the fluctuation of cross section

Asked by Heng-Yu Chen

Dear Madgraph experts,
                                               I want to calculate the cross section of standard charge current ve p > e- j in the SM. To be general, I turn off the cutoff of pt and rapidity. Below is my run card.

    When the beam energy is around 10^5 GeV x 10^5 GeV, running at the same energy for five times , the cross section fluctuates about 10-15%. But when I use the original settings for cutoff of pt and rapidity, the fluctuation becomes much smaller and is basically stable.

    Apparently the parameter space of integration is different. Is it because the fluctuation is due to the contribution of infrared divergence to the cross section when the cutoff is turned off? I am not quite sure what's the main reason for the fluctuation?
I really appreciate your help.

# Standard Cuts
#*******************
#
#*********************************************************************
# Minimum and maximum pt's (for max, -1 means no cut) *
#*********************************************************************
  0 = ptj ! minimum pt for the jets
  0 = ptb ! minimum pt for the b
  0 = pta ! minimum pt for the photons
  0 = ptl ! minimum pt for the charged leptons
  0 = misset ! minimum missing Et (sum of neutrino's momenta)
  0 = ptheavy ! minimum pt for one heavy final state
 1.0 = ptonium ! minimum pt for the quarkonium states
 -1 = ptjmax ! maximum pt for the jets
 -1 = ptbmax ! maximum pt for the b
 -1 = ptamax ! maximum pt for the photons
 -1 = ptlmax ! maximum pt for the charged leptons
 -1 = missetmax ! maximum missing Et (sum of neutrino's momenta)
#*********************************************************************
# Minimum and maximum E's (in the center of mass frame) *
#*********************************************************************
  0 = ej ! minimum E for the jets
  0 = eb ! minimum E for the b
  0 = ea ! minimum E for the photons
  0 = el ! minimum E for the charged leptons
 -1 = ejmax ! maximum E for the jets
 -1 = ebmax ! maximum E for the b
 -1 = eamax ! maximum E for the photons
 -1 = elmax ! maximum E for the charged leptons
#*********************************************************************
# Maximum and minimum absolute rapidity (for max, -1 means no cut) *
#*********************************************************************
  -1 = etaj ! max rap for the jets
  -1 = etab ! max rap for the b
  -1 = etaa ! max rap for the photons
  -1 = etal ! max rap for the charged leptons
 0.6 = etaonium ! max rap for the quarkonium states
   0 = etajmin ! min rap for the jets
   0 = etabmin ! min rap for the b
   0 = etaamin ! min rap for the photons
   0 = etalmin ! main rap for the charged leptons
#*********************************************************************
# Minimum and maximum DeltaR distance *
#*********************************************************************
 0.4 = drjj ! min distance between jets
 0 = drbb ! min distance between b's
 0.4 = drll ! min distance between leptons
 0.4 = draa ! min distance between gammas
 0 = drbj ! min distance between b and jet
 0.4 = draj ! min distance between gamma and jet
 0 = drjl ! min distance between jet and lepton
 0 = drab ! min distance between gamma and b
 0 = drbl ! min distance between b and lepton
 0 = dral ! min distance between gamma and lepton
 -1 = drjjmax ! max distance between jets
 -1 = drbbmax ! max distance between b's
 -1 = drllmax ! max distance between leptons
 -1 = draamax ! max distance between gammas
 -1 = drbjmax ! max distance between b and jet
 -1 = drajmax ! max distance between gamma and jet
 -1 = drjlmax ! max distance between jet and lepton
 -1 = drabmax ! max distance between gamma and b
 -1 = drblmax ! max distance between b and lepton
 -1 = dralmax ! maxdistance between gamma and lepton
#*********************************************************************
# Minimum and maximum invariant mass for pairs *
# WARNING: for four lepton final state mmll cut require to have *
# different lepton masses for each flavor! *
#*********************************************************************
 0 = mmjj ! min invariant mass of a jet pair
 0 = mmbb ! min invariant mass of a b pair
 0 = mmaa ! min invariant mass of gamma gamma pair
 0 = mmll ! min invariant mass of l+l- (same flavour) lepton pair
 -1 = mmjjmax ! max invariant mass of a jet pair
 -1 = mmbbmax ! max invariant mass of a b pair
 -1 = mmaamax ! max invariant mass of gamma gamma pair
 -1 = mmllmax ! max invariant mass of l+l- (same flavour) lepton pair
#*********************************************************************
# Minimum and maximum invariant mass for all letpons *
#*********************************************************************
 0 = mmnl ! min invariant mass for all letpons (l+- and vl)
 -1 = mmnlmax ! max invariant mass for all letpons (l+- and vl)
#*********************************************************************
