Non-Abelian bremsstrahlung and azimuthal asymmetries in high energyp+Areactions

Abstract

We apply the GLV reaction operator solution to the Vitev-Gunion-Bertsch (VGB) boundary conditions to compute the all-order in nuclear opacity non-abelian gluon bremsstrahlung of event-by-event fluctuating beam jets in nuclear collisions. We evaluate analytically azimuthal Fourier moments of single gluon, $v_n^M\{1\}$, and even number $2\ell$ gluon, $v_n^M\{2\ell\}$ inclusive distributions in high energy p+A reactions as a function of harmonic $n$, %independent target recoil cluster number, $M$, and gluon number, $2\ell$, at RHIC and LHC. Multiple resolved clusters of recoiling target beam jets together with the projectile beam jet form Color Scintillation Antenna (CSA) arrays that lead to characteristic boost non-invariant trapezoidal rapidity distributions in asymmetric $B+A$ nuclear collisions. The scaling of intrinsically azimuthally anisotropic and long range in $\eta$ nature of the non-abelian \br leads to $v_n$ moments that are similar to results from hydrodynamic models, but due entirely to non-abelian wave interference phenomena sourced by the fluctuating CSA. Our analytic non-flow solutions are similar to recent numerical saturation model predictions but differ by predicting a simple power-law hierarchy of both even and odd $v_n$ without invoking $k_T$ factorization. A test of CSA mechanism is the predicted nearly linear $\eta$ rapidity dependence of the $v_n(k_T,\eta)$. Non-abelian beam jet \br may thus provide a simple analytic solution to Beam Energy Scan (BES) puzzle of the near $\sqrt{s}$ independence of $v_n(p_T)$ moments observed down to 10 AGeV where large $x$ valence quark beam jets dominate inelastic dynamics. Recoil \br from multiple independent CSA clusters could also provide a partial explanation for the unexpected similarity of $v_n$ in $p(D)+A$ and non-central $A+A$ at same $dN/d\eta$ multiplicity as observed at RHIC and LHC.