FaRe: a Mathematica package for tensor reduction of Feynman integrals

We present FaRe, a package for Mathematica that implements the decomposition of a generic tensor Feynman integral, with arbitrary loop number, into scalar integrals in higher dimension. In order for FaRe to work, the package FeynCalc is needed, so that the tensor structure of the different contributions is preserved and the obtained scalar integrals are grouped accordingly. FaRe can prove particularly useful when it is preferable to handle Feynman integrals with free Lorentz indices and tensor reduction of high-order integrals is needed. This can then be achieved with several powerful existing tools.Comment: Matches version to appear on the International Journal of Modern Physics

Supersymmetric SO(10)SO(10)-inspired leptogenesis and a new N2N_2-dominated scenario

We study the supersymmetric extension of $SO(10)$-inspired thermal leptogenesis showing the constraints on neutrino parameters and on the reheat temperature $T_{\rm RH}$ that derive from the condition of successful leptogenesis from next-to-lightest right handed (RH) neutrinos ($N_2$) decays and the more stringent ones when independence of the initial conditions (strong thermal leptogenesis) is superimposed. In the latter case, the increase of the lightest right-handed neutrino ($N_1$) decay parameters helps the wash-out of a pre-existing asymmetry and constraints relax compared to the non-supersymmetric case. We find significant changes especially in the case of large $\tan\beta$ values $(\gtrsim 15)$. In particular, for normal ordering, the atmospheric mixing angle can now be also maximal. The lightest (ordinary) neutrino mass is still constrained within the range $10 \lesssim m_1/{\rm meV} \lesssim 30$ (corresponding to $75\lesssim \sum_i m_i/{\rm meV} \lesssim 120$). Inverted ordering is still disfavoured, but an allowed region satisfying strong thermal leptogenesis opens up at large $\tan\beta$ values. We also study in detail the lower bound on $T_{\rm RH}$ finding $T_{\rm RH}\gtrsim 1 \times 10^{10}\,{\rm GeV}$ independently of the initial $N_2$ abundance. Finally, we propose a new $N_2$-dominated scenario where the $N_1$ mass is lower than the sphaleron freeze-out temperature. In this case there is no $N_1$ wash-out and we find $T_{\rm RH} \gtrsim 1\times 10^{9}\,{\rm GeV}$. These results indicate that $SO(10)$-inspired thermal leptogenesis can be made compatible with the upper bound from the gravitino problem, an important result in light of the role often played by supersymmetry in the quest of a realistic model of fermion masses.Comment: 35 pages, 10 figures; v3: matches JCAP versio

Neutrino parameters and the N2N_2-dominated scenario of leptogenesis

We briefly review the main aspects of leptogenesis, describing both the unflavoured and the flavoured versions of the $N_2$-dominated scenario. A study of the success rates of both classes of models has been carried out. We comment on these results and discuss corrective effects to this simplest scenario. Focusing on the flavoured case, we consider the conditions required by strong thermal leptogenesis, where the final asymmetry is fully independent of the initial conditions. Barring strong cancellations in the seesaw formula and in the flavoured decay parameters, we show that strong thermal leptogenesis favours a lightest neutrino mass m_1\gtrsim10\,\mbox{meV} for normal ordering (NO) and m_1\gtrsim 3\,\mbox{meV} for inverted ordering (IO). Finally, we briefly comment on the power of absolute neutrino mass scale experiments to either support or severely corner strong thermal leptogenesis.Comment: Contribution to the Proceedings of the NuPhys2013 Conference: Prospects in Neutrino Physics, 19-20 December 2013, IOP, Londo

A consistent model for leptogenesis, dark matter and the IceCube signal

We discuss a left-right symmetric extension of the Standard Model in which the three additional right-handed neutrinos play a central role in explaining the baryon asymmetry of the Universe, the dark matter abundance and the ultra energetic signal detected by the IceCube experiment. The energy spectrum and neutrino flux measured by IceCube are ascribed to the decays of the lightest right-handed neutrino $N_1$, thus fixing its mass and lifetime, while the production of $N_1$ in the primordial thermal bath occurs via a freeze-in mechanism driven by the additional $SU(2)_R$ interactions. The constraints imposed by IceCube and the dark matter abundance allow nonetheless the heavier right-handed neutrinos to realize a standard type-I seesaw leptogenesis, with the $B-L$ asymmetry dominantly produced by the next-to-lightest neutrino $N_2$. Further consequences and predictions of the model are that: the $N_1$ production implies a specific power-law relation between the reheating temperature of the Universe and the vacuum expectation value of the $SU(2)_R$ triplet; leptogenesis imposes a lower bound on the reheating temperature of the Universe at 7\times10^9\,\mbox{GeV}. Additionally, the model requires a vanishing absolute neutrino mass scale $m_1\simeq0$.Comment: 19 pages, 4 figures. Constraints from cosmic-ray antiprotons and gamma rays added, with hadrophobic assignment of the matter multiplets to satisfy bounds. References added. Matches version published in JHE

Epidemic Threshold in Continuous-Time Evolving Networks

Current understanding of the critical outbreak condition on temporal networks relies on approximations (time scale separation, discretization) that may bias the results. We propose a theoretical framework to compute the epidemic threshold in continuous time through the infection propagator approach. We introduce the {\em weak commutation} condition allowing the interpretation of annealed networks, activity-driven networks, and time scale separation into one formalism. Our work provides a coherent connection between discrete and continuous time representations applicable to realistic scenarios.Comment: 13 pages, 2 figure

