Abstract: Neutrinos are the only particles in the Standard Model that could be Majorana fermions, that is, completely neutral fermions that are their own antiparticles. The most sensitive known experimental method to verify whether neutrinos are Majorana particles is the search for neutrinoless double-beta decay. The last 2 decades have witnessed the development of a vigorous program of neutrinoless double-beta decay experiments, spanning several isotopes and developing different strategies to handle the backgrounds masking a possible signal. In addition, remarkable progress has been made in the understanding of the nuclear matrix elements of neutrinoless double-beta decay, thus reducing a substantial part of the theoretical uncertainties affecting the particle-physics interpretation of the process. On the other hand, the negative results by several experiments, combined with the hints that the neutrino mass ordering could be normal, may imply very long lifetimes for the neutrinoless double-beta decay process. In this report, we review the main aspects of such process, the recent progress on theoretical ideas and the experimental state of the art. We then consider the experimental challenges to be addressed to increase the sensitivity to detect the process in the likely case that lifetimes are much longer than currently explored, and discuss a selection of the most promising experimental efforts.

Abstract: Metalenses are composed of nanostructures for focusing light and have been widely explored in many exciting applications. However, their expanding dimensions pose simulation challenges. We propose a method to simulate metalenses in a timely manner using vectorial wave and ray tracing models. We sample the metalens's radial phase gradient and locally approximate the phase profile by a linear phase response. Each sampling point is modeled as a binary blazed grating, employing the chosen nanostructure, to build a transfer function set. The metalens transmission or reflection is then obtained by applying the corresponding transfer function to the incoming field on the regions surrounding each sampling point. Fourier optics is used to calculate the scattered fields under arbitrary illumination for the vectorial wave method, and a Monte Carlo algorithm is used in the ray tracing formalism. We validated our method against finite -difference time domain simulations at 632 nm, and we were able to simulate metalenses larger than 3000 wavelengths in diameter on a personal computer.

Abstract: We consider a flavour conserving two Higgs doublet model that consists of a type I (or X) quark sector and a generalized lepton sector where the Yukawa couplings of the charged leptons to the new scalars are not proportional to the lepton masses. The model, previously proposed to solve both muon and electron g – 2 anomalies simultaneously, is also capable to accommodate the ATLAS excess in pp -> S -> tau(+)tau(-) with gluon-gluon fusion production in the invariant mass range [0.2; 0.6] TeV, including all relevant low and high energy constraints. The excess is reproduced taking into account the new contributions from the scalar H, the pseudoscalar A, or both. In particular, detailed numerical analyses favoured the solution with a significant hierarchy among the vevs of the two Higgs doublets, t(beta)similar to 10, and light neutral scalars satisfying m(A) > m(H) with sizable couplings to tau leptons. In this region of the parameter space, the muon g – 2 anomaly receives one and two-loop (Barr Zee) contributions of similar size, while the electron anomaly is explained at two loops. An analogous ATLAS excess in b-associated production and the CMS excess in ditop production are also studied. Further New Physics prospects concerning the anomalous magnetic moment of the tau lepton and the implications of the CDF M-W measurement on the final results are discussed.