High p_{T} Top Quarks at the Large Hadron Collider

High Top Quarks at the Large Hadron Collider

U. Baur111baur@ubhex.physics.buffalo.edu Department of Physics, State University of New York,
Buffalo, NY 14260, USA
   L.H. Orr222orr@pas.rochester.edu Dept. of Physics and Astronomy, University of Rochester,
Rochester, NY 14627, USA
Abstract

Many new physics models predict resonances with masses in the TeV range which decay into a pair of top quarks. With its large cross section, production at the Large Hadron Collider (LHC) offers an excellent opportunity to search for such particles. The identification of very energetic top quarks is crucial in such an analysis. We consider in detail the () final state for high top quarks. In this phase space region, two or more of the final state quarks can merge into a single jet due to the large Lorentz boost of the parent top quark. As a result, a large fraction of events with an invariant mass in the TeV region contains less than four observable jets. Requiring one or two tagged -quarks, we calculate the jets, jets, jets, , and single top plus jets backgrounds for these final states, and identify cuts which help to suppress them. In particular, we discuss whether a cut on the jet invariant mass may be useful in reducing the background in the  jets channel. We also investigate how next-to-leading order QCD corrections affect high top quark production at the LHC. We find that the  jets and  jets final states with one or two -tags will significantly improve the chances for discovering new heavy particles in the channel at the LHC.

preprint:

I Introduction

The Large Hadron Collider (LHC) is scheduled to have its first physics run in 2008. Investigating jet, weak boson and top quark production are some of the goals of the 2008 run. Top pair production at the LHC, with a cross section which is about a factor 100 larger than at the Fermilab Tevatron, will make it possible to precisely determine the top quark properties [1]. It also offers an excellent chance to search for new physics in the early operational phase of the LHC. Once the LHC reaches design luminosity, production will provide access to new phenomena in the multi-TeV region. Many extensions of the Standard Model (SM) predict particles which decay into pairs, and thus show up as resonances in the invariant mass, , distribution. The masses of these particles are typically in the TeV range. For example, topcolor [2, 3] and Little Higgs [4, 5, 6] models predict weakly coupled new vector bosons, models with extra dimensions [7, 8, 9] can have Kaluza-Klein (KK) excitations of the graviton [10, 11] the weak [9, 12] and the strong gauge bosons [13, 14, 15, 16, 17, 18, 19, 20] which couple to top quarks, while massive axial vector bosons appear in torsion gravity models [21]. Resonances in the channel also occur in technicolor [22, 23], chiral color [24] and models with a strong gauge symmetry [25, 26]. In some models [10, 13, 14, 15, 16], the couplings of the new particles to light quarks and gluons is suppressed, and the final state becomes their main discovery channel.

Top quarks decay either hadronically, (), or semileptonically, (; decays with leptons in the final state are ignored here). Pair production of top quarks thus results in so-called “di-lepton+jets” events, , “lepton+jets” events, , or the “all-hadronic”,  quarks, final state. For sufficiently small top quark transverse momenta, , a substantial fraction of events has a number of isolated jets within the and rapidity range covered by the detector which is equal to or greater (when large angle, hard QCD radiation is included) than the number of quarks in the final state. This is reflected in the standard selection criteria of the LHC experiments. For example, to identify lepton+jets events, ATLAS and CMS require an isolated charged lepton, missing transverse momentum, and at least four isolated hadronic jets. For events with more than four jets, the four leading (highest transverse momentum) jets are selected. Of these four jets two have to be tagged as a -quarks [27, 28]. The main background in this case originates from  jets and  jets production, and is quite small [27, 28].

While the standard top quark selection criteria work well for top quark transverse momenta less than a few hundred GeV and invariant masses below 1 TeV, they are not adequate in the TeV region where signatures from new resonances are expected. In this region the top quark decay products are highly boosted and thus almost collinear. This frequently results in non-isolated leptons and/or merged or overlapping jets for lepton+jets and all-hadronic events, ie. the number of jets may be smaller than the number of final state quarks. Furthermore, the -tagging efficiency in the TeV region may be significantly smaller than at low energies [6, 14, 19]. Imposing standard selection criteria for very energetic top quarks therefore may dramatically reduce the observable cross section for invariant masses in the TeV range, and severely limit the sensitivity of the LHC experiments to resonances in this range.

Extending the selection criteria to include topologies with fewer jets is an obvious strategy for improving the selection efficiency for very energetic top quarks. On the other hand, this may significantly increase the background. For example, for lepton+jets events where all three quarks originating from the hadronically decaying top quark merge into one jet, and production contribute to the background. These processes occur at a lower order in perturbation theory than  jets and  jets and therefore are potentially more dangerous. Relaxing the selection criteria further by requiring only one tagged -quark in events may partially compensate for the reduced -tagging efficiency at very high energies. However, this will also increase the reducible background where a light quark or gluon jet is misidentified as a -quark. Since the mistagging probability worsens significantly with energy [6, 19], the background for final states with only one -tag is potentially much larger than if two -tags are required.

