Qualitative features of multiparticle correlations in light-heavy ion (<math><mi>p</mi><mo>+</mo><mi>A</mi></math>) collisions at RHIC and LHC are reproduced in a simple initial state model of partons in the projectile coherently scattering off localized domains of color charge in the heavy nuclear target. These include (i) the ordering of the magnitudes of the azimuthal angle <math><mi>n</mi></math>th Fourier harmonics of two-particle correlations <math><msub><mi>v</mi><mi>n</mi></msub><mo>{</mo><mn>2</mn><mo>}</mo></math>, (ii) the energy and transverse momentum dependence of the four-particle Fourier harmonic <math><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>4</mn><mo>}</mo></math>, and (iii) the energy dependence of four-particle symmetric cumulants measuring correlations between different Fourier harmonics. Similar patterns are seen in an Abelian version of the model, where we observe <math><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>2</mn><mo>}</mo><mo>&gt;</mo><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>4</mn><mo>}</mo><mo>≈</mo><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>6</mn><mo>}</mo><mo>≈</mo><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>8</mn><mo>}</mo></math> of two, four, six, and eight particle correlations. While such patterns are often interpreted as signatures of collectivity arising from hydrodynamic flow, our results provide an alternative description of the multiparticle correlations seen in <math><mi>p</mi><mo>+</mo><mi>A</mi></math> collisions.

United States

Kevin Dusling

Mark Mace

Raju Venugopalan

Multiparticle Collectivity from Initial State Correlations in High Energy Proton-Nucleus Collisions

In K. Dusling et al. [arXiv:1705.00745.], an initial-state “parton model” of quarks scattering off a dense nuclear target was shown to qualitatively reproduce the systematics of multiparticle azimuthal anisotropy cumulants measured in proton/deuteron-nucleus (<math><mi>p</mi><mi>A</mi></math>) collisions at the Relativistic Heavy Ion Collider and the LHC. The systematics included (i) the behavior of the four-particle cumulant <math><msub><mi>c</mi><mn>2</mn></msub><mo>{</mo><mn>4</mn><mo>}</mo></math>, which generates a real four-particle second Fourier harmonic <math><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>4</mn><mo>}</mo></math>; (ii) the ordering <math><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>2</mn><mo>}</mo><mo>&gt;</mo><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>4</mn><mo>}</mo><mo>≈</mo><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>6</mn><mo>}</mo><mo>≈</mo><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>8</mn><mo>}</mo></math> for two-, four-, six-, and eight-particle Fourier harmonics; and (iii) the behavior of so-called symmetric cumulants SC(2,3) and SC(2,4). These features of azimuthal multiparticle cumulants were previously interpreted as a signature of hydrodynamic flow; our results challenge this interpretation. We expand here upon our previous study and present further details and novel results on the saturation scale and transverse momentum (<math><msub><mi>p</mi><mo>⊥</mo></msub></math>) dependence of multiparticle azimuthal correlations. We find that the dependence of <math><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>2</mn><mo>}</mo></math> and <math><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>4</mn><mo>}</mo></math> on the number of color domains in the target varies with the <math><msub><mi>p</mi><mo>⊥</mo></msub></math> window explored. We extend our prior discussion of symmetric cumulants and compute as yet unmeasured symmetric cumulants. We investigate the <math><msub><mi>N</mi><mi>c</mi></msub></math> dependence of <math><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>2</mn><mo>}</mo></math> and <math><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>4</mn><mo>}</mo></math>. We contrast our results, which include multiple scatterings of each quark off the target, to the Glasma graph approximation, where each quark suffers at most two-gluon exchanges with the target. We find that coherent multiple scattering is essential to obtain a positive definite <math><msub><mi>v</mi><mn>2</mn></msub><mo>{</mo><mn>4</mn><mo>}</mo></math>. We provide an algorithm to compute expectation values of arbitrary products of the “dipole” lightlike Wilson line correlators.