Two-Loop Massive Operator Matrix Elements and Unpolarized Heavy Flavor Production at Asymptotic Values Q^2 >> m^2

Abstract

We calculate the $O({\alpha }_s^2)$ massive operator matrix elements for the twist--2 operators, which contribute to the heavy flavor Wilson coefficients in unpolarized deeply inelastic scattering in the region $Q^2\gg m^2$. The calculation has been performed using light--cone expansion techniques. We confirm an earlier result obtained in \cite{Buza:1995ie}. The calculation is carried out without using the integration-by-parts method and in Mellin space using harmonic sums, which lead to a significant compactification of the analytic results derived previously. The results allow to determine the heavy flavor Wilson coefficients for $F_2(x,Q^2)$ to $O({\alpha }_s^2)$ and for $F_L(x,Q^2)$ to $O({\alpha }_s^3)$ for all but the power suppressed terms $\propto (m^2/Q^2{)}^k,k\ge 1$.

1 style file, 5 figures, 38 pages latex

References in corpus (28)

• Harmonic sums, Mellin transforms and Integrals
• Automatized analytic continuation of Mellin-Barnes integrals
• The third-order QCD corrections to deep-inelastic scattering by photon exchange
• Harmonic Sums and Mellin Transforms up to two-loop Order
• The 3-loop QCD calculation of the moments of deep inelastic structure functions
• Deep Inelastic Structure Functions at two Loops
• Heavy quark coefficient functions at asymptotic values $Q^2\gg m^2$
• The Longitudinal Structure Function at the Third Order
• Algebraic Relations Between Harmonic Sums and Associated Quantities
• Rates for Inclusive Deep-Inelastic Electroproduction of Charm Quarks at HERA
• Some higher moments of deep inelastic structure functions at next-to-next-to leading order of perturbative QCD
• Non--Singlet QCD Analysis of Deep Inelastic World Data at \boldmath $O({\alpha }_s^3)$
• Analytic Continuation of Mellin Transforms up to two-loop Order
• The Evolution of Unpolarized Singlet Structure Functions at Small x
• On the Twist 2 and Twist 3 Contributions to the Spin-dependent Electroweak Structure Functions
• The massless two-loop two-point function
• The Longitudinal Heavy Quark Structure Function F_{L}^{Q\bar{Q}} in the Region Q^2 \gg m^2 at O(α_s^3)
• Analytic Continuation of the Harmonic Sums for the 3--Loop Anomalous Dimensions
• Mellin Moments of the Next-to-next-to Leading Order Coefficient Functions for the Drell-Yan Process and Hadronic Higgs-Boson Production
• Mellin Representation for the Heavy Flavor Contributions to Deep Inelastic Structure Functions
• $O({\alpha }_s^2)$ Timelike Wilson Coefficients for Parton-Fragmentation Functions in Mellin Space
• The 16th Moment of the Non--Singlet Structure Functions $F_2(x,Q^2)$ and $F_L(x,Q^2)$ to $O({\alpha }_s^3)$
• The evolution of parton distributions beyond leading order: the singlet case
• Parton Distributions: Summary Report
• Calculation of Massive 2-Loop Operator Matrix Elements with Outer Gluon Lines
• Universal Higher Order QED Corrections to Polarized Lepton Scattering
• Evaluating Two-Loop massive Operator Matrix Elements with Mellin-Barnes Integrals
• Mathematical Structure of Anomalous Dimensions and QCD Wilson Coefficients in Higher Order

Cited by in corpus (77)

