Double_t dif_p2e_t(Double_t *t, Double_t *par) // decay-in-flight p2e pdf 
 { 
   double yield = 0.;
   double tau_pi = 26.03;
   double tau_mu = 2197.;
   double pg_start = -69.70; // opening of PiGate
   double pg_close = 222.50; // closing of PiGate
   double sigma = 1.;        // gate edge resolution, ns

   if ( t[0] > 0 && t[0] < pg_close ) {
       if ( t[0]>0. )                // causality
       yield = exp( -t[0]/tau_mu);
       return par[0]*yield; } // end if
   else if ( t[0] < 0 && fabs(t[0] )< 3*sigma ) {
     yield = exp(0./tau_mu)*
             exp( -0.5*t[0]*t[0]/(sigma*sigma) );
       return par[0]*yield; } // end else if
   else if ( t[0] > pg_close && fabs(t[0]- pg_close )< 3*sigma ) {
     yield = exp(0./tau_mu)*
       exp( -0.5*( t[0] -pg_close )*( t[0] - pg_close ) /(sigma*sigma) );
       return par[0]*yield; } // end else if
    else 
      return yield ;
}