«MADPH-95-909 RAL-TR-95-063 University of Wisconsin - Madison hep-ph/9511459 November 1995 Top pair production with an extra gluon at the Tevatron V. ...»
University of Wisconsin - Madison
Top pair production with an extra gluon at the Tevatron
V. Bargera, P.G. Mercadantea and R.J.N. Phillipsb
Physics Department, University of Wisconsin, Madison, WI 53706, USA
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, UK
We calculate top pair production and decay at the Tevatron p¯ collider, with
the emission of an extra gluon, and study the corresponding W + 5 jet top signals including full spin correlations in the W → ν leptonic and W → jj hadronic decays. We study the feasibility of reconstructing W + 5 jet top events with a single b-tag, including realistic energy resolution. Our suggested basic procedure based on kinematic ﬁtting achieves about 74% reconstruction eﬃciency, with 74% of the reconstructed events correctly classiﬁed (purity); this improves to 82% eﬃciency with 77% purity in double-b-tagged events. We suggest possible reﬁnements, based on virtuality criteria, that give higher purity at the cost of lower reconstruction eﬃciency.
and single-lepton + 4 jets channels and by both the CDF and D0 collaborations [1,2], it is interesting to explore other channels where top signals may be found. The underlying parton mechanism for producing these signals at the Tevatron energy is dominantly q + q → t + t → (bW +)(¯ −), ¯ ¯ bW (1) with either one or both of the W bosons decaying leptonically: W → ν ( = e, µ).
It is important to tag one or more of the b-jets, by a displaced vertex or by a lepton from b-decay, in order to establish the signal and discriminate against background. For determining the top quark mass, it is preferable to study the (W → ν) + 4 jets channels, where one of the W -bosons decays hadronically (W → jj) and a suitably chosen three-jet combination has invariant mass m(bjj) mt, avoiding problems with invisible neutrinos. The principal background in the W + 4 jets channel comes from the electroweak production of a single W -boson plus four QCD jets , but with the usual acceptance cuts and b-tagging this background is much smaller than the signal.
In high-Q2 processes like top pair production, it is not uncommon that additional hard QCD radiation (typically a gluon) will be emitted, viz
Here the gluon can be radiated either from the incident quarks, or from the produced top quarks before they decay, or from subsequent top decays into bW, and complete calculations have recently been performed  exploiting the MADGRAPH program .
These improve on previous calculations that omitted radiation from top decay ; the new results coherently combine the eﬀects of radiation during both production and decay processes, together with their interference. The radiation of gluons from the colordisconnected process of hadronic W -decay (W → jj) can be ignored here, since the hadronically decaying W is identiﬁed experimentally as a dijet with invariant mass m(jj) MW. In the ﬁve-jet channel, it seems very likely that the background from W + 5 QCD jets will also be small compared to the signal, after b-tagging.
There are four conﬁgurations in each class, corresponding to two W → ν solutions and two diﬀerent ways to pair the b-quarks with W -bosons. Although we evaluate all the diagrams in each event, Class A is well represented by diagrams a,b,e,f,g shown in Figure 1, Class B by d,f and Class C by c,e (in the case of W + → + ν leptonic decay).
We note that gluon emission from a top quark can contribute to Class A or B or C.
The underlying idea for event reconstruction is that events are most likely to occur in regions of phase space where one class of Feynman diagrams has both a top propagator and an antitop propagator near the mass shell, and are unlikely otherwise; the near-shell propagators deﬁne the event class. Thus almost all events fall into one of the Classes A,B,C, although a very small fraction may defy this classiﬁcation (e.g. one top may decay far oﬀ-shell).
Lepton-tagging of the b-jet would distinguish b from ¯ and hence reduce the number b of competing conﬁgurations to six (two in each class), improving the prospects for a correct reconstruction. Our analysis neglects this positive feature, implicitly assuming vertex-tagging; however, we also neglect for simplicity the negative eﬀects of possible mistagging (illustrated in Ref. ).
