/* This file calculates the pion wavefunction. */

/**************************************************************************/
/*                                                                        */
/* IMPORTANT : all dimensional quantities in this program                 */
/*             are in units GeV                                           */  
/*                                                                        */
/**************************************************************************/


#include <pion_wavefunction.h>

/* the function pion_distribution_ampl() returns the 
   asymptotic pion distribution amplitude 
   as function of the quark longitudinal momentum fraction x */

double pion_distribution_ampl(double x)
{
     return sqrt(3.) * F_PI * x * (1. - x);     
}


/* The function pion_wavef_impactpar() returns the pion wavefunction 
   as function of the quark longitudinal momentum fraction x and 
   as function of the transverse distance b (in GeV^-1)
   between the quark and antiquark. 
   To model the transverse momentum dependence, a gaussian ansatz is used. */

double pion_wavef_impactpar(double x, double b)
{
     double pi_avmom_sqr;

     pi_avmom_sqr = 8. * pow(PI * F_PI,2.);  /* average squared transverse 
                                                quark momentum in pion 
                                                wavefunction in units GeV^2 */
   
     return 4. * PI * pion_distribution_ampl(x) 
            * exp(- .5 * pi_avmom_sqr * x * (1. - x) * pow(b,2.));        
}


/* The function pion_wavef_momspace() returns the pion wavefunction 
   in momentum space as function of 
   the quark longitudinal momentum fraction x and as function of 
   the transverse momentum k_perp between the quark and antiquark. 
   To model the transverse momentum dependence, a gaussian ansatz is used. */

double pion_wavef_momspace(double x, double k_perp)
{
     double pi_avmom_sqr;

     pi_avmom_sqr = 8. * pow(PI * F_PI,2.);  /* average squared transverse 
                                                quark momentum in pion 
                                                wavefunction in units GeV^2 */
 
     return 8. * pow(PI,2.) / pi_avmom_sqr
            * pion_distribution_ampl(x) / (x * (1. - x)) 
            * exp(- .5 * pow(k_perp,2.)/(pi_avmom_sqr * x * (1. - x)) );
        
}