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:
- 1206.2381 [hep-ph]
Report number:
- HU-EP-12-16
View in:
Citations per year
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
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