Our procedure is ﬁrst to identify the gluon and other jets as indicated above (with W → jj the best ﬁt of untagged jet pairs), and then to evaluate the invariant masses m1, m2 of the two “top” candidate clusters in each conﬁguration, and to assign a closeness
Tests with Monte Carlo events We have tested this procedure with Monte Carlo (W → ν) + 5 jet events generated by the MADGRAPH program , using the observed top mass mt = 174 GeV [1,2] and calculated decay width Γt = 1.53 GeV. To simulate detector energy resolution we add
realistic gaussian smearing:
where η = ln tan(θ/2) is pseudorapidity, (∆R)2 = (∆η)2 + (∆φ)2 measures angular separation, while θ and φ are the usual polar and azimuthal angles with respect to the beam. These cuts are applied at the parton level, interpreting quarks and gluons as jets.
In the absence of smearing, we ﬁnd that our procedure correctly reconstructs about 95% of single-b-tagged events that pass the acceptance cuts; misreconstructions and failures occur in the 5% of events where the gluon has higher pT than the untagged b-jet (and is therefore incorrectly identiﬁed). There are very few events where the top-quark propagators are so far oﬀ-shell that they alone give Fmin 500 GeV.
For smeared Monte Carlo events, the success of our reconstruction procedure (after acceptance cuts) is shown in Table 1. The ﬁrst two columns give the percentage of events in true classes, determined from event kinematics before smearing. Columns 3–6 show Table 1: Basic reconstruction for smeared single-b-tagged events after cuts.
the corresponding percentages that are reconstructed in Classes A–C or fail (because Fmin 500 GeV2). Failures and misreconstructions typically arise in events where, after smearing, the wrong pair of jets gives the best ﬁt to W → jj, or the gluon has higher pT than the untagged b-jet.
These results show that 55% of events passing the cuts are correctly reconstructed in Class A, B or C, while 19% are incorrectly reconstructed (in the wrong class) and 26% fail to reconstruct; in other words, our procedure has 74% reconstruction eﬃciency and 74% purity (correctness of classiﬁcation), albeit with diﬀerent degrees of purity (83%,61%,65%) in diﬀerent reconstructed classes (A,B,C). We surmise that a similar success rate would be achieved with real data.
It is interesting to investigate how well such reconstructed events reproduce the correct dynamical distributions for gluons emitted before (Class A) or during (Classes B,C) the top quark decay, i.e. whether the reconstruction procedure introduces signiﬁcant biases.
Figure 2 shows distributions versus gluon transverse momentum pT (g) for Class A,B,C events; solid histograms represent true unsmeared events while dashed histograms compare the behaviour of reconstructed smeared events (normalized to the same area). The solid/dashed discrepancies can be qualitatively understood as follows. Class A events with soft gluons (hence small pT ) can rather easily fake B or C after smearing, because such gluons aﬀect invariant masses rather little, so we lose A and gain B,C events at small pT (g). There is a ﬂow the other way, too, which apparently wins out at larger pT (g). We see that the true A,B,C pT (g)-dependences are very similar (solid histograms), but the misidentiﬁcation probabilities change with pT (g) and the dashed histograms are rather diﬀerent.
Similarly, Fig. 3 compares true and reconstructed distributions of the separation ∆R(gb) between the gluon jet and its associated b-jet in Class B and C events. True at ∆R = 0.4), due to the propagator of the oﬀ-shell b∗ -quark in the radiation process b∗ → bg. Reconstructed histograms, however, contain 20-30% backgrounds of misidentiﬁed events (mostly from Class A) with diﬀerent dynamical origins that give no such peak.
Figure 4 compares true and reconstructed distributions versus gluon energy E(g) in the parent top rest-frame, for Class B and C events. The same 20–30% backgrounds are present here too, but apparently have much the same E(g)-dependence as the true signal.
Reﬁned reconstruction for single-tagged events The results above show that many misreconstructed events do not have the expected close correlation with the beam line (Class A, see Fig. 2(a)) or with the associated b-jet (Classes B and C, see Fig. 3). We have therefore investigated ways to incorporate such correlations into the reconstruction procedure; it seems that the best-motivated way is to introduce the relevant virtuality in each conﬁguration, as follows. For Class A, we consider the virtuality [p(q ∗)]2 = [p(q) − p(g)]2 = −2p(q).p(g) of the oﬀ-shell quark q ∗ that would be recoiling against a gluon g radiated from an initial quark or anti-quark q; we choose the lowest of the two possible values corresponding to the incident quark and anti-quark; this quantity is ≤ 0 and vanishes at the q ∗ -propagator pole. For Classes B and C, we consider the virtuality [p(b∗)]2 − m2 = [p(b) + p(g)]2 − m2 = 2p(b).p(g) b b of the oﬀ-shell b∗-quark that would be radiating the gluon in these conﬁgurations; this quantity is ≥ 0 and vanishes at the b∗-propagator pole. Clearly, a small virtuality implies a large matrix element and hence a large likelihood that the gluon was emitted in the corresponding conﬁguration; this suggests minimum-virtuality as an additional criterion in choosing the best ﬁt.
