Transverse single-spin asymmetries in proton-proton collisions at the AFTER@LHC experiment

We present results for transverse single-spin asymmetries in proton-proton collisions at kinematics relevant for AFTER, a proposed fixed-target experiment at the Large Hadron Collider. These include predictions for pion, jet, and direct photon production from analytical formulas already available in the literature. We also discuss specific measurements that will benefit from the higher luminosity of AFTER, which could help resolve an almost 40-year puzzle of what causes transverse single-spin asymmetries in proton-proton collisions.Comment: 10 pages, 4 figures; more details/discussion added to the text, references added/updated, version to appear in Advances in High Energy Physics for the Special Issue "Physics at a Fixed-Target Experiment Using the LHC Beams

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

Single-spin asymmetries in the leptoproduction of transversely polarized Λ\Lambda hyperons

We analyze single-spin asymmetries (SSAs) in the leptoproduction of transversely polarized $\Lambda$ hyperons within the collinear twist-3 formalism. We calculate both the distribution and fragmentation terms in two different gauges (lightcone and Feynman) and show that the results are identical. This is the first time that the fragmentation piece has been analyzed for transversely polarized hadron production within the collinear twist-3 framework. In lightcone gauge we use the same techniques that were employed in computing the analogous piece in $p^\uparrow p\to \pi\,X$, which has become an important part to that reaction. With this in mind, we also verify the gauge invariance of the formulas for the transverse SSA in the leptoproduction of pions.Comment: 12 pages, 1 figure, reference added, version to appear in Phys. Lett.