Comparing efficient computation methods for massless QCD tree amplitudes: Closed analytic formulas versus Berends-Giele recursion

Jun, 2012
13 pages
Published in:
  • Phys.Rev.D 87 (2013) 3, 034011
  • Published: Feb 6, 2013
e-Print:
Report number:
  • HU-EP-12-16

Citations per year

20122015201820212024012345
Abstract: (APS)
Recent advances in our understanding of tree-level QCD amplitudes in the massless limit exploiting an effective (maximal) supersymmetry have led to the complete analytic construction of tree amplitudes with up to four external quark-antiquark pairs. In this work we compare the numerical efficiency of evaluating these closed analytic formulas to a numerically efficient implementation of the Berends-Giele recursion. We compare calculation times for color-ordered tree amplitudes with parton numbers ranging from 4 to 25 with no, one, two, and three external quark lines. We find that the analytic results are generally faster in the case of maximally helicity-violating and next-to-maximally helicity-violating amplitudes. Starting with the next-to-next-to-maximally helicity-violating amplitudes the Berends-Giele recursion becomes more efficient. In addition to the runtime we also compare the numerical accuracy. The analytic formulas are on average more accurate than the off-shell recursion relations, though both are well-suited for complicated phenomenological applications. In both cases we observe a reduction in the average accuracy when phase-space configurations close to singular regions are evaluated. In summary, our findings show that for up to nine gluons the closed analytic formulas perform best.
Note:
  • 22 pages, 9 figures, Mathematica package GGT.m and example notebook is included in submission
  • 12.38.Bx
  • quantum chromodynamics: scattering amplitude
  • quantum chromodynamics: massless
  • quark antiquark: pair
  • tree approximation
  • numerical calculations