Leptogenesis is a class of scenarios where the baryon asymmetry of the Universe is produced from a lepton asymmetry generated in the decays of a heavy sterile neutrino. We explain the motivation for leptogenesis. We review the basic mechanism, and describe subclasses of models. We then focus on recent developments in the understanding of leptogenesis: finite temperature effects, spectator processes, and in particular the significance of flavor physics.Comment: 111 pages, 8 figures. Added Sect. 3 on anomalous B+L violation. Corrected equations (6.30) and (6.31). Added Sect. 9.1 with a simple example of the effects of flavours. Revised Sect. 10.1 on susy leptogenesis. Added several references, and other minor improvements. To be published in Physics Report

In the seesaw model, the baryon asymmetry of the Universe can be generated by the decay of the lightest right-handed neutrino, ν R . For a hierarchical spectrum of right-handed neutrinos, we show that there is a model independent upper bound on the CP asymmetry produced in these decays: ǫ < 3 m ν3 M νR /(8π H u 2 ). This implies that ǫ and the mass M νR of the lightest right-handed neutrino are not independent parameters, as is commonly assumed. If m ν3 = ∆m 2 atm and the ν R are produced thermally, then leptogenesis requires a reheat temperature of the Universe T reh > M νR > 10 8 GeV. Reasonable estimates of ν R production and the subsequent washout of the asymmetry, as made by Buchmüller and Plümacher, imply M νR > 10 9 GeV, and T reh > 10 10 GeV. Implications for the gravitino problem are also discussed. IntroductionThe discovery of neutrino oscillations has been one of the most exciting experimental results in the last years. Although a deficit in the flux of solar neutrinos, observed for the first time in the late 60s [1], suggested that neutrinos oscillate, it was not until the Super-Kamiokande experiment [2] that the oscillation hypothesis acquired strength 1 . As is widely known, these results are nicely explained if neutrinos have a small mass. Explaining why the neutrino mass scale is so small is one of the current unsolved problems in particle physics. An elegant solution is the see-saw mechanism [4], which consists on adding a heavy Majorana fermion per generation to the Standard Model (SM) particle content, singlet with respect to the SM gauge group, and coupled to the Higgs doublet through a Yukawa coupling. Although very appealing, this model suffers from a serious hierarchy problem, since the right-handed neutrinos produce a (large) quadratically-divergent radiative correction to the Higgs mass. Hence, in this letter we will concentrate on the supersymmetric version of the see-saw mechanism, that stabilizes the Higgs mass against the dangerous quadratic divergences that otherwise appear.The leptonic part of the corresponding superpotential readswhere L i and e Ri (i = e, µ, τ ) are the left-handed lepton doublet and the right-handed charged-lepton singlet, respectively, and H d (H u ) is the hypercharge −1/2 (+1/2) Higgs doublet. Y e and Y ν are the Yukawa couplings that give masses to the charged leptons and generate the neutrino Dirac mass, and M is a 3 × 3 Majorana mass matrix that does not break the SM gauge symmetry.1 Other hints for neutrino oscillations have been reported in [3].

This paper describes the physics case for a new fixed target facility at CERN SPS. The SHiP (search for hidden particles) experiment is intended to hunt for new physics in the largely unexplored domain of very weakly interacting particles with masses below the Fermi scale, inaccessible to the LHC experiments, and to study tau neutrino physics. The same proton beam setup can be used later to look for decays of tau-leptons with lepton flavour number non-conservation, [Formula: see text] and to search for weakly-interacting sub-GeV dark matter candidates. We discuss the evidence for physics beyond the standard model and describe interactions between new particles and four different portals-scalars, vectors, fermions or axion-like particles. We discuss motivations for different models, manifesting themselves via these interactions, and how they can be probed with the SHiP experiment and present several case studies. The prospects to search for relatively light SUSY and composite particles at SHiP are also discussed. We demonstrate that the SHiP experiment has a unique potential to discover new physics and can directly probe a number of solutions of beyond the standard model puzzles, such as neutrino masses, baryon asymmetry of the Universe, dark matter, and inflation.

We update the bounds on fermions with electric charge ǫe and mass m ǫ . For m ǫ < ∼ m e we find 10 −15 < ∼ ǫ < 1 is excluded by laboratory experiments, astrophysics and cosmology. For larger masses, the limits are less restrictive and depend on m ǫ . For milli-charged neutrinos, the limits are stronger, especially if the different flavors mix as suggested by current experimental evidence.

