Lepton number symmetry as a way to testable leptogenesis

Transcription

1 Lepton number symmetry as a way to testable leptogenesis ichele Lucente 5st Rencontres de oriond (arch th 6) ased on:. bada, G. rcadi, V. Domcke and.l., JP 5 (5), 4 [arxiv:57.65 [hep-ph]]

2 Leptogenesis in a nutshell The Universe is matter dominated, Standard odel cannot account for observed U Y (8.6 ±.) This result calls for physics beyond S.. Gavela, P. Hernandez, J. Orloff and O. Pene, hep-ph/95 P. Huet and E. Sar, hep-ph/944 Sphalerons: non-perturbative solutions of S Δ( - L) + L While sphalerons in rmal equilibrium GeV. T. GeV. y convert any lepton asymmetry into a net baryon asymmetry aryogenesis via leptogenesis

3 Neutrino masses and leptogenesis Type-I seesaw mechanism: S + gauge singlet fermions NI L L S + in I /@N I Y I` e NI + IJ e N I cn J + h.c. fter electroweak phase transition < Φ > v 74 GeV m ' v Y Y The Lagrangian provides ingredients for leptogenesis too Sakharov conditions omplex Yukawa couplings Y as a source of P from sphaleron transitions until TEW 4 GeV { sterile neutrinos deviations from rmal equilibrium

4 Thermal leptogenesis Sterile neutrinos in rmal equilibrium if ' Y & 7 Thermal leptogenesis: sterile neutrinos in equilibrium at large temperatures Y decoupling x Yeq out of equilibrium decay before TEW Generation of a lepton asymmetry due to ajorana character of particles. Fukugita and T. Yanagida, Phys. Lett. 74 (986) 45 > 8 GeV to reproduce observed U (relaxed to > TeV for degenerate masses) xm/t Prohibitive to test in laboratory S. Davidson, E. Nardi and Y. Nir, arxiv:8.96 [hep-ph]. bada, S. Davidson,. Ibarra, F.-X. Josse-ichaux,. Losada and. Riotto, hep-ph/658. Pilaftsis and T. E. J. Underwood, hep-ph/94 4

5 RS mechanism E. K. khmedov, V.. Rubakov and. Y. Smirnov, hep-ph/9855 Sterile neutrinos out of equilibrium at large temperatures Y deviation from equilibrium before TEW TEW Yeq e xm/t From seesaw relation m ' ~ GeV to reproduce ν masses v Y GeV Y Y '. 4 & Testable ev 5

6 Flavoured leptogenesis ~ GeV T Negligible ajorana character total lepton number is conserved generation of sterile neutrinos How do mechanism work? E. K. khmedov, V.. Rubakov and. Y. Smirnov, hep-ph/9855 T. saka and. Shaposhnikov, hep-ph/55. Shaposhnikov, arxiv: [hep-ph] T. saka and H. Ishida, arxiv:4.549 [hep-ph] T. saka, S. Eijima and H. Ishida, arxiv:.5565 [hep-ph] L. anetti,. Drewes and. Shaposhnikov, arxiv:4.486 [hep-ph] L. anetti,. Drewes, T. Frossard and. Shaposhnikov, arxiv:8.467 [hep-ph] P. Hernández,. Kekic, J. López-Pavón, J. Racker and N. Rius, arxiv: [hep-ph] oscillation of sterile neutrinos asymmetries in individual flavours arise ΔL Sterile neutrinos ctive leptons Δ aryons Sphalerons 6

7 Naturalness argument Need a pair of degenerate neutrinos or hierarchical fine-tuning or pproximate lepton number at origin of mass degeneracy {z} {z } {z} L + {z } L6 degenerate pseudo-dirac pairs of sterile neutrinos inimal setup: S + sterile fermions with opposite lepton number L L- { { Field content: νl + N + vy vy m ν Λ Lepton number conserving mass spectrum 7

8 Table : Table : / (some) inimal mechanisms 4/ sin TEW vy 4/ Yvy / (5/6) vy vy L. (). c c vy asis:. () vy vy (ν, N, N ) L sin L h i X The mass spectrum given by this mass matrix Im F F F F The massisspectrum given by this mass matrix is is mass matrix is I J given by this mass matrix is IJ Need to perturb to generate mν I>J and Δheavy m, m, m, q q qm, T q + n, d H (), m, d + n m, d + n, m, () m, d + n, () dd small ΔL operators (assume ε, ζ, ζ ) e L F ` H NI + h.c. I L linear vy vy vy vy.,,,linear @ vy Toy model (one active neutrino) + {z } + {z } {z} {z} } ISS + {z Linear L6 L6 L {z} L L m L6 v y v y y 4 v vy (4). vy (5) Loop v y f (6) ( + {z } (5) (5) {z} L6 L mν ), Λ (6) W (6) 8

9 Toy model Viable mechanisms (minimal setup) ISS Linear Loop m y v y v y v f ( W ) 4 v y Requirements m ν, Λ Neutrino data Successful leptogenesis q ' Need a pair of y < p 7 out of equilibrium m & q p m atm ' 5 ev ev apple,. GeV N bound. kev relativistic degenerate sterile neutrinos Only ISS: too large mass splitting or too small neutrino masses Only linear: no mass splitting when Higgs VEV v 9

10 The minimal framework Linear + inverse seesaw perturbations S + RH neutrinos with opposite lepton number inimal flavour seesaw.. Gavela, T. Hambye, D. Hernandez and P. Hernandez, arxiv:96.46 [hep-ph] vy vy T vy T { ζ small mass splitting Sterile neutrino oscillations ε large mixing angle )

