Non-Abelian bremsstrahlung and azimuthal asymmetries in high energy p plus A reactions

We apply the GLV reaction operator solution to the Vitev-Gunion-Bertsch (VGB) boundary conditions to compute to all orders in nuclear opacity the 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 numbered 2l gluon distribution, v(n)(M) {2l}, inclusive distributions in high-energy p + A reactions as a function of harmonic n, target recoil cluster number, M, and gluon number, 2l, at the 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-noninvariant trapezoidal rapidity distributions in asymmetric B + A nuclear collisions. The scaling of the intrinsically azimuthally anisotropic and long range in eta nature of the non-Abelian bremsstrahlung 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 nonflow 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 the CSA mechanism is the predicted nearly linear. rapidity dependence of the v(n)(k(T), eta). Non-Abelian beam jet bremsstrahlung may, thus, provide a simple analytic solution to the beam energy scan puzzle of the near root s independence of v(n)(p(T)) moments observed down to 10 AGeV, where large-x valence-quark beam jets dominate inelastic dynamics. Recoil bremsstrahlung from multiple independent CSA clusters could also provide a partial explanation for the unexpected similarity of v(n) in p(D) + A and noncentral A + A at the same dN / d eta multiplicity as observed at the RHIC and LHC.