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848d4b7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 | 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())) |