• Parton distribution functions and benchmark cross sections at NNLO
• The 3-, 4-, and 5-flavor NNLO Parton from Deep-Inelastic-Scattering Data and at Hadron Colliders
• The ABM parton distributions tuned to LHC data
• Mellin Moments of the {$O({\alpha }_s^3$)} Heavy Flavor Contributions to unpolarized Deep-Inelastic Scattering at $Q^2\gg m^2$ and Anomalous Dimensions
• b-Initiated processes at the LHC: a reappraisal
• Structural Relations of Harmonic Sums and Mellin Transforms up to Weight w = 5
• A Critical Appraisal and Evaluation of Modern PDFs
• Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra
• The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for the Structure Function $F_2(x,Q^2)$ and Transversity
• The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function $F_2(x,Q^2)$ and the Anomalous Dimension
• The Theory of Deeply Inelastic Scattering
• The Gluonic Operator Matrix Elements at O(α_s^2) for DIS Heavy Flavor Production
• The O(α_s^3) Massive Operator Matrix Elements of O(n_f) for the Structure Function F_2(x,Q^2) and Transversity
• Hadron structure in high-energy collisions
• Two--Loop Massive Operator Matrix Elements for Unpolarized Heavy Flavor Production to $O(ε)
• Heavy-quark deep-inelastic scattering with a running mass
• Iterated Binomial Sums and their Associated Iterated Integrals
• The Transition Matrix Element A_{gq}(N) of the Variable Flavor Number Scheme at O(α_s^3)
• Precise charm-quark mass from deep-inelastic scattering
• General-mass treatment for deep inelastic scattering at two-loop accuracy
• Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms
• Modern Summation Methods and the Computation of 2- and 3-loop Feynman Diagrams
• Massive 3-loop Ladder Diagrams for Quarkonic Local Operator Matrix Elements
• Determining the closed forms of the $O(a_s^3)$ anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra
• On the next-to-next-to-leading order QCD corrections to heavy-quark production in deep-inelastic scattering
• The Logarithmic Contributions to the O(α_s^3) Asymptotic Massive Wilson Coefficients and Operator Matrix Elements in Deeply Inelastic Scattering
• The $O({\alpha }_s^3{n}_f{T}_F^2{C}_{A,F})$} Contributions to the Gluonic Massive Operator Matrix Elements
• A Symbolic Summation Approach to Feynman Integral Calculus
• The Three-Loop Splitting Functions $P_{qg}^{(2)}$ and $P_{gg}^{(2,N_F)}$
• The $O({\alpha }_s^2)$ Heavy Quark Corrections to Charged Current Deep-Inelastic Scattering at large Virtualities
• The O(α_s^3 T_F^2) Contributions to the Gluonic Operator Matrix Element
• Three Loop Massive Operator Matrix Elements and Asymptotic Wilson Coefficients with Two Different Masses
• Higher Twist Contributions to the Structure Functions F_2^p(x,Q^2) and F_2^d(x,Q^2) at Large x and Higher Orders
• Two-loop QED Operator Matrix Elements with Massive External Fermion Lines
• Analytic Computing Methods for Precision Calculations in Quantum Field Theory
• The 3-Loop Non-Singlet Heavy Flavor Contributions to the Structure Function g_1(x,Q^2) at Large Momentum Transfer
• $O({\alpha }_s^2)$ and $O({\alpha }_s^3)$ Heavy Flavor Contributions to Transversity at $Q^2\gg m^2$
• $O({\alpha }_s)$ Heavy Flavor Corrections to Charged Current Deep-Inelastic Scattering in Mellin Space
• The two-mass contribution to the three-loop pure singlet operator matrix element
• The effect on PDFs and ${\alpha }_S(M_Z^2)$ due to changes in flavour scheme and higher twist contributions
• Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order epsilon-expansion of generalized hypergeometric functions with one half-integer value of parameter
• Higher order QCD corrections to charged-lepton deep-inelastic scattering and global fits of parton distributions
• The Variable Flavor Number Scheme at Next-to-Leading Order
• Probing the dark photon via polarized DIS scattering at the HERA and EIC
• The N${}^3$LO Scheme-invariant QCD Evolution of the Non-singlet Structure Functions \boldmath $F_2^{\mathrm{NS}}(x,Q^2)$ and $g_1^{\mathrm{NS}}(x,Q^2)$
• The Polarized Transition Matrix Element $A_{gq}(N)$ of the Variable Flavor Number Scheme at $O({\alpha }_s^3)$
• The Two-mass Contribution to the Three-Loop Gluonic Operator Matrix Element $A_{gg,Q}^{(3)}$
• The Polarized Two-Loop Massive Pure Singlet Wilson Coefficient for Deep-Inelastic Scattering
• On the Perturbative Stability of the QCD Predictions for the Ratio $R=F_L/F_T$ in Heavy-Quark Leptoproduction
• The Unpolarized and Polarized Single-Mass Three-Loop Heavy Flavor Operator Matrix Elements $A_{gg,Q}$ and $\Delta A_{gg,Q}$
• Advanced Computer Algebra Algorithms for the Expansion of Feynman Integrals
• Determination of the charm-quark mass in the MS-bar scheme using charm production data from deep inelastic scattering at HERA
• The Logarithmic Contributions to the Polarized and Operator Matrix Elements in Deeply Inelastic Scattering
• Structural Relations between Harmonic Sums up to w=6
• The Two-mass Contribution to the Three-Loop Polarized Operator Matrix Element $A_{gg,Q}^{(3)}$
• Charm Production and QCD Analysis at HERA and LHC
• The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals
• The unpolarized two-loop massive pure singlet Wilson coefficients for deep-inelastic scattering
• $O({\alpha }_s^2$) Polarized Heavy Flavor Corrections}to Deep-Inelastic Scattering at $Q^2\gg m^2$
• Heavy-flavor PDF evolution and variable-flavor number scheme uncertainties in deep-inelastic scattering
• The Two-Loop Massless Off-Shell QCD Operator Matrix Elements to Finite Terms
• Difference Equations in Massive Higher Order Calculations
• The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$
• First $O({\alpha }_s^3)$ heavy flavor contributions to deeply inelastic scattering
• Heavy Flavor DIS Wilson coefficients in the asymptotic regime
• Three-Loop Contributions to the Gluonic Massive Operator Matrix Elements at General Values of N
• Benchmark of deep-inelastic-scattering structure functions at $\mathcal{O}({\alpha }_s^3)$
• General mass variable flavor number scheme for $Z$ boson production in association with a heavy quark at hadron colliders
• Structural Relations between Nested Harmonic Sums
• Resummation of large logarithms in the heavy quark effects on the parton distributions inside the virtual photon
• Z-Sum Approach to Loop Integrals using Taylor Expansion
• Photon Structure Function in Supersymmetric QCD Revisited
• Proton structure at the LHC
• The QCD Coupling and Parton Distributions at High Precision
• Status of Deeply Inelastic Parton Distributions
• Summary of the Heavy Flavor Working Group
• IRC-safe jet flavour at leading power