The three-loop ratio function
Computer-readable files associated with the paper
"Bootstrapping an NMHV amplitude through three loops''
arXiv:1408.1505
by Lance Dixon and Matt von Hippel

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Symbol

The symbol of the three-loop parity-even function V3 has 19,986 terms (gzipped): V3_symb.gz

The symbol of the three-loop parity-odd function Vt3 has 16,402 terms (gzipped): Vt3_symb.gz

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Coproduct Representation

The independent {5,1} coproduct components of V3, in terms of the weight-5 hexagon function basis in arXiv:1308.2276: VVt3_coprod

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Near collinear limit

The expansion of V3 and Vt3 in the near collinear limit w -> 0, as a function of T, F and S, through order T^2 (gzipped): V_T2.wl.gz

The expansion of V3 and Vt3 in the near collinear limit v -> 0, as a function of T, F and S, through order T^3, in a different format (gzipped): V_T3.gz

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Near collinear/soft limits

The expansion of V3 and Vt3 in the near collinear limit v -> 0, as a function of T, F and S, through order T^5, but also expanded around S=0 (gzipped): V3_TS.gz

Same order T^5 expansion for the two-loop functions V2 and Vt2 (gzipped): V2_TS.gz

The advantage of these formulas is that all the harmonic polylogarithms (HPLs) are gone, there are only T, S, F, lnT = ln(T), lnS = ln(S), and the Riemann zeta values z2, z3, z4, z5 and z6. And a lot of big rational numbers.

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Multi-Regge limit

The transcendental functions p_n^{(L)} and q_n^{(L)} are given through three loops in terms of single-valued harmonic polylogarithms (SVHPLs) NMHVMRK.m

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Similar files for the four-loop remainder function

and the four-loop ratio function