| from mpmath import mp | |
| mp.dps = 110 | |
| def sunset_2d(m1, m2, m3, s): | |
| m1 = mp.mpf(m1) | |
| m2 = mp.mpf(m2) | |
| m3 = mp.mpf(m3) | |
| s = mp.mpf(s) | |
| m1sq = m1 * m1 | |
| m2sq = m2 * m2 | |
| m3sq = m3 * m3 | |
| def F(x1, x2, x3): | |
| U = x1 * x2 + x2 * x3 + x3 * x1 | |
| A = m1sq * x1 + m2sq * x2 + m3sq * x3 | |
| return A * U - s * x1 * x2 * x3 | |
| def integrand(u, v): | |
| # Map unit square (u,v) -> simplex via: | |
| # x1 = u*(1-v), x2 = u*v, x3 = 1-u, Jacobian = u | |
| x1 = u * (1 - v) | |
| x2 = u * v | |
| x3 = 1 - u | |
| return u / F(x1, x2, x3) | |
| with mp.extradps(40): | |
| # Use native 2D quadrature (faster than nested 1D quad) | |
| val = mp.quad(integrand, [0, 1], [0, 1]) | |
| # Standard D=2 normalization from Feynman parameters: | |
| # I = 1/(4*pi)^(L*D/2) * integral, with L=2, D=2 -> 1/(4*pi)^2 | |
| val *= 1 / (4 * mp.pi) ** 2 | |
| return mp.re(val) | |
| def compute(): | |
| # Representative "generic masses" and a nontrivial kinematic point below threshold: | |
| # m1=1, m2=2, m3=3, threshold s_th=(1+2+3)^2=36, choose s=30 | |
| return sunset_2d(1, 2, 3, 30) | |
| if __name__ == "__main__": | |
| print(str(compute())) |