PHYSICAL REVIEW D VOLUME 37, NUMBER 1 1 JANUARY 1988

Semileptonic decays of top mesons

L. M. Jones Physics Department, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801

R. Migneron Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada N6A 5B9

(Received 20 July 1987)

We use a QCD approach to model the hadrons produced in semileptonic decays of top-quark mesons. We examine the validity of a "one-jet-plus-lepton-pair" approach to the final state, and show that it is useful but not a completely accurate description. We also cover some additional properties of the hadrons in the final state: their multiplicity, quantum numbers, and energy dis- tribution. A range of top-quark masses from 20 to 43 GeV is considered.

I. INTRODUCTION

With the start of new accelerators in the past few months, and more expected in the next year, particle physicists are expecting to fill in one of the few remain- ing holes in the standard model-the top quark. Since this quark will be very much heavier than the b quark into which it decays, there is a lot of phase space for the decay and many particles will show up in the final state.

The detection of the top quark then hinges on the question of whether this large multiplicity of final-state particles will prove confusing. In the first approxima- tion, one might expect a meson containing a top quark to decay semileptonically into a lepton pair and one en- ergetic jet containing a b quark. In this paper we inves- tigate the extent to which this pattern for the decay is good, assuming a particular model for the fragmentation of the produced quarks and their hadronization.

In Sec. I1 we review the model briefly: it is based on a standard QCD Monte Carlo model for the splitting of quarks and gluons, followed by cluster-phase-space had- ronization. In Sec. I11 we discuss the properties of the hadronic final state when analyzed in terms of jets. In Sec. IV we discuss some of the properties of the hadrons in the final state-their multiplicity and quantum num- bers. Section V contains conclusions and summary.

11. MODEL

We focus on the semileptonic decays of the top mesons because this seems to be the easiest place to see the signal. The method discussed below can be general- ized in a straightforward way to the purely hadronic final states, but we leave the results of that to another paper.

In addition, we deal with "generic" top mesons. That is, these are mesons formed from a top quark and a light antiquark, without assuming any particular wave func- tion binding them together. We believe this is a good approximation to the sum over all spin states of the top- meson system. Basically, all we have is a "colorless clus- ter" with top-quark quantum numbers and an appropri-

ate mass. This is, however, probably more useful for the present than anything more specific since (i) it is the ex- act quantity which enters into the QCD calculations and (ii) it is likely that identification of the spin states of the top mesons will be a second stage in the experimental process. At first, the interest will be simply in establish- ing that a top exists.

We begin with a top quark and a light antiquark ( i i , z, S; or T. since the calculations in which we have used these to date' have not required any tb colorless clus- ters). The top quark decays into a b quark and a lepton pair (eve or pv, in our case). We therefore have a prob- ability for this basic process governed by four-body phase space (ev,bd, say) multiplied by the square of the decay matrix element for the top quark.

The bd quark-antiquark pair is then used as input to the Webber-Marchesini Monte Carlo program.2 This uses QCD probabilities to compute the radiation of gluons from the quarks, the splitting of these gluons into further gluons or quark-antiquark pairs, etc., until all of the partons concerned have come down to some Q: at which the nonperturbative effects of hadronization take over. (See Fig. 1.)

These "end-stage" partons then form colorless clus- ters, which turn into hadrons. A t this stage there are several models to choose from. We continue to use the Webber-Marchesini approach, involving cluster-phase- space hadronization. At some level of detail, this is al- most certainly an oversimplification. However, it has been shown to give good results for the final-state hadrons in standard two- and three-jet events produced by e + e - collision^,^ and we expect it to be a reasonable first approximation to the details of the hadronization in our case also.

