Azimuthal anisotropies in p + Pb collisions from classical Yang–Mills dynamics

We compute single and double inclusive gluon distributions in classical Yang–Mills simulations of proton–lead collisions and extract the associated transverse momentum dependent Fourier harmonics v2(pT)v2(pT) and v3(pT)v3(pT). Gluons have a large v2v2 in the initial state, while odd harmonics such as v3v3 vanish identically at the initial time τ=0+τ=0+. By the time τ≲0.4 fm/cτ≲0.4 fm/c final state effects in the classical Yang–Mills evolution generate a non-zero v3v3 and only mildly modify the gluon v2v2. Unlike hydrodynamic flow, these momentum space anisotropies are uncorrelated with the global spatial anisotropy of the collision. A principal ingredient for the generation of v2v2 and v3v3 in this framework is the event-by-event breaking of rotational invariance in domains the size of the inverse of the saturation scale QsQs. In contrast to our findings in p + Pb collisions Yang–Mills simulations of lead–lead collisions generate much smaller values of v2,3(pT)v2,3(pT) and additional collective flow effects are needed to explain experimental data. This is because the locally generated anisotropy due to the breaking of rotational invariance is depleted with the increase in the number of uncorrelated domains.