Study of High Transverse Momentum Jets with 5.95 fb -1 of CDF Run II Data.

Raz Alon, Ehud Duchovni and Gilad Perez (Weizmann Institute of Science)

Pekka Sinervo (University of Toronto),   [Contact]

Abstract [Link to public note]

We present the preliminary results of a study of the very highest energy jets observed by CDF and their substructure. Jets are reconstructed using the Midpoint algorithm (without search cones) with cone sizes of 0.4 and 0.7 and corrected with the standard jet energy corrections. We select events with at least one jet with transverse momentum > 400 GeV/c in a sample of 5.95 fb^-1, and study the angular structure of the energy flow within the jet, as well as the overall jet mass. We have performed various studies to validate and calibrate these jet data, as well as understand their possible sources. We measure the jet mass and two measures of substructure, angularity and planar flow.

Link to Previous Webpage

Introduction

High p_T massive QCD jets are interesting to study from various aspects [1, 2, 3]. From the experimental perspective, these objects have never been studied even though a data is potentially available in the inclusive jet data collected by CDF. Furthermore, the CDF detector is understood quite well, which allows us to measure and correct these boosted jets and to analyze the corresponding mass distribution and other jet shapes. Theoretically, the observation of massive collimated jets provides an important test of perturbative QCD, an opportunity to tune the various Monte Carlo (MC) event generators and gives insight into the QCD showering mechanism. Furthermore, massive boosted jets comprise perhaps the most important background for new physics [4, 5, 6, 7, 8, 9, 10] and even Higgs searches [11, 12, 13]. Particularly relevant is the case where microscopic dynamics, for instance via a decay of a heavy resonance, produces high-p_T , standard model (SM) massive particles that decay hadronically. Consequently, these new physics signals are expected to be of the form of highly boosted W, Z, h and top jets. Finally, the results as well as the techniques presented may be useful in follow-up studies at the LHC experiments.

As mentioned, there have been no CDF or D0 studies of high-p_T jet substructure performed using Run II data, despite both experiments having large samples of high-p_T jets. CDF did publish a study [15] that looked at the radial energy flow within a jet, but this was limited to clusters with p_T < 380 GeV/c. Initial estimates based on CDF's measurements of differential jet cross sections suggests that we would expect to have of order 500 fb of events with at least one jet with p_T > 400 GeV/c. The D0 Collaboration published a study [16] on subjet multiplicity using the k_T algorithm at lower momenta. An initial look at the jet mass distribution was performed in the context of the SLEUTH analysis [17] but there was no detailed analysis or explanation of the apparent discrepancies between MC predictions and data.

Finally, we note that there have been relatively few studies at the Tevatron that explore the production of very highly boosted top quarks. The first top quark p_T measurement was by CDF [18] using 0.1 fb^-1 of Run I data. The D0 collaboration has recently published a new measurement using 1 fb^-1 of Run II data [19]. In both cases, the statistics of these measurements have been limited by the integrated luminosity and the efficiency for reconstructing t tbar lepton+jet final states, and no data is available for top quarks with p_T > 400 GeV/c. Perhaps the measurement most sensitive to high p_T top quarks has been a study of the invariant mass distribution of top quark pairs [20], though that did not look explicitly at the top quark p_T distribution. It also appeared to give little information about top quark production above a p_T of 300-350 GeV/c.

Theoretical predictions for the differential top quark production cross section as a function of p_T now exist up to next-to-next-to-leading order (NNLO) [21] so that a measurement or upper limit on the top quark production cross section for p_T > 400 GeV/c will add in a unique way to our understanding of top quark production.

Theoretical Background

Jet Mass

The mass of a jet is defined experimentally using the "E-scheme" [41], where each tower in the calorimeter associated with a jet cluster is considered a mass-less 4-vector with momentum given by the energy in the tower. The jet 4-vector and mass arises from the 4-vector sum of the towers. Based on QCD factorization [22], a semi-analytic calculation of QCD jet mass distribution has been derived where the mass is dominantly due to a single gluon emission [23]. The jet function can be defined via the total differential rate

where σ^q,G is the factorized Born cross section. Corrections of O(R²) are neglected and the analysis is applied to the high mass tail, m_J^peak << m_J << p_TR (m_J^peak corresponds to the peak of the jet mass distribution). A simple approximation for the full result [23] is

where α_s(p_T) is the strong coupling constant at the appropriate scale and C_q,G = 4/3,3 for quark and gluon jets, respectively.

We note that the above result contains two non-trivial pieces of information. The first is that the overall scale of the jet mass distributions (i.e., the probability of having a jet at a given mass) is a physical observable and has no arbitrary or unknown normalization. The second is that the shape of the distribution is well defined. Both predictions should be tested by the data. The former can be translated into a rejection power as a function of a mass cut, or a mass window, both useful in distinguishing between new physics signal and QCD background [24, 25]. The shape prediction can be used to improve the sensitivity to new physics searches by reducing the number of free parameters in a side-band analysis.