# Minimum and maximum pt for 4-momenta sum of leptons *
#*********************************************************************
 0 = ptllmin ! Minimum pt for 4-momenta sum of leptons(l and vl)
 -1 = ptllmax ! Maximum pt for 4-momenta sum of leptons(l and vl)
#*********************************************************************
# Inclusive cuts *
#*********************************************************************
 0 = xptj ! minimum pt for at least one jet
 0 = xptb ! minimum pt for at least one b
 0 = xpta ! minimum pt for at least one photon
 0 = xptl ! minimum pt for at least one charged lepton
#*********************************************************************
# Control the pt's of the jets sorted by pt *
#*********************************************************************
 0 = ptj1min ! minimum pt for the leading jet in pt
 0 = ptj2min ! minimum pt for the second jet in pt
 0 = ptj3min ! minimum pt for the third jet in pt
 0 = ptj4min ! minimum pt for the fourth jet in pt
 -1 = ptj1max ! maximum pt for the leading jet in pt
 -1 = ptj2max ! maximum pt for the second jet in pt
 -1 = ptj3max ! maximum pt for the third jet in pt
 -1 = ptj4max ! maximum pt for the fourth jet in pt
 0 = cutuse ! reject event if fails any (0) / all (1) jet pt cuts
#*********************************************************************
# Control the pt's of leptons sorted by pt *
#*********************************************************************
 0 = ptl1min ! minimum pt for the leading lepton in pt
 0 = ptl2min ! minimum pt for the second lepton in pt
 0 = ptl3min ! minimum pt for the third lepton in pt
 0 = ptl4min ! minimum pt for the fourth lepton in pt
 -1 = ptl1max ! maximum pt for the leading lepton in pt
 -1 = ptl2max ! maximum pt for the second lepton in pt
 -1 = ptl3max ! maximum pt for the third lepton in pt
 -1 = ptl4max ! maximum pt for the fourth lepton in pt
#*********************************************************************
# Control the Ht(k)=Sum of k leading jets *
#*********************************************************************
 0 = htjmin ! minimum jet HT=Sum(jet pt)
 -1 = htjmax ! maximum jet HT=Sum(jet pt)
 0 = ihtmin !inclusive Ht for all partons (including b)
 -1 = ihtmax !inclusive Ht for all partons (including b)
 0 = ht2min ! minimum Ht for the two leading jets
 0 = ht3min ! minimum Ht for the three leading jets
 0 = ht4min ! minimum Ht for the four leading jets
 -1 = ht2max ! maximum Ht for the two leading jets
 -1 = ht3max ! maximum Ht for the three leading jets
 -1 = ht4max ! maximum Ht for the four leading jets
#***********************************************************************
# Photon-isolation cuts, according to hep-ph/9801442 *
# When ptgmin=0, all the other parameters are ignored *
# When ptgmin>0, pta and draj are not going to be used *
#***********************************************************************
   0 = ptgmin ! Min photon transverse momentum
 0.4 = R0gamma ! Radius of isolation code
 1.0 = xn ! n parameter of eq.(3.4) in hep-ph/9801442
 1.0 = epsgamma ! epsilon_gamma parameter of eq.(3.4) in hep-ph/9801442
 .true. = isoEM ! isolate photons from EM energy (photons and leptons)
#*********************************************************************
# WBF cuts *
#*********************************************************************
 0 = xetamin ! minimum rapidity for two jets in the WBF case
 0 = deltaeta ! minimum rapidity for two jets in the WBF case
#*********************************************************************
# KT DURHAM CUT *
#*********************************************************************
 -1 = ktdurham
 0.4 = dparameter
#*********************************************************************
# maximal pdg code for quark to be considered as a light jet *
# (otherwise b cuts are applied) *
#*********************************************************************
 4 = maxjetflavor ! Maximum jet pdg code
#*********************************************************************
# Jet measure cuts *
#*********************************************************************
 0 = xqcut ! minimum kt jet measure between partons
#*********************************************************************
#
#*********************************************************************
# Store info for systematics studies *
# WARNING: If use_syst is T, matched Pythia output is *
# meaningful ONLY if plotted taking matchscale *
# reweighting into account! *
#*********************************************************************
   F = use_syst ! Enable systematics studies
#
#**************************************

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Olivier Mattelaer (olivier-mattelaer) said :
#1

I guess that the Phase-Space integration has some difficulty to integrate efficiently in this case.

Cheers,

Olivier

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