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: Newer lattice results indicate that, in the Landau gauge at low spacelike momenta, the gluon propagator and the ghost dressing function are finite non-zero. This leads to a definition of the QCD running coupling, in a specific scheme, that goes to zero at low spacelike momenta. We construct a running coupling which fulfills these conditions, and at the same time reproduces to a high precision the perturbative behavior at high momenta. The coupling is constructed in such a way that it reflects qualitatively correctly the holomorphic (analytic) behavior of spacelike observables in the complex plane of the squared momenta, as dictated by the general principles of quantum field theories. Further, we require the coupling to reproduce correctly the nonstrange semihadronic decay rate of tau lepton which is the best measured low-momentum QCD observable with small higher-twist effects. Subsequent application of the Borel sum rules to the V + A spectral functions of tau lepton decays, as measured by OPAL Collaboration, determines the values of the gluon condensate and of the V + A six-dimensional condensate, and reproduces the data to a significantly higher precision than the usual (MS) over bar running coupling.

Abstract: Production cross-sections of prompt charm mesons are measured using data from pp collisions at the LHC at a centre-of-mass energy of 5TeV. The data sample corresponds to an integrated luminosity of 8 : 60 +/- 0 : 33 pb(-1) collected by the LHCb experiment. The production cross-sections of D-0, D+, D-s(+), and D*(+) mesons are measured in bins of charm meson transverse momentum, p(T), and rapidity, y. They cover the rapidity range 2 : 0 < y < 4 : 5 and transverse momentum ranges 0 < p(T) < 10 GeV/c for D-0 and D+ and 1 < p(T) < 10 GeV/c for D-s(+) and D*(+) mesons. The inclusive cross- sections for the four mesons, including charge-conjugate states, within the range of 1 < p(T) < 8 GeV/c are determined to be sigma (pp -> D-0 X) – 1004 +/- 3 +/- 54 μb; sigma ( pp -> D+ X) = 402 +/- 2 +/- 30 μb; sigma ( pp -> Ds+X) = 170 +/- 4 +/- 16 μb; sigma ( pp -> D*(+) X) = 421 +/- 5 +/- 36 μb; where the uncertainties are statistical and systematic, respectively.