Jet Shape and Substructure

QCD jets and ones resulting from hadronic decay of massive boosted particles fundamentally differ from each other and we should be able to find observables which exploit this essential difference. As we have discussed, jet mass has non-negligible rejection power when one is seeking parent particles that decay into heavy objects. Once the jet mass is fixed at a high scale, it is important to note that a large class of other jet shapes becomes perturbatively calculable. An interesting way to proceed beyond the jet mass is to look at energy distribution and substructure within the jet itself.

Since this is an initial study, we focus below on measuring angularity and planar flow jet shape variables. At small cone sizes and large jet mass, these variables are expected to be quite robust against soft radiation and allow in principle a comparison with theoretical predictions in addition to comparison with MC results.

Angularity

Angularity corresponds to a class of jet shapes [32, 26]:

where ω_i is the energy of a component inside the jet (such as a calorimeter tower). Limiting the parameter a ≤ 2 ensures IR safety, as can be directly seen from the expression on the right hand side of the equation which is valid for small angle radiation θ_i << 1.

The angularity distribution, dσ/dτ_a, is similar over a large class of jet definitions in the limit of R<<1 and high jet mass [26]. Since angularity basically measures the energy distribution inside the jet, it is particularly sensitive to the degree of symmetry in the energy deposition. It therefore can distinguish jets originating from QCD production of light quarks and gluons from boosted heavy particle decay, in a similar manner to the k_T distance measurement that is often describe by the Y-splitter variable [2, 4]. The key point here is that for high mass jets, the distribution of the leading parton and the emitted gluon is expected to be peaked around a symmetric p_T configuration where both partons are at the same distance, θ_i, from the jet axis, θ_1,2 = z = m/p_T [26]. This implies that there is a minimum value for angularity:

This is true both for the signal and background events and hence provides an important test for the energy distribution of massive jets. In particular, in our case this is a test for the two pronged description of the QCD energy distribution of boosted massive jets and the corresponding showering mechanism. It is worth noting that the above implies that the angularity distribution of the signal (say of the form of a W/Z/h jet) and background (QCD jet) are similar in shapes. The comparison is only qualititative, however, as the QCD distribution has a broader tail towards larger angularity value. A similar conclusion holds for the Y-splitter variable since the leading order kinematics is characterized by a single parameter.

We can also get an estimate for the maximal value of τ_a that arises due to radiation towards the edge of the cone when θ_s~R:

The leading-order (LO) energy distribution of massive QCD jets [26] can be characterized by the angular distribution of the softer particle in the two-pronged description. It can be simplified in the limit of z,|θ_s|,R<<1 to give the jet angularity distribution:

Planar Flow

Another IR-safe jet shape, denoted as planar flow (P_f), can be used to distinguish planar from linear configurations [23, 26, 28]. Planar flow is defined as follows. We first construct for a given jet a matrix I_w as

where m_J is the jet mass, w_i is the energy of particle i in the jet, and p_i,k is the k^th component of its transverse momentum relative to the jet momentum axis. Given I_w, we define Pf for that jet as

where λ_1,2 are the eigenvalues of I_w. P_f vanishes for linear shapes and approaches unity for isotropic depositions of energy.

Jets with pure two-body kinematics have a planar flow distribution peaked at a low value close to zero. This would apply to leading order for events with highly boosted weak gauge boson, Higgs and QCD jets. On the other hand, events that are characterized by ≥ 3-body kinematics have a smooth distribution [3, 26]. The QCD planar flow distribution, even though not calculated analytically, is expected to be that of a typical QCD distribution and similar to the jet mass distribution. At very small P_f it should vanish due to Sudakov suppression from soft gluon emission, then peak around a small value and then have a long tail that is characterized by perturbation theory due to emission of an extra hard gluon at a wide angle.

Event Selection

We used the standard Jet100 samples triggered with the inclusive jet trigger with a nominal transverse energy threshold of 100 GeV. The data sample corresponds to 5.95 fb^-1 of Run II data. Our strategy was to take advantage of the significant amount of work done to understand the Run II high p_T jet sample, encapsulated in the measurement of the differential jet cross section as a function of transverse momentum and rapidity [40]

The entire inclusive jet sample consisted of 75,764,270 events for 5.95 fb^-1. This corresponds to an effective triggered cross section of 12.7 nb. Jets in these events were subsequently reconstructed with a Midpoint cone algorithm with cone sizes of R = 0.4, 0.7 and 1.0 using the Fastjet software package. We compare the results obtained with the Midpoint algorithm with the results obtained using the anti-kT algorithm and the Midpoint algorithm with search cones.

Given our interest in high p_T objects, we kept the event selection as simple as possible. We made the following requirements, using the data up to and including period 27:

1. The run and event satisfy the standard requirements for high quality data.
2. The event is required to have a high quality primary event vertex within |z_vtx| < 60 cm.
3. The event is required to have a jet cluster formed with R=0.7 with a p_T > 400 GeV/c in the pseudoradipity intervals |η| ∈ (0.1, 0.7). The p_T requirement is made after jet energy corrections have been applied. We also accept events that satisfy these requirements when an R=0.4 or an R=1.0 cone is used.
4. The event satisfy an extremely loose E_T^miss significance requirement of S_MET < 10 (this variable is the observed missing transverse energy divided by the summed total transverse energy in the calorimeter).

