DØ Note: XXXX
V0.2
Inclusive + jet Cross-Section
and
Inclusive b-jet Cross-Section
Don Lincoln, Yevgeny Galyaev, Hong Luo, Neal Cason, Paul Bierdz, Phil Buksa, Markus Wobisch
ABSTRACT
In this Note, we describe the details of a measurement of the + jet cross-section at a s of 1.96 TeV. An attempt is made to extract the inclusive b jet cross-section for the central region | y | < 0.5.
Introduction
While the Standard Model of particle physics does a brilliant job of explaining the bulk of measurements made by modern experimenters, it is well known that there exist a number of questions that can be easily asked but not as easily answered. One of these questions is the nature and cause of three particle generations, each similar in gross properties, yet somehow different among other things, including increasing mass. In a simple argument by analogy, one might compare this situation with the chemical Periodic Table, in which a similar phenomenon was successfully explained by atomic structure. Consequently a possible explanation of the problem of particle generations is the idea of quark compositeness. If quarks are composite (taking the quarks with charge –1/3), then one might envision that a down quark is in the ground state, while the strange and bottom quarks are in low-lying excited states. A parallel structure would describe the +2/3 charge quarks.
By this reasoning, it might be true that a study of the quarks of the third generation might exhibit deviation from point-like behavior. Thus one might choose to study the process
pp X qq, where the final state quarks would be either bottom or top. Given the resources at hand, it was decided to study X bb. A more compelling discussion of the theoretical concerns of such a search will be given in a forthcoming note however for the moment, one can restrict oneself to a study of the relevant concerns and performances of b-tagging in very high Pt jets and high mass di-b jets. If a quality job of high Pt b-tagging is impossible, then theoretical concerns are moot. If successful, an intermediate result of this study will naturally yield an inclusive jet cross section for jets originated by b quarks. Subsequent work will explore the dijet question.
In addition to the goal of this measurement, study of high Pt b jets will provide useful feedback to the Higgs group. It is also true that there exist possible physics mechanisms which might generate enhanced b-quark production at high Pt (i.e. any hypothetical heavy-mass object preferentially decaying into quarks of the third generation.) Conventional inclusive jet cross-section measurements would not reveal this behavior, being over shadowed by the more common light-quark and gluon behavior.
Analysis Techniques
The analysis technique used in this study is based heavily on Ariel Schwartzman’s d0root package [1]. This is a root-based package, in which one can quickly change the nature and details of the cuts, without the inconvenience involved in recompiling RECO and framework-based analyses.
The basic premise of the analysis utilizes the strength of DØ’s calorimeter. First jets are found using the conventional () 0.5 cone based jet finder. Objects that are relevant to heavy flavor identification are then appended to the jet. For example, RECO muons and secondary vertices that are collinear to the jet are attached, as are (when relevant) the initiating parton as specified by leading order Monte Carlo. In addition, Monte Carlo truth muons, b and c quark carrying hadrons are associated.
Within the context of the d0root package, this heavy flavor identification, calorimeter jet based construct is called a “D0JetInfo”. The details of each object, as well as the cuts that must be fulfilled to associate each object to the calorimeter jet are given below:
Calorimeter Jet:
Standard ( jet, with cone of 0.5 [corrJCCB]. This includes JES and jet quality cuts.
Track-based Jet:
A track based jet finding algorithm was run. Tracks that can be used to create a track jet are required to have
Aspect / ValueMinimum track Pt / 1.0 GeV
Minimum # of SMT hits on track / 2
Track (x,y) DCA / < 0.15 cm
Track z DCA / < 0.4 cm
DCA significance / < 3.0
2 / < 10
In addition, via btags_cert, I run a prefilter of 2PPV_NoV0 which removes tracks that come from Vo’s (Ko, o and conversions). As this prefiltering comes before track jet finding, this will slightly reduce the number of track jets, but will not affect the desired vertices.
With these “Vo-free” tracks, the track jet finder is run, requiring the following cuts.