We have stored these events at the "hadron reso- nance" level; i.e., we have not allowed resonances such as K * or 2* particles to decay. This means that our multiplicity is low by a factor of about 2. There is no difficulty in allowing all particles to decay completely; in fact, the Webber package makes this simple. Our main reason for stopping at this level is that we have no good model for the ultimate decay of the b-containing had-

130 @ 1988 The American Physical Society

37 - SEMILEPTONIC DECAYS O F TOP MESONS 131

rons. We have inserted a reasonable spectrum of b- containing mesons and baryons, with masses computed from quark model consideration^.^ Hence we are treat- 3 ing the b hadrons in the same way as the lighter ones by $ 600

stopping the decay chains at the hadron resonance level; ' the complete decay chains require a model of the b de- ' 400

confident that it will not change the results presented here.

cays. This will doubtless come in time, but we feel 9 0

0 2 4 6 8 1 0 0 2 4 6 8 1 0 0 2 4 6 8 1 0

111. JET ANALYSIS

The naive expectation one would have is that the final 3 state, albeit very messy in terms of number of hadrons, $ 600 might look particularly simple when the hadrons are @

clumped together into jets. Since most modern detectors c0 400

will find jet identification simpler than particle 9 identification, this is a good place to begin.

All the calculations in this paper assume that the top o meson is in its rest frame. We refer readers to another 0 2 4 6 8 1 0 0 2 4 6 8 1 0 0 2 4 6 8 1 0

work in which similar analysis has been done on moving Number of Jets

tops (Ref. 1). Choice of frame has no effect on our basic conclusions, but the energy spectra prepared here are in the rest frame of the top. FIG. 2. Number of 45" jets formed by outgoing hadrons.

A. Number and energy of jets

Our jet-finding routine begins with the most energetic particle, and searches for the next most energetic parti- cle within a cone of angle a of the first. These four- vectors are then added, and the process is continued un- til no more hadrons can be found within the cone. The remaining most energetic particle is then used to start the next jet. We present here results using a=45", as a fairly representative value. There are occasional events in which several jets cluster together, so possibly a larger value of the cone could be used. We discuss this further below.

As we see in Fig. 2, this results in several jets per event. However, as shown in Fig. 3, many of these jets have rather low energy and would normally be ignored.

FIG. 1. Our model for the semileptonic decays. After the weak decay, the b i system (bd in this case) fragments using QCD and cluster-phase-space hadronization.

In Fig. 4 we show the number of jets per event with en- ergy greater than 5.3 GeV (which might, therefore, be candidates for b jets). Note that although most events for 20-GeV tops have only one such jet, by the time we reach the 43-GeV mesons half of the events have two such jets.

A sample event of this kind is shown in Fig. 5; we see

0 10 20 30 400 10 20 30 40

Jet Energy (GeV)

(f) M,=43 GeV

Ll FIG. 3. Energy spectrum of the jets in Fig. 2. Notice that

many of the jets are very soft.

132 L. M. JONES AND R. MIGNERON - 3 7

25 GeV 20 GeV V1 i

w

I

L(c)M,-30 G e V ~

(e) Mt=40 GeY

KO of Energetic 45' Jets Number of Energetic 60' Jets

FIG. 6. Number of jets with energy greater than 5.3 GeV if the cone angle is widened to 60". We see that there are still a

FIG. 4. Number of jets from Fig. 2 that have energy greater large number of two-jet events at the larger values of m,, show- than 5.3 GeV (and thus could contain a B particle). ing that these jets are well separated.

that the two energetic jets are well separated. The hy- B. Use of the most energetic jet pothesis that most such pairs of jets are well separated may be checked by running the jet finder over again with In spite of possible confusion, let us assume that the a cone angle of a=6OQ. As we see in Fig. 6, there still most energetic jet in each event is the one of interest remains a large fraction of the events with two jets ener- (this will, in fact, usually be the case). In Fig. 7 we show getic enough to contain a b quark. the spectrum of the most energetic jet; in Fig. 8 the

FIG. 5. A sample two-jet event at m, =25 GeV showing that the two jets are well separated and not very different in energy.

/ (c ) Mt=30 GeV

g 100

0 0 10 20 30 400 10 20 30 40

Energy of Jet 1 (GeV)

FIG. 7. Energy distribution of the most energetic jet (jet 1)

SEMILEPTONIC DECAYS OF TOP MESONS 133

Energy (GeV) Electron Spec t rum (GeV)

FIG. 8. Same as Fig. 7 with the energy distribution of the FIG. 10. Spectrum of the final-state electron. Solid curve b-containing hadron superimposed. We see that the hypothesis shows the actual electrons in our multibody calculation; dashed that the most energetic jet contains the b hadron is reasonable. curve shows the same spectrum for three-body decay model.

spectrum of the particles containing b quarks is shown superimposed on this. We see that the spectra are simi- lar, but that the most energetic jet typically has more en- ergy than the b particle. It is therefore not a bad ap- proximation to assume that this most energetic jet is the b jet.

