Double_t single_mich_t(Double_t *t, Double_t *par) // single Michel 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 = 2;         // gate edge resolution, ns

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