We present recent analytic results for the 3-loop corrections to the massive operator matrix element A (3) Qg for further color factors. These results have been obtained using the method of arbitrarily large moments. We also give an overview on the results which were obtained solving all difference and differential equations for the corresponding master integrals that factorize at first order.
We present an update of the ABM12 PDF analysis including improved constraints due to the final version of the inclusive DIS HERA data, the Tevatron and LHC data on the W -and Z-production and those on heavy-quark production in the electron-and neutrino-induced DIS at HERA and the fixed-target experiments NOMAD and CHORUS. We also check the impact of the Tevatron and LHC top-quark production data on the PDFs and the strong coupling constant. We obtain α s (M Z ) = 0.1145(9) and 0.1147(8) with and without the top-quark data included, respectively.
We report an updated version of the ABKM09 NNLO PDF fit, which includes the most recent HERA collider data on the inclusive cross sections and an improved treatment of the heavy-quark contribution to deep-inelastic scattering using advantages of the running-mass definition for the heavy quarks. The ABM11 PDFs obtained from the updated fit are in a good agreement with the recent LHC data on the W -and Z-production within the experimental and PDF uncertainties. We also perform a determination of the strong coupling constant α s in a variant of the ABM11 fit insensitive to the influence of the higher twist terms and find the value of α s = 0.1133(11) which is in good agreement with the nominal ABM11 one and our earlier determination.
We describe the analytic calculation of the master integrals required to compute the two-mass three-loop corrections to the ρ parameter. In particular, we present the calculation of the master integrals for which the corresponding differential equations do not factorize to first order. The homogeneous solutions to these differential equations are obtained in terms of hypergeometric functions at rational argument. These hypergeometric functions can further be mapped to complete elliptic integrals, and the inhomogeneous solutions are expressed in terms of a new class of integrals of combined iterative non-iterative nature.
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