The importance of modifying the selection criteria for very energetic top quarks to optimize the search for KK excitations of the gluon in bulk Randall-Sundrum models has been discussed in Refs. [13] and [14]. In this paper we follow a more general approach and investigate whether it is feasible to improve the selection efficiency for very energetic top quarks. In Sec. II we discuss the signatures and the selection of events with high top quarks in the lepton+jets, di-lepton+jets, and the all-hadronic decay modes. We also investigate how next-to-leading order (NLO) QCD corrections affect the cross section for the lepton+jets channel in the phase space region of interest. The main result of Sec. II is that the  jets and  jets final state topologies with one or two tagged -jets offer the best chances to improve the selection efficiency. In Sec. III we calculate the differential cross sections of the SM background processes as a function of the invariant mass and the top quark transverse momentum for these final states. More precisely, we consider the jets, jets, jets,  jets,  jets, , and backgrounds. We also show that cluster transverse mass and invariant mass cuts are sufficient to control the background at large values of and . Of particular interest for suppressing the background is a cut on the jet invariant mass in and production. In Sec. IV we investigate the efficiency of such a cut. Our conclusions are presented in Sec. V.

Considering the  jets and  jets final state topologies with one or two tagged -jets in production is, of course, not new. These final states have been successfully used to search for the top quark in Run 1 of the Fermilab Tevatron [29, 30] where it was essential to maximize the number of signal events. This is also the case at the LHC in the high invariant mass and region when searching for signals of new physics. However, there is an important difference between the top quark search at the Tevatron and the search for new physics in the channel at the LHC. At the Tevatron, most  jets and  jets events are the result of one or two jets which do not pass the and rapidity cuts imposed. For very energetic top quarks at the LHC, jet merging is the main source of such events.

All tree level (NLO QCD) cross sections in this paper are computed using CTEQ6L1 (CTEQ6M) [31] parton distribution functions (PDFs). For the CTEQ6L1 PDF’s, the strong coupling constant is evaluated at leading order with . The factorization and renormalization scales for the calculation of the signal are set equal to , where  GeV is the top quark mass. The value of the top quark mass chosen is consistent with the most recent experimental data [32]. The choice of factorization and renormalization scales of the background processes is discussed in Sec. III. The Standard Model (SM) parameters used in all tree-level calculations are [33]

(1)
(2)
(3)

where is the Fermi constant, and are the and boson masses, is the weak mixing angle, and is the electromagnetic coupling constant in the scheme.

Ii Detecting very energetic top quarks

ii.1 The lepton+jets final state at leading order

We begin our discussion by examining the lepton+jets final state in more detail. The di-lepton+jets and the all-hadronic final states will be discussed in Sec. II.4. Approximately 30% of all top quark pairs yield lepton+jets events. We calculate the SM cross section at leading-order (LO), including all decay correlations. Top quark and decays are treated in the narrow width approximation. We require that both -quarks are tagged with a constant efficiency of and that there are two additional jets in the event which are not tagged. We sum over electron and muon final states and impose the following acceptance cuts on events at the LHC ( collisions at  TeV):

(4)
(5)
(6)
(7)

Here, () is the pseudo-rapidity (rapidity), , and is the missing transverse momentum originating from the neutrino in which escapes undetected. We include minimal detector effects via Gaussian smearing of parton momenta according to ATLAS [27] expectations, and take into account the -jet energy loss via a parametrized function. Charged leptons are assumed to be detected with an efficiency of . All numerical results presented in this paper include the appropriate combination of -tagging and lepton detection efficiencies unless specified otherwise. In addition to the cuts listed in Eqs. (4) – (7), the LHC experiments will also impose isolation cuts on all final state objects except the missing transverse momentum by requiring the separation in pseudo-rapidity – azimuth space to be larger than a minimum value, :

(8)

The minimum separation usually is in the range .

New particles which decay into a pair of top quarks lead to resonances in the invariant mass distribution and to a Jacobian peak in the top quark transverse momentum distribution. In the following we therefore concentrate on these observables. Since the neutrino escapes undetected, cannot be directly reconstructed. However, assuming that the charged lepton and the missing transverse momentum come from a boson with a fixed invariant mass , it is possible to reconstruct the longitudinal momentum of the neutrino, , albeit with a twofold ambiguity. In our calculations of the distribution in the lepton+jets final state, we reconstruct the invariant mass using both solutions for with equal weight. The energy loss of the -quarks slightly distorts the distribution. As a result, the quadratic equation for does not always have a solution. Events for which this is the case are discarded in our analysis. This results in a reduction of the cross section in the distribution. More advanced algorithms [34] improve the reconstruction of the mass of the new physics signal, however, they have little effect on the shape of the SM distribution.

In order to reconstruct the or transverse momentum one has to correctly assign the and momenta to the parent top or anti-top quark. Since it is impossible to determine the -charge on an event-by-event basis, we combine , , and the transverse momentum of the tagged -jet with the smaller separation from the charged lepton to form the transverse momentum of the semileptonically decaying top quark. The ’s of the two non-tagged jets and the other -jet form the transverse momentum of the hadronically decaying top333Alternatively, one could select the combination which minimizes  [35].. We find that the reconstructed and true top quark transverse momentum distributions are virtually identical except for transverse momenta below 50 GeV where deviations at the few percent level are observed.