We give analytic approximations to the baryon asymmetry produced by thermal leptogenesis with hierarchical right-handed neutrinos. Our calculation includes flavour-dependent washout processes and CP violation in scattering, and neglects gauge interactions and finite temperature corrections. Our approximate formulae depend upon the three CP asymmetries in the individual lepton flavours as well as on three flavour-dependent efficiency factors. We show that the commonly used expressions for the lepton asymmetry, which depend on the total CP asymmetry and one single efficiency factor, may fail to reproduce the correct lepton asymmetry in a number of cases. We illustrate the importance of using the flavour-dependent formulae in the context of a two right-handed neutrino model.Note Added: In the published version of this paper, we applied incorrectly the A matrix [8], which relates the asymmetries in B/3 − L α to the asymmetries Y αα carried by the lepton doublets. This over-estimated the baryon asymmetry by a factor of order one (or a few). In this revised version, we modify sections 4.1.4 and 4.2 to give a more correct relation between our analytic estimates for the flavour asymmetries, and the final baryon asymmetry. We thank E.J. Chun and M. Plumacher for discussions on this issue, and in particular A Strumia for details of his calculations and results.Second Note Added: There are various other errors (we thank S Antusch, P Di Bari, EJ Chun, and C Gonzalez-Garcia for comments) which we correct in this version:1. In the previous net version (modified to use more correctly the A matrix), the overall sign of the baryon asymmetry was wrong in eqns (55) and (57).2. The coefficient of the washout term in the Boltzmann Equations was a factor of 2 too large: in the last term of eqns (11), (18), and (36), and in the corresponding coefficients of the analytic solutions, the numerical factor should be 1/4 (not the 1/2 of the published version).3. The vev of the Higgs should be taken 175 GeV, not 246 GeV(given after eqn (1)). This changes m * from the 2 − 3 × 10 −3 eV used in the published version (at eqns (5),(20)) to m * ≃ 10 −3 eV. NB: in the analytic approximations this erroneous factor of 2 cancels against the one of point 2 above. So the analytic approximations remain acceptable , using m * ≃ 10 −3 eV. (22), (23) and (28) have been corrected. Factors of two in eqns 5.In the published version, the captions of Figures 1,2, and 3 indicate that e was taken distinguishable from µ. However, for M 1 > 10 9 GeV, only the τ is distinguishable 1 . We therefore interchanged the e and τ indices on the inputs (ǫ ee → ǫ τ τ , K τ τ → K ee ,...). We also changed a washout factor in the caption of Figure 2 to account for points 2 and 3 above. We have remade the plots, with these modified inputs, and the plots remain unchanged.

We study the impact of flavour in thermal leptogenesis, including the quantum oscillations of the asymmetries in lepton flavour space. In the Boltzmann equations we find different numerical factors and additional terms which can affect the results significantly. The upper bound on the CP asymmetry in a specific flavour is weaker than the bound on the sum. This suggests that -when flavour dynamics is included -there is no modelindependent limit on the light neutrino mass scale, and that the lower bound on the reheat temperature is relaxed by a factor ∼ (3 − 10).

We present model independent constraints on the masses and couplings to fermions of B and L conserving leptoquarks. Such vector or scalar particles could have masses below 100 GeV and be produced at HERA; we list the generation dependent bounds that can be calculated from rare lepton and meson decays, meson-anti-meson mixing and various electroweak tests.

We consider Non-Standard neutrino Interactions (NSI), described by four-fermion operators of the form (ναγν β )(f γf ), where f is an electron or first generation quark. We assume these operators are generated at dimension ≥ 8, so the related vertices involving charged leptons, obtained by an SU (2) transformation ν δ → e δ , do not appear at tree level. These related vertices necessarily arise at one loop, via W exchange. We catalogue current constraints from sin 2 θW measurements in neutrino scattering, from atmospheric neutrino observations, from LEP, and from bounds on the related charged lepton operators. We estimate future bounds from comparing KamLAND and solar neutrino data, and from measuring sin 2 θW at the near detector of a neutrino factory. Operators constructed with νµ and νe should not confuse the determination of oscillation parameters at a νfactory, because the processes we consider are more sensitive than oscillations at the far detector. For operators involving ντ , we estimate similar sensitivities at the near and far detector. * Reference [9] found that NSI induced in the R-parity violating MSSM could not explain the solar neutrino deficit. However, their operators were otherwise constrained to be at least an order of magnitude smaller than the solutions found in [8].