We make a number of additional jet quality cuts to eliminate instrumental backgrounds and cosmic ray sources.

These event and jet selection requirements result in 2699 events with at least one jet with p_T > 400 GeV/c and with |η| ∈ (0.1, 0.7). Within this sample, there are 3290 jets with p_T > 400 GeV/c and 3079 jets with p_T ∈ (400, 500) GeV/c.

Rejection of Top Quark Events

The primary goal of this study was to compare the jet substructure associated with highly boosted QCD jets. From this point of view, any top quark contributions are in fact a background that could distort these substructure distributions. We therefore used the the correlations predicted by the MC to develop a strategy to reject ttbar backgrounds.

The key element of the strategy was to recognize that there are essentially three ttbar topologies that we should actively reject:

1. The case where both top quarks decay hadronically and result in two massive jets. We call this the "1+1" topology. Such events would be characterized by a second-leading jet with large mass and with S_MET consistent with no high-energy neutrinos.
2. The case where the recoil top quark decays semileptonically, resulting in an energetic neutrino, a b-jet and a charged lepton. Hence, this "SL" topology is characterized by large E_T^miss (and S_MET), an additional lower energy jet and possibly a charged lepton candidate.
3. The case where the recoil top quark decays hadronically, but where the decay daughters result in 2 or perhaps 3 jets. Because of the high p_T of the top quark, we would expect these events to be characterized by perhaps 2 jets with an invariant mass consistent with a top quark, and with low E_T^miss. We call this the "2+1" topology.

As a preliminary selection that targets two out of three of these topologies, we chose to apply the following relatively simple cuts to reject ttbar events:

• Reject any event with a second-leading jet with m^jet2 > 100 GeV/c².
• Reject any event with S_MET > 4.

We also require that the second-leading jet have a pT > 100 GeV/c so that we have a well-defined second-leading jet.

We find that with these cuts, only 35% of the ttbar MC events that would make it into this sample otherwise survive. On the other hand, 82% of the QCD MC events survive this "top rejection". Hence, this rejection strategy reduces any remaining contamination of ttbar events contributing to the leading jet to 0.3 fb, or to a level of approximately 2 observed events in our data sample.

The resulting number of events in data after making this selection is 2108.

W and Z boson Contamination

We note that there is a suggestion in the mass distribution of a "shoulder" in the region of 70-110 GeV/c². This may be evidence of a small sample of W/Z bosons decaying hadronically.

Based on MC calculations, we would expect a total production W/Z rate for boson p_T > 400 GeV/c of 4.5 pb and 3.0 pb for W and Z boson production, respectively. Factoring in the hadronic branching fractions of 0.68 and 0.70 for these two bosons and assuming that something like 70% of the bosons are reconstructed on a cone of R = 0.7 and make our jet p_T and η cuts, we end up with a predicted cross section of observed jets of ~ 3.6 fb. In our data sample, this would yield approximately 20 events with a jet in the 70-110 GeV/c² mass region where we see 197 events. These jets would naturally fall into this event sample where we have rejected top quark contamination (as opposed to an "enriched top quark sample"), given that we would expect the boson to be recoiling against one or a few QCD jets with little if any E_T^miss.

We expect the number of "boson jets" to be even less in the sample with jets formed with a cone size R = 0.4 though the number of QCD jets are expected to be less as well.

Corrections to Jet Mass for Multiple Interactions

The jet mass is sensitive to additional energy in the event coming from underlying event (UE) and multiple interactions (MI), as any additional energy in the jet cone will result in an increase in the jet mass. This mass shift is only partly included in the PYTHIA MC sample, and is not incorporated in any theoretical calculation of the jet mass. We therefore developed a correction scheme, based on a correction procedure suggested by S. Pronko, that corrected the jet mass for the effect of the underlying event (UE) and multiple interactions (MI) in the sample.

The scheme uses the complementary cone techniques to measure the average energy flow in the event as a function of the UE and MI together (UEMI). Restricting the jet sample to those events with N_vtx = 1, we could use the same technique to determine the energy flow in events where only UE was contributing. The mass shift associated with the UEMI and UE alone was determined on an event-by-event basis by collecting the energy in the complementary cone and adding it as an additional four-vector to the observed jet four vector of the jet. The shift in jet mass upward would be an estimate of the shift of the jet mass associated with this low energy flow, and therefore could be used to correct the observed jet mass downward. This makes the assumption that the jet mass correction is small compared to the jet mass itself and one could assume that the shift upward in mass adding the additional energy flow should be equal to the additional mass the jet inherits from the UE and/or MI.

We see that the average jet mass shift is approximately 6.5 GeV/c², and decreases somewhat with jet mass. We also see that the event-to-event fluctuations in this jet mass are quite large (the RMS is about the size of the average shift), arising from the stochastic nature of the energy flow in the UE and MI. We therefore decided to fit the profile plot of this distribution to an empirical parameterization, assuming that the dominant term would have a 1/m^jet behaviour.