11 dy are based on Ref. [7]. N Weak washout regime: analytical solution sin ht Y (8.6 ±.) Finally we calculate 64 baryon asymmetry in.) oscillations of th (8.6 ± py8 generated F I < X h 7 e F Y )6 : utrinos (cf. ppendix Y n Im F I F F I>J 945 / sin / / 5/ g (T T 58 (5/6) s W ) IJ FJ TW ( 4/ m )/ Fj. IJ i h T r 4/ F F i, 4/ / H Y sin F I 4/ / T (5/6) (), / F sin isew I ere F Y e with Y e definedy in Eq. m mass squared 4/ T (5/6) EW e L F ` H N + h.c. I I N h sin Y EW (8.6 ±.) - set to heavy neutrinos, TW is ofl phase transition ttemperature N ht sin 64 and diag( GeV, sin. P asymmetry in os h i ) is X 64 8 i h X Im F I F F FJ fined as: IJ FJ X I>J Im F I F F.. s ImI>J F i F F ij T i>j 4/ H T / i, j run before index corresponds to a flavour index, while indices YH sin F 4/ TEW / (5/6) in [8 rile mass eigenstates. derivation of this expression, firstly introduced ISS The Linear Loop N h sin. efully revisited in appendix. In this. analytical determina t v v next v section,.. ) m y y y f ( W h hierarchy i light neut For simplicity we are reporting just casex of a normal regarding

12 Weak washout regime: numerical comparison Sterile neutrino abundances Sterile neutrino asymmetry Temperature resonance Lepton flavour asymmetry aryon asymmetry

13 Weak washout: viable solutions ζ LNV parameters ε Normal Hierarchy Inverted Hierarchy Uμ4 Sterile fermions phenomenology. dams et al., arxiv:7.75 [hep-ex] S. lekhin et al., arxiv: [hep-ph] 4 [GeV]

14 Strong washout regime: numerical solution The analysis is computationally demanding: only a set of benchmark points is solved Sterile neutrino abundances Sterile neutrino asymmetry Temperature resonance Lepton flavour asymmetry aryon asymmetry 4

15 onclusions Lepton number violation as a key to low scale leptogenesis nalytical solution in weak washout regime Viable leptogenesis in weak washout, but solutions cannot be probed Viable leptogenesis in strong washout, testable at future facilities 5

16 ackup

17 Strong washout regime: flavoured GeV, m 8.5keV.5 7 i i.5 7 Y i i.57 Y e eq ' p 7.4GeV, m.6kev. 7 + i i. 8 Y 8 i i i i

18 Strong strong washout regime Y e O 6 Sterile neutrino abundances Sterile neutrino asymmetry Temperature resonance Lepton flavour asymmetry aryon asymmetry 8

19 Dirac and ajorana phase dependence Y Δ Y Δ ajorana ajorana Dirac Dirac Strong dependence on ajorana vy vy vy T vy T UPNS with one massless ν Weak dependence on Dirac phase ) complex phases complex phases Dirac + ajorana 9

20 The ISS setup p p Yv p NPNS m ˆ R fields, respectively. Schematically, mass matrix can be written p Y T p Y v ZT nt, where orthogonal matrix R is defined as With Eq. (4), Yukawa couplings between activeflavours and n bounded from below by, R ( ) cos sin cos 9 X X.5 ev e Y.. Eac and complex angle is randomly varied in range i max jj v i4 required to accommodate neutrino oscillation data, laboratory bounds on direc Z. We show that neutrino data impose a lower bound on Yukawa couplings (9) sterile fermions and N bounds. The values of e ective Yukawas for li Finally, imposing lower inaeq. (8) to lie below out-of equil Pbound p e e is understood as I and J J matrices. Z I J state, Y Y as a function of lightest sterile mass are reported 4 4 e 7P p ' & (.5 Gev) for > max value GeV e 4 Y < e ] &.7 IJ Y < for all heavy states i, implies [ The horizontal green line represents out of equilibrium Y jj i 4 up Y and are Imposing rder unity. The entries of Z and Y matrices areis taken complex ) degeneracy colour code related to mass lighter pair corresponding to a mass splitting O( & (.5 in GeV), inpseudo-dirac good agreeme Validated by scan taken real and diagonal [5].. 45 mation obtained in toy model using Eq. (9). In conclusion, ISS( + splitting which is significantly large m two heavy pseudo-dirac pairsa mass of mass O( ) with squared too mass- ), ISS(,) case features for8 viable leptogenesis in t. ev []. oreover, scale max wh regime, which requires m jj in addition a sterile state at scale of potential D candidate in ISS(,) model is found to be unpleasa nges of ev or kev, latter is an interesting candidate to address observations exclude sterile neutrinos heavier than about kev contribu o oscillation data or to explain dark matter [6], respectively. The two to D abundance [45]. Since lower bound inasymmetry, Eq. (8) reliesas on assumption i ' for irs are promising candidates for generating a baryon may expect above are invalidated Given that we are now dealing with a 7 7that or 8 8 massconclusions matrix, re if a large mass di e di erent pseudo-dirac pairs is present. In order to probe feasibility of t ities for cancellations in equations and we can no longer trust we performed a numerical scan of simpler phenomenologically viab on., which as we recall, lead ISS(,). us to disfavour pure ISS due to complex a We generated entries of evscan Zof ISS(,) 4 GeV and ev ij of heavy states. Indeed, a detailed parameter ij submatrices Z and GeV, taking d No viable leptogenesis in weak washout regime in ISS setup each submatrix be sub-ev of same order of magnitude. found solutions for light sterile state in to to kev The Dirac submatr using a modified version of asas-ibarra parametrisation [46] adapted f