LOW-SCALE LEPTOGENESIS WITH 3 RIGHT-HANDED NEUTRINOS
Michele Lucente
39th International Conference on High Energy Physics ICHEP 2018 Seoul July 6th 2018, Coex Center in Seoul
Based on work in collaboration with A. Abada, G. Arcadi, V. Domcke, M. Drewes and J. Klaric Normal Ordering ( 2 =0.97) Inverted Ordering (best fit) Any Ordering bfp 1 3 range bfp 1 3 range 3 range ± ± 2 +0.013 +0.013 sin ✓12 0.304 0.012 0.270 0.344 0.304 0.012 0.270 0.344 0.270 0.344 ! ! ! +0.78 +0.78 ✓12/ 33.48 0.75 31.29 35.91 33.48 0.75 31.29 35.91 31.29 35.91 ! ! ! 2 +0.052 +0.025 sin ✓23 0.452 0.028 0.382 0.643 0.579 0.037 0.389 0.644 0.385 0.644 ! ! ! +3.0 +1.5 ✓23/ 42.3 1.6 38.2 53.3 49.5 2.2 38.6 53.3 38.3 53.3 ! ! ! 2 +0.0010 +0.0011 sin ✓13 0.0218 0.0010 0.0186 0.0250 0.0219 0.0010 0.0188 0.0251 0.0188 0.0251 ! ! ! +0.20 +0.20 tions.✓13/ The discrepancy8.50 0.21 7.85 is at9.10 the [2.83.51, 50..3]21 level,7.87 depending9.11 7.87 on the9.11 adopted analysis [228], ! ! ! +39 +63 and CP constitutes/ 306 70 the so-called0 360 Lithium254 62 problem0. It360 is not clear0 360 if the discrepancy is due ! ! ! to systematic m2 errors in the observed abundances, to uncertainties in the nuclear inputs, 21 7.50+0.19 7.02 8.09 7.50+0.19 7.02 8.09 7.02 8.09 5 2 0.17 0.17 to10 underestimated eV processes! that may reduce the! Lithium abundance! during the stellar 2 m3` +0.047 +0.048 +2.325 +2.599 2 +2.457 0.047 +2.317 +2.607 2.449 0.047 2.590 2.307 ! evolution10 3 eV or to new physics! at work. ! 2.590 2.307 !
Observational3.5.2Table 1. Cosmic Three-flavor oscillation Microwave problems parameters Background from of our the fit to globalSM data after the NOW 2014 conference. The results are presented for the “Free Fluxes + RSBL” in which reactor fluxes have Thebeen study left free in of the the fit and CMB short baseline anisotropies reactor data provides (RSBL) with aL . precise100 m are measurement included. The of the baryon to Two seeminglynumbers in the 1st unrelated (2nd) column are observations obtained assuming NO cannot (IO), i.e., relativebe to the respective photonlocal minimum, ratio whereas at the in decoupling the 3rd column we epoch minimize via also the with determination respect to the ordering. of theNote parameter ⌦b, which thataccounted m2 m2 > for0 for in NO the and mStandard2 m2 < 0 Model for IO. is related3` ⌘ to the31 BAU via the3` ⌘ relation32 [229]
leptonic mixing matrix to be: ⇢c ⌘ = ⌦ , (3.86) B m n0 b Neutrinos are 0.801 0.845 0.514 0.580 0.137 0.158 ! ! h i ! U = 0.225 0.517 0.441 0.699 0.614 0.793 . (3.1) massive and0 | | 0 ! ! ! 1 where n is the present0.246 0.529 photon 0.464 number0.713 density 0.590 and0.776m is the mean mass per baryon, leptons mix B ! ! ! h Ci which is slightly@ lowerM.C. Gonzalez-Garcia, than the M. Maltoni proton and T. Schwetz, one arXiv:1409.5439 due to the [hep-ph] HeliumA binding energy. We already By construction the derived limits in Eq. (3.1) are obtained under the assumption of the discussedmatrix U being the unitary. effects In otherof ⌦ words,b on the the ranges CMB in the angular di↵erent entries power of spectrumthe matrix are in Section 3.3.4. The analysiscorrelated performed due to the constraints by the imposed Planck by collaboration unitarity, as well as gives the fact the that, value in general, [178] the result of a given experiment restricts a combination of several entries of the matrix. As The Universe has a negligible 10 a consequence choosing a specific value⌘ B for=(6 one element.10 0 further.04) restricts10 the, range of the (3.87) amountothers. of antimatter ± ⇥ whichThe is present in remarkable status of the determination agreement of with leptonic the CP violation value derived is illustrated from in Fig. BBN,3 eq.(3.85). Notice where we show the dependence of the 2 of the global analysis on the Jarlskog invariant that this observation is a probe of the BAU at an epoch when the temperature was T which gives a convention-independent measure of CP violation [51], defined as usual by: ⇠ eV, and is thus complementary!2 to the BBN one that probes the BAU at T MeV. max Im U U ⇤ U ⇤ U J ✏ ✏ J sin . (3.2) ⇠ We notice here↵i ↵j that i j the⌘ CMB angularCP ↵ powerijk ⌘ spectrumCP CP also depends on the parameter =e,µ,⌧ k=1,2,3 ⇥ ⇤ X X Yp, that sets the number of free electrons between helium and hydrogen recombination, Using the parametrization in Eq. (1.1) we get that in turns determine the mean free path of photons due to Thomson scattering. max 2 Thus the parametersJCP = cos(⌦✓b12,H,Ysin ✓12pcos) are✓23 sin directly✓23 cos ✓13 probedsin ✓13 . by CMB(3.3) observation: since they are correlated in BBN, it is possible to test the BBN scenario from CMB [229].
