Threshold singularities, dispersion relations and fixed-order perturbative calculations

Abstract

We show how to correctly treat threshold singularities in fixed-order perturbative calculations of the electron anomalous magnetic moment and hadronic pair production processes such as top pair production. With respect to the former, we demonstrate the equivalence of the "non-perturbative", resummed treatment of the vacuum polarization contribution, whose spectral function exhibits bound state poles, with the fixed-order calculation by identifying a threshold localized term in the four-loop spectral function. In general, we find that a modification of the dispersion relation by threshold subtractions is required to make fixed-order calculations well-defined and provide the subtraction term. We then solve the apparent problem of a divergent convolution of the partonic cross section with the parton luminosity in the computation of the top pair production cross section starting from the fourth-order correction. We find that when the computation is performed in the usual way as an integral of real and virtual corrections over phase space at a given order in the expansion in the strong coupling, an additional contribution has to be added at N3LO.

15 pages, 3 figures

References in corpus (4)

• Parton distributions for the LHC
• The total top quark pair production cross-section at hadron colliders through O(alpha_S^4)
• Reconstruction of heavy quark current correlators at O(α_s^3)
• Inclusive top-pair production phenomenology with TOPIXS

Cited by in corpus (7)

• Top quark pair production near threshold: single/double distributions and mass determination
• Light-cone distribution amplitudes of light mesons with QED effects
• Soft-gluon and Coulomb corrections to hadronic top-quark pair production beyond NNLO
• Ambiguities of the principle of maximum conformality procedure for hadron collider processes
• Spin Correlations in $t\bar{t}$ Production and Decay at the LHC in QCD Perturbation Theory
• Nonintegrable threshold singularities of two-point functions in perturbation theory
• NNLO QCD corrections to $\gamma \gamma \to Q\bar{Q}$ from Local Unitarity combined with Coulomb resummation and NLO EW effects