Abstract: In modular invariant models of flavor, observables must be modular invariant. The observables discussed so far in the literature are functions of the modulus tau and its conjugate, (tau) over bar. We point out that certain combinations of observables depend only on tau , i.e. are meromorphic, and in some cases even holomorphic functions of tau. These functions, which we dub “invariants” in this Letter, are highly constrained, renormalization group invariant, and allow us to derive many of the models' features without the need for extensive parameter scans. We illustrate the robustness of these invariants in two existing models in the literature based on modular symmetries, Gamma(3) and Gamma(5). We find that, in some cases, the invariants give rise to robust relations among physical observables that are independent of tau. Furthermore, there are instances where additional symmetries exist among the invariants. These symmetries are relevant phenomenologically and may provide a dynamical way to realize symmetries of mass matrices.

Abstract: In the presence of electromagnetic fields, both axions and gravitational waves (GWs) induce oscillating magnetic fields: a potentially detectable fingerprint of their presence. We demonstrate that the response is largely dictated by the symmetries of the instruments used to search for it. Focussing on low mass axion haloscopes, we derive selection rules that determine the parametric sensitivity of different detector geometries to axions and GWs, and which further reveal how to optimise the experimental geometry to maximise both signals. The formalism allows us to forecast the optimal sensitivity to GWs in the range of 100 kHz to 100 MHz for instruments such as ABRACADABRA, BASE, ADMX SLIC, SHAFT, WISPLC, and DMRadio.

Abstract: In this note we study the tensor and vector exchange contributions to the elastic reactions involving the pseudoscalars mesons pi(+) pi(-), K+ K- and D+D-. In the case of the tensor-exchange contributions we assume that an intermediate tensor f(2)(1270) is dynamically generated from the interaction of two virtual rho mesons, with the use of a pole approximation. The calculation of the two-loop amplitude is facilitated since the triangle loops can be factorized and computed separately. The results show very small contributions coming from the tensor-exchange mechanisms when compared with those from the vector-exchange processes. We compare our results for pi pi and K (K) over bar scattering with those obtained in other works where the f2(1270) is considered as an ordinary q (q) over bar meson. Our picture provides a smaller contribution but of similar order of magnitude for pion scattering and stabilizes the results in the case of K (K) over bar, allowing us to make estimates for D (D) over bar scattering.

Abstract: In this paper, we have estimated the neutrino mass ordering and the CP violation sensitivity of the proposed Protvino to ORCA (P2O) experiment after 6 years of data-taking. Both unitary and non-unitary 3x3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3\times 3$$\end{document} neutrino mass mixing have been considered in the simulations. A forecast analysis deriving possible future constraints on non-unitary parameters at P2O have been performed.

Abstract: Kaon physics is at a turning point – while the rare-kaon experiments NA62 and KOTO are in full swing, the end of their lifetime is approaching and the future experimental landscape needs to be defined. With HIKE, KOTO-II and LHCb-Phase-II on the table and under scrutiny, it is a very good moment in time to take stock and contemplate about the opportunities these experiments and theoretical developments provide for particle physics in the coming decade and beyond. This paper provides a compact summary of talks and discussions from the Kaons@CERN 2023 workshop, held in September 2023 at CERN.