Aspect / Value() cone size / 0.5
Z between tracks (unused) / < 2.0 cm
Minimum track Pt / 0.5 GeV [overridden by track criteria]
Minimum Jet Pt / 0.0 GeV
Minimum Pt of highest Pt track / 1.0 GeV
Minimum # of SMT hits on track / 1 [overridden by track criteria]
Track (x,y) DCA / < 0.2 cm
Track z DCA / < 0.4 cm
A track jet is associated with a calorimeter jet if they match in space with a R of less than 0.7 and a Z of less than 1.5 cm.
Vertexing:
Primary vertexing was done within the context of btags_cert. The objects returned were the two-pass primary vertices. If multiple primary vertices were returned, the first one was used as the event primary vertex.
Secondary vertices were found using SVKalmanBtagger. First trackjets were found using the above-described algorithm. Then the algorithm tries to create secondary vertices using a “build up” method. Tracks are added to a secondary vertex if they pass the following cuts and a vertex candidate is retained if the cuts listed below are satisfied.
Aspect / ValueTrack addition to VTX 2 / < 15.
Total VTX 2 / < 100
# Tracks / > 1
Zdca / < 0.4 cm
DCA Significance / > 0
VTX Collinearity / > 0.9
When secondary vertices were found, they were inspected to find the “best” secondary vertex. A best secondary vertex satisfied the following cuts. The dot product between the vector starting at the primary vertex and ending on the secondary vertex and the vector of the momentum of the secondary vertex must be positive. This essentially means that the secondary vertex is on the same side of the primary vertex as the secondary vertex’ direction of motion. The two dimensional decay length separating the primary and secondary vertex must be less than 2.5 cm (to suppress Ks, ’s and other strange quark carrying hadron decays). Finally the secondary vertex with the greatest three-dimensional decay length significance (defined to be the decay length divided by the combined uncertainty of the two vertices) was chosen. This cut uses the 3D decay length significance, rather than 2D, for historical reasons.
RECO Muons:
RECO muons were associated to the JetInfo object if they were of MEDIUM quality as specified by the Muon ID group. In addition, the Pt of the muon was required to exceed 5.0 GeV, the reasons for which will be mentioned in the text below. A RECO muon is associated with a calorimeter jet if they match in space with a R of less than 0.5 and a Z of less than 1.5 cm.
D0JetInfo Kinematics:
In addition to the kinematics of the calorimeter jet and the associated muon, the standard heavy flavor JES (v5.3, no T42) is applied, resulting in an approximate energy for the parent parton. This is done separately to allow for cuts on both the calorimeter jet and the “right” (i.e. jet + ) energy.
Run and Event number:
Each jet had the run and event number associated with it.
Leading Order Primary Parton:
InMonte Carlo, it is frequently convenient to know the partonic parentage of a particular jet. Within the context of the Pythia Monte Carlo, two leading order partons are generated which are subsequently modified by parton shower models. There was not available when the study began a method to unambiguously determine the original partons, so a simple algorithm was devised. The program loops over all partons in the event (including ones from parton showers). It finds the parton with the largest Pt and declares this a leading-order parton. It then loops again over the remaining partons and finds the highest Pt parton which also has a from the hot parton of more than ( – 0.7). This parton is declared to be the second leading order parton.
These two potential leading order partons are then compared to the two leading jets. The partons and jets are associated if they match in space with a R of less than 1.0 and a Z of less than 100 cm. This matching was intentionally left loose to enhance efficiency and, since there are only two leading order partons allowed, this can be done without much effect on fake matches.
Monte Carlo Secondary Vertices:
Monte Carlo secondary vertices are those particles in the event record containing either a bottom or charm quark and decay weakly. The parent heavy flavor hadron is recorded, as are all daughters with no attention paid to the stability or charge state of the daughters. The correspondence between the parent b-hadron and its daughter c-hadron is lost.
The MC secondary vertices and calorimeter jets are associated if they match in space with a R of less than 0.5 and a Z of less than 3 cm.
Monte Carlo Muons:
Monte Carlo muons are those muons recorded in the truth table. They include heavy flavor as well as light meson decay. While in principle a source of muons might be Hadronic showers in the calorimeter or from light meson decay even in the magnet or calorimeter, the MC generated for this study restricted the radius of the decay vertex of the particle decaying inclusively into muons to be less than 53 cm. The MC muons and calorimeter jets are associated if they match in space with a R of less than 0.5 and a Z of less than 3 cm.