We note, incidentally, that minimum-virtuality alone cannot select a unique conﬁguration in our analysis, since each B-type conﬁguration has the same b∗ -virtuality as a C-type conﬁguration where the (b, W ) pairings are interchanged; similarly, each A-type conﬁguration has the same q ∗-virtuality as another A-type with (b, W ) pairings reversed.
However, in the particular case of lepton-tagging the pairings would be ﬁxed and this degeneracy would disappear.
Accordingly, we propose to combine kinematic ﬁtting with a minimum-virtuality criTable 2: Reﬁned reconstruction for smeared single-b-tagged events after cuts.
terion. We now accept a given conﬁguration as the best ﬁt if it has both (a) the minimum F with value 500 and (b) the minimum absolute value of virtuality, compared to all the competing conﬁgurations. The results of this more reﬁned strategy are shown in Table 2.
These results shows a marked improvement in purity, which is now 95%, 70%, 73% in reconstructed classes A,B,C respectively (81% overall). Figure 5 presents the corresponding ∆R(gb) distributions in Class B and C events. We can see that the extra virtuality criterion brings the reconstructed distribution much closer to the true unsmeared case than previously (Fig. 3).
However, eﬃciency has now dropped to about 41% overall and is particularly low (34%) in events of true class A. The reason for the latter is that the diﬀerent virtuality distributions are aﬀected in quite diﬀerent ways by our acceptance cuts, as we now describe. In true class B events, the relevant virtuality [p(b∗)]2 peaks at zero before cuts, but this peak is removed by the ∆R(bg) cut and the remaining events have a peak around (18 GeV)2 that is not much smeared by energy resolution; in contrast, the “wrong” virtualities (corresponding to incorrect A or C assignments) have broader distributions peaking near (50–60 GeV)2 instead, so the minimum-virtuality criterion usually points to the correct B assignment. In true class A events, the relevant virtuality [p(q ∗ )]2 also peaks at zero before cuts; this peak is cut out by the pT (g) and |η(g)| cuts and the remaining distribution now vanishes below about (20 GeV)2 and has a broad shape peaking around (40–50 GeV)2. The “wrong” virtualities both have rather broad distributions peaking near (60 GeV)2, but with wings extending down even below (20 GeV)2, so the minimumvirtuality criterion now quite often points to an incorrect B or C assignment; increased conﬂict with the minimum-F criterion gives more failures and lower eﬃciency.
This overlap of right and wrong virtualities happens because the acceptance cuts Table 3: Compromise reconstruction for smeared single-b-tagged events after cuts.
act more harshly against small [p(q ∗ )]2 than against small [p(b∗ )]2. This overlap might be reduced if there were diﬀerent jet cuts, but as things stand the minimum-virtuality criterion is not particularly helpful in Class A reconstructions. We therefore propose the following compromise strategy.
Compromise strategy for single-tagged events Since the minimum-virtuality criterion is apparently helpful in classes B and C, but not in class A reconstructions, a simple compromise strategy is to apply it only in the former cases. First select the best-ﬁt conﬁguration by minimizing F; if the result is Class A, accept it; if the result is Class B or C, accept it only if it also has minimum virtuality.
The result of this strategy is to obtain column A from Table 1 with columns B and C from Table 2, as shown in Table 3.
This gives purity 83%, 70%, 73% in reconstructed classes A,B,C, respectively. The overall eﬃciency is 63%, and is roughly the same (62%, 67%, 63%) for the three true classes A,B,C.
A caveat should now be voiced. The measurement of ﬁnal-state b-quark virtualities [p(b∗)]2 − m2 is rather straightforward, involving just the gluon-jet and associated b-jet b kinematics, but initial-state virtualities [p(q ∗)]2 require a complete reconstruction of the event and accumulate large uncertainties (that have in fact been included in our calculations). As an alternative approach, we could choose not to rely on these q ∗ virtualities.