The angle between the momentum vector of a top quark decay particle and the flight direction of the parent quark tends to be small for very energetic top quarks, due to the large Lorentz boost. Imposing a standard isolation cut on the charged lepton and the jets in events thus significantly reduces the cross section at large values of and . This is seen in Fig. 1, where we show the invariant mass and the distribution for the final state and three choices of , with corresponding to no isolation cut being imposed.

[3mm]

Figure 1: The LO differential cross section at the LHC for three choices of as a function of a) the reconstructed invariant mass, and b) the reconstructed of the semileptonically decaying top quark. The cuts imposed are listed in Eqs. (4) – (7).

The smallest differential cross section shown in Fig. 1,  pb/GeV, corresponds to 1 event in a 100 GeV bin for an integrated luminosity of 100 fb. It can be viewed as a crude measure of the LHC reach once it operates at design luminosity. At LO, the transverse momentum distributions of the and the quark are identical. We therefore do not show the transverse momentum distribution of the hadronically decaying top quark in Fig. 1. The figure demonstrates that the isolation cut greatly reduces the cross section in the TeV region, in particular in the distribution.

Events which fail the isolation cut either have a charged lepton which is embedded inside a jet, or some of the final state quark jets merge and one observes lepton+jets events with fewer than four jets. Events with non-isolated leptons are difficult to utilize. In most lepton+jets events with a non-isolated lepton, the lepton is embedded in the -jet which originates from the same parent top quark. Such a lepton can easily be confused with a charged lepton originating from semileptonic -decay. Furthermore, such events look similar to QCD jets events where one or more badly mismeasured jets result in a significant amount of missing transverse momentum. Finally, since the neutrino is not required to be isolated, the cut affects the decay much less than . Trying to utilize lepton+jets events with fewer than four jets thus is potentially more beneficial than attempting to use events where the lepton is not isolated.

In the following we therefore focus on  jets events with . If we require two -tagged jets, the final state does not contribute. This leaves the  jets and  jets final states.

We calculate LO  jets production by merging light quark jets from and -quark jets if

(9)

. If a -quark jet and a light quark jet merge, their momenta are combined into a -jet. Jets are counted and used in the reconstruction of if they satisfy Eqs. (5) and (6) after merging. The and differential cross sections for  jets with two -tags and are shown in Fig. 2a and 2b, respectively. For comparison, we also show the  jets distributions.

[3mm]

Figure 2: The LO  jets differential cross section at the LHC as a function of a) the reconstructed invariant mass, and b) the reconstructed of the semileptonically decaying top quark. Shown are the cross sections for two (blue), three (red) and four (black) jets in the final state. Two of the jets are assumed to be -tagged. The cuts imposed are listed in Eqs. (4) – (7). In addition an isolation cut (see Eq. (8)) with is imposed and jets with are merged.

Taking into account the  jets and  jets final states is seen to increase the cross section for very large values of by more than a factor of 3. The effect is even more pronounced in the distribution where the 2 jet and 3 jet final states extend the range which is accessible from 900 GeV to about 1.4 TeV. The LO results shown in Fig. 2 are, of course, expected to be somewhat modified by QCD corrections. The QCD corrections for the lepton+jets final state topologies will be discussed in more detail in Sec. II.2. They do not qualitatively change the results presented in Fig. 2.

At small transverse momenta and invariant masses, most of the 2 jet and 3 jet final states originate from 4 jet events where one or both light quark jets do not pass the and rapidity cuts of Eq. (5). With increasing energies, more and more  jet events with contain jets which originate from jet merging. This is most pronounced in the case where it leads to a shoulder in the differential cross section at  TeV and  GeV. At large invariant masses or ’s,  jet events originate almost exclusively from the merging of all three quarks in into one “-jet” which, however, is tagged as a -jet. The invariant mass of such jets, which is close to , and their shower profile [36] are potential tools for discriminating signal and QCD / background events [13, 14]. The jet invariant mass cut will be discussed in more detail in Sec. IV. Alternatively, one can pursue a strategy similar to that discussed in Refs. [37] and [38]. jet events at high energies originate either from the merging of the two light quark jets from , or from the merging of one light quark jet with a -jet.

SM production at the LHC is dominated by gluon fusion and the -channel top quark exchange diagram is playing an important role in this process. As a result, top quarks tend to be produced with a fairly large rapidity, ie. with a large invariant mass but a relatively small top quark . The steeply falling distribution (see Fig. 2b) reflects this behavior. New physics particles decaying into , , manifest themselves as -channel resonances, leading to a Jacobian peak in the top quark transverse momentum distribution which peaks at , where is the mass. The relatively larger impact the  jet final states have on the SM distribution, therefore, should carry over to the distribution in the vicinity of the resonance, ie. the resonance should be significantly more pronounced in lepton+jets events with 2 or 3 jets. This is borne out in Fig. 3, where we show the invariant mass and top quark distributions for the  jet final states with in the SM (black solid lines), and for two types of KK excitations of the gluon. For comparison, we also show the differential cross sections for .