3.6 BAU and the Standard–7– Model Having established the presence of a small but finite BAU at the BBN epoch makes it necessary to determine the mechanism at its origin. The first question to answer is whether the SM can account for this asymmetry. Qualitatively, it complies with Sakharov’s conditions. The C and CP symmetries and the baryon number are violated by weak interactions. The violation of the C symmetry relies on the chiral structure of the SU(2)L gauge group, with the weak current given by the sum of a vector component (odd under C) and an axial one (even under C)[13]. The CP violation is related to the presence of a physical phase in the Lagrangian, the CKM phase in the Cabibbo- Kobayashi-Maskawa quark mixing matrix [56]. Baryon number is conserved in the SM at the perturbative level, however non-perturbative effects violate the sum of the baryon plus lepton numbers B + L, while conserving B L [230–232]. Indeed, the ground state of an SU(N) gauge theory is not unique, but is composed by an infinite series of vacua,
60 The natural (simple) way Complete the SM field pattern with right-handed neutrinos
Figure from S. Alekhin et al., arXiv:1504.04855 [hep-ph] !3 Parameter Y Y Y Y m [eV] ⇤ [GeV] Phases Osc. data | e| ⇥ | µ| | e| | µ| 1 4 5 3 4 Range (0, 10 ) ( 0.1, 0.1) (10 , 1) (10 , 10 ) (0, 2⇡) fixed Parameter Y Y Y Y m [eV] ⇤ [GeV] Phases Osc. data | e| ⇥ | µ| | e| | µ| 1 Range (0, 10 4) ( 0.1, 0.1) (10 5, 1) (103, 104) (0, 2⇡) fixed Table 1: The 9 free parameters of our scan: the modulus and phase of the electron and muon Yukawas Y , Y , ↵ and ↵ , the Majorana mass scale ⇤, the absolute neutrino mass m and Table| e 1:| The| µ| 9 freee parametersµ of our scan: the modulus and phase of the electron and muon 1 the 3 yetYukawas unknownY , Y CP-violation, ↵ and ↵ , phases the Majorana (Dirac mass and scale Majorana)⇤, the absolute in the neutrino PMNS mass mixingm matrix:and , ↵1 | e| | µ| e µ 1 and ↵2the. The 3 yet PMNS unknown mixing CP-violation angles phases and (Dirac mass and splittings Majorana) are in fixed the PMNS to their mixing best matrix: fit from , ↵1 the global analysisand in↵2 Ref.. The [? PMNS]. mixing angles and mass splittings are fixed to their best fit from the global analysis in Ref. [?]. Neutrino masses and leptogenesis
Type-I seesaw mechanism: SM + gauge singlet fermions NI M / IJMcIJ c = = SM++iiNNI @/NNI Y↵YI `↵ `N I N+ + NI NJN+ Nh.c. + h.c. (1) (1) L L LSML I I ↵I ↵ I 2 2 I J ✓✓ ◆ ◆ e After electroweak phase transition e< Φ > = v ≃ 174 GeV lim mi =0, 2 mi µ, m M 0 v) /1 !m Y ⇤ Y † (2) lim ⌫mi =0, mi n, d (2) M 0 ' 6 2) M/ !
The Lagrangian provides the ingredients for leptogenesis too (3) lim mi =0!, mi µ, m M 0 ) / • Complex! Yukawav couplings Y as a source of CP lim mdi==0,Y ⇤ mi n, d (3) Sakharov M 0 6 p2 ) / • B from! sphaleron transitions until TEW ≃ 140 GeV conditions ! (4) • sterile neutrinos deviations from thermal equilibrium (4) ! ⌫R(0,0) (5) 4 { v d = 2 5Y 2 G m sin⇤ ✓I Fp2I , (6) EW ' 192⇡3 ! (5)
2 ⌦mh =0.1426 0.0020 (7) 2 ± ⌦bh =0.02226 0.00023 (8) 2 ± ⌦ h =0⌫R.1186(0,0) 0.0020 (9) (6) c ±
2 5 2 G m sin13✓I BR < 5F.7 I 10 (10) EWµe ⇥ , (7) ' 192⇡38 BR⌧e < 3.3 10 (11) ⇥ 8 BR < 4.4 10 (12) ⌧µ ⇥ 2 ⌦mh =0.1426 0.0020 (8) ↵ =(7.2973525698 0.0000000024) 10 3 2 ± ⌦bh =0.±02226 0.00023⇥ (9) MZ = (91.1876 0.0021) GeV± (13) 2 ± 5 2 G =(1⌦.c1663787h =00.0000006)1186 0.002010 GeV (10) µ ± ± ⇥
1 13 BRµe < 5.7 10 (11) ⇥ 8 BR⌧e < 3.3 10 (12) ⇥ 8 BR < 4.4 10 (13) ⌧µ ⇥
1 Parameter Y Y Y Y m [eV] ⇤ [GeV] Phases Osc. data | e| ⇥ | µ| | e| | µ| 1 4 5 3 4 ParameterRange Y(0, 10 Y ) (Y 0.1,Y0.1) m(10 [eV], 1) ⇤(10[GeV], 10 ) Phases(0, 2⇡) Osc.fixed data | e| ⇥ | µ| | e| | µ| 1 4 5 3 4 Table 1:RangeParameter The 9 free(0 parameters,Y10 ) Y ( of0 ourY.1, 0 scan:.1)Y (10 the m modulus, 1)[eV](10 and⇤, 10[GeV] phase) (0, ofPhases2⇡ the) electronfixedOsc. data and muon | e| ⇥ | µ| | e| | µ| 1 Yukawas Ye , Yµ , ↵e and ↵µ4, the Majorana mass scale5 ⇤, the3 absolute4 neutrino mass m1 and Table 1: The| Range| 9| free| parameters(0, 10 ) of our( 0. scan:1, 0.1) the(10 modulus , 1) and(10 , phase10 ) of(0 the, 2⇡) electronfixed and muon Parameter Ye Yµ Ye Yµ m1 [eV] ⇤ [GeV] Phasesthe 3 yetOsc. unknown data CP-violation phases (Dirac and Majorana) in the PMNS mixing matrix: , ↵1 | | ⇥ | | | | | | Yukawas Ye , Yµ , ↵e and ↵µ, the Majorana mass scale ⇤, the absolute neutrino mass m1 and and ↵2.