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 production cross-sections of Υ mesons, namely Υ(1S), Υ(2S) and Υ(3S), in pp collisions at root s = 5TeV are measured with a data sample corresponding to an integrated luminosity of 9.13 +/- 0.18 pb(-1) collected by the LHCb detector. The Υ mesons are reconstructed in the decay mode Υ -> mu(+)mu(-). Double differential cross-sections times branching fractions, as functions of the transverse momentum p(T) and the rapidity y of the Υ mesons, are measured in the range pT < 20 GeV/ c and 2.0 < y < 4.5. The results integrated over these pT and y ranges are sigma((sic)(1S)) x B((sic)(1S) -> mu(+) mu(-)) = 2101 +/- 33 +/- 83 pb, sigma((sic)(2S)) x B((sic)(2S) -> mu(+) mu(-)) = 526 +/- 20 +/- 21 pb, sigma((sic)(3S)) x B((sic)(3S) -> mu(+) mu(-)) = 242 +/- 16 +/- 10 pb, where the first uncertainties are statistical and the second are systematic. The ratios of cross-sections between measurements of two different (sic) states and between measurements at different centre-of-mass energies are determined. The nuclear modification factor of (sic)(1S) at root s = 5TeV is updated as well using the directly measured cross-section results from this analysis.

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: The amount of energy carried by gamma-rays during the fission process is an important consideration when developing new reactor designs. Many studies of gamma-ray energy and multiplicity, from a multitude of fissioning systems, were measured during the 1970s. However the data from such experiments largely underestimates the heating effect caused by gamma-rays in the structure of a reactor. It is therefore essential to obtain more accurate measurements of the energy carried during gamma-ray emission. As such, the OECD Nuclear Energy Agency has put out a high priority request [1] for measurements of the mean gamma-ray energy and multiplicity to an accuracy better than 7.5 percent from several fissioning systems; including U-235(n(thermal)). Measurements of the rays from these fissioning nuclei were performed with the SpecTrometer for Exotic Fission Fagments (STEFF).

Abstract: In this paper, we explore in detail the cosmological implications of an abelian L – L gauge extension of the Standard Model featuring a light and weakly coupled Z. Such a scenario is motivated by the longstanding approximate to 4 sigma discrepancy between the measured and predicted values of the muon's anomalous magnetic moment, (g – 2), as well as the tension between late and early time determinations of the Hubble constant. If sufficiently light, the Z population will decay to neutrinos, increasing the overall energy density of radiation and altering the expansion history of the early universe. We identify two distinct regions of parameter space in this model in which the Hubble tension can be significantly relaxed. The first of these is the previously identified region in which a approximate to 10 – 20 MeV Z reaches equilibrium in the early universe and then decays, heating the neutrino population and delaying the process of neutrino decoupling. For a coupling of g (-) similar or equal to (3 – 8) x 10(-4), such a particle can also explain the observed (g – 2) anomaly. In the second region, the Z is very light (mZ approximate to 1eV to MeV) and very weakly coupled (g (-) approximate to 10(-13) to 10(-9)). In this case, the Z population is produced through freeze-in, and decays to neutrinos after neutrino decoupling. Across large regions of parameter space, we predict a contribution to the energy density of radiation that can appreciably relax the reported Hubble tension, N-eff similar or equal to 0.2.