 6 φ s with φ s = π s n, where k = 0 (k = 1) for cos 2 θ R > 0 (cos 2 θ R < 0) and r = 0 (r = 1) for NO (IO). Restricts the ight neutrino contribution to 0νββ: m ββ 1 mso ( 1) s+k+1 sin 2 θ L e 6 i φs m 2 atm (NO). m ( 1) s+k e 6 i φs cos 2 θ L 2 atm (IO). For n = 26, θ L 0.18 and best-fit vaues of m 2 so and m 2 atm, we get ev m ββ ev (NO) ev m ββ ev (IO). Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 29 / 45

38 High Energy CP Phases and Leptogenesis At eading order, three degenerate RH neutrinos. Higher-order corrections can break the residua symmetries, giving rise to a quasi-degenerate spectrum: M 1 = M N (1 + 2 κ) and M 2 = M 3 = M N (1 κ). CP asymmetries in the decays of N i are given by ε i Im ( ) ( (Ŷ ) ) ŶD,iŶD,j Re DŶD ij j i F ij are reated to the reguator in RL and are proportiona to the mass spitting of N i. We find ε 3 = 0 and ε 1 y 2 y 3 9 ( 2 y y 2 3 (1 cos 2 θ R )) sin 3 φ s sin θ R sin θ L, F 12 (NO) ε 1 y 1 y 2 9 ( 2 y y 2 1 (1 + cos 2 θ R )) sin 3 φ s cos θ R cos θ L, F 12 (IO) with θ L, = θ L + ρ 4π/3 and ρ e = 0, ρ µ = 1, ρ τ = 1. ε 2 are the negative of ɛ 1 with F 12 being repaced by F 21. F ij Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 30 / 45

39 Correation between BAU and 0νββ ηb ,9, ,12,14 6,7, ,11, m ββ [ev] 23 5,8,18 0, ,10,16 NO [BD, Hagedorn, Moinaro (in prep)] Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 31 / 45

40 Correation between BAU and 0νββ ηb ,9, ,7,20 2,11, ,8,18 0 0, ,10, ,12,14 17 IO m ββ [ev] [BD, Hagedorn, Moinaro (in prep)] Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 32 / 45

41 Correation between BAU and 0νββ 30 ηb ,9, nexo ,12,14 LEGEND 1k 6,7, ,11,24 15 LEGEND ,8,18 0, ,10,16 IO m ββ [ev] [BD, Hagedorn, Moinaro (in prep)] Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 33 / 45

42 Decay Length For RH Majorana neutrinos, Γ = M (Ŷ D ŶD) /(8 π). We get Γ 1 M ( ) N 2 y 2 1 cos 2 θ R + y y3 2 sin 2 θ R, 24 π Γ 2 M ( ) N y 2 1 cos 2 θ R + 2 y2 2 + y3 2 sin 2 θ R, 24 π Γ 3 M ( ) N y 2 1 sin 2 θ R + y3 2 cos 2 θ R. 8 π For y 1 = 0 (NO), Γ 3 = 0 for θ R = (2j + 1)π/2 with integer Long Lived j. Partice Searches at LHC For y 3 = 0 (IO), Γ 3 = 0 for jπ with integer j. In either case, N 3 is an utra ong-ived partice. Suitabe for MATHUSLA [Chou, Curtin, Lubatti 16] see Henry s tak In addition, N 1,2 can have dispaced vertex signas at the LHC. MATHUSLA Surface Detector SHiP experiment Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 34 / 45

43 Decay Length L (m ) MATHUSLA LHC dispaced NO θ R /π N 1 (red), N 2 (bue), N 3 (green). M N =150 GeV (dashed), 250 GeV (soid). Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 35 / 45

44 Decay Length L (m ) MATHUSLA LHC dispaced IO θ R /π N 1 (red), N 2 (bue), N 3 (green). M N =150 GeV (dashed), 250 GeV (soid). Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 36 / 45

45 Coider Signa Need an efficient production mechanism. yi (our case) suppresses the Dre-Yan production pp W ( ) Ni `. Let us consider a minima U(1)B L porta. Production cross section is no onger Yukawa-suppressed, whie the decay is, giving rise to dispaced vertex at the LHC. [Deppisch, Desai, Vae 13] Z0! q BrHmÆegL=5.7â10-13 eµ The and para neut ' cays N Z Dm2so < q2mn < 0.3 ev bran favo N LLHC=1 mm 10-8 β As u 100 mm so th d W the L q 10 m a m neut q Figu ing FIG. 2: Average decay ength of a heavy neutrino N produced FIG. 1: Feynman diagram for heavy Majorana neutrino proand in Z 0! N N with mz 0 = 3 TeV as a function of its mass 0 a de duction through the Z porta at the LHC. mn and the ight-heavy mixing (soid bue contours). The Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI 45 dashed red contours denote constant vaues forworkshop Br(µ! e ) 37 / cons W 10-4 q q u d

46 Coider Signa NO ee eμ μμ ττ σlnv (fb) M N (GeV) At s = 14 TeV LHC and for M Z = 3.5 TeV. Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 38 / 45