Figure 3: The LO  jets, , differential cross section at the LHC as a function of the reconstructed invariant mass, and the reconstructed of the semileptonically decaying top quark. Two of the jets are assumed to be -tagged. Shown are the cross sections for two, three and four jets in the final state in the SM (black lines) and for two types of KK gluon excitations (see text). The cuts imposed are listed in Eqs. (4) – (7). In addition an isolation cut (see Eq. (8)) with is imposed and jets with are merged.

The red curves give predictions for a KK gluon, , with  TeV, vector like couplings to quarks and coupling strength , where is the QCD coupling constant [18, 19]. The solid and dashed blue lines show the cross sections for bulk RS KK gluons, , with  TeV and 3 TeV, respectively [13, 14]. Bulk RS KK gluons have vector-like couplings with strength to all quarks except the top and bottom quarks for which , , and . The width of the KK gluons is taken to be . They do not couple to gluons at LO. It is obvious that the  jet and  jet final states offer a much better chance to discover such resonances, especially if the mass of the resonance is larger than 2 TeV. Qualitatively similar results are obtained for other types of resonances. However, if they couple weakly to top quarks, such as bosons appearing in Little Higgs or topcolor models, their significance may be very much reduced.

ii.2 NLO QCD corrections to the lepton+jets final state at high energies

So far, our calculations have been limited to lowest order in perturbation theory. Since QCD corrections to top pair production are known to be significant, we now study how NLO QCD corrections affect the lepton+jets final state topologies. QCD corrections may change the normalization and/or the shape of distributions. In addition, hard QCD bremsstrahlung may produce additional isolated jets which complicate the reconstruction of the invariant mass and the top quark transverse momentum distribution. QCD corrections apply to both the top production and decay processes; interference between the two is negligible in the narrow width approximation, which we employ. For very energetic top quarks, most extra jets originate from production-stage radiation, i.e. from QCD corrections for production. Jets coming from decay-stage radiation, i.e. from QCD corrections to and , rarely lead to additional isolated jets, due to the large Lorentz boost for very energetic top quarks.

We first investigate how NLO QCD corrections to production modify the shape and normalization of the , and distributions for a given number of decay jets. This assumes that the jets from the hadronic top decay have been correctly identified, for example by imposing an invariant mass cut on one or several jets. Subsequently, we will then discuss how QCD corrections affect these distributions for fixed observed jet multiplicities.

The NLO QCD corrections to production have been know for more than 15 years [39]. A more recent calculation [40] includes top quark decays and spin correlations. The NLO QCD corrections to production have been interfaced with the HERWIG shower Monte Carlo[41] in the program MC@NLO [42]. This produces a realistic transverse momentum distribution. Furthermore, MC@NLO includes top quark decay [43] and thus makes it possible to include acceptance cuts in the calculation. Using MC@NLO to compute the cross section including QCD corrections, we show the NLO to LO cross section ratio (-factor) for  jets, , as a function of the reconstructed invariant mass in Fig. 4 (solid histograms). Here, and in all other figures in this Section, is the number of jets resulting from the decay of the pair, not the number of jets in the event. Furthermore, we call the cross section obtained with MC@NLO the “NLO” cross section, although this is, strictly speaking, not correct: MC@NLO does take into account multiple gluon radiation in the leading log approximation.

Figure 4: The NLO to LO  jets cross section ratio (solid histograms) at the LHC as a function of the reconstructed invariant mass. Here, is the number of decay jets. The dashed histograms display the fraction of the NLO  jets events for which  GeV. Shown are the cross section ratios for two (blue), three (red) and four (black) decay jets. Two of the jets are assumed to be -tagged. The cuts imposed are listed in Eqs. (4) – (7). In addition an isolation cut (see Eq. (8)) with is imposed. decay jets with a separation have been merged.

For 3 jet and 4 jet final states, Fig. 4 shows that the -factor increases slowly with . In the 2 jet case, it rises at low invariant masses, and then decreases somewhat for  TeV. We also show the fraction of NLO  jet events with  GeV in Fig. 4 (dashed histograms). The fraction increases from about 25% at low invariant mass to at  TeV.

Figures 5 and 6 show the -factor and the

[3mm]

Figure 5: The NLO to LO cross section ratio (solid histograms) for  jets at the LHC as a function of the (black) and (blue) transverse momentum for a) two () and b) three () decay jets. The dashed histograms display the fraction of the NLO  jet events () for which  GeV. Two of the jets are assumed to be -tagged. The cuts imposed are listed in Eqs. (4) – (7). In addition an isolation cut (see Eq. (8)) with is imposed. decay jets with a separation have been merged.
Figure 6: The NLO to LO  jets cross section ratio (solid histograms) at the LHC as a function of the (black) and (blue) transverse momentum. The dashed histograms display the fraction of the NLO  jet events for which  GeV. The number of jets here refers to decay jets, and we assume that two of them are -tagged. The cuts imposed are listed in Eqs. (4) – (7). In addition an isolation cut (see Eq. (8)) with is imposed. decay jets with a separation have been merged.

