BCFW recursion for TMD parton scattering

Abstract

Abstract:We investigate the application of the BCFW recursion relation to scattering amplitudes with one off-shell particle in a Yang-Mills theory with fermions. We provide a set of conditions of applicability of the BCFW recursion, stressing some important differences with respect to the pure on-shell case. We show how the formulas for Maximally-HelicityViolating (MHV) configurations with any number of partons, which are well known in the fully on-shell case, are generalized to this kinematic regime. We also derive analytic expressions for all the helicity configurations of the 5-point color-stripped tree-level amplitudes for any of the partons being off the mass shell.

Angular correlations in pair production at the LHC in the parton Reggeization approach

“…Also it has been verified, that in the collinear limit q (1,2)T → 0, squared amplitudes (1) and (3) transform to the squared amplitudes of the corresponding parton subprocesses in the CPM after averaging over the azimuthal angles. Additionally, we have compared our results for the both squared amplitudes numerically with the results obtained from the Monte-Carlo generator Katie [20], which is based on the recently suggested scheme to obtain gaugeinvariant matrix elements in the k T −factorization by exploiting the spinor-helicity representation and recursion relations for the tree-level amplitudes [21,22].…”

Off-shell amplitudes and four-jet production inkT-factorization

“…If a complete calculation of 4-jet production in k T factorization was still missing in the literature, it was mainly because computing gauge-invariant amplitudes with off-shell legs is definitely non trivial. Techniques to compute such amplitudes in gauge invariant ways are by now analytically and numerically well established [3][4][5].…”

“…Using a proper generalisation of the Britto-Cachazo-Feng-Witten recursion relation [1,2] for on-shell QCD amplitudes, we can recursively compute fully gauge-invariant amplitudes with initial state offshell particle both analytically [3,4] and numerically [5] and use them to assess both the Single Parton Scattering and Double Parton Scattering contributions to four-jet production. This allows us to expand the analysis of Ref.…”

Progress in off-shell amplitudes

“…This spinor inherits the opposite helicity of the on-shell end of the spinor line. In [13] it is shown how to calculate amplitudes with off-shell quarks and/or anti-quarks via on-shell recursion. One observation worth highlighting was that the recursion may involve intermediate amplitudes with off-shell gluons, also when the original amplitude to be calculated does not involve any.…”