# The unpolarized two-loop massive pure singlet Wilson coefficients for deep-inelastic scattering

## TL;DR

This paper analytically computes the two-loop massive pure singlet Wilson coefficients for heavy quark production in deep-inelastic scattering, introducing new classes of iterated integrals and providing numerical results across all kinematic regions.

## Contribution

It introduces the calculation of massive two-loop pure singlet Wilson coefficients with novel elliptic iterated integrals and improved asymptotic representations for structure functions.

## Key findings

- Complete expressions with elliptic letters are derived.
- New Kummer-elliptic integrals are introduced.
- Numerical results demonstrate the applicability across kinematic regions.

## Abstract

We calculate the massive two--loop pure singlet Wilson coefficients for heavy quark production in the unpolarized case analytically in the whole kinematic region and derive the threshold and asymptotic expansions. We also recalculate the corresponding massless two--loop Wilson coefficients. The complete expressions contain iterated integrals with elliptic letters. The contributing alphabets enlarge the Kummer-Poincar\'e letters by a series of square-root valued letters. A new class of iterated integrals, the Kummer-elliptic integrals, are introduced. For the structure functions $F_2$ and $F_L$ we also derive improved asymptotic representations adding power corrections. Numerical results are presented.

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Source: https://tomesphere.com/paper/1903.06155