Related papers: Helicity at Small $x$: Oscillations Generated by B…
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 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-$N_c$…
In this Letter, we analytically solve the evolution equations for the small-$x$ asymptotic behavior of the (flavor singlet) quark helicity distribution in the large-$N_c$ limit. These evolution equations form a set of coupled…
We construct an exact analytic solution of the revised small-$x$ helicity evolution equations, where the contributions of the quark-to-gluon and gluon-to-quark transition operators were newly included. These evolution equations are written…
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 an exact analytic solution of the revised small-$x$ helicity evolution equations derived recently. The equations we solve are obtained in the large-$N_c$ limit (with $N_c$ the number of quark colors) and are double-logarithmic…
We construct an exact analytic solution of the revised small-$x$ helicity evolution equations derived recently. The equations we solve are obtained in the large-$N_c$ limit (with $N_c$ the number of quark colors) and are double-logarithmic…
The proton spin puzzle is a longstanding problem in high-energy nuclear physics: how the proton spin distributes among the spin and orbital angular momenta of the quarks and gluons inside. Two of the unresolved pieces of the puzzle are the…
We extend our earlier results for the quark helicity evolution at small $x$ to derive the small-$x$ asymptotics of the flavor singlet and flavor non-singlet quark helicity TMDs and PDFs and of the $g_1$ structure function. In the flavor…
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…
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…
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 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…
The proton spin puzzle denotes the challenge of describing the proton's spin in terms of the angular momenta of the quarks and gluons which comprise it. These quarks and gluons carry a fraction $x$ of the proton's momentum. Contributions…
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 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…
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 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 rederive the small-$x$ evolution equations governing quark helicity distribution in a proton using solely an operator-based approach. In our previous works on the subject, the evolution equations were derived using a mix of diagrammatic…
We construct a numerical solution of the small-$x$ evolution equations recently derived in \cite{Kovchegov:2015pbl} for the (anti)quark helicity TMDs and PDFs as well as the $g_1$ structure function. We focus on the case of large $N_c$…