We investigate whether the Balitsky-Fadin-Kuraev-Lipatov (BFKL) low x evolution equation is capable to describe the energy dependence of the exclusive photo-production cross-section of vector mesons J/Ψ and Υ on protons. Such cross-sections have been measured by both HERA experiments H1 and ZEUS in electron-proton collisions and by LHC experiments ALICE, CMS and LHCb in ultra-peripheral proton-proton and ultraperipheral proton-lead collisions. Our approach provides a perturbative description of the rise with energy and relies only on a fit of the initial transverse momentum profile of the proton impact factor, which can be extracted from BFKL fits to inclusive HERA data. We find that BFKL evolution is capable to provide a very good description of the energy dependence of the current data set, while the available fits of the proton impact factor require an adjustment in the overall normalization.

The collective interactions of many partons in the first stage of the collisions is the usual accepted explanation of the sizable elliptical flow. The clustering of color sources provides a framework of partonic interactions. In this scheme, we show a reasonable agreement with RHIC data for p T < 1.5 GeV/c in both the dependence of v 2 on transverse momentum and in the shape of the nuclear modified factor on the azimuthal angle for different centralities. We show the predictions at LHC energies for Pb-Pb. In the case of proton-proton collisions a sizable v 2 is obtained at this energy.

We use multiple scattering and energy conservation arguments to describe dn/dη| N A N A as a function of dn/dη| pp in the framework of string percolation. We discuss the pseudorapidity η and beam rapidity Y dependence of particle densities. We present our results for pp, Au-Au, and Pb-Pb collisions at RHIC and LHC.

For field theories with a topological charge Q, it is often of interest to measure the topological susceptibility χ t = ( Q 2 − Q 2 )/V . If we manage to perform a Monte Carlo simulation where Q changes frequently, χ t can be evaluated directly. However, for local update algorithms and fine lattices, the auto-correlation time with respect to Q tends to be extremely long, which invalidates the direct approach. Nevertheless, the measurement of χ t is still feasible, even when the entire Markov chain is topologically frozen. We test a method for this purpose, based on the correlation of the topological charge density, as suggested by Aoki, Fukaya, Hashimoto and Onogi. Our studies in non-linear σ-models and in 2d Abelian gauge theory yield accurate results for χ t , which confirm that the method is applicable. We also obtain promising results in 4d SU(2) Yang-Mills theory, which suggest the applicability of this method in QCD.