Abstract
We study factorization in single transverse spin asymmetries for dijet production in proton-proton collisions, by considering soft gluon radiation at one-loop order. We show that the associated transverse momentum dependent (TMD) factorization is valid at the leading logarithmic level. At next-to-leading-logarithmic (NLL) accuracy, however, we find that soft gluon radiation generates terms in the single transverse spin dependent cross section that differ from those known for the unpolarized case. As a consequence, these terms cannot be organized in terms of a spin independent soft factor in the factorization formula. We present leading logarithmic predictions for the single transverse spin dijet asymmetry for $pp$ collisions at RHIC, based on quark Sivers functions constrained by semi-inclusive deep inelastic scattering data. We hope that our results will contribute to a better understanding of TMD factorization breaking effects at NLL accuracy and beyond.
Highlights
There has been a strong interest in correlated dijet production in various hadronic collisions [1,2,3,4,5,6,7,8,9], where the two jets are produced mainly in the back-to-back configuration in the transverse plane,A þ B → Jet1 þ Jet2 þ X: ð1ÞHere A and B represent the two incoming hadrons with momenta PA and PB, respectively
We show that the associated transverse momentum dependent (TMD) factorization is valid at the leading logarithmic level
We have investigated the single transverse spin asymmetry in dijet correlations in hadronic collisions
Summary
There has been a strong interest in correlated dijet production in various hadronic collisions [1,2,3,4,5,6,7,8,9], where the two jets are produced mainly in the back-to-back configuration in the transverse plane,. Some subleading logarithmic terms can be factorized in this form as well These include collinear gluon radiation associated with the incoming hadrons and the final state jets. The former can be resummed by including the scale evolution of the integrated parton distribution and the Qiu-Sterman matrix elements, e.g., by evaluating these distributions at the scale μb 1⁄4 b0=b⊥. The basic formalism, including the eikonal approximation, the phase space integrals to obtain the leading contributions, and the subtraction method to derive the soft gluon radiation associated with the final state jets will be introduced. We introduce the general framework, the twist-three collinear expansion, and derive the soft gluon radiation amplitude in this formalism We apply these techniques to different partonic channels and demonstrate that the leading double logarithmic contributions factorize, and we verify our resummation formula at LLA0.
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