| The| PMNS| | mixing angles and mass splittings are fixed to their best fit from the global 4 5 3 4 Table 1: The 9 free parameters of our scan: the modulus and phase of the electron and muon↵ Range (0, 10 ) ( 0.1, 0.1) (10 , 1) (10 , 10 ) (0,the2analysis⇡) 3 yet in unknownfixed Ref. [?]. CP-violation phases (Dirac and Majorana) in the PMNS mixing matrix: , 1 Parameter Y Y Y Y m [eV] ⇤ [GeV] Phases Osc.Yukawas data Ye , Yµ , ↵e and ↵µ, the Majorana mass scale ⇤, the absolute neutrino mass m1 and e µ e µ 1 and ↵2. The| PMNS| | | mixing angles and mass splittings are fixed to their best fit from the global | | ⇥ | | | | | | ↵ 4 5 3 4 analysisthe 3 inyet Ref. unknown [?]. CP-violation phases (Dirac and Majorana) in the PMNS mixing matrix: , 1 Range (0, 10 ) ( 0.1, 0.1) (10 , 1) (10 , 10 ) (0, 2⇡) fixed Table 1: The 9 free parameters of our scan: the modulus and phase of theand electron↵2. The PMNS and muon mixing angles and mass splittings are fixed to their best fit from the global Yukawas Y , Y , ↵ and ↵ , the Majorana mass scale ⇤, the absolute neutrinoanalysis in Ref.mass [?].m and Table| e 1:| The| µ| 9 freee parametersµ of our scan: the modulus and phase of the electron and muon 1 the 3 yet unknown CP-violation phases (Dirac and Majorana) in the PMNS mixing matrix: , ↵1 MIJ Yukawas Ye , Yµ , ↵e and ↵µ, the Majorana mass scale ⇤, the absolute neutrino mass m1 and = + iN @/N Y ` N + N cN + h.c. (1) | | | | L LSM I I ↵I ↵ I 2 I J and ↵2the. The 3 yet PMNS unknown mixing CP-violation angles phases and (Dirac mass and splittings Majorana) are in fixed the PMNS to their mixing best matrix: fit from , ↵1 the global ✓ ◆ MIJ c and ↵ . The PMNS mixing angles and mass splittings are fixed to their best fit from the global = + iNI @/NI Y↵I `↵ NI + N NJ + h.c. (1) analysis in2 Ref. [?]. L LSM e 2 I ✓ 2 ◆ analysis in Ref. [?]. v 1 MIJ c = + iNm @/N YY⇤ ` Y †N + N N + h.c. (2)(1) L LSM I⌫ ' I 2 ↵MIe↵ I 2 I J Neutrino masses and leptogenesis v2 ✓ 1 ◆ m Y ⇤ Y † (2) ⌫ ' 2 M e Type-I seesaw mechanism: SM + gauge singlet fermions NI v2 1 lim mmi⌫ =0, Ym⇤i Yµ,† m (2) M M 0 ' )2 M/ = + iN @/N Y ` N + IJMN cIJN +ch.c. ! = SM+ iNII @/NII ↵YI↵↵I `↵ I NI + I JN NJ + h.c. (1) (1) lim m =0, m n, d L SML 2 I lim mi =0i , mi i µ, m (3) L L ✓ 2 ◆ M M 0 0 6 )) // ✓ ◆ !! e limlimmim=0=0, , mim n,µ, d m (3) After electroweak phase transition e< Φ > = v ≃ 174 GeV M 0 6 i ) /i !M 0 ) / lim mi =0, 2 mi µ, m ! M 0 v) /1 lim mi =0, mi n, d (4)(3) !m Y ⇤ Y † (2) M 0 6! ) / lim ⌫mi =0, mi n, d (2) ! M 0 ' 6 2) M/ ! v (4) d =! Y ⇤ p2 (4) The Lagrangian provides the ingredients for leptogenesis too v ! (3) d = Y ⇤! (5) lim mi =0!, mi µ, m p2 M 0 ) / v • Complex! Yukawav couplings Y as a source of CP d = !Y ⇤ (5) lim mdi==0,Y ⇤ mi n, d (3) p2 Sakharov M 0 6 p2 ) / • B from! sphaleron transitions until TEW ≃ 140 GeV ⌫R(0,0) ! (6)(5) conditions ! (4) • ⌫ (6) sterile neutrinos deviations from thermal equilibrium R(0,20) 5 2 G m sin ✓I (1) F I (4) EW 3 , (7) ' ⌫R(0192,0) ⇡ (6) ! 2 5 2 ⌫R(0,0) (5) G m sin ✓I 5 F I , (7) EW ' 192⇡3 { v 2 2 5 2 G m sin ✓ d = 2 5Y ⇤2 ⌦mh =0.1426F I 0.0020I (8) G m sin ✓I EW ± , (7) Fp2I , 2 ' 192⇡3 EW 3 (6) ⌦bh =0.02226 0.00023 (9) ' 192⇡ ⌦ h2 =0.1426 ±0.0020 (8) ! m 2 (5) ⌦ch =0.1186± 0.0020 (10) ⌦ h2 =0.02226± 0.00023 (9) b⌦ h2 =0.1426 0.0020 2 m2 ± (8) ⌦mh =0.1426 0.0020 (7) ⌦ch 2=0.1186 0±.0020 (10) 2 ± ⌦bh =0.02226± 0.00023 (9) ⌦bh =0.02226 0.00023 (8) 2 ± 13 2 ± ⌦BRchµe =0< 5.1186.7 10 0.0020 (11)(10) ⌦ch =0⌫R.1186(0,0) 0.0020 (9) (6) ⇥ ± 8 ± BR⌧e < 3.3 10 13 (12) BRµe < 5.7 ⇥10 8 (11) BR⌧µ < 4.4⇥ 10 8 (13) 2 5 2 BR⌧e < 3.3 ⇥10 13 (12) G m sin13✓I BRµe < 5⇥.7 10 (11) BR < 5F.7 I 10 (10) ⇥ 8 EWµe , (7) BR⌧µ < 4.4 10 8 (13) ⇥ 3 BR⌧e <1 3⇥.3 10 (12) BR '< 3.319210⇡ 8 ⌧e (11) ⇥ 8 ⇥ 8 BR⌧µ < 4.4 10 (13) BR < 4.4 10 (12) 1 ⇥ ⌧µ ⇥ 2 ⌦mh =0.1426 0.0020 (8) 1 ↵ =(7.2973525698 0.0000000024) 10 3 2 ± ⌦bh =0.±02226 0.00023⇥ (9) MZ = (91.1876 0.0021) GeV± (13) 2 ± 5 2 G =(1⌦.c1663787h =00.0000006)1186 0.002010 GeV (10) µ ± ± ⇥
1 13 BRµe < 5.7 10 (11) ⇥ 8 BR⌧e < 3.3 10 (12) ⇥ 8 BR < 4.4 10 (13) ⌧µ ⇥
1
1 Leptogenesis realisations
3rd Sakharov condition: deviation from thermal equilibrium
At which temperature(s) do sterile neutrinos enter/deviate from thermal equilibrium?
