Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams [PDF]
, 2014 Nested sums containing binomial coefficients occur in the computation of massive operator matrix elements. Their associated iterated integrals lead to alphabets including radicals, for which we determined a suitable basis.
Ablinger, Jakob +3 more
core +1 more source
The Method of Arbitrarily Large Moments to Calculate Single Scale Processes in Quantum Field Theory [PDF]
, 2017 We device a new method to calculate a large number of Mellin moments of single scale quantities using the systems of differential and/or difference equations obtained by integration-by-parts identities between the corresponding Feynman integrals of loop ...
Blümlein, Johannes, Schneider, Carsten
core +2 more sources
3-Loop Heavy Flavor Corrections in Deep-Inelastic Scattering with Two Heavy Quark Lines [PDF]
, 2014 We consider gluonic contributions to the heavy flavor Wilson coefficients at 3-loop order in QCD with two heavy quark lines in the asymptotic region $Q^2 \gg m_{1(2)}^2$.
Ablinger, J. +7 more
core +1 more source
Recent Symbolic Summation Methods to Solve Coupled Systems of Differential and Difference Equations [PDF]
, 2014 We outline a new algorithm to solve coupled systems of differential equations in one continuous variable $x$ (resp. coupled difference equations in one discrete variable $N$) depending on a small parameter $\epsilon$: given such a system and given ...
Bluemlein, Johannes +2 more
core +2 more sources
Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering: Recent Results [PDF]
, 2017 We present recent analytic results for the 3-loop corrections to the massive operator matrix element $A_{Qg}^{(3)}$for further color factors. These results have been obtained using the method of arbitrarily large moments.
Ablinger, J. +5 more
core +2 more sources
Massive three loop form factors in the planar limit [PDF]
, 2018 We present the color planar and complete light quark QCD contributions to the three loop heavy quark form factors in the case of vector, axial-vector, scalar and pseudo-scalar currents.
Ablinger, Jakob +4 more
core +1 more source
The massive 3-loop operator matrix elements with two masses and the generalized variable flavor number scheme [PDF]
, 2017 We report on our latest results in the calculation of the two--mass contributions to 3--loop operator matrix elements (OMEs). These OMEs are needed to compute the corresponding contributions to the deep-inealstic scattering structure functions and to ...
Ablinger, J. +6 more
core +2 more sources
The Three Loop Two-Mass Contribution to the Gluon Vacuum Polarization [PDF]
, 2017 We calculate the two-mass contribution to the 3-loop vacuum polarization of the gluon in Quantum Chromodynamics at virtuality $p^2 = 0$ for general masses and also present the analogous result for the photon in Quantum Electrodynamics.Comment: 5 pages ...
Blümlein, J. +3 more
core +1 more source
Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations [PDF]
, 2017 Various of the single scale quantities in massless and massive QCD up to 3-loop order can be expressed by iterative integrals over certain classes of alphabets, from the harmonic polylogarithms to root-valued alphabets.
Ablinger, J. +8 more
core +1 more source
A toolbox to solve coupled systems of differential and difference equations
, 2016 We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do {\it not} request special choices of bases.
Ablinger, Jakob +3 more
core +1 more source