Conservative binary dynamics to third post-Minkowskian order beyond General Relativity

Ancillary file for the paper "Conservative binary dynamics to third Post-Minkowskian order beyond General Relativity" by G. L. Almeida, Y. Du, Z. Liu and H. Wang. This file contains machine-readable expressions for: - The 3PM impulse expanded according to eq. (9); - Scattering angle, as in eq. (12); - Coefficients c_n's and d_n's defined in eq. (9); - Polynomial functions sigma_i appearing in eq. (11) (Table I). We use the following notation for the variables used in this file: - m1, m2 are the masses of two particles, and u1 and u2 are respectively their initial velocities; - m = m1+m2 is the total mass; - nu = m1 m2/m^2 is the symmetric mass ratio, introduced below eq. (8); - s1, s2, sp1, sp2, spp1, spp2 are the sensitivities s1, s2, s1', s2', s1'', s2'', respectively, introduced in eq. (4); - y = \gamma = u1.u2, scalar product of initial velocities (we use the Minkowski metric eta=diag(1,-1,-1,-1)); - x = y - Sqrt[ y^2 - 1], the variable entering the Log[x]; - Gamma = \Gamma = E/m = Sqrt[1+2nu(y - 1)], introduced in eq. (8); - bHat = \hat{b}: normalized impact parameter, introduced in eq. (10); - w = w^\mu: linear combination of the initial velocities introduced eq. (10); - aGB is the Gauss-Bonnet coupling constant; - be = Sqrt[-b^2], absolute value of the impact parameter introduced below eq. (10); - J = (G m/be)^{-1}, the dimensionless impact parameter introduced in eq. (9); - sign is the sign of the term (2 y^2 - 1 + s1*s2) introduced below eq. (12); - f1 and f2 are the coefficients of the function f(\phi) introduced in eq. (5); - c1, c2, c3, d2, d3 are the coefficients c_n's and d_n's defined in eq. (9); - sig1, sig2, ..., are the coefficient polynomials sigma_i defined in Table I.