no SUSY contribution is fitted in the CR introducing a bias in our estimate.
There is a second issue with the naive approach, which is that the shape of the MT(ETmiss) distribution might be different for lower or higher ETmiss(MT). This turns out to be the case for some backgrounds and we have to take these correlations into account as described in section 6.4.2.
The first section will describe the samples that were generated for the backgrounds and possible mSUGRA signals.
In the second section we will describe the models for the different backgrounds and for the SUSY signal. In this analysis all the aspects of working with PDFs mentioned in chapter 5 are used. A product of three PDFs is used to get a 3-dimensional model of the backgrounds and signal, taking correlations between observables into account using conditional PDFs. Different aspects of a 1D PDF are described by summing PDFs, for instance a Gaussian peak on top of an exponential tail in the MT models. In 3 dimensions, the models of all background contributions and the SUSY signal are combined through addition into one model describing the data.
The control region used in this analysis is non-square, but rather built from two square elements. Together with the signal range that means that the model has to be consistently defined and evaluated in three different ranges. Thus the tools and formalisms developed in the previous chapter will be needed. All the descriptions of the models, and all fitting in this thesis was done using the RooFit framework [46], which is part of the ROOT framework [47] commonly used in high energy physics.
Finally, a proof of principle will be given where the combined fit method will be applied to a pseudo dataset made by combining background and signal MC. It will be shown that the input yields of the different components can be correctly estimated with the method.
This analysis was developed together with A. Koutsman. Most of the text in this chapter was already published in the ATLAS internal note [48], which is only available for members of the ATLAS collaboration, and appeared as a chapter in Koutsman’s thesis [49].
6.2
Signal and Background generation
In the following section we briefly describe our simulation of signal and background samples. The simulated data documented here has been produced by Monte Carlo (MC) simulation inside the official ATLAS software framework ATHENA [50]. Then we will describe the criteria for event selection, and the number of events for each background are expected to pass these cuts.
The ATHENA framework incorporates different packages for generating events. Simulation of the ATLAS detector was done using the ATLFAST2 [51] simulation package. ATLFAST2 includes state of the art GEANT4 [52] simulation of the inner detector and muon system sup- plemented by a fast calorimeter simulation. GEANT4 handles the interaction of the particles with the magnetic field and with the detector material, handling multiple scattering, energy loss and much more. This is the most extensive and CPU intensive for the calorimeters, where very many particles are produced in the hadronic/electromagnetic showers. ATLFAST2 has been designed to be able to produce large numbers of models/events with less computing power than would be needed for the full GEANT4 simulation of the whole detector.
10 TeV. During the year of 2009 the energy at which the LHC was going to collide once restarted after the accident of 19 September 2008 was not clear. Hence the choice of the collaboration is somewhat off from the mark of√s = 7 TeV at which the LHC started colliding protons in 2010. Chapter 7 will deal with applying the method described in this chapter to the data measured in 2010. The next two sections will describe the signal and background MC samples that were used in this analysis.
6.2.1
Backgrounds
Different MC generators were used for different background samples. This was done in an attempt to optimize the reliability of the estimate and cross check the results for the Standard Model samples.
Top quark production One of the two largest backgrounds for one lepton SUSY searches
is t¯t pair production. As the top quark almost always decays into a W and a bottom quark, the signature of a t¯t decay is determined by the decay channels of the two W bosons. In the case of the fully hadronic t¯t both W s decay into a pair of quarks. This case is not interesting from the point of view of one lepton analyses, so we will not mention it again. The other two cases of t¯t decay are of great interest. If one of the W s decays into a lepton and a neutrino, we speak of semileptonic (lνqq) decays, and if both W s decay leptonically we speak of dileptonic (lνlν) decay.
As t¯t pair production at the LHC can occur well beyond the immediate mass threshold we need to use the next-to-leading order (NLO) generator MC@NLO [53, 54] to accurately describe the hard interaction for t¯t production with initial and final state radiation (ISR/FSR) of hard jets. Parton showering and fragmentation are performed by the HERWIG [55, 56] program. The cross section for the joint semileptonic and dileptonic t¯t sample as calculated by MC@NLO is 217 pb [57] as can be seen in Table 6.1.
