Abstract
We calculate the massive polarized three-loop pure singlet operator matrix element AQq(3),PS in the single mass case in the Larin scheme. This operator matrix element contributes to the massive polarized three-loop Wilson coefficient HQq(3),PS in deep-inelastic scattering and constitutes a three-loop transition matrix element in the variable flavor number scheme. We provide analytic results in Mellin N and in x space and study the behaviour of this operator matrix element in the region of small and large values of the Bjorken variable x.
Highlights
Higher order heavy flavor corrections to deeply–inelastic structure functions are important both in the unpolarized and polarized case [1,2]
We present the result for the O(ε0) term of the unrenormalized pure singlet polarized operator matrix elements (OMEs), namely, aQ(3q),PS
An expression for the pure singlet contribution to the structure function can be obtained, referring to parton distribution functions in the Larin scheme, which are obtained in fits describing the evolution in the Larin scheme [21,35]
Summary
Higher order heavy flavor corrections to deeply–inelastic structure functions are important both in the unpolarized and polarized case [1,2]. In order to describe the transition of massive partons becoming effectively massless, the variable flavor number scheme can be used [6,7,8] This transition is described by massive operator matrix elements (OMEs), and after its application, effective calculations for scattering reactions at hadron colliders are possible, based on heavy quark parton distributions. Several of these transition matrix elements have been already computed in the unpolarized and polarized case in the single, cf [9,10,11,12,13,14,15,16], and two–mass case [7,8,17,18,19,20]. In an ancillary file to this paper we give the massive OME in computer readable form
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