fraction of events with  GeV (at NLO) as a function of the of the semileptonically and the hadronically decaying top quark. As mentioned before, at LO the distributions of the two top quarks in production are identical. This is no longer the case at NLO. Figures 5 and 6 show that the differential -factors can be quite different for and . The difference is most pronounced in the 2 jet final state (Fig. 5a). In the region  GeV most jets merge into a single jet. This favors a kinematical configuration where , ie. where the QCD jet(s) and the semileptonically decaying top quark are in the same hemisphere. As a result, the fraction of events with  GeV for  GeV is larger than that for in the same range. In turn, the fraction of events with  GeV for  GeV is smaller than that for . Below a of about 250 GeV, a new effect comes into play. If  GeV and is small, the hadronically decaying top quark has to carry a transverse momentum of  GeV). This makes it likely that one of the light quark jets originating from satisfies the jet acceptance cuts. On the other hand, the top quark transverse momentum is not high enough for jet merging. For small , events with a large transverse momentum of the system thus are very unlikely (black dashed histogram).

The evolution of the event fraction with  GeV as a function of is directly reflected in the corresponding -factor. The preference for events with for  GeV leads to a very large -factor for  GeV. The suppression of events with high transverse momentum at small then causes the -factor to sharply drop for  GeV (solid black histogram). While the -factor varies significantly with , it is essentially uniform for  GeV.

The -factor and the fraction of events with  GeV for the 3 jet and the 2 jet final state show the same qualitative behavior. In the 3 jet final state, an even larger fraction of events has a transverse momentum larger than 100 GeV, especially for very large top quark (dashed histograms in Fig. 5b). At low , the suppression of events with high is less pronounced than in the 2 jet final state. Consequently, the variation of the -factor with is smaller than for  jets. The -factor slowly increases with over the entire range.

In the 4 jet final state, the -factor is uniform for  GeV (see Fig. 6). For higher values, it becomes very large. For very large , the transverse momentum of essentially all events exceeds 100 GeV (dashed black histogram in Fig. 6). In contrast, the -factor stays uniform up to transverse momenta of about 800 GeV for the hadronically decaying top quark. The extremely large -factor for  GeV is a consequence of the separation cut which affects much more than at large . As a result, events which contain one or more hard QCD jets in the hemisphere opposite to that of the decay products are kinematically favored. For the same reason, and production becomes important for large values of  [44].

NLO QCD corrections mostly change the normalization of the and distributions. For these distributions, the cross section hierarchy for 2, 3 and 4  decay jets shown in Fig. 2 remains unchanged. With the extremely large -factor for the 4 jet final state, this is not obvious for the distribution. Figure 7 shows that for  GeV ( GeV) the cross section for the final state with 3 (2) jets from decays still exceeds that of the channel with 4  decay jets when NLO QCD corrections are taken into account.

Figure 7: The NLO  jets cross section at the LHC as a function of the transverse momentum. is the number of decay jets in the event, and two of these jets are assumed to be -tagged. The solid blue and red histograms show the cross sections for and , respectively. The dashed histogram represents the cross section. The cuts imposed are listed in Eqs. (4) – (7). In addition an isolation cut (see Eq. (8)) with is imposed. decay jets with a separation have been merged.

In phase space regions where most top pair events have a large transverse momentum, the NLO cross section is dominated by the tree level process . As a result, the NLO cross section depends significantly on the choice of the factorization and renormalization scale in these regions.

So far we have classified events by the number of decay jets. The number of extra jets from QCD radiation in production was not specified. At large top quark transverse momentum, we found that most events have  GeV and thus have one or more extra hard jets. These extra jets introduce a combinatorial background. Considering final states with a fixed jet multiplicity of 2, 3 or 4 jets, and requiring that the invariant mass of the jet(s) excluding the -jet with the smaller separation from the charged lepton is consistent with is expected to suppress hard extra QCD jets in the event, and thus the combinatorial background. As we shall demonstrate in Secs. III and IV, such a cut will also be helpful in reducing the background to an acceptable level. If no hard QCD jets are produced, the transverse momentum will be small. A rough estimate of the QCD corrections to  jets with no hard extra QCD jets can be obtained from the -factor for events with  GeV, . can be calculated from the inclusive -factor, , and the ratio of the NLO cross section with  GeV and the inclusive NLO rate, ,

(10)

which are both shown in Figs. 4 – 6. The distributions as a function of , , and are qualitatively very similar. is found to decrease smoothly from at low and to at large values. QCD corrections for top quark pairs with small transverse momentum thus are smaller than in the inclusive case, and result in somewhat steeper falling and distributions than at LO.

Quantitative results of course depend on the jet threshold considered; for a lower (higher) threshold of , a smaller (larger) -factor is found. More detailed simulations, which are beyond the scope of our paper, are required to develop a better understanding how QCD corrections affect the and distributions for fixed jet multiplicities when an invariant mass cut on one or more jets is imposed.

ii.3 -tagging for very energetic top quarks

So far, in our analysis, we have assumed that both -quarks in are tagged with an efficiency of each. However, for very energetic top quarks, the -tagging efficiency is expected to degrade [14]. This is easy to understand. The energy of the -quark in or is on average about 1/3 of that of the parent top quark. The higher the energy of the -quark, the more collimated the decay products are. Due to the finite angular resolution of the LHC detectors, this will increase the uncertainty in the position of the reconstructed secondary vertex, and thus decrease the tagging efficiency. In hadronic top decays where two or more jets merge, the overlapping of the -jet with one or several light quark jets may additionally complicate the reconstruction of the secondary vertex which is expected to result in a further decrease in . The increased decay length of very energetic -quarks, which makes it easier to tag -quarks, is not expected to compensate these effects.

