I want to plot the definite integral of the following function
Integrand[p_, Q2_, ν_, θ_] := p^2/(M^2 (M - 2*E3[p])^2)
1/(E3[p] E4[p, Q2, ν, θ]) 1/D[f[p, Q2, ν, θ], p]
DiracDelta[p - p3zero1[Q2, ν, θ]]+p^2/(M^2 (M - 2*E3[p])^2)
1/(E3[p] E4[p, Q2, ν, θ]) 1/D[f[p, Q2, ν, θ], p]
DiracDelta[p - p3zero2[Q2, ν, θ]]
Where the integration over p
runs from 0
to Infinity
and the integration over θ
runs from 0
to Pi
. The definitions of p3zero1
and p3zero2
are bad enough that I can't analytically integrate the function and I don't know a priori if they are always greater or smaller than 0 for all points on the integration region. I then came up with the following code to plot it.
Plot3D[NIntegrate[Integrand[p, Q2, ν, θ], {p, 0, Infinity},
{θ, 0, π}], {Q2, 0, 5000}, {ν, 0, 2000}]
The problem that I'm facing is that the Dirac delta function is not defined for numerical integrals. Numerical integrations of Dirac deltas appear to always return 0. But I need a way to plot the function in terms of Q2
and ν
.
Thanks.