Abstract: The dynamics of the QCD gauge sector give rise to non-perturbative phenomena that are crucial for the internal consistency of the theory; most notably, they account for the generation of a gluon mass through the action of the Schwinger mechanism, the taming of the Landau pole, the ensuing stabilization of the gauge coupling, and the infrared suppression of the three-gluon vertex. In the present work, we review some key advances in the ongoing investigation of this sector within the framework of the continuum Schwinger function methods, supplemented by results obtained from lattice simulations.

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: We present novel results for the three-gluon vertex, obtained from an extensive quenched lattice simulation in the Landau gauge. The simulation evaluates the transversely projected vertex, spanned on a special tensorial basis, whose form factors are naturally parametrized in terms of individually Bosesymmetric variables. Quite interestingly, when evaluated in these kinematics, the corresponding form factors depend almost exclusively on a single kinematic variable, formed by the sum of the squares of the three incoming four-momenta, q, r, and p. Thus, all configurations lying on a given plane in the coordinate system (q2, r2, p2) share, to a high degree of accuracy, the same form factors, a property that we denominate planar degeneracy. We have confirmed the validity of this property through an exhaustive study of the set of configurations satisfying the condition q2 = r2, within the range [0, 5 GeV]. This drastic simplification allows for a remarkably compact description of the main bulk of the data, which is particularly suitable for future numerical applications. A semi-perturbative analysis reproduces the lattice findings rather accurately, once the inclusion of a gluon mass has cured all spurious divergences.