I.1)

- number fo events:

Main:numberOfEvents = 1000

- beam type:

Beams:idA = 2212                   ! first beam, p = 2212, pbar = -2212
Beams:idB = 2212                   ! second beam, p = 2212, pbar = -2212

- center of mass energy:

Beams:eCM = 14000.

- physics process

Top:gg2ttbar = on                  ! g g -> t tbar
Top:qqbar2ttbar = on               ! q qbar -> t tbar


I.2)

Pythia8 card: examples/Pythia8/config_ee_zh_zmumu.cmd

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Main:numberOfEvents = 10000         ! number of events to generate

Beams:idA = 11                   ! first beam, e- = -11
Beams:idB = -11                  ! second beam, e+ = 11
Beams:eCM = 240.                 ! CM energy of collision

! Higgsstrahlung process
HiggsSM:ffbar2HZ = on

! 5) Force the Z decays to muons
23:onMode = off
23:onIfAny = 13 -13

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

I.3)

./DelphesPythia8 cards/delphes_card_CEPC.tcl examples/Pythia8/config_ee_zh_zmumu.cmd delphes_ee_zh_zmumu.root


II.2)

Delphes->Draw("Muon_size");
Delphes->Draw("Jet_size");

III.1)

m_recoil = sqrt( (sqrt(s) - E_ll)^2 - p_ll^2 )

III.2)

# Recoil Mass macro
#!/usr/bin/env python

import sys
import ROOT

if len(sys.argv) < 2:
  print " Usage: python examples/MissingMass.py delphes_ee_zh_zmumu.root hist_mrec.root"
  sys.exit(1)

ROOT.gSystem.Load("libDelphes")

try:
  ROOT.gInterpreter.Declare('#include "classes/SortableObject.h"')
  ROOT.gInterpreter.Declare('#include "classes/DelphesClasses.h"')
  ROOT.gInterpreter.Declare('#include "external/ExRootAnalysis/ExRootTreeReader.h"')
except:
  pass

inputFile = sys.argv[1]
outputFile = sys.argv[2]

# Create chain of root trees
chain = ROOT.TChain("Delphes")
chain.Add(inputFile)

# Create object of class ExRootTreeReader
treeReader = ROOT.ExRootTreeReader(chain)
numberOfEntries = treeReader.GetEntries()

# Get pointers to branches used in this analysis
branchMuon = treeReader.UseBranch("Muon")

# Book histograms
histMass = ROOT.TH1F("mass", "M_{recoil} [GeV]", 60, 100.0, 160.0)

ptot = ROOT.TLorentzVector(0.,0.,0.,240.)
# Loop over all events
for entry in range(0, numberOfEntries):
  # Load selected branches with data from specified event
  treeReader.ReadEntry(entry)

  # If event contains at least 2 muons
  if branchMuon.GetEntries() > 1:

    mu1 = branchMuon.At(0)
    mu2 = branchMuon.At(1)

    pll = mu1.P4() + mu2.P4()
    ph = ptot - pll

    histMass.Fill(ph.M())

out_root = ROOT.TFile(outputFile,"RECREATE")
histMass.Write()


IV.1)

The two parameters are the muon momentum resolution and the reconstruction efficiency.
One can for instance worsen both of them by replacing the existing parameterisations by:

IV.2)

The relevant modules are called "MuonMomentumSmearing" and "MuonTrackingEfficiency"

IV.3)


###############################
# Momentum resolution for muons
###############################

module MomentumSmearing MuonMomentumSmearing {
  set InputArray MuonTrackingEfficiency/muons
  set OutputArray muons

  # set ResolutionFormula {resolution formula as a function of eta and pt}

   # resolution formula for charged hadrons
  set ResolutionFormula {    (abs(eta) <= 1.0)                   * 10 * sqrt(0.001^2 + pt^2*1.e-5^2) +
                             (abs(eta) > 1.0 && abs(eta) <= 3.0) * 10 * sqrt(0.01^2 + pt^2*1.e-4^2)}

}

##########################
# Muon tracking efficiency
##########################

module Efficiency MuonTrackingEfficiency {
  set InputArray ParticlePropagator/muons
  set OutputArray muons

  # set EfficiencyFormula {efficiency formula as a function of eta and pt}

  # tracking efficiency formula for muons
  set EfficiencyFormula {                                                    (pt <= 0.1)   * (0.00) +
                                           (abs(eta) <= 3.0)               * (pt > 0.1)    * (0.80) +
                                           (abs(eta) >  3.0)                               * (0.00)}
}


IV.4)

./DelphesPythia8 cards/delphes_card_CEPC_mod.tcl examples/Pythia8/config_ee_zh_zmumu.cmd delphes_ee_zh_zmumu_mod.root
./DelphesPythia8 cards/delphes_card_CEPC_mod2.tcl examples/Pythia8/config_ee_zh_zmumu.cmd delphes_ee_zh_zmumu_mod2.root


root -l hist_mrec.root hist_mrec_mod.root hist_mrec_mod2.root

((TH1F *)_file0->Get("mass"))->SetLineColor(kGreen+1);
((TH1F *)_file1->Get("mass"))->SetLineColor(kBlue);
((TH1F *)_file2->Get("mass"))->SetLineColor(kRed);

((TH1F *)_file0->Get("mass"))->SetLineWidth(3);
((TH1F *)_file1->Get("mass"))->SetLineWidth(3);
((TH1F *)_file2->Get("mass"))->SetLineWidth(3);

_file0->Get("mass")->Draw();
_file1->Get("mass")->Draw("SAME");
_file2->Get("mass")->Draw("SAME");