Abstract
We present the two-mass QCD contributions to the polarized pure singlet operator matrix element at three loop order in x-space. These terms are relevant for calculating the polarized structure function g1(x,Q2) at O(αs3) as well as for the matching relations in the variable flavor number scheme and the polarized heavy quark distribution functions at the same order. The result for the operator matrix element is given in terms of generalized iterated integrals. These integrals depend on the mass ratio through the main argument, and the alphabet includes square–root valued letters.
Highlights
Massive operator matrix elements (OMEs) are essential building blocks for the massive Wilson coefficients in deep–inelastic scattering in the limit Q2 m2, and they are the transition matrix elements in the variable flavor number scheme (VFNS) [1,2]
In the unpolarized case the two–mass corrections have been calculated for all OMEs to three–loop order in Refs. [3,4,5,6,7]
In order to compute the corresponding contribution to the structure function g1(x, Q2) or for the transition rate in the VFNS, we have to perform the convolution with parton distribution functions, which can be obtained straightforwardly
Summary
Massive operator matrix elements (OMEs) are essential building blocks for the massive Wilson coefficients in deep–inelastic scattering in the limit Q2 m2, and they are the transition matrix elements in the variable flavor number scheme (VFNS) [1,2]. In the result we obtain iterative integrals, partly with limited support in x ∈ [0, 1] This has been observed in the single mass pure singlet case [8]. Is one of the contributions of the two–mass variable flavor number scheme [4,10] in the polarized case, describing the respective transitions of the polarized parton densities in the case the heavy quarks become light. They contribute in particular to the charm- and bottom quark distributions. In the appendix we provide complete analytic expressions for a number of Mellin moments N ∈ N
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