Abstract: Recent lattice data on pi pi -scattering phase shifts in the vector-isovector channel, pseudoscalar meson masses and decay constants for strange-quark masses smaller or equal to the physical value allow us to study the strangeness dependence of these observables for the first time. We perform a global analysis on two kind of lattice trajectories depending on whether the sum of quark masses or the strange-quark mass is kept fixed to the physical point. The quark mass dependence of these observables is extracted from unitarized coupled-channel one-loop Chiral Perturbation Theory. This analysis guides new predictions on the rho (770) meson properties over trajectories where the strange-quark mass is lighter than the physical mass, as well as on the SU(3) symmetric line. As a result, the light- and strange-quark mass dependence of the rho (770) meson parameters are discussed and precise values of the Low Energy Constants present in unitarized one-loop Chiral Perturbation Theory are given. Finally, the current discrepancy between two- and three-flavor lattice results for the rho (770) meson is studied.

Abstract: The numerical evaluation of multi-loop scattering amplitudes in the Feynman representation usually requires to deal with both physical (causal) and unphysical (non-causal) singularities. The loop-tree duality (LTD) offers a powerful framework to easily characterise and distinguish these two types of singularities, and then simplify analytically the underling expressions. In this paper, we work explicitly on the dual representation of multi-loop Feynman integrals generated from three parent topologies, which we refer to as Maximal, Next-to-Maximal and Next-to-Next-to-Maximal loop topologies. In particular, we aim at expressing these dual contributions, independently of the number of loops and internal configurations, in terms of causal propagators only. Thus, providing very compact and causal integrand representations to all orders. In order to do so, we reconstruct their analytic expressions from numerical evaluation over finite fields. This procedure implicitly cancels out all unphysical singularities. We also interpret the result in terms of entangled causal thresholds. In view of the simple structure of the dual expressions, we integrate them numerically up to four loops in integer space-time dimensions, taking advantage of their smooth behaviour at integrand level.

Abstract: The inclusive b (b) over bar- and c (c) over bar -dijet production cross-sections in the forward region of pp collisions are measured using a data sample collected with the LHCb detector at a centre-of-mass energy of 13TeV in 2016. The data sample corresponds to an integrated luminosity of 1.6 fb(-1). Differential cross-sections are measured as a function of the transverse momentum and of the pseudorapidity of the leading jet, of the rapidity difference between the jets, and of the dijet invariant mass. A fiducial region for the measurement is defined by requiring that the two jets originating from the two b or c quarks are emitted with transverse momentum greater than 20 GeV/c, pseudorapidity in the range 2.2 < eta < 4.2, and with a difference in the azimuthal angle between the two jets greater than 1.5. The integrated b (b) over bar -dijet cross-section is measured to be 53.0 +/- 9.7 nb, and the total c (c) over bar -dijet cross-section is measured to be 73 +/- 16 nb. The ratio between c (c) over bar- and b (b) over bar -dijet cross-sections is also measured and found to be 1.37 +/- 0.27. The results are in agreement with theoretical predictions at next-to-leading order.