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Low-Scale Leptogenesis with 3 Right-Handed Neutrinos

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Low-Scale Leptogenesis with 3 Right-Handed Neutrinos 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 (∆χ2 =0.97) Inverted Ordering (best fit) Any Ordering bfp 1σ 3σ range bfp 1σ 3σ range 3σ 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 σ level,7.87 depending9.11 7.87 on the9.11 adopted analysis [228], − ! − ! ! +39 +63 andδCP 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 0.137γ 0.158 ! ! h i ! U = 0.225 0.517 0.441 0.699 0.614 0.793 . (3.1) massive and0 | | 0 ! ! ! 1 where nγ 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 ∆χ2 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 δ . (3.2) ⇠ We notice here↵i ↵j thatβi βj the⌘ CMB angularCP ↵γ powerijk ⌘ spectrumCP CP also depends on the parameter γ=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 δCKM 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 δ, ↵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 fromδ, ↵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 `↵φ`NφI 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 Γ 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) ΓEWµe ⇥ , (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.
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