6 Parameter Y Y Y Y m [eV] ⇤ [GeV] Phases Osc. data | e| ⇥ | µ| | e| | µ| 1 Range (0, 10 4) ( 0.1, 0.1) (10 5, 1) (103, 104) (0, 2⇡) fixed Table 1: The 9 free parameters of our scan: the modulus and phase of the electron and muon Yukawas Y , Y , ↵ and ↵ , the Majorana mass scale ⇤, the absolute neutrino mass m and | e| | µ| e µ 1 the 3 yet unknown CP-violation phases (Dirac and Majorana) in the PMNS mixing matrix: , ↵1 and ↵2. The PMNS mixing angles and mass splittings are fixed to their best fit from the global analysis in Ref. [?].
MIJ = + iN @/N Y ` N + N cN + h.c. (1) L LSM I I ↵I ↵ I 2 I J ✓ ◆ e v2 1 m Y ⇤ Y † (2) BAU I: Thermal leptogenesis⌫ ' 2 M 7 Sterile neutrinos in thermal equilibrium if Y 10 (3) | | & Thermal leptogenesis: sterile neutrinos in equilibrium at large temperatures
Y lim mi =0, mi µ, m decoupling M 0 ) / ! lim mi =0, mi n, d (4) M 0 6 ) / ! x (5) ! out of equilibrium Yeq v d = decayY ⇤ before TEW p2 x=m/T ! (6) Generation of a lepton asymmetry due to the Majorana character of the particles M. Fukugita and T. Yanagida, Phys. Lett. B 174 (1986) 45 M > 108 GeV to reproduce observed BAU ⌫RDi(0,0)fficult to test (7) (relaxed to M > TeV for degenerate masses) in laboratory S. Davidson, E. Nardi and Y. Nir, arXiv:0802.2962 [hep-ph] 2 5 2 G m sin ✓I A. Abada, S. Davidson, A. Ibarra, F.-X. Josse-Michaux, M. Losada and A. Riotto, hep-ph/0605281F I , (8) A. Pilaftsis and T. E. J. Underwood, hep-ph/0309342EW ' 192⇡3 7
⌦ h2 =0.1426 0.0020 (9) m ± ⌦ h2 =0.02226 0.00023 (10) b ± ⌦ h2 =0.1186 0.0020 (11) c ±
13 BRµe < 5.7 10 (12) ⇥ 8 BR⌧e < 3.3 10 (13) ⇥ 8 BR < 4.4 10 (14) ⌧µ ⇥
1 BAU II: ARS mechanism ParameterE. K. Akhmedov,Y V. A. RubakovY andY A. Y. Smirnov,Y hep-ph/9803255m [eV] ⇤ [GeV] Phases Osc. data | e| ⇥ | µ| | e| | µ| 1 SterileRange neutrinos(0 out, 10 of4 )equilibrium( 0.1, 0. 1)at large(10 temperatures5, 1) (103, 104) (0, 2⇡) fixed Y Table 1: The 9 free parameters of our scan: the modulus and phase of the electron and muon Yukawas Y , Y , ↵ and ↵ , the Majorana mass scale ⇤, the absolute neutrino mass m and | e| | µ| e µ 1 the 3 yet unknown CP-violation phases (Dirac and Majorana) in the PMNS mixing matrix: , ↵1 and ↵2. The PMNS mixing angles and mass splittings are fixed to their best fit from the global deviationanalysis from in Ref. [?]. equilibrium before TEW
Yeq MIJ c = SM + iNI @/NI Y↵I `↵ NI + N NJ + h.c. (1) L L TEW x=m/T2 I ✓ ◆ e From the seesaw v2 1 GeV Y 2 m Y ⇤ Y † 0.3 eV (2) ⌫ ' 2 M ' M 10 14 relation ✓ ◆✓ ◆ 7 Y & 10 (3) M ~ GeV to reproduce ν masses | | Testable
8 lim mi =0, mi µ, m M 0 ) / ! lim mi =0, mi n, d (4) M 0 6 ) / !
(5) ! v d = Y ⇤ p2 ! (6)
⌫R(0,0) (7)
2 5 2 G m sin ✓I F I , (8) EW ' 192⇡3
⌦ h2 =0.1426 0.0020 (9) m ± ⌦ h2 =0.02226 0.00023 (10) b ± ⌦ h2 =0.1186 0.0020 (11) c ±
13 BRµe < 5.7 10 (12) ⇥ 8 BR⌧e < 3.3 10 (13) ⇥ 8 BR < 4.4 10 (14) ⌧µ ⇥
1 ULB-TH/17-07
Baryogenesis from L-violating Higgs-doublet decay in the density-matrix formalism
Thomas Hambye⇤ and Daniele Teresi† Service de Physique Th´eorique - Universit´eLibre de Bruxelles, Boulevard du Triomphe, CP225, 1050 Brussels, Belgium
We compute in the density-matrix formalism the baryon asymmetry generated by the decay of the Higgs doublet into a right-handed (RH) neutrino and a Standard Model lepton. The emphasis is put on the baryon asymmetry produced by the total lepton-number violating decay. From the derivation of the corresponding evolution equations, and from their integration, we find that this contribution is fully relevant for large parts of the parameter space. This confirms the results found recently in the CP-violating decay formalism with thermal corrections and shows in particular that the lepton-number violating processes are important not only for high-scale leptogenesis but also when the RH-neutrino masses are in the GeV range. For large values of the Yukawa couplings, we also find that the strong washout is generically much milder for this total lepton-number violating part than for the usual RH-neutrino oscillation flavour part.
