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Transverse Momentum Moments

ORAL

Abstract

We establish robust relations between Transverse Momentum Dependent distributions (TMDs) and collinear functions. We define weighted integrals of TMDs which we call Transverse Momentum Moments (TMMs). We demonstrate that TMMs are related to collinear distributions via calculable scheme-coefficients

and we derive expressions for them up

to three loops. We prove that TMMs obey the same evolution equations as the corresponding collinear quantities. We discuss in details the zeroth, the first, and the second TMMs and provide phenomenological results for those based on the current extractions of TMDs. Results of this paper open new avenues for theoretical and phenomenological investigation of the three-dimensional and collinear hadron structures.

* This work was partially supported by the National Science Foundation under Grants No.~PHY-2012002, No.~PHY-2310031, No.~PHY-2335114 (A.P.), and the U.S. Department of Energy contract No.~DE-AC05-06OR23177, under which Jefferson Science Associates, LLC operates Jefferson Lab (A.P.).A.V. is funded by the \textit{Atracci\'on de Talento Investigador} program of the Comunidad de Madrid (Spain) No. 2020-T1/TIC-20204. O. dR. is supported by the MIU (Ministerio de Universidades, Spain) fellowship FPU20/03110. This project is supported by the Spanish Ministry grant No. PID2022-136510NB-C31. This project has received funding from the European Union Horizon 2020 research and innovation program under grant agreement Num. 824093 (STRONG-2020).

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Presenters

  • Alexei Prokudin

    Penn State Berks

Authors

  • Alexei Prokudin

    Penn State Berks

  • Alexey Vladimirov

    UCM

  • Ignazio Scimemi

    UCM

  • Óscar del Río García

    UCM