Abstract
We present the two-mass QCD contributions to the pure singlet operator matrix element at three loop order in x-space. These terms are relevant for calculating the structure function F2(x,Q2) at O(αs3) as well as for the matching relations in the variable flavor number scheme and the heavy quark distribution functions at the same order. The result for the operator matrix element is given in terms of generalized iterated integrals that include square root letters in the alphabet, depending also on the mass ratio through the main argument. Numerical results are presented.
Highlights
Starting at 2-loop order, massive operator matrix elements (OME) Aij, which are the transition matrix elements in the variable flavor number scheme (VFNS), receive two-mass contributions [1,2]
Details on new iterated integrals emerging in the representation, the G-functions, and a series of fixed moments as a function of the mass ratio of the two heavy quarks for the unrenormalized OME are given in the Appendix
The transition relations for the renormalization of the heavy quarks in the MS-scheme is given in [3], Eq (5.100), but it only applies to the equal mass case since for the unequal mass case the first contributions emerge at 3-loop order
Summary
Starting at 2-loop order, massive operator matrix elements (OME) Aij , which are the transition matrix elements in the variable flavor number scheme (VFNS), receive two-mass contributions [1,2]. This applies to the Wilson coefficients in deeply inelastic scattering. The single mass contributions to the pure singlet (PS) OME, APQSq,(3), have been calculated in Ref. Ablinger et al / Nuclear Physics B 927 (2018) 339–367 present paper we present the corresponding 2-mass contributions For all OMEs a series of moments has been calculated in the single mass case in Ref. Details on new iterated integrals emerging in the representation, the G-functions, and a series of fixed moments as a function of the mass ratio of the two heavy quarks for the unrenormalized OME are given in the Appendix
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