integration_contour Class Reference

Static Public Member Functions
static double	nonsinglet (const partondistribution &f, double Q, double x, double u)
static vector_d	singlet (const partondistribution &s, const partondistribution &g, double Q, double x, double u)
static vector_d	singlet_with_qed (const partondistribution &Delta, const partondistribution &s, const partondistribution &g, const partondistribution &phot, const partondistribution &lept, double Q, double x, double u)

Detailed Description

This class provides some helper methods to perform numerically an inverse Mellin transform along a parabolic contour.

This method returns

$\frac{c_2}{2 \pi} \mbox{Re}\; \left( e^u \left( 1 - i c_2 c_3 \sqrt{u} \right) EF(x,z) \right)$

where

$z = c_0 + i c_2 \sqrt{u} + \frac{1}{2} c_2^2 c_3 u,$

$c_2 = \sqrt{\frac{2 F F''}{F''^2 - F' F'''}},$

$c_3 = \frac{F'''}{3 F''},$

$F(x,z) = x^{-z} \sum\limits_{i=0}^{n-1} A_i B(z+\alpha_i-1,1+\beta_i),$

$EF(x,z) = x^{-z} E^z(Q^2,Q_0^2) \sum\limits_{i=0}^{n-1} A_i B(z+\alpha_i-1,1+\beta_i),$

and $c_0$ is the minimum of $F$ on the real axis right to the rightmost pole.

Same as integration_contour::nonsinglet, but now for the singlet case.

Same as integration_contour::singlet, but now with the inclusion of QED effects.

The documentation for this class was generated from the following files: