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HELAS and MadGraph/MadEvent with spin-2 particles

Kaoru Hagiwara, Junichi Kanzaki, Qiang Li, Kentarou Mawatari

TL;DR

The work extends the HELAS library with a complete set of subroutines for massive spin-2 gravitons, enabling automatic generation of graviton production and decay amplitudes within MadGraph/MadEvent. It introduces tensor wavefunctions and a broad suite of vertices (SST, FFT, VVT, FFVT, VVVT, VVVVT) with couplings scaled by the relevant energy scale, and handles the challenging 5-point VVVT/HVVVT structures by hand for MG compatibility. The authors implement ADD and RS graviton models, integrate the new HELAS routines, and modify MG/ME to handle external spin-2 states and KK summation, validating the approach via gauge and general-coordinate invariance tests. They demonstrate practical LHC phenomenology with graviton-plus-jet signatures, illustrating the method's utility for extra-dimension studies and collider predictions.

Abstract

Fortran subroutines to calculate helicity amplitudes with massive spin-2 particles (massive gravitons), which couple to the standard model particles via the energy momentum tensor, are added to the {\tt HELAS} ({\tt HEL}icity {\tt A}mplitude {\tt S}ubroutines) library. They are coded in such a way that arbitrary scattering amplitudes with one graviton production and its decays can be generated automatically by {\tt MadGraph} and {\tt MadEvent}, after slight modifications. All the codes have been tested carefully by making use of the invariance of the helicity amplitudes under the gauge and general coordinate transformations.

HELAS and MadGraph/MadEvent with spin-2 particles

TL;DR

The work extends the HELAS library with a complete set of subroutines for massive spin-2 gravitons, enabling automatic generation of graviton production and decay amplitudes within MadGraph/MadEvent. It introduces tensor wavefunctions and a broad suite of vertices (SST, FFT, VVT, FFVT, VVVT, VVVVT) with couplings scaled by the relevant energy scale, and handles the challenging 5-point VVVT/HVVVT structures by hand for MG compatibility. The authors implement ADD and RS graviton models, integrate the new HELAS routines, and modify MG/ME to handle external spin-2 states and KK summation, validating the approach via gauge and general-coordinate invariance tests. They demonstrate practical LHC phenomenology with graviton-plus-jet signatures, illustrating the method's utility for extra-dimension studies and collider predictions.

Abstract

Fortran subroutines to calculate helicity amplitudes with massive spin-2 particles (massive gravitons), which couple to the standard model particles via the energy momentum tensor, are added to the {\tt HELAS} ({\tt HEL}icity {\tt A}mplitude {\tt S}ubroutines) library. They are coded in such a way that arbitrary scattering amplitudes with one graviton production and its decays can be generated automatically by {\tt MadGraph} and {\tt MadEvent}, after slight modifications. All the codes have been tested carefully by making use of the invariance of the helicity amplitudes under the gauge and general coordinate transformations.

Paper Structure

This paper contains 35 sections, 122 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. HELAS subroutines for spin-2 particles
  3. Tensor wavefunction
  4. TXXXXX
  5. SST vertex
  6. SSTXXX
  7. HSTXXX
  8. USSXXX
  9. FFT vertex
  10. IOTXXX
  11. FTIXXX
  12. FTOXXX
  13. UIOXXX
  14. VVT vertex
  15. VVTXXX
  16. ...and 20 more sections

Figures (2)

  • Figure 1: $P^{{\rm miss}}_T$ dependence of the total cross sections for the graviton productions with 1-jet (via the $gg$, $qg$ and $q\bar{q}$ channels) and 2-jets (via the $gg$, $qg$ and $qQ$ channels) in the ADD model at the LHC, where $q,Q=u,d,s,c$.
  • Figure 2: Distributions of the azimuthal angle separation between the two jets for the first KK graviton plus di-jet productions in the RS model at the LHC, via the $gg$, $qg$ and $qQ$ channels ($q,Q=u,d,s,c$).