Abstract
We consider one of the most fundamental sets of hadronic matrix elements, namely the generalized transverse momentum dependent distributions (GTMDs), and argue that their existing definitions lack proper evolution properties. By exploiting the similarity of GTMDs with the much better understood transverse momentum distributions, we argue that the existing definitions of GTMDs have to include an additional dependence on soft gluon radiation in order to render them properly defined. With this, we manage to obtain the evolution kernel of all (un)polarized quark and gluon GTMDs, which turns out to be spin independent. As a byproduct, all large logarithms can be resummed up to next-to-next-to-leading-logarithmic accuracy with the currently known perturbative ingredients.
Highlights
MotivationIt has been known for quite some time that hadronic matrix elements such as generalized parton distributions [1,2,3] (GPDs) and transverse momentum dependent parton distribution/fragmentation functions [4,5,6] (TMDs in general) are indispensable objects for studying fundamental properties of hadrons
By exploiting the similarity of generalized transverse momentum dependent distributions (GTMDs) with the much better understood transverse momentum distributions, we argue that the existing definitions of GTMDs have to include an additional dependence on soft gluon radiation in order to render them properly defined
As we show below for an unpolarized quark target, the existing definition of GTMDs suffers from unwanted rapidity divergences (RDs)
Summary
It has been known for quite some time that hadronic matrix elements such as generalized parton distributions [1,2,3] (GPDs) and transverse momentum dependent parton distribution/fragmentation functions [4,5,6] (TMDs in general) are indispensable objects for studying fundamental properties of hadrons. The last assertion results from the observation that these matrix elements lack proper evolution properties with respect to the renormalization scale μ and the rapidity scale Q Their operator product expansion into generalized parton distributions breaks down even for large enough transverse momentum, contrary to what the case should be. The upshot is that such matrix elements, formulated from the basic QCD fields and being gauge invariant, cannot be admissible in the group of genuine QCD hadronic quantities, such as the integrated PDFs, GPDs or the more recently reformulated TMDs. When calculated perturbatively, as we show below for an unpolarized quark target, the existing definition of GTMDs suffers from unwanted rapidity divergences (RDs). The importance of properly defining quark and gluon GTMDs, extracting their evolution kernels, motivating their lattice calculation and experimental measurements, relies on them being fundamental objects of QCD, and on their connection to orbital angular momentum of partons inside hadrons [24,25,26,27,28,29]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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 callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
