Abstract: The first measurement of the Z boson production cross-section at centre-of-mass energy v s = 5.02TeV in the forward region is reported, using pp collision data collected by the LHCb experiment in year 2017, corresponding to an integrated luminosity of 100 +/- 2 pb-1. The production cross-section is measured for final-state muons in the pseudorapidity range 2.0 <. < 4.5 with transverse momentum pT > 20 GeV/c. The integrated cross-section is determined to be sZ.mu+mu- = 39.6 +/- 0.7(stat) +/- 0.6(syst) +/- 0.8(lumi) pb for the di-muon invariant mass in the range 60 < M μμ< 120 GeV/c2. This result and the differential cross-section results are in good agreement with theoretical predictions at next-to-next-to-leading order in the strong coupling constant. Based on a previous LHCb measurement of the Z boson production cross-section in pPb collisions at v sNN = 5.02TeV, the nuclear modification factor RpPb is measured for the first time at this energy. The measured values are 1.2+0.5 -0.3(stat) +/- 0.1(syst) in the forward region (1.53 < y* μ< 4.03) and 3.6+1.6 -0.9(stat)+/- 0.2(syst) in the backward region (-4.97 < y* μ< -2.47), where y* μrepresents the muon rapidity in the centre-of-mass frame.

Abstract: In this work we compute, at the “one-loop-dressed” level, the nonperturbative contribution of the ghost loops to the self-energy of the gluon propagator, in the Landau gauge. This is accomplished within the PT-BFM formalism, where the contribution of the ghost-loops is inherently transverse, by virtue of the QED-like Ward identities satisfied in this framework. At the level of the “one-loop dressed” approximation, the ghost transversality is preserved by employing a suitable gauge-technique Ansatz for the longitudinal part of the full ghost-gluon vertex. Under the key assumption that the undetermined transverse part of this vertex is numerically subleading in the infrared, and using as nonperturbative input the available lattice data for the ghost dressing function, we show that the ghost contributions have a rather sizable effect on the overall shape of the gluon propagator, both for d = 3, 4. Then, by exploiting a recently introduced dynamical equation for the effective gluon mass, whose solutions depend crucially on the characteristics of the gluon propagator at intermediate energies, we show that if the ghost loops are removed from the gluon propagator then the gluon mass vanishes. These findings suggest that, at least at the level of the Schwinger-Dyson equations, the effects of gluons and ghosts are inextricably connected, and must be combined suitably in order to reproduce the results obtained in the recent lattice simulations.

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.