I. INTRODUCTION the final state of this decay, see Fig. 1 (as this absorp- tive part vanishes at zero temperature). In Ref. [14] this thermal cut of the self-energy has been computed in the In the framework of the type-I seesaw model of neu- Kadano↵-Baym formalism. The production takes advan- trino masses with right-handed (RH) neutrinos below tage of the fact that, for RH neutrino masses below the the electroweak scale, there exists a well-known mech- sphaleron cut, the Yukawa interactions do not thermal- anism to account for the baryon asymmetry of the Uni- ize the RH neutrinos so easily as for higher masses. This verse, through oscillations of right-handed neutrinos [1– results in a large departureARS from equilibrium leptogenesis for the RH- 13]. This Akhmedov-Rubakov-Smironv (ARS) scenario neutrino number densities in the final state, boosting the is based on the generation of particle-antiparticle asym-Howasymmetry does the production. A. Abada, S. Antusch, E. K. Akhmedov, G. Arcadi, T. Asaka, S. Blanchet, L. Canetti, E. metries for the various lepton flavours. These asymme- Cazzato, V. Domcke, M. Drewes, S. Eijima, O. Fischer, T. Frossard, B. Garbrecht, D. This total (SM + RH neutrino) lepton number violat- tries cancel each other in the total Standard-Model (SM)mechanism Gueter, T. Hambye, P. Hernández, H. Ishida, M. Kekic, J. Klaric, J. López-Pavón, M.L., J. ing scenario is in many respects di↵erent from the ARS lepton-number asymmetry but, thanks to washout ef- Racker, N. Rius, V. A. Rubakov, J. Salvado, M. Shaposhnikov, A. Y. Smirnov, D. Teresi… total lepton-number conserving scenario. One di↵erence fects, which do not a↵ect the di↵erent flavours in the work? is that it gives a non-vanishing asymmetry already for same way, a net lepton asymmetry remains. In this one lepton flavour. Another is that, as a result of the framework, since the relevant processes do not involve a fact that it involves a MajoranaTwo kinds mass insertion, of CP it gives processes RH neutrino Majorana mass insertion, a lepton number rates for the relevant processes that are proportional to can be assigned to the two helicities of the RH neutri- m2 /T 2, relatively to the total lepton-number conserv- nos. Thus, in the ARS scenario, the total lepton number N ing ARS piece. As a result,Lepton the asymmetry number is typically conserving L, i.e. the sum of the SM and the RH-neutrino ones, produced at lower temperatures than in the ARS case, is conserved, but not both components separately, due (neutrino generation and oscillations) basically not long before the sphaleron decoupling. Also, to flavour e↵ects. The SM lepton-number asymmetry since this mechanism does not require an asymmetric component which is produced in this way before the washout for the di↵erent flavours, its contribution in the sphalerons decouple is reprocessed in part into a baryon weak-washout regime is proportional to 4 powers of the asymmetry, unlike the other component. The evolution Yukawa couplings, rather than to 6 for the ARS one. of the lepton asymmetries as a function of the tempera- ture of the thermal bath can be calculated in the density- The purpose of this paper is twofold. The first goal matrix formalism, which properly takes into accountFigure theFigure 2:FigureFeynman 2:isFeynman to 2: determineFeynman diagrams diagrams diagrams for how scatteringfor this scattering for L-violating scattering processes processes processes of contribution production of production of production an canddestructionrates. anddestructionrates. anddestructionrates.Figure 1: Feynman diagram for self energy of sterile neutrinos. arXiv:1705.00016v1 [hep-ph] 28 Apr 2017 coherences between various RH neutrinos and their asso- develop itself in the framework of the density-matrix formalism, rather than in theLepton usual leptogenesis number CP- violating ciated oscillations. Fig.Fig. 2. Here 2.Fig. HereQ 2. HereandQL andtQLdenotetandR denotetR left-handeddenote left-handed left-handed quark quark doublet quark doublet doublet of third of third of generation third generation3KineticEquations generation and and right-h and right-handed right-handedanded violatingL R decay formalism considered in [14], and to com- In the di↵erent CP-violating decay formalismtop usuallytop quark. quark.top We quark. Wethen then We divide then divide the divide the rates rates the into rates into three threeinto parts:(thermal three parts: parts: Higgs decay) T. Hambye and D. Teresi, arXiv:1606.00017 [hep-ph],Now we are arXiv:1705.00016 atT the position to [hep-ph] derive the kinetic equations for ρN,N¯ and ρL,L¯ . First of all, let used for leptogenesis, it has been shown recently [14] that d,p (A) d,p (B) d,p (C) d,p d,p d,p d,p (A)d,p (A) d,p (B)d,p (B) d,p (C)d,p (C) us consider the time evolution of ρ . Our construction is based on Ref. [15] (as in [4, 7]) and ΓN (kN )=ΓN (kN )+ΓN (kN )+ΓN x (kN=) . (5) N the total lepton-number violating decay of the Higgs dou- ΓN (ΓkNN )=(kN )=ΓN ΓN(kN ()+kN )+ΓN ΓN(kN()+kN )+ΓN ΓN (kN()k.N ) . (5)(5) blet into a RH neutrino and a SM lepton, i.e. the de- starts withTEW TheThe destruction destructionThe destruction rates rates of each rates of each process of each process are process are found found areL to found be to be to be cays which do involve a Majorana mass insertion, could 2 dρN (kN ) 1 d 1 p H L M = −i HN (kN ), ρN (kN ) − ΓN (kN ), ρN (kN ) + ΓN (kN ), 1 − ρN (kN ) , (3) also account for the baryon asymmetry. This is possible d (A) d (B) d † d (A)d (A) d (B)d (B) d † dt 2 2 Γ Γ(kN )(kN=) NΓ= Γ(kN )(kN =)d γ =(kγN)†(kFN )FF F, relevant, at late times (1) thanks to thermal e↵ects which induce a non-zero ab- Γ (NkN ) N =IJ Γ IJ N(kN ) N =IJγN (IJkNN ) NF F , IJ IJ N IJ N IJ 2IJ ! " # $ #1# $ d (C) H / T where 1 denotes the unit matrix with appropriate dimensions. HN is the effective Hamilto- sorptive part for the self-energy of the RH neutrino in d (C)! " d ! d † †" d d ! " d (C)! ΓN "(kNd) ! = γN†(kN") F F d + δ!ΓN (k"N ) . (6) !Γ Γ(NkN )("kN )= !