FIG. 9. "Dalitz plot" of electron energy and energy of jet 1, superimposed on boundaries drawn for a genuine three-body decay with two massless leptons and one 6-GeV particle.

One is therefore tempted to imagine the decay of the top meson as a sort of three-body decay, with the three bodies being the neutrino, electron (or muon), and the fastest jet. Of course this is not exactly correct, but in many cases it will be impossible to decide whether or not the slower jets "belong" to the particular top in question so we will have to make do with the fastest one.

To see how good an approximation this is, we com- pare the "Dalitz plots" generated by plotting the energy of the electron and the energy of the fastest jet with the boundary of a Dalitz plot calculated from true three- body kinematics (see Fig. 9). We have assumed a B mass of 6 GeV for calculating the three-body boundaries. Note that while the bulk of the events do fall within the three-body Dalitz plot, everything is shifted to lower en- ergy (reflecting the fact that other jets take away some energy).

We have also generated events using the three-body kinematics and the weak decay matrix element. In Fig. 10 we display the energy spectrum of electrons from this calculation superimposed on the exact electron energy from the multibody calculation. As one can see from Fig. 9, the peak energy is lower.

One can thus conclude that the "three-body decay model" is reasonably good for "bulk" properties, but that one should not formulate tests based on the extreme kinematic limits calculated from this model.

IV. HADRONIC CONTENT

As one might expect, the hadron multiplicity grows slowly with the mass of the top meson. This multiplicity is plotted in Fig. 11; we remind the reader that many of the "particles" plotted here are resonances which will

134 L. M. JONES A N D R. MIGNERON - 37

(b) Mt=25 G e V r--l 1000 Ha) Mt=20 G e V I 1 (b) Mt=25 G e V I ( (c) Mt=30 G e V I I LC) M ~ 3 0 GeV 1 t (a) Mt=20

(e) Mt=40 GeV u Mt=43 GeV 1

Hadron Multiplicity Number of Baryons

FIG. 13. Production of baryon pairs in the final state. We FIG. 11. Multiplicity of hadrons (including resonances). see that even at m, =20 GeV almost 10% of the events have a

Actual hadron multiplicity is about twice this. baryon pair.

decay into further pions, kaons, etc. This means that there can easily be 30 "elementary" particles in the final state.

As we pointed out in the previous section, the parti- cles carrying the b quarks will typically be the leading particle (at least in energy) in the most energetic jet. The expected spectrum is shown in Fig. 12. A fair num- ber of these are baryons; once we get to the b mass scale baryons are not "disadvantaged" by their masses and

their number is determined mainly by the probability for production of a light-diquark-antidiquark pair (this is typically a parameter in most hadronization models).

Even at the smaller energies, a fair number of the events (8% or so) have a baryon-antibaryon pair pro- duced. By the time we get to 43 GeV, some events even have two such pairs (see Fig. 13).

In Fig. 14 we display the baryon energy spectrum. At the lower energies, a fair proportion of the baryons

(b) Mt=25 G e V c) Mt=30 GeV / "I Ti r (c) Mt=30 G e V r-i

Energy of B hadron (GeV) Baryon Energy (GeV)

FIG. 12. Energy distribution of b-quark hadrons. FIG. 14. Energy spectrum of the produced baryons.

SEMILEPTONIC DECAYS OF TOP MESONS 135

800 l (d) Mt=35 GeV (e) Mt=40 GeV ( f ) Mt=43 G e V

-UL " 0 2 4 6 8 1 0 0 2 4 6 8 1 0 0 2 4 6 8 1 0

Number of s Quarks

FIG. 15. Number of particles containing a strange quark in the final state of the E meson. Note that as many as three strange pairs may be produced at the larger m,.

present are the leading b-containing ones. By the time we get to the higher-mass tops, there is more phase space for production of light baryon pairs and these dominate the spectrum even though there are still some leading ones left.

