Probing the two-scale-factor universality hypothesis by exact rotation symmetry-breaking mechanism

We probe the two-scale factor universality hypothesis by evaluating, firstly explicitly and analytically at the one-loop order, the loop quantum corrections to the amplitude ratios for O($N$) $\lambda\phi^{4}$ scalar field theories with rotation symmetry-breaking in three distinct and independent methods in which the rotation symmetry-breaking mechanism is treated exactly. We show that the rotation symmetry-breaking amplitude ratios turn out to be identical in the three methods and equal to their respective rotation symmetry-breaking ones, although the amplitudes themselves, in general, depend on the method employed and on the rotation symmetry-breaking parameter. At the end, we show that all these results can be generalized, through an inductive process based on a general theorem emerging from the exact calculation, to any loop level and physically interpreted based on symmetry ideas.Comment: 17 pages, 3 figure

Coherent and incoherent J/ΨJ/\Psi photoproduction in PbPbPbPb collisions at the LHC, HE -- LHC and FCC

The coherent and incoherent $J/\Psi$ photoproduction in $PbPb$ collisions are investigated considering the possible states of nucleon configurations in the nuclear wave function and taking into account of the non - linear corrections to the QCD dynamics. The cross sections and the rapidity and transverse momentum distributions are estimated for the energies of the next run of the LHC, High -- Energy LHC and Future Circular Collider. Our results indicate that a future experimental analysis of these processes will be useful to discriminate between different approaches for the QCD dynamics as well to improve our description of the gluon saturation effects.Comment: 7 pages, 3 figures, 1 tabl