Although detailed simulations of -tagging for very energetic top quarks do not exist yet, preliminary studies [6, 19] indicate that may decrease by a factor in the TeV region. Simultaneously, the probability for misidentifying a light quark, gluon or -jet as a -jet may increase by up to a factor 3.

A decrease of by a factor in the high energy regime results in a reduction of the observable cross section by up to a factor 10. However, the efficiency for tagging only one -quark in a event,

(11)

is much less sensitive to than . For , , ie. it varies by less than a factor of two. For small , the cross section of the lepton+jets final state with one -tag is much larger than that for two -tags. For example, for , . This, and the relative stability of the one tag cross section to variations of , make the lepton+jets final state with one -tag an attractive channel in the search for resonances in the channel.

The increase in rate in the lepton+jets channel with one -tag comes at the price of a potentially much larger background. The background for both one and two -tags in the lepton+jets channel will be examined in detail in Sec. III.

ii.4 The di-lepton+jets and all-hadronic final states

Our discussion, so far, has been focused on the lepton+jets final state. In this section we investigate whether the di-lepton and all-hadronic final states can significantly increase the range in and/or which can be accessed at the LHC.

In the di-lepton channel, (), one requires two isolated leptons with opposite charge, two jets with at least one -tag, and a substantial amount of . The main disadvantages of the di-lepton final state are its small branching ratio of , and the two neutrinos in the final state which make it impossible to reconstruct the invariant mass or the of the individual top quarks. However, the  jets final state is much less sensitive to the isolation cut at high energies than  jets which makes it worthwhile to investigate. The main background in this channel comes from jets and production [28].

Since the invariant mass cannot be reconstructed in the di-lepton final state, one has to use the cluster transverse mass,

(12)

where and are the transverse momentum and invariant mass of the system, respectively, to search for resonances. The cluster transverse mass distribution in the SM and for the KK gluon states discussed in Sec. II.1 is shown in Fig. 8.

Figure 8: The LO differential cross section at the LHC as a function of the cluster transverse mass (see Eq. (12)). At least one of the -quarks is assumed to be tagged. Shown are the cross sections in the SM (black lines) and for two types of KK gluon excitations (see Sec. II.1). The cuts imposed are listed in Eqs. (4) – (7). In addition an isolation cut (see Eq. (8)) with is imposed.

We require at least one -quark to be tagged and impose the same cuts as in Secs. II.1 and II.2. The cluster transverse mass distribution is seen to fall much more rapidly than that of the invariant mass. The di-lepton final state therefore will not be competitive with the lepton+jets final state when searching for resonances, and we will not discuss it further in this paper.

The all-hadronic final state, has the largest branching ratio () but also the largest background. In order to reduce the QCD multi-jet background to an acceptable level, two -tags have to be required. Imposing a standard isolation cut on the -jets and the four light quark jets, the main background originates from QCD  jet production, which is approximately one order of magnitude larger than the signal [27, 28].

As in the lepton+jets mode, the isolation cut strongly reduces the observable cross section in the all-hadronic final state for very energetic top quarks. In this region of phase space, some or all of the jets originating from top quark decay may merge, ie. the LO signal is spread out over the  jets final states with . The QCD background for is expected to be of the same size or larger than that in the  jet channel.

The large background makes it difficult to utilize the all-hadronic final state in a search for resonances. In the following, we therefore concentrate on the lepton+jets final state with one or two -tags.

Iii Background Calculations for the lepton+jets Final State

In Sec. II, we have shown that extending the search criteria for the lepton+jets final state to include topologies with less than 4 jets and/or one -tag may considerably increase the number of candidate events. These final states, however, will be useful in a search for resonances only if the backgrounds are sufficiently small. It is well known [27, 28, 45] that the background is indeed small in the 4 jet case with two -tags. Here we calculate the backgrounds contributing to the 2 jet and 3 jet final states and compare it with that obtained in the 4 jet case. We consider final states with one or two -tags. Backgrounds where one or two light quark, gluon or -quark jets are misidentified as a -jet are included in our calculation. Numerical results are presented for and misidentification probabilities of () and  [27, 28]. Since these numbers may well be considerably higher for very energetic top quarks [6, 19] we comment wherever appropriate on how our results change if is increased by a factor 3 and the -tagging efficiency, , is decreased by a factor 3.

