Alexander Hasselhuhn

Massive 3-loop Ladder Diagrams for Quarkonic Local Operator Matrix Elements

Abstract 3-loop diagrams of the ladder-type, which emerge for local quarkonic twist-2 operator matrix elements, are computed directly for general values of the Mellin variable N using Appell-function representations and applying modern summation technologies provided by the package Sigma and the method of hyperlogarithms. In some of the diagrams generalized harmonic sums with ξ ∈ { 1 , 1 / 2 , 2 } emerge beyond the usual nested harmonic sums. As the asymptotic representation of the corresponding integrals shows, the generalized sums conspire giving well behaved expressions for large values of N . These diagrams contribute to the 3-loop heavy flavor Wilson coefficients of the structure functions in deep-inelastic scattering in the region Q 2 ≫ m 2 .

The

The

O(\alpha_s^3 n_f T_F^2 C_{A,F})

O(\alpha_s^3 n_f T_F^2 C_{A,F})

} Contributions to the Gluonic Massive Operator Matrix Elements

terms to the massive gluonic operator matrix elements are calculated for general values of the Mellin variable

The O(αs3nfTF2CA,F) contributions to the gluonic massive operator matrix elements

N

Heavy Flavor DIS Wilson coefficients in the asymptotic regime

. These twist-2 matrix elements occur as transition functions in the variable flavor number scheme at NNLO. The calculation uses sum-representations in generalized hypergeometric series turning into harmonic sums. The analytic continuation to complex values of

O(α

N

_s^3

is provided.

) heavy flavor contributions to the charged current structure function

The

xF_3(x,Q^2)

O(\alpha_s^3 n_f T_F^2 C_{A,F})