The massive 3-loop operator matrix elements with two masses and the generalized variable flavor number scheme

TL;DR

This paper presents advanced calculations of two-mass three-loop operator matrix elements crucial for improving the variable flavor number scheme in deep-inelastic scattering, including charm and bottom quark effects.

Contribution

It introduces new two-mass three-loop operator matrix element results, extending previous single-mass calculations and enhancing the variable flavor number scheme.

Findings

Calculated non-singlet and $A_{gq,Q}$ OMEs with two masses

Compared two-mass contributions to single-mass cases

Provided gluonic OME $A_{gg,Q}$ results beyond previous scalar diagram computations

Abstract

We report on our latest results in the calculation of the two--mass contributions to 3--loop operator matrix elements (OMEs). These OMEs are needed to compute the corresponding contributions to the deep-inealstic scattering structure functions and to generalize the variable flavor number scheme by including both charm and bottom quarks. We present the results for the non-singlet and $A_{gq,Q}$ OMEs, and compare the size of their contribution relative to the single mass case. Results for the gluonic OME $A_{gg,Q}$ are given in the physical case, going beyond those presented in a previous publication where scalar diagrams were computed. We also discuss our recently published two--mass contribution to the pure singlet OME, and present an alternative method of calculating the corresponding diagrams.