The main background processes contributing to the  jet final states with are  jets,  jets, and  jets production,  jets,  jets production with , and , and production with . For each process, , and represents a light quark or gluon jet, or a -jet. production only contributes to the 2 jet and 3 jet final states. The  jets ( jets) background originates from  jets ( jets) production where one of the -quarks is not detected. We calculate these processes in the -quark structure function approximation. We have verified that, for , the differential cross sections for () and () where one -jet is not detected are very similar. For the 2 jet final state (), the NLO QCD corrections for all background processes except and production are known [46, 47, 48, 49, 50, 51, 52]. The background processes relevant for the 3 jet and 4 jet final states, however, are only known at LO. We therefore calculate all background cross sections consistently at LO, and comment wherever appropriate how NLO QCD corrections modify our results. To calculate  jets and  jets we use ALPGEN [33]. All other background processes are calculated using MadEvent [53].

 jets production where one -quark decays semileptonically also contributes to the background. Once a lepton isolation cut has been imposed, this background is known to be small for standard lepton+jets cuts [45]. For  jets events to mimic a production with very energetic top quarks, the -quarks also have to be very energetic. This will make the lepton isolation cut even more efficient. We therefore ignore the  jets background here.

 jets production in ALPGEN includes -jets in the final state. Since , this underestimates the background from  charm production. However, the cross section of  charm final states is only a tiny fraction of the full  jets rate, resulting in an error which is much smaller than the uncertainty on the background from other sources. One can also estimate the  charm cross section from that of  jets and  jets. For the phase space cuts imposed, quark mass effects are irrelevant. The  jets ( jets) cross section thus is about a factor 10 (100) smaller than the  jets ( jets) rate.

In the following we impose the standard acceptance cuts of Eqs. (4) – (8) with and reconstruct the invariant mass using the procedure described in Sec. II.1. The reconstruction of depends on the number of -tags and is discussed in more detail below. For the background processes, the distribution is replaced by the reconstructed  jets and  jets invariant mass distribution. The renormalization and factorization scales of background processes involving top quarks are set to ; for all other background processes we choose the mass. Since our calculations are performed at tree level, the cross section of many background processes exhibits a considerable scale dependence. However, uncertainties on the current -tagging efficiencies and the light jet mistag probability at high energies introduce an even larger uncertainty.

iii.1 Background for lepton+jets events with two -tags

The differential cross section of the SM  jets signal and the combined background from the processes discussed above as a function of the reconstructed and is shown in Fig. 9.

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Figure 9: The LO differential cross section of the SM  jets signal and the combined background as a function of a) the reconstructed invariant mass and b) the transverse momentum at the LHC. The two jets are assumed to be -tagged. The black and blue curves show the signal and background, respectively, imposing standard cuts (Eqs. (4) – (8)) with ). The dashed and red curves show signal and background if in addition a cluster transverse mass cut is imposed on the system (see Eq. (14)).

To reconstruct for signal and background  jet final states with two -tags, we use the method discussed in Sec. II.1. Imposing the standard cuts of Eqs. (4) – (8) with , signal and background are seen to be about equal. Only for  TeV and  TeV does the background dominate. The main background source is , except at very high and where production dominates.

The signal to background ratio can be significantly improved by imposing a cut

(13)

on the cluster transverse mass, , of the system which is defined by

(14)

where and are the transverse momentum and invariant mass of the system, respectively, and is the - or -quark which has the smaller separation from the charged lepton. sharply peaks at the top mass. The cluster transverse mass reduces the signal by about a factor 2 (1.5) at small (large) invariant masses and ’s (dashed curves). The background, on the other hand, decreases by a factor . At large and , production is the dominant contribution to the background after the cut has been imposed. At low energies, is still the largest background source.

The signal in the  jets final state with two -tags necessarily requires a small transverse momentum of the system. As discussed in Sec. II.2, the NLO and distributions fall somewhat faster than those at LO if the transverse momentum of the system is small. It is important to know whether the corresponding distributions of the dominant background processes, and , show the same behavior, or whether QCD corrections worsen the signal to background ratio. Calculating the NLO corrections to these processes using the program MCFM [54] and imposing a veto on additional hard jets, we find that they have a similar effect on the signal and the background distributions. QCD corrections thus will not change the signal to background ratio significantly.

In Fig. 10, we show the signal and the combined background for the 3 jet final state.

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Figure 10: The LO differential cross section of the SM  jets signal and the combined background as a function of a) the reconstructed invariant mass and b) the transverse momentum at the LHC. Two jets are assumed to be -tagged. The black and blue curves show the signal and background, respectively, imposing standard cuts (Eqs. (4) – (8)) with ). The dashed and red curves show signal and background if in addition a cluster transverse mass cut is imposed on the system (see Eq. (14)). The blue dashed and magenta curves, finally, show signal and background if in addition the invariant mass cut of Eq. (15) is imposed.

Imposing the standard cuts of Eqs. (4) – (8) only, the background is small at low values of and but dominates over the signal in the TeV region. Imposing a cut (see Eq. (13)) improves the situation. However, the background is still larger than the signal for  TeV and  TeV. To further improve the signal to background ratio one can impose an invariant mass cut on the system,

(15)

where is the non-tagged jet and is the -quark with the larger separation from the charged lepton. The cut suppresses the background by an additional factor for  TeV (magenta line), while it has a much smaller effect on the signal in this region (dashed blue curve). Note that the cut does reduce the signal by up to a factor 10 at small invariant masses. In this region most  jets events are the result of one jet not satisfying the and pseudo-rapidity cuts, and not of the merging of jets. If a jet fails the acceptance cuts, the system usually will not be in the vicinity of the top quark mass.

