Abstract
The transverse momentum-dependent (TMD) and collinear higher twist theoretical factorization frameworks are the most frequently used approaches to describe spin-dependent hard cross sections weighted by and integrated over transverse momentum. Of particular interest is the contribution from small transverse momentum associated with the target bound state. In phenomenological applications, this contribution is often investigated using transverse momentum weighted integrals that sharply regulate the large transverse momentum contribution, for example, with Gaussian parametrizations. Since the result is a kind of hybrid of TMD and collinear (inclusive) treatments, it is important to establish if and how the formalisms are related in applications to weighted integral observables. The suppression of a large transverse momentum tail, for example, can potentially affect the type of evolution that is applicable. We find that a naive version of a widely used identity relating the ${k}_{T}^{2}$-weighted and integrated Sivers TMD function to a renormalized twist-3 function has strongly ambiguous ultraviolet contributions, and that corrections to it are not necessarily perturbatively suppressed. We discuss the implications for applications, arguing in particular that the relevant evolution for transverse momentum weighted and integrated cross sections with sharp effective large transverse momentum cutoffs is of the TMD form rather than the standard renormalization group evolution of collinear correlation functions.
Highlights
Understanding fully the single transverse-spin asymmetries (SSAs) of high energy scattering cross sections with the momentum transfer Q ≫ ΛQCD is still one of the most fascinating and challenging subjects in QCD since its discovery in hadronic Λ0 production over 40 years ago [1]
The two schemes we considered were (1) standard collinear renormalization for the twist-3 collinear correlation function and (2) direct integration of the transverse momentum-dependent (TMD) function with suppression of the large transverse momentum contribution
This implies that it is the evolution of the Sivers function, performed using standard TMD evolution techniques and before the integration over kT, that governs the evolution of the weighted-integrated asymmetries as they are normally determined
Summary
Understanding fully the single transverse-spin asymmetries (SSAs) of high energy scattering cross sections with the momentum transfer Q ≫ ΛQCD is still one of the most fascinating and challenging subjects in QCD since its discovery in hadronic Λ0 production over 40 years ago [1]. In an overlap region where ΛQCD ≪ QT ≪ Q, the TMD and twist-3 collinear factorization formalisms for the SSAs were shown to be consistent with each other [21,22,23] when the active parton kT and the phase of the Sivers TMD function are perturbatively generated by the twist-3 mechanism Both TMD and twist-3 collinear factorization approaches have been used frequently to describe the transverse moment of two-scale spin-dependent hard cross sections and their asymmetries, by integrating over transverse momentum QT while weighting by a single power of QT, leaving the observables with only a single large momentum transfer Q [24,25,26,27,28].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