Monte Carlo Truth Particles:
Monte Carlo truth particles are ALL truth particles collinear with the calorimeter jet, even if the particle subsequently decays into other particles that will also be listed as collinear with the calorimeter jet. Restricting the particles to the stable ones is done via JetInfo methods. The truth particles and calorimeter jets are associated if they match in space with a R of less than 0.5.
Monte Carlo Partons:
Monte Carlo truth partons are ALL truth partons collinear with the calorimeter jet, even if the parton subsequently showers into other partons that will also be listed as collinear with the calorimeter jet. The truth partons and calorimeter jets are associated if they match in space with a R of less than 0.5. Note this is distinct from the leading order parton, as it provides another way to look at b and c quark content.
Monte Carlo Samples
Initially, twenty thousand events were requested at three different Pt ranges. These Pt ranges were 080-160, 160-320 and 320-980 GeV. Separate requests were made for direct b-quark production, direct c-quark production and also light quark (standard jet production). Later, additional requests were made. The low-numbered requests are used for the following PtRel discussion. The high-numbered requests were used for all others. The following tables list the available statistics, as well as the original MC production job number and SAM dataset definition.
MC Request# / Request Type / # Events / SAM Dataset Definition
13334 / bb 80-160 / 20000 / req-id-13334-tmb-good
13383 / bb 80-160 / 18490 / req-id-13383-tmb-good
13336 / bb 160-320 / 18193 / req-id-13336-tmb-good
13385 / bb 160-320 / 27000 / req-id-13385-tmb-good
13338 / bb 320-980 / 18297 / req-id-13338-tmb-good
13387 / bb 320-980 / 17259 / req-id-13387-tmb-good
13335 / cc 80-160 / 20500 / req-id-13335-tmb-good
13384 / cc 80-160 / 20397 / req-id-13384-tmb-good
13337 / cc 160-320 / 21000 / req-id-13337-tmb-good
13386 / cc 160-320 / 20000 / req-id-13386-tmb-good
13339 / cc 320-980 / 20140 / req-id-13339-tmb-good
13388 / cc 320-980 / 20750 / req-id-13388-tmb-good
13372 / qcd 80-160 / 51000 / req-id-13372-tmb-good
13373 / qcd 80-160 / 51000 / req-id-13373-tmb-good
13374 / qcd 80-160 / 50500 / req-id-13374-tmb-good
13375 / qcd 80-160 / 51000 / req-id-13375-tmb-good
13376 / qcd 160-320 / 33500 / req-id-13376-tmb-good
13377 / qcd 160-320 / 24108 / req-id-13377-tmb-good
13378 / qcd 320-980 / 20000 / req-id-13378-tmb-good
Data Selection: (skim, cuts, etc.)
The initial data processing was from the Common Samples group’s CSG_QCD skim. The following URL gives more details.
All data, spanning the run range 161973-193780 (15 August 2002 - 07 June 2004) was used. The total number of the events in the CSG QCD skim was 40,460,043 events and ALL events were present in our TMBTrees. We subsequently skimmed the data so as to have a more manageable data set. One skim, the Muon_skim, required that at least one of the two leading jets have a collinear MEDIUM RECO muon, with Pt > 4.0 GeV. This data set comprised 405,671 events. In addition, although not directly germane to this analysis, a 2VTX_skim was done, which required that at least one of the two leading jets contain a “Best Secondary Vertex” (see above). This data set comprised 1,538,291 events. For both of these skims, the offline data quality database was consulted and if any of the following fields were listed as bad, the event was rejected: SMT, CAL, MET, CFT, MUO & JET.
After reasonable (yet loose) jet thresholds were determined (discussed below), a “micro skim” was performed. The requirement for this skim was that for each QCD trigger, the jet containing the tag was required to be above a threshold, for which the trigger was 90% efficient. The thresholds are [JT25 – 70, JT45 – 90, JT65 – 120, JT95 – 165]. Also, the “tagged” jet was required to have a rapidity [| y | < 0.5]. When the muon-based micro skim was completed, 18,328 events remained. Microskims were also performed on the SVX data set (for both Pt and Mass thresholds), but these skims are not relevant to this analysis.
