HELAS and MadGraph with goldstinos

Abstract

Fortran subroutines to calculate helicity amplitudes with goldstinos, which appear as the longitudinal modes of massive gravitinos in high energy processes, are added to the HELAS (HELicity Amplitude Subroutines) library. They are coded in such a way that arbitrary amplitudes with external goldstinos can be generated automatically by MadGraph, after slight modifications. All the codes have been tested carefully by making use of the goldstino equivalence theorem and the gauge invariance of the helicity amplitudes. Hadronic total cross sections for associated gravitino productions with a gluino and a squark are also presented.

Associated production of light gravitinos in e + e − and e − γ collisions

“…where the four-momentum (p i ) and helicity (λ i = ±1) of each particle are defined in the center-of-mass (CM) frame collisions, generated by MadGraph [22]. N1, gld, el, and er denote a lightest neutralino, a gravitino, a left-handed selectron, and a right-handed selectron, respectively.…”

“…Moreover, our analytic amplitudes are checked numerically for each helicity combination by using the gravitino/goldstino code in MG/ME [17,22].…”

“…In Table 2, the selection efficiencies for the signal and background processes with different polarizations 6 are presented, where the above kinematical cuts, (20) and (21), are taken into account. The cross sections both for the signal and background are calculated by MG/MEv4 [21] supporting gravitino interactions [17,22]. Here, we assume the branching ratio of the neutralino decay is unity, B(χ 0 1 → γG) = 1, although other decay modes can be significant in some parameter space [27].…”

“…(7) of [12] for the squark associated process qg →qG after substitutions for the masses and the couplings as in (16) and the exchange of t ↔ u. Moreover, we checked our amplitudes for each helicity combination numerically by the gravitino/goldstino code in MG/ME [17,22].…”

“…They are implemented in such a way that amplitudes with external gravitinos can be generated automatically by MG/ME. 2 Since goldstinos appear as the longitudinal modes of massive gravitinos and their interactions become dominant over the transverse modes in high-energy processes, two of the authors also implemented effective goldstino interactions [22] as an alternative to the gravitino code.…”