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The Two-mass Contribution to the Three-Loop Polarized Operator Matrix Element A_(gg,Q)⁽³⁾

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arxiv 2004.08916 v1 pith:DZOWX4N7 submitted 2020-04-19 hep-ph hep-exhep-th

The Two-mass Contribution to the Three-Loop Polarized Operator Matrix Element A_(gg,Q)⁽³⁾

J. Ablinger , J. Bl\"umlein , A. De Freitas , A. Goedicke , M. Saragnese , C. Schneider , K. Sch\"onwald This is my paper
classification hep-ph hep-exhep-th
keywords elementharmonicintegralsmatrixoperatorpolarizedspacetwo-mass
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We compute the two-mass contributions to the polarized massive operator matrix element $A_{gg,Q}^{(3)}$ at third order in the strong coupling constant $\alpha_s$ in Quantum Chromodynamics analytically. These corrections are important ingredients for the matching relations in the variable flavor number scheme and for the calculation of Wilson coefficients in deep--inelastic scattering in the asymptotic regime $Q^2 \gg m_c^2, m_b^2$. The analytic result is expressed in terms of nested harmonic, generalized harmonic, cyclotomic and binomial sums in $N$-space and by iterated integrals involving square-root valued arguments in $z$ space, as functions of the mass ratio. Numerical results are presented. New two--scale iterative integrals are calculated.

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