Related papers: Small-$x$ Helicity Evolution: an Operator Treatmen…
We construct small-$x$ evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the $g_1$ structure function. These evolution equations resum powers of $\alpha_s \, \ln^2 (1/x)$ in the…
We apply the formalism developed earlier for studying transverse momentum dependent parton distribution functions (TMDs) at small Bjorken $x$ to construct the small-$x$ asymptotics of the quark Sivers function. First, we explicitly…
We revisit the problem of small Bjorken-$x$ evolution of the gluon and flavor-singlet quark helicity distributions in the shock wave ($s$-channel) formalism. Earlier works on the subject in the same framework resulted in an evolution…
We construct small-x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the $g_1$ structure function. These evolution equations resum powers of $\alpha_s \, \ln^2 (1/x)$ in the…
We determine the small-$x$ asymptotics of the gluon helicity distribution in a proton at leading order in perturbative QCD at large $N_c$. To achieve this, we begin by evaluating the dipole gluon helicity TMD at small $x$. In the process we…
We generalize the JIMWLK evolution equation to include the small-$x$ evolution of helicity distributions. To derive helicity JIMWLK, we use the method devised by A.H. Mueller for the usual unpolarized JIMWLK, and apply it to the helicity…
We include the quark to gluon and gluon to quark shock-wave transition operators into the small Bjorken-$x$ evolution equations for helicity in the flavor-singlet channel derived earlier. While such transitions do not affect the large-$N_c$…
A small-$x$ helicity evolution has been derived in 2016-18 and received an important modification in 2022. This article discusses its general framework and summarizes the recent theoretical developments, including the asymptotic behaviors…
The recently revised small-$x$ helicity evolution, resumming the double-logarithmic factor, $\alpha_s\ln^2(1/x)$, allows for the study of helicity distributions of quarks and gluons at small Bjorken $x$, corresponding to high center-of-mass…
The small-$x$ quark helicity evolution equations at double-logarithmic order, with the kernel $\sim\alpha_s\ln^2(1/x)$, have been derived previously. In this work, we derive the single-logarithmic corrections to the equations, to order…
The contribution to proton helicity from the spins of quarks and gluons at small Bjorken $x$ can be conveniently studied through the small-$x$ helicity evolution. Recently, it has been employed in a global analysis that includes polarized…
We present a numerical solution of the revised version of the small-$x$ helicity evolution equations at large $N_c$ and $N_f$. (Here $N_c$ and $N_f$ are the numbers of quark colors and flavors, respectively.) The evolution equations are…
We revisit the problem of the small Bjorken-$x$ asymptotics of the quark and gluon orbital angular momentum (OAM) distributions in the proton utilizing the revised small-$x$ helicity evolution derived recently. We relate the quark and gluon…
We revisit the problem of the small Bjorken-$x$ asymptotics of the quark and gluon orbital angular momentum (OAM) distributions in the proton utilizing the revised formalism for small-$x$ helicity evolution derived recently in a paper by…
It is well-known that the back-to-back (correlation) limit of inclusive quark-antiquark dijet production in unpolarized high energy electron-proton collisions can probe the Weizs\"{a}cker-Williams (WW) gluon transverse momentum-dependent…
We apply the valence quark model recently calculated for polarized proton to constrain the non-perturbative initial condition for the small-$x$ helicity evolution. The remaining free parameters are constrained by performing a global…
The small-$x$ deep inelastic scattering in the saturation region is governed by the non-linear evolution of Wilson-line operators. In the leading logarithmic approximation it is given by the BK equation for the evolution of color dipoles.…
The small-$x$ deep inelastic scattering in the saturation region is governed by the non-linear evolution of Wilson-lines operators. In the leading logarithmic approximation it is given by the BK equation for the evolution of color dipoles.…
Helicity of quarks and gluons inside the proton at small Bjorken $x$ is one of the missing pieces of the proton spin puzzle, with limited experimental results due to various challenges. To address the problem, we derive under the framework…
We perform a phenomenological study of helicity-dependent parton distribution functions (PDFs) using small-$x$ helicity evolution equations, incorporating for the first time single-inclusive jet production data in polarized proton-proton…