γ=(IJγkN ()kNF)"FF FN+ δ+ΓIJδ(Γ!kNN()kN"). . IJ 0 (6)(6) 0 2 2 N IJ IJ N IJ IJ N IJ IJnian, HN = HN + VN , where the free part is [HN (kN )]IJ = ENI δIJ with ENI = kN + MI and ! " ! " ! " d p Here we have! introduced! " " ! ! " " ! ! " " VN is the effective potential induced by the medium effects. ΓN and ΓN are the destruction HereHere we have we have introduced introduced 9 % ⇤ [email protected] FIG. 1. Thermal cut in the H NL decay, which gives riseand production rates of N . From now on we shall apply the approximation of the Boltzmann References ! 2 2 I to its purely-thermal L-violating CP-violation.NC N2 Dh2 T p p † [email protected] d NC N2Dh2 T t 1 d d γNN(kCNN)=Dht T t , statistics and replace the third(7) term of Eq. (3) as 2 {ΓN , 1 − ρN } → ΓN . γN (kN )= 3 , (7) γN (kN )= 3 364π, kN (7) 64π64π kN kN The first term of Eq. (3) describes the coherent evolution of ρN and the oscillation of sterile wherewhereN =N 3C is= a 3 color is a color factor factor and h and≃h1t is≃ the1 is top the Yukawa top Yukawa coupling couplingneutrinos constant, constant, occurs and and due to the off-diagonal elements of VN , which is essential for baryogenesis where NC =C 3 is a color factor and ht ≃ t1 is the top Yukawa coupling constant, and ∞ under consideration. It is found from the self energy for sterile neutrinos at finite temperatures d d∞ ∞ dkLkL † T eq d δΓ (k ) d = γ (k ) dkLkL † FT ρ (k ) − Neq ρ (k )1 F d δΓ (k N) Nd= IJγ (k N) dkN LkL † FT2 ρ (k L)¯ −LNeq ρ Din(k Fig.)1 LF 1 that the effective potential for the mode k = kN is given by [19] δΓ (kNN) N =IJγ (kN ) N 0 FN2 DρT¯ (kL¯) −L NDρ D(kL)1LF IJ N IJ N N2DT L IJ 0 N0 DT# $ IJ ' ! " # d # † −$1 % '& 2 ! " d = γ (k †) F−1$(A −%1)F , '& (8) NDT † ! " d N† N−1 1% IJ & V (k ) = F F , (4) = γ=(kγN )(kNF) (AF (A− 1−)F )F, IJ , (8)(8) N N IJ IJ N N IJ 16 kN ! " ! " ! " where we have used Eq. (2) in! the! last equality." " On the other hand, the production rates are #2 wherewhere we have we have used used Eq. Eq. (2) in(2) the in the last last equality. equality. On On the the other other hand, hand, the twhere productionhe production we disregard rates rates are the are correction to VN from the asymmetries in active leptons. d,p p (A) p (B) d eq † In thep estimation of V (as well as Γ below) all masses including M are neglected since p (A)Γ (kN ) p=(B)Γ (kN ) d= γ (keqN ) ρ (kN†) F F +p δΓ (kN ) , N N I p (A) N p (B)IJ N d IJ eqN † IJp N IJ ΓN (kN ) IJ = ΓN (kN ) IJ = γN (kN ) ρ (kN ) F F IJ + δΓN (kN ) IJ , 0 ΓN (kN ) IJ = ΓN (kN ) IJ = γN (kN ) ρ (kN ) F F IJ + δΓtheyN (k areN ) irrelevantIJ , for temperatures of interest. (Note, however, that we keep MI in HN because p (C) d eq † p (C)!Γ (k )" = γ! (k ) ρ ("k ) F F , ! " ! " (9) p (C)! N " N IJ! d N eqN" N† IJ ! " they! are crucial" for the oscillation of sterile neutrinos.) Further, we first calculate them in the ! ΓN ("kN ) ! d= γN (kNeq)"ρ (kN )† F F , ! " ! " (9) ΓN (kN ) =IJγN (kN ) ρ (kN ) F F , IJ (9) ! IJ " IJ! " basis where neutrino Yukawa matrix is diagonal, and then find the expression in the original where! ! " " ! ! " " wherewhere basis shown in Eq. (1). kN eq p d eq kN dkL 1eq− ρ (kL) † Let us theneq estimate the destruction and production rates of NI with momentum kN .In p δΓN (kN ) d = γN (keqN ) ρ (kkN ) dkL 1 eq− ρ (kL) † F ρL(kL) − NeqDρ (kL)1 F p δΓ (k ) d= γIJ (k eq) ρ (k ) dkL 1 N− ρk (kLρ)eq(k† F) ρ (k the) − consideringNeq ρ (k )1 temperaturesF IJ the dominant contributions come from the scattering processes δΓ (k N) N =IJγ (kN) ρN (k ) N ( 0 D Neq F Lρ (kL) −L N ρ D(k )1L F N N IJ N N N 0 #NDkN eq ρ (kL) L $ L D L IJ ' ! " 0( # NDkN ρ (kL) % IJ & ¯ ¯ ¯ ¯ ! " ( # ∞ eq $ % (A) NI + QL ↔ &Lα'+ tR,(B)NI + tR ↔ Lα + QL,and(C)NI + Lα ↔ tR + QL [4], shown in ! " ∞ dkL 1eq− ρ$ (k%N ) † eq& ' ∞ + dkL 1 eq− ρ (kN ) † F ρL(#1kL) − NeqDρ (kL)1 F dkL 1 − ρ (kN )eq We have neglected theIJ non-linear effects of ρN since the interaction rates between sterile neutrinos are + kN NDkN ρ (k†NF) ρL(kL) − NeqDρ (kL)1 F + # eq F ρL(kL) − NDρ (kL)1 F IJ ) kN NDkN eq ρ (kN ) $ sufficiently small. Otherwise,)' see Ref. [17, 18]. k #NDkN ρ (kN ) % IJ & d #eq N † $ #2 We have numerically)' confirmed that the change of the final baryon asymmetry by this effect is negligibly = γ (kN ) ρ (kN ) F (A − 1)F .$ % '& (10) = γd (k N) ρeq(k ) F †(A − 1)F . IJ % small. & (10) = γd (kN) ρNeq(k ) NF †(A − 1)F . IJ (10) N N N ! IJ " ! " ! "
6 5 6 6
1 T x = T TEW x = 2 TEW M M 2 / T 2 2 Y Y ⇤ (1) / T $ Y Y ⇤ (1) $ MIJ = + iN¯ @/N F `¯ N + N¯cN + h.c. , (2) L LSM I I ↵I ↵ I 2 I J ¯ ¯ MIJ ¯c ✓ ◆ = SM + iNI @/NI F↵I `↵ NI + NI NJ + h.c. , (2) L L 2 e ✓ 2 ◆ v 1 e m⌫ F ⇤M F † (3) 2 ' 2 v 1 m F ⇤M F † (3) ⌫ ' 2 Asymmetry generation exampleR : with 3 RHN T x = TEW = 140 GeV R :sterile neutrinos(1) density matrix µ↵ : active flavours chemical potentials (4) TEW
Deviation Sterile neutrinos abundancesµ↵ : Active flavours asymmetries (4) References 10-8 from 1 thermal Referencesequilibrium value equilibrium 10-9 References 0.100 10-10 0.010 α ii R Δμ 10-11 0.001 We switch of sterile 10-12 neutrino oscillations when they become 10-4 10-13 inefective
10-5 10-4 0.001 0.010 0.100 1 10-5 10-4 0.001 0.010 0.100 1 x x Sterile flavours asymmetries Total asymmetries
10-12 10-10
i Lepton number R -14
Δ 10 -12 i violating processes
ii 10 c
; relevant at low
R α - ii Washout when -16 temperatures R Δμ 10 -14 10 states equilibrate α active 10-18 10-16 sterile
10-5 10-4 0.001 0.010 0.100 1 10-5 10-4 0.001 0.010 0.100 1 x x 10
1 1 1 Parameter Y Y Y Y m [eV] ⇤ [GeV] Phases Osc. data | e| ⇥ | µ| | e| | µ| 1 Range (0, 10 4) ( 0.1, 0.1) (10 5, 1) (103, 104) (0, 2⇡) fixed Table 1: The 9 free parameters of our scan: the modulus and phase of the electron and muon Yukawas Y , Y , ↵ and ↵ , the Majorana mass scale ⇤, the absolute neutrino mass m and | e| | µ| e µ 1 the 3 yet unknown CP-violation phases (Dirac and Majorana) in the PMNS mixing matrix: , ↵1 and ↵2. The PMNS mixing angles and mass splittings are fixed to their best fit from the global analysis in Ref. [?].