In considering the theoretical implications of this sort of correction, we argue that it would be inappropriate to correct the jet mass for both the UE and MI, primarily because some part of the UE is coherent with the jet final state and some part is not, as has been shown by recent studies of the underlying event. The N_vtx = 1 events give us a correction that only includes the UE, so the difference between the jet mass corrections for N_vtx > 1 and for N_vtx = 1 provides us with an estimate of the jet mass correction associated with MI effects alone.

Below an uncorrected jet mass of 30 GeV/c², we do not expect such a shift to have real meaning given that the jets themselves would be very collimated and a low mass would suggest that the UE and/or MI have not contributed significantly to the jet mass. We therefore changed the parameterization for m^jet < 30 GeV/c² to be linear with an intercept at zero. This has no change in the overall correction for higher jet masses and allows us to have a continuous parameterization over the entire jet mass range.

We show in the below a comparison of the MI-corrected mass distributions for the data and MC jets (to be blessed soon). Although there is still a difference between these two samples, we are confident that this is not due to multiple interactions or underlying event effects, but likely arising from the modelling of jet hadronization in the Monte Carlo generator.

We have created similar jet mass corrections for R = 0.4 and the average jet mass correction for MI for the smaller cone is of order 1 GeV/c². The same method applied to R=1.0 cones does not work as well given that the complementary cones overlap with the jet cone (leading to cross-contamination for higher mass jets). We therefore use the R=0.7 corrections scaled up to the R=1.0. We use a scaling formula of R⁴ as the average number of additional towers from MI in the cone goes like R² and the average mass contribution of a single tower scales like R². Finally, we also scale the R = 0.7 correction down to R = 0.4 due to the low statistics we have for R = 0.4 when requiring high jet mass and 1 reconstructed vertex.

Unfolding

The jet mass distribution was unfolded back to particle level. The figure below shows the unfolding factors used for the high mass region for R = 0.7. Some uncertainties are added due to this procedure, see the next section.

The unfolding factors for angularity and planar flow are consistent with unity given the available statistics, and therefore these observables were not unfolded. An exception for this is the planar flow distribution for a cone size of R = 1.0.

Systematic Uncertainties

The systematic uncertainties associated with this analysis arise from the calculation and calibration of the jet mass for these high p_T jets. We find that there are four sources of systematic uncertainty:

1. The calibration of the calorimeter for energy depositions of different sizes in a given tower.
2. The MI correction
3. The unfolding proceduere
4. The PDF uncertainties on the PYTHIA calculations.

We determined an uncertainty in the overall energy flow as a function of radius from the centroid of the jet by comparing the ratio of charged particle momentum flow to calorimeter energy with data and MC and detector simulations. This allowed us to set a systematic uncertainty of 1 GeV/c² for m^jet=60 GeV/c² and 10 GeV/c² for m^jet=120 GeV/c², with the growth in this arising from the change in the shape of the jet.

We estimated the uncertainty on the MI correction to be approximately half the size of the correction, or 2 GeV/c² for R=0.7 jets.

Overall, we estimate that the jet mass systematic uncertainty is 10.2 GeV/c² for jets with masses > 70 GeV/c². This is a conservative estimate, especially at the jet masses below 100 GeV/c².

In order to study the effects of the hadronization model on the unfolding procedure, we compared the unfolding factors derived from parton level jets to those derived from hadron level jets. For the jet mass range of m^jet > 70 GeV/c², we found a difference of 10% in the unfolding factors. We also considered the uncertainty in the unfolding factor that arises from the 3% uncertainty on the jet energy scale. We shifted the detector level jet p_T cut up and down by 3% and re-derived the jet mass unfolding factors. We assigned an additional 10% uncertainty in the unfolding factor. We combined these two sources of uncertainty together in quadrature.

PDF uncertainties are estimated using the standard eigenvector approach.

