Collinearly improved JIMWLK evolution in Langevin form

The high-energy evolution of Wilson line operators, which at leading order is described by the Balitsky-JIMWLK equations, receives large radiative corrections enhanced by single and double collinear logarithms at next-to-leading order and beyond. We propose a method for resumming such logarithmic corrections to all orders, at the level of the Langevin formulation of the JIMWLK equation. The ensuing, collinearly-improved Langevin equation features generalized Wilson line operators, which depend not only upon rapidity (the logarithm of the longitudinal momentum), but also upon the transverse size of the color neutral projectile to which the Wilson lines belong. This additional scale dependence is built up during the evolution, via the condition that the successive emissions of soft gluons be ordered in time. The presence of this transverse scale in the Langevin equation furthermore allows for the resummation of the one-loop running coupling corrections.Comment: 24 pages, 1 figur

Building up the elliptic flow: analytical insights

In this paper, we present a fully analytical description of the early-stage formation of elliptic flow in relativistic viscous hydrodynamics. We first construct an elliptic deformation of Gubser flow which is a boost invariant solution of the Navier-Stokes equation with a nontrivial transverse profile. We then analytically calculate the momentum anisotropy of the flow as a function of time and discuss the connection with the empirical formula by Bhalerao {\it et al.} regarding the viscosity dependence of elliptic flow.Comment: 8 pages;v2. To be published in physics letters

On the small-xx behavior of the orbital angular momentum distributions in QCD

We present the numerical solution of the leading order QCD evolution equation for the orbital angular momentum distributions of quarks and gluons and discuss its implications for the nucleon spin sum rule. We observe that at small-$x$, the gluon helicity and orbital angular momentum distributions are roughly of the same magnitude but with opposite signs, indicating a significant cancellation between them. A similar cancellation occurs also in the quark sector. We explain analytically the reason for this cancellation.Comment: 12 pages. v2: two figures added, version to appear in Physics Letters

Proton Spin Structure at Small-xx

We generalize the Bartels-Ermolaev-Ryskin approach for the $g_1$ structure function at small-$x$ to determine the small-$x$ asymptotic behavior of the orbital angular momentum distributions in QCD. We present an exact analytical solution of the evolution equation in the double logarithmic approximation and discuss its implications for the proton spin problem.Comment: 6 pages and 3-page appendix; v2:minor correction, references adde

Hemisphere jet mass distribution at finite NcN_c

We perform the leading logarithmic resummation of nonglobal logarithms for the single-hemisphere jet mass distribution in $e^+e^-$ annihilation including the finite-$N_c$ corrections. The result is compared with the previous all-order result in the large-$N_c$ limit as well as fixed-order perturbative calculations.Comment: 10 pages, 1 figure. v2: the numerical result revised after removing a systematic error; v3: added more statistics, new fitting parameters, accepted for publication in Phys.Lett.

Gluon polarization in the nucleon demystified

Recently, X. Chen et al. proposed a new approach to the gauge invariant decomposition of the nucleon spin into helicity and orbital parts. The key ingredient in their construction is the separation of the gauge field into `physical' and `pure gauge' parts. We suggest a simple separation scheme and show that the resulting gluon helicity coincides with the first moment of the conventional polarized gluon distribution measurable in high energy experiments.Comment: 6 page