Double_t tpileup_mich(Double_t *t, Double_t *par) // Michel pileup 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 T = 19.75;         // rf Period, ns

   if ( t[0] > pg_start && t[0] < pg_close ) {
     for (int n= -500; n<11; n++ ) {  // 5 muon lifetimes into past
       if ( t[0]>n*T )                // causality
       yield+ = exp( (-t[0]+n*T)/tau_mu) - exp( (-t[0] + n*T)/tau_pi); } // end for
     return par[0]*yield; } // end if
    else 
      return yield ;
 }