An Observation Concerning the Process Dependence of the Sivers Functions

TL;DR

The paper investigates a potential inconsistency between the Sivers function, extracted from SIDIS, and the twist-3 ETQS function, related to the Sivers function via its $k_⊥$-moment. By computing the $k_⊥$-moments for two SIDIS-based Sivers parameterizations and applying the operator relation to obtain $T_{q,F}(x,x)$, they compare these with ETQS functions directly extracted from $p^\uparrow p$ SSAs, correcting a sign convention issue. They find a sign mismatch for both $u$ and $d$ quarks, suggesting either that the Sivers mechanism is not the dominant source of pp SSAs or that SIDIS data do not fully constrain the $k_⊥$-moment, with caveats about UV renormalization and $k_⊥$-dependence. The authors discuss possible explanations, including additional hadronization effects and alternative SSA mechanisms, and advocate further measurements in $pp$ and $ep$ scattering (e.g., direct photons, jets, Drell–Yan, and future EIC SIDIS) to resolve the discrepancy and clarify the process dependence of the Sivers effect.

Abstract

The $k_\perp$-moment of a quark's Sivers function is known to be related to the corresponding twist-three quark-gluon correlation function $T_{q,F}(x, x)$. The two functions have been extracted from data for single-spin asymmetries in semi-inclusive deep inelastic scattering and in single-inclusive hadron production in $pp$ collisions, respectively. Performing a consistent comparison of the extracted functions, we find that they show a "sign mismatch": while the magnitude of the functions is roughly consistent, the $k_\perp$-moment of the Sivers function has opposite sign from that of $T_{q,F}(x, x)$, both for up and for down quarks. Barring any inconsistencies in our theoretical understanding of the Sivers functions and their process dependence, the implication of this mismatch is that either, the Sivers effect is not dominantly responsible for the observed single-spin asymmetries in $pp$ collisions or, the current semi-inclusive lepton scattering data do not sufficiently constrain the $k_\perp$-moment of the quark Sivers functions. Both possibilities strengthen the case for further experimental investigations of single-spin asymmetries in high-energy $pp$ and $ep$ scattering.

Figures (4)

• Figure 1: The quark-gluon correlation function $gT_{q,F}(x, x)$ as a function of momentum fraction $x$ for $u$-quarks (left) and $d$-quarks (right). The dashed (dotted) lines are $gT_{q, F}(x, x)|_{\rm new~Sivers}$ ($gT_{q, F}(x, x)|_{\rm old~Sivers}$) obtained by taking the $k_\perp$-moments of the corresponding quark Sivers functions according to the right-hand-side of Eq. (\ref{['rel']}). The solid lines represent the correlation functions extracted directly from data on SSAs for inclusive pion production in proton-proton collisions, $p^\uparrow p\to \pi+X$newpion, after correcting for the sign convention (see text).
• Figure 2: The SSAs for direct photon (left) and single inclusive jet (right) production in $p^\uparrow p$ collisions at $\sqrt{S}=200$ GeV, as functions of $x_F$ for rapidity $y=3.3$. The various curves correspond to the $T_{q, F}(x, x)$ shown in Fig. \ref{['fig:sivers']}.
• Figure A.1: Illustration of the sign convention for $A_N$: positive $A_N$ means that more hadrons are produced to the left of the beam direction when the beam's spin is vertically upward.
• Figure A.2: The SSA, $A_N$, for inclusive single pion production in $p^\uparrow p\to\pi+X$ at $\sqrt{s}=200$ GeV, as a function of $x_F$ and at rapidity $y=3.7$, evaluated by using the old Sivers functions in Eq. (\ref{['old']}) (left), and the new Sivers functions in Eq. (\ref{['new']}) (right).