Results

☆Cut Flow
The data distribution of jet pT for jets with pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7
The data distribution of jet2 η for jets with pT > 400 GeV/c, cone R=0.7
★The data mean mass shift (from complementary cone) vs jet mass, for Nvtx=1 and Nvtx>1 for jets with pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7
Jet Mass Unfolding Factors for jets with pT > 400 GeV/c, cone R=0.7
☆The data distribution of jet mass (MI corrected, unfolded, and with top rejection cuts) for jets with pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.4
☆The data distribution of jet mass (MI corrected, unfolded, and with top rejection cuts) for jets with pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7
☆The data distribution of jet mass (MI corrected, unfolded, and with top rejection cuts) for jets with pT > 400 GeV/c, |η| < 0.7, cone R=1.0
☆The data distribution of jet mass (MI corrected, unfolded, and with top rejection cuts) for jets with pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.4 and 0.7, and |η| < cone R=1.0
☆Distribution of jet mass (MI corrected, unfolded, and with top rejection cuts) for jets with pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.4. Black crosses are the data, red dashed is QCD MC, theoretical "all quarks" and "all gluons" curves are presented as well. The inset plot compares the results with Midpoint/SC and Anti-kT
☆Distribution of jet mass (MI corrected, unfolded, and with top rejection cuts) for jets with pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7. Black crosses are the data, red dashed is QCD MC, theoretical "all quarks" and "all gluons" curves are presented as well. The inset plot compares the results with Midpoint/SC and Anti-kT
☆Distribution of jet mass (MI corrected, unfolded, and with top rejection cuts) for jets with pT > 400 GeV/c, |η| < 0.7, cone R=1.0. Black crosses are the data, red dashed is QCD MC, theoretical "all quarks" and "all gluons" curves are presented as well. The inset plot compares the results with Midpoint/SC and Anti-kT
★The data mean planar flow shift (from complementary cone) vs planar flow, for Nvtx≥1 for jets with mass ∈ (130, 210) GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7
The data fit results for mean planar flow shift (from complementary cone) vs planar flow, for Nvtx≥1 for jets with mass ∈ (130, 210) GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7
☆Planar flow for jets with mass ∈ (130, 210) GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7. Black crosses are the data, red dashed is QCD MC, blue dotted is ttbar MC. The inset plot compares the results with Midpoint/SC and Anti-kT
☆Planar flow for jets with mass ∈ (130, 210) GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7 with top rejection cuts applied. Black crosses are the data, red dashed is QCD MC, blue dotted is ttbar MC. The inset plot compares the results with Midpoint/SC and Anti-kT
☆Unfolded planar flow distribution for jets with mass ∈ (130, 210) GeV/c2, pT > 400 GeV/c, |η| < 0.7, cone R=1.0. Black crosses are the data, red dashed is QCD MC, blue dotted is ttbar MC. The inset plot compares the results with Midpoint/SC and Anti-kT
☆Unfolded planar flow distribution for jets with mass ∈ (130, 210) GeV/c2, pT > 400 GeV/c, |η| < 0.7, cone R=1.0 with top rejection cuts applied. Black crosses are the data, red dashed is QCD MC, blue dotted is ttbar MC. The inset plot compares the results with Midpoint/SC and Anti-kT
★The data mean angularity shift (from complementary cone) vs angularity, for Nvtx≥1 for jets with mass ∈ (90, 120) GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7
The data fit results for mean angularity shift (from complementary cone) vs angularity, for Nvtx≥1 for jets with mass ∈ (90, 120) GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7
☆Angularity for jets with mass ∈ (90, 120) GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.4. Black crosses are the data, red dashed is QCD MC, τmin and τmax predictions are also shown. The inset plot compares the results with Midpoint/SC and Anti-kT
☆Angularity for jets with mass ∈ (90, 120) GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7. Black crosses are the data, red dashed is QCD MC, τmin and τmax predictions are also shown. The inset plot compares the results with Midpoint/SC and Anti-kT
☆Angularity for jets with mass ∈ (100, 130) GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.4. Black crosses are the data, red dashed is QCD MC, τmin and τmax predictions are also shown. The inset plot compares the results with Midpoint/SC and Anti-kT
☆Angularity for jets with mass ∈ (100, 130) GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7. Black crosses are the data, red dashed is QCD MC, τmin and τmax predictions are also shown. The inset plot compares the results with Midpoint/SC and Anti-kT
★The QCD MC mean mass shift (from complementary cone) vs jet mass, for Nvtx=1 and Nvtx>1 for jets with pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7
★The QCD MC mean planar flow shift (from complementary cone) vs planar flow, for Nvtx≥1 for jets with mass ∈ (130, 210) GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7
The QCD MC fit results for mean planar flow shift (from complementary cone) vs planar flow, for Nvtx≥1 for jets with mass ∈ (130, 210) GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7
★The QCD MC mean angularity shift (from complementary cone) vs angularity, for Nvtx≥1 for jets with mass ∈ (90, 120) GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7
The QCD MC fit results for mean angularity shift (from complementary cone) vs angularity, for Nvtx≥1 for jets with mass ∈ (90, 120) GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7
☆The data distribution of leading jet mass after applying top rejection cuts, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R = 0.4 and R=0.7
In the following plots showing PDF uncertainties, the full error bars on the data represent the total uncertainties, while the horizontal ticks mark the statistical uncertainties.
☆The data and QCD MC distributions of leading jet mass after applying top rejection cuts and unfolding zoomed in on high mass range, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.4, showing PDF uncertainties
☆The data and QCD MC distributions of leading jet mass after applying top rejection cuts and unfolding zoomed in on high mass range, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7, showing PDF uncertainties
☆The data and QCD MC distributions of leading jet mass after applying top rejection cuts and unfolding zoomed in on high mass range, pT > 400 GeV/c, |η| < 0.7, cone R=1.0, showing PDF uncertainties
☆The data and QCD MC distributions of planar flow without any jet mass cut, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7, showing PDF uncertainties