47 Coider Signa IO ee eμ μμ ττ σlnv (fb) M N (GeV) At s = 14 TeV LHC and for M Z = 3.5 TeV. Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 39 / 45

48 s at very [7]. Bound Weon Z Mass M Z' GeV vaues of s, and for FIG. 1: Regions in the space (M Z Z M N )whereeptogenesis interactions induce additiona diution effects, e.g. NN Z jj. 3foreach can be tested for the case of norma or inverted hierarchy. The Successfu eptogenesis requires a ower bound on M Z. [Banchet, Chacko, Granor, Mohapatra hy, where regions the right and above the coored curves are aowed. 09; Heeck, Teresi 17; BD, Hagedorn, Moinaro (in prep)] essed [15]. saity and 2500 t reaxing y factors (2 K atm ) M N M Z' 2 > 300 if 1500 egenerate enchmark 1000 hierarchy, i K i = reasonabe etries ε i, inverted This is efficiency re present assumed MN GeV 500 ε 1 ε M Z' GeV FIG. 2: Same as Fig. 1 but for the case of quasi-degenerate neutrinos. Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 40 / 45

49 RL in LR and Bound on W R Mass Additiona diution effects induced by W R, e.g. Ne R W R ū R d R. Lower imit on M WR 10 TeV. [Frere, Hambye, Vertongen 09; BD, Lee, Mohapatra 15] Y tot =1 mw R (TeV) Y tot =3 Strong Washout Weak Washout m N > m W 5 R Log 10 [m N /TeV] Figure 4: Contour pots of L (z c) = for h = (dashed ines) and h = (soid ines) with " Y tot = 1 (red ines) and " Y tot = 3 (bue ines). The green dot corresponds to the exampe fit vaue presented in Section 3. Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 41 / 45

50 Concusion Leptogenesis provides an attractive ink between neutrino mass and observed baryon asymmetry of the universe. Resonant Leptogenesis provides a way to test this idea in aboratory experiments. Favor effects are important in the cacuation of epton asymmetry. Testabe modes of RL. Predictive in both ow and high-energy sectors. Correation between BAU and 0νββ. In gauge-extended modes, LNV signas (incuding dispaced vertex) at the LHC. Discovery of a heavy gauge boson coud fasify eptogenesis. Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 42 / 45

51 Concusion Leptogenesis provides an attractive ink between neutrino mass and observed baryon asymmetry of the universe. Resonant Leptogenesis provides a way to test this idea in aboratory experiments. Favor effects are important in the cacuation of epton asymmetry. Testabe modes of RL. Predictive in both ow and high-energy sectors. Correation between BAU and 0νββ. In gauge-extended modes, LNV signas (incuding dispaced vertex) at the LHC. Discovery of a heavy gauge boson coud fasify eptogenesis. Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 42 / 45

52 Backup Sides

53 Favor Transformations L N Under U(N L ) U(N N ), h = h L Φ NR, NC R, [M N ] β N R,β + H.c.. L L = V m L m, L (L ) L = V m L m, N R, N R, = U β N R,β, NR (N R,) N R h = V m = U β N β R. U β h β m, [M N ] β [M N] β = U γ U β δ [M N] γδ. Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 44 / 45

54 Favor Transformations L N Under U(N L ) U(N N ), h = h L Φ NR, NC R, [M N ] β N R,β + H.c.. L L = V m L m, L (L ) L = V m L m, N R, N R, = U β N R,β, NR (N R,) N R h = V m Number densities: Tota number density: n N (t) = U β N β R. U β h β m, [M N ] β [M N] β = U γ U β δ [M N] γδ. [n L s 1 s 2 (p, t)] m 1 V 3 b m (p, s 2, t) b (p, s 1, t) t, [ n L s 1 s 2 (p, t)] m 1 V 3 d (p, s 1, t) d,m (p, s 2, t) t, [n N r 1 r 2 (k, t)] β 1 V 3 a β (k, r 2, t) a (k, r 1, t) t, [ n N r 1 r 2 (k, t)] β 1 V 3 G γ a γ (k, r 1, t) G βδ a δ (k, r 2, t) t, n N rr (k, t), n L (t) Tr iso r=,+ k s=,+ p Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 44 / 45 n L ss(p, t).

55 Favor Covariant Transport Equations for RL Expicity, for charged-epton and heavy-neutrino matrix number densities, d dt [nl s 1 s 2 (p, t)] m = i [ E L (p), ns L 1 s 2 (p, t) ] m d dt [nn r 1 r 2 (k, t)] β = i [ E N (k), nr N 1 r 2 (k, t) ] β Coision terms are of the form + [C L s 1 s 2 (p, t)] m + [CN r 1 r 2 (k, t)] β + G λ [C N r 2 r 1 (k, t)] λ µ G µβ [C L s 1 s 2 (p, t)] m 1 2 [Fs 1s r 1 r 2 (p, q, k, t)] n β [Γs s 2r 2 r 1 (p, q, k)] m n β, where F are statistica tensors, and Γ are the rank-4 absorptive rate tensors describing heavy neutrino decays and inverse decays. Bhupa Dev (Washington U.) Leptogenesis and Coiders ACFI Workshop 45 / 45