Abstract
We complete the analytic calculation of the full set of two-loop Feynman integrals required for computation of massless five-particle scattering amplitudes. We employ the method of canonical differential equations to construct a minimal basis set of transcendental functions, pentagon functions, which is sufficient to express all planar and nonplanar massless five-point two-loop Feynman integrals in the whole physical phase space. We find analytic expressions for pentagon functions which are manifestly free of unphysical branch cuts. We present a public library for numerical evaluation of pentagon functions suitable for immediate phenomenological applications.
Highlights
Scattering amplitudes are among the central objects of interest in quantum field theories (QFT)
We employ the method of canonical differential equations to construct a minimal basis set of transcendental functions, pentagon functions, which is sufficient to express all planar and nonplanar massless five-point two-loop Feynman integrals in the whole physical phase space
Approaching the surface ∆ = 0 from the opposite sides — δ > 0 and δ < 0 — inside any physical channel, we find a discontinuity in the parity-odd uniform transcendental (UT) master integrals if they do not vanish at ∆ = 0
Summary
Scattering amplitudes are among the central objects of interest in quantum field theories (QFT). Differential equations in canonical form provide a natural framework for expressing master integrals in terms of functions of uniform transcendental (UT) weight order by order in the dimensional regulator It is advantageous, both for analyzing analytic structure of scattering amplitudes and for their efficient numerical evaluations, to have a good grasp on the analytic understanding of the relevant space of transcendental function. Finding a minimal set of transcendental functions that is sufficient to express all master integrals is essential for deriving compact analytic representations of scattering amplitudes and studying their asymptotic behavior in singular limits (soft, collinear, high-energy, etc.). We construct a basis set of pentagon functions that is sufficient to express all planar and nonplanar massless five-point two-loop master integrals in any physical scattering channel.
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