Numerical integration of one-loop Feynman diagrams for N-photon amplitudes

By Zoltán Nagy, Davison E. Soper. 2006

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In the calculation of cross sections for infrared-safe observables in high energy collisions at nextto-leading order, one approach is to perform all of the integrations, including the virtual loop integration, numerically. One would use a subtraction scheme that removes infrared and collinear divergences from the integrand in a style similar to that used for real emission graphs. Then one would perform the loop integration by Monte Carlo integration along with the integrations over final state momenta. In this paper, we explore how one can perform the numerical integration. We study the N-photon scattering amplitude with a massless electron loop in order to have a case with a singular integrand that is not, however, so singular as to require the subtractions. We report results for N = 4, N = 5 with left-handed couplings, and N = 6.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/35db909e8af1f3be2a0165d73892f0225becee62

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In Nuclear and High Energy Physics

Citations in the corpus

Loop amplitudes in gauge theories: modern analytic approaches (2010, result): “Both analytic forms confirmed the numerical results of [101].”
Sector Decomposition (2008, methodology): “We explain the general algorithm in detail and review its application to multi-loop Feynman parameter integrals as well as infrared divergent phase-space integrals over real radiation matrix elements.”
On the characterisation of the underlying event (2009, background): “ref. [14]), or because they can have a common origin from an initial-state collinear splitting, as in figure 1b. However the contribution of figure 1b is itself also part of the 2 → 4 1-loop scattering diagram figure 1c (as discussed for example in [ 15 ]), which is relevant as a N 4 LO correction t”
Collider physics at the precision frontier (2020, background): “ iin eq. (28), tells us that the contour deformation into the complex plane should be such that the imaginary part of Fis negative. For real masses and Mandelstam invariants sij, the following Ansatz[775, 789, 787, 886{888] is therefore convenient: zk(~x) = xk i˝k(~x) ;˝k= xk(1 xk) @F(~x) @xk : (63)”