Abstract: We review lattice results related to pion, kaon, D-meson, B-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor f(+) (0) arising in the semileptonic K -> pi transition at zero momentum transfer, as well as the decay constant ratio Alf, and its consequences for the CKM matrix elements V-us and V-ud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)(L) x SU(2)(R) and SU(3)(L) x SU(3)(R) Chiral Perturbation Theory. We review the determination of the B-K parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for m(c) and m(b) as well as those for the decay constants, form factors, and mixing parameters of charmed and bottom mesons and baryons. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant alpha(s). We consider nucleon matrix elements, and review the determinations of the axial, scalar and tensor bilinears, both isovector and flavor diagonal. Finally, in this review we have added a new section reviewing determinations of scale-setting quantities.

Abstract: With the establishment and maturation of the experimental programs searching for new physics with sizeable couplings at the LHC, there is an increasing interest in the broader particle and astrophysics community for exploring the physics of light and feebly-interacting particles as a paradigm complementary to a New Physics sector at the TeV scale and beyond. FIPs 2020 has been the first workshop fully dedicated to the physics of feebly-interacting particles and was held virtually from 31 August to 4 September 2020. The workshop has gathered together experts from collider, beam dump, fixed target experiments, as well as from astrophysics, axions/ALPs searches, current/future neutrino experiments, and dark matter direct detection communities to discuss progress in experimental searches and underlying theory models for FIPs physics, and to enhance the cross-fertilisation across different fields. FIPs 2020 has been complemented by the topical workshop “Physics Beyond Colliders meets theory”, held at CERN from 7 June to 9 June 2020. This document presents the summary of the talks presented at the workshops and the outcome of the subsequent discussions held immediately after. It aims to provide a clear picture of this blooming field and proposes a few recommendations for the next round of experimental results.

Abstract: We study the scaling of kaon decay amplitudes with the number of colours, N-c, in a theory with four degenerate flavours, N-f = 4. In this scenario, two current-current operators, Q(+/-), mediate Delta S = 1 transitions, such as the two isospin amplitudes of non-leptonic kaon decays for K -> (pi pi)(I=0,2), A(0) and A(2.) In particular, we concentrate on the simpler K -> pi amplitudes, A(+/-), mediated by these two operators. A diagrammatic analysis of the large-N-c scaling of these observables is presented, which demonstrates the anticorrelation of the leading O(1/N-c) and O(N-f/N-c(2)) corrections in both amplitudes. Using our new N-f = 4 and previous quenched data, we confirm this expectation and show that these corrections are naturally large and may be at the origin of the Delta I = 1/2 rule. The evidence for the latter is indirect, based on the matching of the amplitudes to their prediction in Chiral Perturbation Theory, from which the LO low-energy couplings of the chiral weak Hamiltonian, g(+/-), can be determined. A NLO estimate of the K -> (pi pi)(I=0,2) isospin amplitudes can then be derived, which is in good agreement with the experimental value.

Abstract: Neutrino masses could originate in seesaw models testable at colliders, with light mediators and an approximate lepton number symmetry. The minimal model of this type contains two quasi-degenerate Majorana fermions forming a pseudo-Dirac pair. An important question is to what extent future colliders will have sensitivity to the splitting between the Majorana components, since this quantity signals the breaking of lepton number and is connected to the light neutrino masses. We consider the production of these neutral heavy leptons at the ILC, where their displaced decays provide a golden signal: a forward-backward charge asymmetry, which depends crucially on the mass splitting between the two Majorana components. We show that this observable can constrain the mass splitting to values much lower than current bounds from neutrinoless double beta decay and natural loop corrections.

Abstract: An extension of the Standard Model with Majorana singlet fermions in the 1-100GeV range can explain the light neutrino masses and give rise to a baryon asymmetry at freeze-in of the heavy states, via their CP-violating oscillations. In this paper we consider extending this scenario to also explain dark matter. We find that a very weakly coupled B-L gauge boson, an invisible QCD axion model, and the singlet majoron model can simultaneously account for dark matter and the baryon asymmetry.