Small-xx Asymptotics of the Quark Helicity Distribution: Analytic Results

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 integro-differential equations, which previously could only be solved numerically. This approximate numerical solution, however, revealed simplifying properties of the small-$x$ asymptotics, which we exploit here to obtain an analytic solution. We find that the small-$x$ power-law tail of the quark helicity distribution scales as $\Delta q^S (x, Q^2) \sim \left(\tfrac{1}{x} \right)^{\alpha_h}$ with $\alpha_h = \tfrac{4}{\sqrt{3}} \sqrt{\tfrac{\alpha_s N_c}{2\pi}}$, in excellent agreement with the numerical estimate $\alpha_h \approx 2.31\sqrt{\tfrac{\alpha_s N_c}{2\pi}}$ obtained previously. We then verify this solution by cross-checking the predicted scaling behavior of the auxiliary "neighbor dipole amplitude" against the numerics, again finding excellent agreement.Comment: 5 pages, 2 figure

Connections between collinear and transverse-momentum-dependent polarized observables within the Collins-Soper-Sterman formalism

We extend the improved Collins-Soper-Sterman (iCSS) $W+Y$ construction recently presented in~\cite{Collins:2016hqq} to the case of polarized observables, where we focus in particular on the Sivers effect in semi-inclusive deep-inelastic scattering. We further show how one recovers the expected leading-order collinear twist-3 result from a (weighted) $q_T$-integral of the differential cross section. We are also able to demonstrate the validity of the well-known relation between the (TMD) Sivers function and the (collinear twist-3) Qiu-Sterman function within the iCSS framework. This relation allows for their interpretation as functions yielding the average transverse momentum of unpolarized quarks in a transversely polarized spin-$\frac{1}{2}$ target. We further outline how this study can be generalized to other polarized quantities.Comment: 14 pages, Version to be published in PL

Polarized hyperon production in single-inclusive electron-positron annihilation at next-to-leading order

We study the production of polarized $\Lambda$-hyperons in electron-positron annihilation. We are particularly interested in the transverse-spin dependence of the cross section for unpolarized incident electron-positron pairs. At high energies this process may be described in the collinear twist-3 framework, where the hadronization transition of partons into a transversely polarized $\Lambda$-hyperon can be written in terms of collinear twist-3 fragmentation matrix elements. We calculate the hard partonic cross sections and interference terms in perturbative QCD to next-to-leading order accuracy. We find that the QCD equation of motion plays a crucial role in our analysis. As a byproduct, assuming the validity of QCD factorization for twist-3 observables at next-to-leading order, we derive the evolution equation for the relevant twist-3 fragmentation matrix element.Comment: 43 pages, 25 figure

Polarized Hyperon Production in Single-Inclusive Electron Positron Annihilation at Next-To-Leading Order

We study the production of polarized A-hyperons in electron-positron annihilation. We are particularly interested in the transverse-spin dependence of the cross section for unpolarized incident electron-positron pairs. At high energies this process may be described in the collinear twist-3 framework, where the hadronization transition of partons into a transversely polarized -hyperon can be written in terms of collinear twist-3 fragmentation matrix elements. We calculate the hard partonic cross sections and interference terms in perturbative QCD to next-to-leading order accuracy. We find that the QCD equation of motion plays a crucial role in our analysis. As a byproduct, assuming the validity of QCD factorization for twist-3 observables at next-to-leading order, we derive the evolution equation for the relevant twist-3 fragmentation matrix element

Updated numerical study of transverse single-spin asymmetries in single-inclusive pion production from lepton-nucleon collisions

We revisit the analysis of transverse single-spin asymmetries $A_N$ in lepton-nucleon scattering where only a single pion is detected in the final state, $\ell\,N^\uparrow\to h\, X$. This observable is the Electron-Ion Collider (EIC) analogue to $A_N$ in proton-proton collisions, $p^\uparrow p\to h\,X$, that has been studied intensely for decades, especially at the Relativistic Heavy Ion Collider (RHIC). We incorporate new theoretical developments in the collinear twist-3 framework and utilize recent extractions of (Sivers-like and Collins-like) quark-gluon-quark correlators in the numerical computations. We compare our calculations to HERMES measurements as well as make predictions for Jefferson Lab, COMPASS, and EIC kinematics. We further explore the role of next-to-leading order (NLO) corrections to the (twist-2) unpolarized cross section (denominator of $A_N$) and consider what can be deduced empirically about the potential numerical significance of the full NLO calculation of $A_N$ in this process. We consider sources of theoretical uncertainty in our predictions, which present potential opportunities then for future measurements to improve our understanding of $A_N$ and multi-parton correlations in hadrons.Comment: 13 pages, 6 figures; extended the discussion in Sec. 3.1 on the role of NLO corrections, version to appear in Phys. Lett.