MIJ = + iN @/N Y ` N + N cN + h.c. (1) L LSM I I ↵I ↵ I 2 I J ✓ 2 1 ◆ m v F ∗ F † (1) Testability?ν ≃− eM 2 v 7 1 M Seesaw scaling m⌫F ! 10Y−⇤ Y † (2)(2) | ' | 2 M!GeV In the absence of any structure mν 5 GeV U 10− (3) in the F and M matrices | αi| ! M ! M ! ! lim mi =0, mi µ, m M 0 ) / Experimentally! -5 c 1 (4) 10 excluded lim mi =0, αβ mi n, d (3) M 0 6 ) ≪ / ! 10-7 Λ
2 GeV (5) |
ei ≈ U | (4) 10-9 ! Naive seesaw -11 scalingv 10 d = Y ⇤ p2 0.1 0.5 1 5 10 50
Mi[GeV] ! (5)
But these are (complex) matrices: cancellations are possible !11
⌫R(0,0) (6)
2 5 2 G m sin ✓I F I , (7) EW ' 192⇡3
⌦ h2 =0.1426 0.0020 (8) m ± ⌦ h2 =0.02226 0.00023 (9) b ± ⌦ h2 =0.1186 0.0020 (10) c ±
13 BRµe < 5.7 10 (11) ⇥ 8 BR⌧e < 3.3 10 (12) ⇥ 8 BR < 4.4 10 (13) ⌧µ ⇥
1
1 eµ 2 J = J = Im U U ⇤ U ⇤ U = c s s c s c sin (8) 12 e1 e2 µ1 µ2 13 13 12 12 23 23
[ ] 4 (1) O
i ⇥ ⇤ c12c13 s12c13 s13e ↵ ↵ i i i 21 i 31 UPMNS = 0 s c c s s e c c s s s e c s 1 diag(1,e 2 ,e 2 ), 12 23 12 13 23 12 23 12 13 23 13 23 ⇥ B i i C B s12s23 c12s13c23e c12s23 s12s13c23e c13c23 C B C @ A (2)
↵i g ↵ i W = eL W/ U † U⌫ ⌫L + h.c. (3) L p2 L ⇣ ↵i ⌘ UPMNS v | {z } eL↵ = UL↵ eL0 8 eR↵ = UR↵ e0 > R <> ⌫Li = U⌫†i↵⌫L0 c v > v > eV M :U M U † = [m ,m ,m ] ↵ l R l L diag e µ ⌧ . ! 8 m U T m U = diag [m ,m ,m ] < ⌫ ! ⌫ ⌫ ⌫ 1 2 3
: ip x ip x (x)= ⌫ ⌫ (x)SSB= U mechanism,⇤ U e i in⌫ a⌫ similar= U ⇤ wayU e as Diraci mass terms(4) are generated in the SM. However ⇤ ⌫↵ ⌫ ↵ j ↵i j i i ↵i A⌧! h | i h | i such mechanism would require a Higgs-like scalar field with isospin I =1, in order to c construct a gauge invariant Yukawa interaction containing the I =1term ⌫L⌫L.Sucha 2 ipix 2 2 2 i(pj pi)x P⌫↵ ⌫ (x)= ⌫↵ ⌫ (x) = U ⇤iU↵ie field (a= HiggsU i triplet)U↵i + is not2 Re presentU jU in↵⇤j theU ⇤iU SM,↵ie and so this possibility is also excluded. ! A ! | | | | i
2 1
2
2 eµ 2 J = J = Im U U ⇤ U ⇤ U = c s s c s c sin (8) 12 e1 e2 µ1 µ2 13 13 12 12 23 23
[ ] 4 (1) O
i ⇥ ⇤ c12c13 s12c13 s13e ↵ ↵ i i i 21 i 31 UPMNS = 0 s c c s s e c c s s s e c s 1 diag(1,e 2 ,e 2 ), 12 23 12 13 23 12 23 12 13 23 13 23 ⇥ B i i C B s12s23 c12s13c23e c12s23 s12s13c23e c13c23 C B C @ A (2)
↵i g ↵ i W = eL W/ U † U⌫ ⌫L + h.c. (3) L p2 L ⇣ ↵i ⌘ UPMNS v | {z } eL↵ = UL↵ eL0 8 eR↵ = UR↵ e0 > R <> ⌫Li = U⌫†i↵⌫L0 c v > v > eV M :U M U † = [m ,m ,m ] ↵ l R l L diag e µ ⌧ . ! 8 m U T m U = diag [m ,m ,m ] < ⌫ ! ⌫ ⌫ ⌫ 1 2 3
: ip x ip x (x)= ⌫ ⌫ (x)SSB= U mechanism,⇤ U e i in⌫ a⌫ similar= U ⇤ wayU e as Diraci mass terms(4) are generated in the SM. However ⇤ ⌫↵ ⌫ ↵ j ↵i j i i ↵i A⌧! h | i h | i such mechanism would require a Higgs-like scalar field with isospin I =1, in order to c construct a gauge invariant Yukawa interaction containing the I =1term ⌫L⌫L.Sucha 2 ipix 2 2 2 i(pj pi)x P⌫↵ ⌫ (x)= ⌫↵ ⌫ (x) = U ⇤iU↵ie field (a= HiggsU i triplet)U↵i + is not2 Re presentU jU in↵⇤j theU ⇤iU SM,↵ie and so this possibility is also excluded. ! A ! | | | | i
1 2 1
2
2 Lagrangian). If there is no symmetry, although at tree-level accidental cancellations can result in small neutrino masses, then the combination of large Yukawa couplings and low-scale seesaw, without any symmetry protecting neutrino masses, will in general result in large loop corrections, spoiling the tree-level result. One can still satisfy the experimental constraints in this framework by invoking accidental cancellations among different orders in the perturbative expansion, although the solution will result quite fine tuned in this case. A well known example of approximate symmetry protecting neutrino masses in the total lepton number L: experimentally there is no evidence for lepton number violation, but small neutrino masses break lepton number conservation if they are Majorana particles. One can thus link the smallness of neutrino masses with the smallness of the lepton-number violating parameters in the theory, rendering small neutrino masses natural since in the massless limit the Lagrangian acquires an additional symmetry. In this framework, after having integrated out the BSM new physics states, there is a decorrelation between the L-violating 5-dimensional operator in the effective theory, giving rise to non-zero neutrino masses, and the 6-dimensional operators, which encode new-physics effects other than neutrino oscillations and which can be either L-violating or L-conserving [60]. Since there is only one unique 5-dimensional operator in the SM [61], whose coefficient is determined by neutrino masses and mixing, any possibility to disentangle among the different models for neutrino mass generation relies