☆The data and QCD MC distributions of leading jet planar flow after top rejection cuts and without any jet mass cut, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7, showing PDF uncertainties
☆The data and QCD MC distributions of planar flow, 130 < mjet < 210 GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7, showing PDF uncertainties
☆The data and QCD MC distributions of leading jet planar flow after top rejection cuts, 130 < mjet < 210 GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7, showing PDF uncertainties
☆The data and ttbar MC distributions of planar flow, 130 < mjet < 210 GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7, showing PDF uncertainties
☆The data and ttbar distributions of leading jet planar flow after top rejection cuts, 130 < mjet < 210 GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7, showing PDF uncertainties
☆The data and QCD MC distributions of planar flow (unfolded), 130 < mjet < 210 GeV/c2, pT > 400 GeV/c, |η| < 0.7, cone R=1.0, showing PDF uncertainties
☆The data and QCD MC distributions of leading jet planar flow after top rejection cuts (unfolded), 130 < mjet < 210 GeV/c2, pT > 400 GeV/c, |η| < 0.7, cone R=1.0, showing PDF uncertainties
☆The data and ttbar MC distributions of planar flow (unfolded), 130 < mjet < 210 GeV/c2, pT > 400 GeV/c, |η| < 0.7, cone R=1.0, showing PDF uncertainties
☆The data and ttbar MC distributions of leading jet planar flow after top rejection cuts (unfolded), 130 < mjet < 210 GeV/c2, pT > 400 GeV/c, |η| < 0.7, cone R=1.0, showing PDF uncertainties
☆The data and QCD MC distributions of leading jet angularity after top rejection cuts, 90 < mjet < 120 GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.4, showing PDF uncertainties
☆The data and QCD MC distributions of leading jet angularity after top rejection cuts, 90 < mjet < 120 GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7, showing PDF uncertainties
☆The data and QCD MC distributions of leading jet angularity after top rejection cuts, 100 < mjet < 130 GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.4, showing PDF uncertainties
The data and QCD MC distributions of leading jet angularity after top rejection cuts, 100 < mjet < 130 GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7, showing PDF uncertainties
The following plots are variants of plots shown above without the Midpoint + Search Cone algorithm.
☆The data distribution of jet mass (MI corrected, unfolded, and with top rejection cuts) for jets with pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.4
☆The data distribution of jet mass (MI corrected, unfolded, and with top rejection cuts) for jets with pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7
☆The data distribution of jet mass (MI corrected, unfolded, and with top rejection cuts) for jets with pT > 400 GeV/c, |η| < 0.7, cone R=1.0
☆Distribution of jet mass (MI corrected, unfolded, and with top rejection cuts) for jets with pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.4. Black crosses are the data, red dashed is QCD MC, theoretical "all quarks" and "all gluons" curves are presented as well. The inset plot compares the results with Anti-kT
☆Distribution of jet mass (MI corrected, unfolded, and with top rejection cuts) for jets with pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7. Black crosses are the data, red dashed is QCD MC, theoretical "all quarks" and "all gluons" curves are presented as well. Inset plot compares the results with Anti-kT
☆Distribution of jet mass (MI corrected, unfolded, and with top rejection cuts) for jets with pT > 400 GeV/c, |η| < 0.7, cone R=1.0. Black crosses are the data, red dashed is QCD MC, theoretical "all quarks" and "all gluons" curves are presented as well. Inset plot compares the results with Anti-kT
☆Planar flow for jets with mass ∈ (130, 210) GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7. Black crosses are the data, red dashed is QCD MC, blue dotted is ttbar MC. The inset plot compares the results with Anti-kT
☆Planar flow for jets with mass ∈ (130, 210) GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7 with top rejection cuts applied. Black crosses are the data, red dashed is QCD MC, blue dotted is ttbar MC. The inset plot compares the results with Anti-kT
☆Unfolded planar flow distribution for jets with mass ∈ (130, 210) GeV/c2, pT > 400 GeV/c, |η| < 0.7, cone R=1.0. Black crosses are the data, red dashed is QCD MC, blue dotted is ttbar MC. The inset plot compares the results with Anti-kT
☆Unfolded planar flow distribution for jets with mass ∈ (130, 210) GeV/c2, pT > 400 GeV/c, |η| < 0.7, cone R=1.0 with top rejection cuts applied. Black crosses are the data, red dashed is QCD MC, blue dotted is ttbar MC. The inset plot compares the results with Anti-kT
☆Angularity for jets with mass ∈ (90, 120) GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.4. Black crosses are the data, red dashed is QCD MC, τmin and τmax predictions are also shown. The inset plot compares the results with Anti-kT
☆Angularity for jets with mass ∈ (90, 120) GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7. Black crosses are the data, red dashed is QCD MC, τmin and τmax predictions are also shown. The inset plot compares the results with Anti-kT
☆Angularity for jets with mass ∈ (100, 130) GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.4. Black crosses are the data, red dashed is QCD MC, τmin and τmax predictions are also shown. The inset plot compares the results with Anti-kT
☆Angularity for jets with mass ∈ (100, 130) GeV/c2, pT > 400 GeV/c, 0.1 < |η| < 0.7, cone R=0.7. Black crosses are the data, red dashed is QCD MC, τmin and τmax predictions are also shown. The inset plot compares the results with Anti-kT
☆pT / ET in Ring 1 for Midpoint/SC R=0.7 jets with 400 < pT < 500 GeV/c and 0.1 < |η| < 0.7 in single-vertex events
☆pT / ET in Ring 2 for Midpoint/SC R=0.7 jets with 400 < pT < 500 GeV/c and 0.1 < |η| < 0.7 in single-vertex events
☆pT / ET in Ring 3 for Midpoint/SC R=0.7 jets with 400 < pT < 500 GeV/c and 0.1 < |η| < 0.7 in single-vertex events
☆The jet mass distribution for Midpoint R=0.7 jets with pT > 400 GeV/c and 0.1 < |η| < 0.7 in multi-vertex events before MI correction, single-vertex events before MI correction, and multi-vertex events after MI correction
☆The jet pT distribution for Midpoint R=0.7 jets with pT > 400 GeV/c and 0.1 < |η| < 0.7 in data and QCD MC
☆The jet pT distribution for Midpoint R=0.7 jets with pT > 400 GeV/c and 0.1 < |η| < 0.7 in ttbar MC
☆The jet1 mass distribution for Midpoint R=0.7 jets with pT > 400 GeV/c and 0.1 < |η| < 0.7 in QCD and ttbar MC
☆The jet2 mass distribution for Midpoint R=0.7 jets in events for which pTjet1 > 400 GeV/c and 0.1 < |ηjet1| < 0.7 in QCD and ttbar MC

