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

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

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

Cosmological horizons

The recently unveiled deep-field images from the James Webb Space Telescope have renewed interest in what we can and cannot see of the universe. Answering these questions requires understanding the so-called "cosmological horizons" and the "Hubble sphere." Here, we review the topic of cosmological horizons in a form that university physics teachers can use in their lessons, using the latest data about the so-called standard "Lambda cold dark matter" (?CDM) model. Graphical representations are plotted in terms of both conformal and proper coordinates as an aid to understand the propagation of light in the expanding universe at various epochs

Substitutional impurities in monolayer hexagonal boron nitride as single-photon emitters

Single-photon emitters in hexagonal boron nitride have attracted great attention over the last few years due to their excellent optoelectronical properties. Despite the vast range of results reported in the literature, studies on substitutional impurities belonging to the 13th and 15th groups have not been reported yet. Here, through theoretical modeling, we provide direct evidence that hexagonal boron nitride can be opportunely modified by introducing impurity atoms such as aluminum or phosphorus that may work as color centers for single-photon emission. By means of density functional theory, we focus on determining the structural stability, induced strain, and charge states of such defects and discuss their electronic properties. Nitrogen substitutions with heteroatoms of group 15 are shown to provide attractive features (e.g. deep defect levels and localized defect states) for single-photon emission. These results may open up new possibilities for employing innovative quantum emitters based on hexagonal boron nitride for emerging applications in nanophotonics and nanoscale sensing devices

Representing seesaw neutrino models and their motion in lepton flavour space

We discuss how seesaw neutrino models can be graphically represented in lepton flavour space. We examine various popular models and show how this representation helps understanding their properties and connection with experimental data showing in particular how certain texture zero models are ruled out. We also introduce a new matrix, the bridging matrix, that brings from the light to the heavy neutrino mass flavour basis, showing how this is related to the orthogonal matrix and how different quantities are easily expressed through it. We then show how one can randomly generate orthogonal and leptonic mixing matrices uniformly covering all flavour space in an unbiased way (Haar-distributed matrices). Using the isomorphism between the group of complex rotations and the Lorentz group, we also introduce the conceptof Lorentz boost in flavour space for a seesaw model and how this has an insightful physical interpretation. Finally, as a significant application, we consider $N_2$-leptogenesis. Using current experimental values of low energy neutrino parameters, we show that the probability that at least one flavoured decay parameter of the lightest right-handed neutrino is smaller than unity is about $49\%$ (to be compared with the tiny probability that the total decay parameter is smaller than unity, $P(K_{\rm I}< 1)\sim 0.1 \%$, confirming the crucial role played by flavour effects). On the other hand when $m_1 \gtrsim 0.1\,{\rm eV}$ this probability reduces to less than $5\%$, showing how also $N_2$-leptogenesis disfavours degenerate light neutrinos.Comment: 27 pages, 8 figures; v3 matching JHEP versio

Understanding and predicting low-energy neutrino parameters with leptogenesis

In this work, we address two major problems of the Standard Model of particle physics: the baryon asymmetry of the Universe and neutrino masses and mixing. A strict link between these two aspects can be established by the seesaw mechanism and leptogenesis. This connection can be fruitfully exploited to gain information on neutrino parameters. To this aim, we first introduce the type-I seesaw mechanism and leptogenesis, moving then to the strong thermal leptogenesis scenario. Here a large pre-existing asymmetry is efficiently erased by leptogenesis, and an analytical lower bound on the absolute neutrino mass scale can be derived. We then consider SO(10)-inspired leptogenesis, in which a set of conditions kindred to those realised in SO(10) Grand Unification Theories is imposed on the seesaw setup. A rigorous analytical study of this scenario is performed, allowing us to obtain analytical explanations of the numerous predictions on neutrino parameters. SO(10)-inspired and strong thermal SO(10)-inspired leptogenesis appear then to represent a very interesting scenario, rich of definite predictions on neutrino parameters that will be in the reach of forthcoming experiments. Finally, we examine the supersymmetric extension of SO(10)-inspired leptogenesis, analysing how the constraints on neutrino parameters change. The lower bound imposed by thermal leptogenesis on the reheating temperature is carefully studied, in light of the gravitino problem. We conclude that the thermal leptogenesis scenario represents an intriguing and viable mechanism also in the supersymmetric framework