in detecting the effects of at least the 6-dimensional effective operators. Neutrino mass generations mechanisms based on an approximate lepton number conservation include for instance supersymmetric models with R-parity violation [62–67], low-scale Seesaw realisations [68–70], the νMSM [12], the Linear Seesaw [71–73] and Inverse Seesaw [29,74–77] mechanisms. The key rˆole of lepton number symmetry in low-scale leptogenesis realisations was previously addressed in [10, 11]. In the exploration of the parameter space we do not impose any symmetry, but we allow the underlying parameters in the theory to varyFine as reportedtuning in Table 1, in order to generate symmetry protected as well as genericIf a symmetry solutions. is present The prediction of an underlying lepton number symmetry is The neutrino mass in the Lagrangian, it will 1,2 indeed a mass spectrum characterised by a pair of sterile neutrinosscale is stableN understrongly degenerate in mass be manifest at any order PD radiative corrections and coupled to form a pseudo-Diracin perturbation theory state, with relative Yukawa couplings F iF , and a third α1 ≃− α2 3 2 state NDec almost decoupled , Fα3 Fα(1,2) [60, 78, 79]. We then quantify a posteriori the level of We| compute| ≪ neutrino masses mν at 1-loop, and fine-tuning for each solution,quantify by defining the! level the of following! fine-tuning quantity of a solution as ! ! 2 3 mloop mtree f.t.(m )= i − i , (27) eq:fine_tuning ν " loop { } # & mi ' #%i=1 $ loop loop tree tree where mi are the light neutrinom massesi computed at 1-loop level,mi while mi are the same observ- ables computed neglecting loop1-loop corrections. neutrino Eq. (27) quantifiestree-level how neutrino important are loop correction in mass spectrum mass spectrum order to reproduce the observed neutrino mass spectrum: the smaller it is the more neutrino masses !14 are stable under radiative corrections, suggesting the presence of an underlying symmetry if Yukawa couplings are sizeable larger than the naive Seesaw scaling F 10 7 M/GeV. | | ! − 2Notice that the third state can equivalently be heavier or lighter with respect to( the pseudo-Dirac pair.
12 Results
Experimentally excluded
Solutions with sizeable mixing exhibit a small degree of fine-tuning Why? !15 Mass spectrum with 3 right-handed neutrinos and B - L approximate symmetry
Pair two states to form a Dirac state (equal masses, maximal mixing, opposite CP) How to preserve lepton number with or Majorana states? Decouple a state
If there is an odd number of right-handed neutrinos and B - L approximate symmetry Mass
Suppressed Yukawa couplings
Pseudo-Dirac state
!16 New mechanism: resonant asymmetry production in the B - L symmetry Mass spectrum with 3 right-handed neutrinos and B - L symmetry Mass
Thermal masses T ≫ TEW Vacuum masses
B
C C
B A A
If the vacuum mass of the decoupled state is heavier than the pseudo- Dirac one, there is necessarily a level crossing at some finite temperature!
!17 T x = T TEW x = 2 TEW M M 2 / T 2 2 Y Y ⇤ (1) / T $ Y Y ⇤ (1) $ MIJ = + iN¯ @/N F `¯ N + N¯cN + h.c. , (2) L LSM I I ↵I ↵ I 2 I J ¯ ¯ MIJ ¯c ✓ ◆ = SM + iNI @/NI F↵I `↵ NI + NI NJ + h.c. , (2) L L 2 e ✓ 2 ◆ v 1 e m⌫ F ⇤M F † (3) 2 ' 2 v 1 m F ⇤M F † (3) ⌫ ' 2 Level crossing: resonant asymmetryR : production T x = TEW = 140 GeV R :sterile neutrinos(1) density matrix µ↵ : active flavours chemical potentials (4) TEW Sterile neutrinos abundancesµ↵ : Active flavours asymmetries (4) References equilibrium value 1 References 10-5
0.100 References 10-6
0.010 α ii 10-7 R Δμ
0.001 10-8
-9 10-4 10
0.001 0.005 0.010 0.050 0.100 0.500 1 0.001 0.005 0.010 0.050 0.100 0.500 1 x x Energy eigenvalues Total asymmetries
10-8 1 i
R 10-9 Δ i ;
0.001 α Level crossing 10-10 at x ~ 0.13 Δμ α nryeigenvalues Energy 10-11 active 10-6 sterile
10-12 0.001 0.005 0.010 0.050 0.100 0.500 1 0.001 0.005 0.010 0.050 0.100 0.500 1 x x !18
1 1 1 Conclusion
We performed the first systematic study of the low-scale leptogenesis scenario in the minimal Standard Model extended with 3 right-handed neutrinos having masses at the GeV scale
Low-scale solutions are testable in current experiments in the large-mixing region
Large mixings can result from fine-tuning or from an underlying B - L symmetry
We find a new mechanism that: • dynamically creates resonantly enhanced asymmetries • protects them from washout • works precisely in the B - L approximate symmetry
!19 Backup Neutrinoless effective mass 0νββ decay is a lepton number It violates the B - L symmetry violating process
!21