New Signatures of the Milky Way Formation in the Local Halo and Inner Halo Streamers in the Era of Gaia

We explore the vicinity of the Milky Way through the use of spectro-photometric data from the Sloan Digital Sky Survey and high-quality proper motions derived from multi-epoch positions extracted from the Guide Star Catalogue II database. In order to identify and characterise streams as relics of the Milky Way formation, we start with classifying, select, and study $2417$ subdwarfs with $\rm{[Fe/H] < -1.5}$ up to $3$ kpc away from the Sun as tracers of the local halo system. Then, through phase-space analysis, we find statistical evidence of five discrete kinematic overdensities among $67$ of the fastest-moving stars, and compare them to high-resolution N-body simulations of the interaction between a Milky-Way like galaxy and orbiting dwarf galaxies with four representative cases of merging histories. The observed overdensities can be interpreted as fossil substructures consisting of streamers torn from their progenitors, such progenitors appear to be satellites on prograde and retrograde orbits on different inclinations. In particular, of the five detected overdensities, two appear to be associated, yelding twenty-one additional main-sequence members, with the stream of Helmi et al. (1999) that our analysis confirms on a high inclination prograde orbit. The three newly identified kinematic groups could be associated with the retrograde streams detected by Dinescu (2002) and Kepley et al. (2007), whatever their origin, the progenitor(s) would be on retrograde orbit(s) and inclination(s) within the range $10^{\circ} \div 60^{\circ}$. Finally, we use our simulations to investigate the impact of observational errors and compare the current picture to the promising prospect of highly improved data expected from the Gaia mission.Comment: 16 pages, 10 figures, 6 Tables. Accepted for publication in The Astronomical Journa

Evidence of a large scale positive rotation-metallicity correlation in the Galactic thick disk

This study is based on high quality astrometric and spectroscopic data from the most recent releases by Gaia and APOGEE. We select $58\,882$ thin and thick disk red giants, in the Galactocentric (cylindrical) distance range $5 < R < 13$~kpc and within $|z| < 3$~kpc, for which full chemo-kinematical information is available. Radial chemical gradients, $\partial \rm{[M/H]} / \partial \rm{R}$, and rotational velocity-metallicity correlations, $\partial V_\phi / \partial \rm{[M/H]}$, are re-derived firmly uncovering that the thick disk velocity-metallicity correlation maintains its positiveness over the $8$~kpc range explored. This observational result is important as it sets experimental constraints on recent theoretical studies on the formation and evolution of the Milky Way disk and on cosmological models of Galaxy formation.Comment: Accepted for publication in Monthly Notices of the Royal Astronomical Societ

Strong thermal leptogenesis and the absolute neutrino mass scale

We show that successful strong thermal leptogenesis, where the final asymmetry is independent of the initial conditions and in particular a large pre-existing asymmetry is efficiently washed-out, favours values of the lightest neutrino mass $m_1 \gtrsim 10\,{\rm meV}$ for normal ordering (NO) and $m_1 \gtrsim 3\,{\rm meV}$ for inverted ordering (IO) for models with orthogonal matrix entries respecting $|\Omega_{ij}^2| \lesssim 2$. . We show analytically why lower values of $m_1$ require a high level of fine tuning in the seesaw formula and/or in the flavoured decay parameters (in the electronic for NO, in the muonic for IO). We also show how this constraint exists thanks to the measured values of the neutrino mixing angles and can be tighten by a future determination of the Dirac phase. Our analysis also allows to place more stringent constraint for a specific model or class of models, such as $SO(10)$-inspired models, and shows that some models cannot realise strong thermal leptogenesis for any value of $m_1$. A scatter plot analysis fully supports the analytical results. We also briefly discuss the interplay with absolute neutrino mass scale experiments concluding that they will be able in the coming years to either corner strong thermal leptogenesis or find positive signals pointing to a non-vanishing $m_1$. Since the constraint is much stronger for NO than for IO, it is very important that new data from planned neutrino oscillation experiments will be able to solve the ambiguity.Comment: 22 pages; 7 figures; v2: matches JCAP versio

The radial metallicity gradients in the Milky Way thick disk as fossil signatures of a primordial chemical distribution

In this letter we examine the evolution of the radial metallicity gradient induced by secular processes, in the disk of an $N$-body Milky Way-like galaxy. We assign a [Fe/H] value to each particle of the simulation according to an initial, cosmologically motivated, radial chemical distribution and let the disk dynamically evolve for 6 Gyr. This direct approach allows us to take into account only the effects of dynamical evolution and to gauge how and to what extent they affect the initial chemical conditions. The initial [Fe/H] distribution increases with R in the inner disk up to R ~ 10 kpc and decreases for larger R. We find that the initial chemical profile does not undergo major transformations after 6 Gyr of dynamical evolution. The final radial chemical gradients predicted by the model in the solar neighborhood are positive and of the same order of those recently observed in the Milky Way thick disk. We conclude that: 1) the spatial chemical imprint at the time of disk formation is not washed out by secular dynamical processes, and 2) the observed radial gradient may be the dynamical relic of a thick disk originated from a stellar population showing a positive chemical radial gradient in the inner regions.Comment: 10 pages, 5 figures, Accepted for publication on Astrophysical Journal Letter