References

1. S. D. Ellis, J. Huston, K. Hatakeyama, P. Loch and M. Tonnesmann, Prog. Part. Nucl. Phys. 60, 484 (2008) [arXiv:0712.2447 [hep-ph]].
2. G. P. Salam, arXiv:0906.1833 [hep-ph].
3. T. Han, S.J. Lee, F. Maltoni, G. Perez, Z. Sullivan, T.M.P. Tait and L. T. Wang, "Topquark Physics at the LHC," part of "The Hunt for New Physics at the Large Hadron Collider," to appear in Nucl. Phys. B, arXiv:1001.2693 [hep-ph].
4. M. H. Seymour, Z. Phys. C 62 (1994) 127; D. Benchekroun, C. Driouichi, A. Hoummada, SN-ATLAS-2001-001, ATL-COM-PHYS-2000-020, EPJ Direct 3, 1 (2001); J. M. Butterworth, B. E. Cox and J. R. Forshaw, "W W scattering at the LHC," Phys. Rev. D 65, 096014 (2002) [arXiv:hep-ph/0201098].
5. K. Agashe, A. Belyaev, T. Krupovnickas, G. Perez and J. Virzi, Phys. Rev. D 77, 015003 (2008) [arXiv:hep-ph/0612015].
6. A. L. Fitzpatrick, J. Kaplan, L. Randall and L. T. Wang, JHEP 0709, 013 (2007) [arXiv:hep-ph/0701150].
7. B. Lillie, L. Randall and L. T.Wang, JHEP 0709, 074 (2007) [arXiv:hep-ph/0701166].
8. K. Agashe, H. Davoudiasl, G. Perez and A. Soni, Phys. Rev. D 76, 036006 (2007) [arXiv:hep-ph/0701186].
9. K. Agashe et al., Phys. Rev. D 76, 115015 (2007) [arXiv:0709.0007 [hep-ph]].
10. J. M. Butterworth, J. R. Ellis, A. R. Raklev and G. P. Salam, Phys. Rev. Lett. 103, 241803 (2009) [arXiv:0906.0728 [hep-ph]].
11. J. M. Butterworth, A. R. Davison, M. Rubin and G. P. Salam, Phys. Rev. Lett. 100, 242001 (2008) [arXiv:0802.2470 [hep-ph]].
12. G. D. Kribs, A. Martin, T. S. Roy and M. Spannowsky, arXiv:0912.4731 [hep-ph].
13. T. Plehn, G. P. Salam and M. Spannowsky, Phys. Rev. Lett. 104, 111801 (2010) [arXiv:0910.5472 [hep-ph]].
14. D. Krohn, J. Shelton and L. T. Wang, arXiv:0909.3855 [hep-ph].
15. D. Acosta et al. (CDF Collaboration), "Study of Jet Shapes in Inclusive Jet Production in p pbar Collisions at √s = 1.96 TeV," Phys. Rev. D 71, 112002 (2005).
16. V.M. Abazov et al (D0 Collaboration), "Subjet Multiplicity of Gluon and Quark Jets Reconstructed with k_T Algorithm in p pbar Collisions" Phys. Rev. D 65, 052008 (2002) [arXiv: hep-ex/0108054].
17. T. Aaltonen et al. (CDF Collaboration), "Model-Independent and Quasi-Model-Independent Search for New Physics at CDF," Phys. Rev. D 78, 012002 (2008).
18. T. Affolder et al. (CDF Collaboration), "Measurement of the Top Quark PT Distribution in p pbar Collisions at √s = 1.8 TeV," Phys. Rev. Lett. 87, 102001 (2001) .
19. V. M. Abozov et al. (D0 Collaboration), "Dependence of the t tbar Production Cross Section on the Transverse Momentum of the Top Quark," arXiv:1001.1900 (January 2010).
20. T. Aaltonen et al. (CDF Collaboration), "First Measurement of the t tbar Differential Cross Section dσ/dM_{t tbar} in p pbar Collisions at √s = 1.96 TeV," Phys. Rev. Lett. 102, 222003 (2009).
21. N. Kidonakis and R. Vogt, "Next-to-Next-to-Leading Order Soft-Gluon Corrections in Top Quark Hadroproduction," Phys. Rev. D 68, 114014 (2003) [hep-ph/0308222].
22. J. C. Collins, D. E. Soper and G. Sterman, Adv. Ser. Direct. High Energy Phys. 5, 1 (1988) [arXiv:hep-ph/0409313].
