Abstract: Lattice QCD has reached a mature status. State of the art lattice computations include u, d, s (and even the c) sea quark effects, together with an estimate of electromagnetic and isospin breaking corrections for hadronic observables. This precise and first principles description of the standard model at low energies allows the determination of multiple quantities that are essential inputs for phenomenology and not accessible to perturbation theory. One of the fundamental parameters that are determined from simulations of lattice QCD is the strong coupling constant, which plays a central role in the quest for precision at the LHC. Lattice calculations currently provide its best determinations, and will play a central role in future phenomenological studies. For this reason we believe that it is timely to provide a pedagogical introduction to the lattice determinations of the strong coupling. Rather than analysing individual studies, the emphasis will be on the methodologies and the systematic errors that arise in these determinations. We hope that these notes will help lattice practitioners, and QCD phenomenologists at large, by providing a self-contained introduction to the methodology and the possible sources of systematic error. The limiting factors in the determination of the strong coupling turn out to be different from the ones that limit other lattice precision observables. We hope to collect enough information here to allow the reader to appreciate the challenges that arise in order to improve further our knowledge of a quantity that is crucial for LHC phenomenology. Crown Copyright & nbsp;(c) 2021 Published by Elsevier B.V. All rights reserved.

Abstract: A theoretical investigation is done to clarify the origin of the peak structure observed near the K-pp threshold in the in-flight He-3(K-, Lambda p)n reaction of the J-PARC E15 experiment, which could be a signal of the lightest kaonic nuclei, i.e., the (K) over bar NN (I = 1/2) state. For the investigation, we evaluate the Lambda p invariant mass spectrum assuming two possible scenarios to interpret the experimental peak. One assumes that the Lambda (1405) resonance is generated after the emission of an energetic neutron from the absorption of the initial K-, not forming a bound state with the remaining proton. This uncorrelated Lambda (1405)p system subsequently decays into the final Lambda p. The other scenario implies that, after the emission of the energetic neutron, a (K) over bar NN bound state is formed, decaying eventually into a Lambda p pair. Our results show that the experimental signal observed in the in-flight He-3(K-, Lambda p)n reaction at J-PARC is qualitatively well reproduced by the assumption that a (K) over bar NN bound state is generated in the reaction, definitely discarding the interpretation in terms of an uncorrelated Lambda (1405)p s tate.