For more than two additional hard partons the matrix elements (ME) for NLO t¯t production are too difficult to calculate. Another approach is to use the ALPGEN generator [58] that can calculate ME up to 6 extra partons, but at Leading Order (LO). Here one has to compensate for the overlap between jets created by matrix elements on one side and by parton showering on the other. The technique that accomplishes this is called MLM-matching [59]. The MLM matching procedure starts from generating events using the ME with n extra partons. Each parton has to meet a minimum transverse momentum pmin
T requirement, and a minimum separation ∆Rminfrom the other partons. A showering algorithm is applied to each outgoing parton, without a veto on hard emission. Jets are created from the showering output using a cone jet algorithm with radius ∆Rmin and pT > pminT . The jets found using this algorithm are matched to the partons from the ME calculation. If m partons are not matched to a jet, this topology belongs to the n − m ME parton sample and it is rejected. Likewise, if m jets are not matched to a parton it belongs to the n + m ME parton sample and is rejected. Thus double counting caused by showering is avoided. To get an inclusive sample including all topologies with extra jets, the last rejection is skipped for the highest multiplicity sample if the extra jets are softer then the ME jets. We mostly use the ALPGEN t¯t events for a study of systematic uncertainties. The cross sections for all the separate ALPGEN samples given in Table 6.1 are calculated after MLM-matching, i.e. the ALPGEN generator cross section is multiplied with MLM-matching efficiency to get the final quoted cross section. The cross
6.2. SIGNAL AND BACKGROUND GENERATION 87
Process Generator Cross Section (pb)
t¯t (lνlν + lνqq) MC@NLO 217 t¯t (lνlν) + 0 partons ALPGEN 12.7 t¯t (lνlν) + 1 parton ALPGEN 13.7 t¯t (lνlν) + 2 partons ALPGEN 9.36 t¯t (lνlν) + 3 partons ALPGEN 7.06 t¯t (lνqq) + 0 partons ALPGEN 51.8 t¯t (lνqq) + 1 parton ALPGEN 57.1 t¯t (lνqq) + 2 partons ALPGEN 38.3 t¯t (lνqq) + 3 partons ALPGEN 27.6
Table 6.1: Cross sections including NLO k-factor for simulated t¯t processes with different generators. The cross sections for processes generated with ALPGEN are given after MLM matching.
section is compensated for the difference between the NLO and LO calculation by multiplying the LO cross section with a calculated k-factor, scaling it to the NLO value.
W+jets Another important background for SUSY searches with one lepton is production
of W -bosons with associated jets. The number of jets in an event is an important selection criterion for this analysis, thus it is very important to correctly produce the kinematics of the additional jets. The ALPGEN generator was chosen to calculate the exact matrix elements for multiparton hard processes, which was interfaced to HERWIG [55, 56] for showering and hadronisation. Alike to the t¯t ALPGEN samples, also here we have to apply the MLM-matching technique, dividing the phase space between matrix elements for hard jets and parton showering only for soft jets, to prevent double counting. Contributions from processes with associated parton multiplicities between zero and five were summed to produce the complete W +jets sample. The cross sections after applying the MLM-matching technique for all lepton flavor separated processes are given in Table 6.2. For the W +jets a NNLO k-factor, calculated using the FEWZ program, was applied to the LO cross section.
W + b¯b+jets The W +jets processes simulated by ALPGEN as described above only
take into account light flavor (u, d, s and c quarks) jets. A separate ALPGEN process takes care of the W +b¯b+jets production. Although these processes have relatively low cross sections, they must be considered to correctly estimate the total cross section and if b-tagging is to be used. A small overlap is expected between the W + b¯b+jets and W +light jets samples, as the latter may contain b¯b pairs generated by parton showering. This small amount of double counting is minimized by the choice of the generator level cuts [57].
QCD multijet Although the requirement of a single isolated lepton and missing transverse
energy strongly suppresses QCD multijet events, the cross sections of these processes are orders of magnitude higher then the processes involving top quarks and W -bosons, and as such still have to be taken into account. ALPGEN was again the generator of choice for it can calculate matrix elements of events with up to 6 partons in the final state. The generation of QCD events was split according to the quark flavor (b-quarks or light quarks) and the transverse momentum of the leading jet, to be able to produce useful amounts of integrated luminosity. The lowest produced pT of the leading jet was set at 35 GeV, due to practical limitations
Process Generator Cross Section (pb)
W(e ν) + 0 partons ALPGEN 12.3 · 103
W(e ν) + 1 parton ALPGEN 2.6 · 103
W(e ν) + 2 partons ALPGEN 8.3 · 102
W(e ν) + 3 partons ALPGEN 2.4 · 102
W(e ν) + 4 partons ALPGEN 67.7
W(e ν) + 5 partons ALPGEN 19.9
W(µν) + 0 partons ALPGEN 12.3 · 103 W(µν) + 1 parton ALPGEN 2.6 · 103 W(µν) + 2 partons ALPGEN 8.3 · 102 W(µν) + 3 partons ALPGEN 2.4 · 102 W(µν) + 4 partons ALPGEN 67.7 W(µν) + 5 partons ALPGEN 19.9 W(τν) + 0 partons ALPGEN 12.3 · 103 W(τν) + 1 parton ALPGEN 2.6 · 103 W(τν) + 2 partons ALPGEN 8.3 · 102 W(τν) + 3 partons ALPGEN 2.4 · 102 W(τν) + 4 partons ALPGEN 67.7 W(τν) + 5 partons ALPGEN 19.9 W(b¯b) + 0 partons ALPGEN 6.2 W(b¯b) + 1 parton ALPGEN 6.1 W(b¯b) + 2 partons ALPGEN 3.5 W(b¯b) + 3 partons ALPGEN 2.0
Table 6.2: Cross sections for simulated ALPGEN W +jets processes including NNLO k-factors, which were calculated for an inclusive W sample. The cross sections are given after MLM-matching was applied.
6.3. EVENT SELECTION 89