Once a cut has been imposed, the background is smaller than the signal over the entire and invariant mass range of interest. The main background sources in this case are and production. Without the cut, the main contributions to the background in the 3 jet final state originate from and production.

For completeness, we show the invariant mass and top quark distribution for the 4 jet final state in Fig. 11.

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Figure 11: The LO differential cross section of the SM  jets signal and the combined background as a function of a) the reconstructed invariant mass and b) the transverse momentum at the LHC. Two jets are assumed to be -tagged. The black and blue curves show the signal and background, respectively, imposing standard cuts (Eqs. (4) – (8)) with ). The dashed and red curves show signal and background if in addition a cluster transverse mass cut is imposed on the system (see Eq. (14)). The blue dashed and magenta curves, finally, show signal and background if in addition the invariant mass cut of Eq. (16) is imposed.

Once a and a

(16)

cut have been imposed, the background is below the signal for all top quark transverse momenta and invariant masses of interest. The cut has essentially no effect on the signal for  GeV and  GeV. The main background source in the 4 jet channel with (without) a cut is (single resonant and ) production. Note that we have not imposed a cut on the invariant mass of the two light quark jets, . It peaks near for both the signal and the , , background. Once a cut has been imposed, a cut thus will have little effect on the signal to background ratio.

As we have mentioned before, the -tagging efficiency at high invariant masses and transverse momenta may be up to a factor 3 smaller, and the misidentification probability for light quark and gluon jets may be up to factor 3 larger, than at small and . If this is indeed the case, production becomes the largest background source in  jets, and exceeds the signal by about a factor 2 in the distribution, even if a cut is imposed. To further improve the signal to background ratio in this channel, a cut on the invariant mass of the “-jet” which originates from the jet merging may be useful. This will be discussed in more detail in Sec. IV. In the distribution, the background remains smaller than the signal for  GeV. For the 3 jet and 4 jet final states, production remains the most important background for very energetic top quarks, and the signal is still larger than the combined background once a cluster transverse mass and cut have been imposed.

iii.2 Background for lepton+jets events with one -tag

As discussed in Sec. II.3, the cross section for  jets with one -tag may be significantly larger than that of final states with two -tags if is small. In this Section, we consider the background to the lepton+jets mode with one -tag. As before, we assume and in our simulations and comment on how the signal to background ratio changes if the -tagging efficiency decreases, and increases, by a factor of 3.

In addition to final states with 2, 3, or 4 jets, production can also contribute to the  jet channel if only one -tag is required. Top pair events where the -quark in is not detected, and the two light quark jets in are either missed or are merged with the tagged -quark are the dominant source for signal events. The invariant mass distribution thus may still carry useful information on heavy resonances. However, as shown in Fig. 12, the background from  jet production where the jet is misidentified as a -quark is much larger than the signal.

Figure 12: The LO differential cross section of the SM  jet signal (black) and the background (red) as a function of the reconstructed () invariant mass at the LHC. The jet is assumed to be -tagged. The cuts imposed are listed in Eqs. (4) – (7). In addition an isolation cut (see Eq. (8)) with is imposed.

Since the -jet from is usually lost, a cut is ineffective. Furthermore, it prevents reconstruction of the top quark transverse momentum. A cut on the jet invariant mass may help to reduce the background (see Sec. IV). However, any gain in the signal to background ratio from such a cut is at least partially canceled by a reduced -tagging efficiency and an enhanced light jet mistagging probability at large invariant masses. Furthermore, the  jet cross section is significantly smaller than that in the 2, 3, and 4 jet channels (see below) at large values of the reconstructed invariant mass. We will not consider the  jet final state further here.

The and distributions of the signal and the combined background in the  jets final state with one -tag are shown in Fig. 13.

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Figure 13: The LO differential cross section of the SM  jets signal and the combined background as a function of a) the reconstructed invariant mass and b) the transverse momentum at the LHC. One of the jets is assumed to be -tagged. The black and blue curves show the signal and background, respectively, imposing standard cuts (Eqs. (4) – (8)) with ). The dashed and red curves show signal and background if in addition a cluster transverse mass cut is imposed on the system (see Eq. (17)).

Even when a cut is imposed in addition to the standard transverse momentum, rapidity and separation cuts, the background is still considerably larger than the signal in the invariant mass distribution. In the distribution, the signal to background ratio is more favorable. Requiring  GeV, signal and background are approximately equal at large .

In final states with two -tags we used the -jet with the smaller separation from the charged lepton to reconstruct and to compute . Now, with only one -tag, we use the jet, , whether it is tagged or not, which is closest to the charged lepton in , ie. we require

(17)

If only the standard cuts of Eqs. (4) – (8) are imposed, production is the dominant background source for the  jet final state with one -tag. If we require in addition that the cluster transverse mass satisfies Eq. (17), and each contribute about one half of the total background.

To improve the signal to background ratio, one may consider a cut on the invariant mass of the jet with the larger separation from the charged lepton. This will be discussed in more detail in Sec. IV.

In Fig. 14 we show signal and background predictions for the 3 jet final state.

[3mm]

Figure 14: The LO differential cross section of the SM