At these energies, strange mesons are produced almost

600 l (d ) Mt=35 GeV 1 (e) Mt=40 GeV n Energy of Strange Hadrons (GeV)

FIG. 16. Energy spectrum of the particles containing strange quarks.

as copiously as nonstrange ones. In Fig. 15 we display the number of strange quarks in the final state of a tS meson (this must be an odd number because we begin with the one J quark). Sometimes as many as three pairs were produced. While some of these "disappear" into v, mesons, most of them will show up as K's.

The particles containing strangeness typically are soft, unless they are leading (and hence likely to be bJ mesons or similar baryons). The energy spectrum of particles containing strange quarks is displayed in Fig. 16.

V. SUMMARY AND CONCLUSIONS

As has been noted b e f ~ r e , ~ we may expect top quarks to produce large multiplicity final states when they de- cay. Hence the jet spectroscopy approach to analysis of these states is necessary as well as natural. In this paper we have explored some aspects of this approach. We find the following for semileptonic top decays.

(i) Low-mass top mesons produce only one energetic jet, whereas larger mass tops frequently produce two jets energetic enough to contain a b quark. These jets are well separated in the rest frame of the top meson.

(ii) Nevertheless, the energy spectrum of the most en- ergetic jet has the same general shape as the energy spec- trum of the b-containing particle from the decay. It is reasonable in most cases to assume that the most ener- getic jet in the decay contains the B meson or baryon.

iiii) If one attempts to approximate the final state by a lepton pair plus one jet, one will overestimate the aver- age energies of both the charged lepton and the jet (if we compare this single jet with the most energetic jet pro- duced in the multiparticle decay).

There will be a large number of hadrons in the final state of even this semileptonic decay, and pairs of baryons and strange mesons will be produced fairly often. We have presented the energy spectra for various particular final-state types. These show the expected features.

(i) Hadrons containing the final b quark are fairly hard; they have the same spread in energy as you would expect from the quark level decay t-bp+v, but their average energy is less than you would expect on this basis (because of the energy which has gone into creating the other hadrons).

(ii) If one examines the energy spectrum of all parti- cles containing s quarks, or the energy spectrum of all baryons, these show typical behavior expected from oth- er jet-dominated reactions. At low top-quark masses there are a few wee (soft) particles, and a substantial number of hard particles associated with the b quark. As the top mass increases, so the jets can evolve further, the spectrum becomes dominated by the creation of soft pairs.

In this paper we have only discussed top quarks with masses up to 43 GeV because of their immediate interest to experiments at Z energies in e + e - . The method can easily be extended to treat higher-mass tops. In fact, the more energy available to the ( b +spectator q ) , the better our QCD calculation of the final-state hadrons.

L. M. JONES AND R. MIGNERON - 37

ACKNOWLEDGMENTS NSERC International Collaborative Research Grants

This work was supported in part by DOE Contract No. DEACO 276 ERO 1195 Task P (L.M.J.); NSERC (Natural Sciences and Engineering Research Council of Canada) Grant No. S100A8 (R.M.); NATO Collabora- tive Research Grant No. 0779/83 (L.M.J. and R.M.);

(R.M.), and NSERC International Scientific Exchange Program (L.M.J.). In addition, we would like to ac- knowledge useful conversations with C-K. Ng, S. Den- ham, D. Haim, A. E. Hodel, K . S. S. Narayanan, and K. Sundaresan.

lL. M. Jones and R. Migneron, Phys. Rev. D 37, 71 (1987). 4 ~ - ~ . Ng (private communication). *B. R. Webber, Nucl. Phys. B238, 492 (1984); B. R. Webber 5 ~ o r a review on the top quark and various Monte Carlo mod-

and G. Marchesini, ibid. B238, 1 (1984). We thank B. R. els, see Proceedings of the Second Mark I1 Workshop on SLC Webber for sending us his program, which we have Physics (SLAC Report No. 306, 1986). Particles of particu- "enhanced" in a minimal fashion to include top-containing lar interest therein are those by K. O'Shaughnessy, G. Han- clusters and a hypothetical spectrum of B mesons. son, A. Petersen, and F. Porter.

3 C - ~ . Ng, Phys. Rev. D 33, 3246 (1986).