23. L. G. Almeida, S. J. Lee, G. Perez, I. Sung and J. Virzi, Phys. Rev. D 79, 074012 (2009) [arXiv:0810.0934 [hep-ph]].
24. W. Skiba and D. Tucker-Smith, Phys. Rev. D 75, 115010 (2007) [arXiv:hep-ph/0701247].
25. B. Holdom, JHEP 0708, 069 (2007) [arXiv:0705.1736 [hep-ph]].
26. L. G. Almeida, S. J. Lee, G. Perez, G. Sterman, I. Sung and J. Virzi, Phys. Rev. D 79, 074017 (2009) [arXiv:0807.0234 [hep-ph]].
27. J. M. Butterworth, J. R. Ellis and A. R. Raklev, "Reconstructing sparticle mass spectra using hadronic decays," JHEP 0705 (2007) 033 [arXiv:hep-ph/0702150].
28. J. Thaler and L. T. Wang, JHEP 0807, 092 (2008) [arXiv:0806.0023 [hep-ph]].
29. D. E. Kaplan, K. Rehermann, M. D. Schwartz and B. Tweedie, Phys. Rev. Lett. 101 (2008) 142001 [arXiv:0806.0848 [hep-ph]].
30. G. Brooijmans, ATLAS note, ATL-PHYS-CONF-2008-008; ATL-COM-PHYS-2008-001;ATL-PHYS-PUB-2009-081; J. Conway, et. al., LPC Workshop on Early Physics at CMS, UC Davis (2007); G. Brooijmans et al., arXiv:0802.3715 [hep-ph].
31. D. Krohn, J. Thaler and L. T. Wang, arXiv:0912.1342 [hep-ph].
32. C. F. Berger, T. Kucs and G. Sterman, Phys. Rev. D 68, 014012 (2003) [arXiv:hep-ph/0303051].
33. M. Cacciari, G. P. Salam and G. Soyez, JHEP 0804 (2008) 063 [arXiv:0802.1189 [hep-ph]]; S. D. Ellis, A. Hornig, C. Lee, C. K. Vermilion and J. R. Walsh, arXiv:1001.0014 [hep-ph]; S. D. Ellis, C. K. Vermilion and J. R. Walsh, arXiv:0912.0033 [hep-ph]; S. D. Ellis, C. K. Vermilion and J. R. Walsh, Phys. Rev. D 80, 051501 (2009) [arXiv:0903.5081 [hep-ph]].
34. R. Alon, O. Gedalia, G. Perez, G. Sterman and I. Sung, unpublished.
35. G. Perez, G. Sterman and I. Sung, private communications.
36. C. F. Berger and L. Magnea, Phys. Rev. D 70, 094010 (2004) [arXiv:hep-ph/0407024].
37. A. Banfi, G. P. Salam and G. Zanderighi, JHEP 0707, 026 (2007) [arXiv:0704.2999 [hep-ph]].
38. S. D. Ellis, A. Hornig, C. Lee, C. K. Vermilion and J. R. Walsh, arXiv:1001.0014 [hep-ph].
39. S. Fleming, A. H. Hoang, S. Mantry and I. W. Stewart, arXiv:0711.2079 [hep-ph]; S. Fleming, A. H. Hoang, S. Mantry and I. W. Stewart, Phys. Rev. D 77, 074010 (2008) [arXiv:hep-ph/0703207]; A. H. Hoang and I. W. Stewart, arXiv:0808.0222 [hep-ph].
40. T. Aaltonen et al. (CDF Collaboration), "Measurement of the Inclusive Jet Cross Section at the Fermilab Tevatron p anti-p Collider Using a Cone-Based Jet Algorithm," arXiv:hep-ex/0807.2204v4, Phys. Rev. D78, 052006 (2008) .
41. G. C. Blazey et al., arXiv:hep-ex/0005012. Published in "Proceedings of the Physics at RUN II: QCD and Weak Boson Physics Workshop," Batavia, Illinois, Nov 1999, pp 47-77.
42. A. Bhatti et al., "Determination of the Jet Energy Scale at the Collider Detector at Fermilab," arXiv:hep-ex/0510047, Nucl. Instrum. Methods in Phys. Res. Sec. A 566, 375 (2006).
43. S. Sabik and P. Savard, "Track Reconstruction Efficiency in Jets," CDF/ANAL/JET/CDFR/6894 (February 2004).
44. T. Aaltonen et al. (CDF Collaboration), CDF Conference Note 9913 (October 2009).
45. M. Cacciari, G.P. Salam and G. Soyez, Phys. Lett. B641, 57 (2006) [hep-ph/0512210]. We use Fastjet Version 2.4.2.