Luminosity:
The luminosity was calculated according to the instructions from the CSG web page. While the full recorded luminosity for this data set was approximately 389 pb-1, when bad runs were removed, the actual luminosity for the unprescaled JT_125TT trigger was 293.8 pb-1. As each trigger was prescaled by an amount that varied with instantaneous luminosity, the luminosity database was used to determine the luminosity for each trigger. These were:
Trigger / Luminosity (pb-1)JT_25TT / 1.81
JT_45TT / 28.48
JT_65TT / 142.46
JT_95TT / 292.8
JT_125TT / 293.8
The error on the luminosity is taken to be 6.5%.
V0 removal:
The technique of V0 removal is given in [2]. The essential point is that it is possible for strange quark-carrying hadrons to decay at a distance from the interaction point and thus be reconstructed as a secondary vertex. Prior to vertex finding, the tracks from each event are scanned and an attempt is made to reconstruct Kos, o or conversions in the silicon system. Tracks which are found to come from one of these occurrences are removed and not used for future secondary vertex finding. This was done within the btags_cert package.
Identification of Muons:
Conventional Wisdom[1] reports that the use of MEDIUM muons gives an optimum separation between muons and fakes. TIGHT muons do not markedly improve the separation, but do decrease the efficiency. This wisdom was generated during studies of isolated muons for Z and W searches.
Our initial analysis effort took this wisdom to heart. However, since this analysis uses muons inside jets (and therefore manifestly not isolated), studies were undertaken to see if conventional wisdom held. Figure 1 shows the distribution for -tagged jets using MEDIUM muons in our event sample.
Figure 1 Left: distribution of -tagged jets (in radians). Right: Same, but in r coordinates. The curve with higher statistics is for jets tagged with MEDIUM muons. The lower statistics curve is for jets containing muons which both satisfy the MEDIUM criteria, as well as the additional scintillator BC cut discussed in the text.
What was observed was the expected lack of muons in the bottom of the detector, where the muon system coverage is restricted. However, there were two regions (near -45º and -135º) for which the cuts for MEDIUM muons are loosened.
The definitions of muon quality criteria are given in [3]. Briefly, the definition of a MEDIUM muon changes dependent on the number of muon segments (nseg) and the octant number in the muon system. A medium nseg = 3 is defined to be a muon with both A and BC segments, nseg = 2 requires a BC segment matched to a central track, while a nseg = 1 muon requires an A segment matched to a central track. The following chart shows the criteria for MEDIUM muons for the various nseg definitions.
Cut Variable / nseg3 / 2 / 1
# A Wire Hit / 2 / / 2
# A Scint Hit / 1 / / 1
# BC Wire Hit / 2 / 2 /
# BC Scint Hit / 1 / 1 /
Octant / / 5,6 / 5,6
| | / / < 1.6 / < 1.6
Table 1Cuts to define a MEDIUM muon. “” indicates no restrictions.
When a muon is on the bottom of the detector, the criteria are loosened. The reason that we are seeing a large muon presence in the bottom of the detector is partly because we are looking inside jets. Even though D has a deep calorimeter, there is often some amount of MIP punch-through which carries minimal energy. However, this MIP punch-through will fire the A layers of the muon system. Coupled by the fact that this activity occurs within a jet (which has a lot of tracks), it is often possible for hits in the muon A layer to be correlated with a track in the central tracker. Consequently there are many muon fakes inside jets for nseg = 1 MEDIUM muons. Requiring a BC scintillator hit greatly reduces the punch-through background. This point is illustrated in Figure 1.
In addition to this very important muon cut, there are some additional muon cuts necessary to clean up the sample. For instance, the Pt of the muon can be measured in three ways: in the local muon system, in the central tracking system and in via a combined fit (global). For a very tiny fraction of the events, the global and central Pt are in disagreement. It was found that imposing the extremely loose cut
|Pt(global) – Pt(central)| < 15 GeV
would substantially improve the cross-section measurement. Failure to impose this cut would give too many jets with improperly-reconstructed high Pt muons. As illustrated in Figure 2, this cut removes far fewer than 1% of the events.