Z. Phys. C Particles and Fields 49, 657-662 (1991) Partkz ,s ~r Physik C

FLUs �9 Springer-Verlag 1991

Degenerate Higgs and Z Boson at LEP200 N. Brown

Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OXll OQX, England

Received 29 August 1990

Abstract. We investigate the problem of detecting the Higgs boson if Mtt ~ Mz at LEP200, the main problem being the large background from Z Z production. Since this background should be accurately calculable, we estimate that the existence of the Higgs can be established with about 3fb -1 of integrated luminosity. We also discuss how the signal can be improved if efficient tagging of b quarks is available.

1 Introduction

The mechanism by which electroweak gauge symmetry is broken from SU(2)L@U(1)r to U(1)~, remains one of the most important problems in high energy physics. In the standard model, this breaking is achieved by means of the Higgs mechanism. In its minimal version, this predicts the existence of a neutral scalar particle, the Higgs boson (H). Although more complicated models are possible with a richer scalar sector, we shall restrict ourselves in this study to the minimal model. Unfortunately the model does not predict the Higgs mass, which is left as an arbitrary parameter, although there are some theoretical reasons for believing MH to be less than about 1 TeV.

The best experimental limits have been set by the LEP experiments [1], where the region 0 < M H < 40 GeV has been ruled out. With greater statistics it should be possible to push the lower limit on M H to about 50 GeV [2]. In the future it will be possible to upgrade LEP to run at more than twice the present energy, known as LEP200. Unfortunately it will be hard to extend the Higgs search much further. The main reason is not that the cross section is too small, but rather one runs into a serious background problem from vector boson pair production. In particular, the Higgs decays predominantly into two jets, and for Mn ~ Mz it will be extremely hard to distinguish Higgs events from hadronic Z decays. The conclusion of extensive studies is that with an integrated luminosity of 500 pb - 1, the discovery limit will be about

80 GeV [3]. If the Higgs becomes heavier than the Z, it should be possible to distinguish it by observing pairs of jets with invariant masses M u > M z. The cross-section falls as M H increases, and the problem of observability becomes one of statistics.

Planned hadron supercolliders (LHC, SSC) are sensitive to much heavier Higgs masses, but will have trouble if MH < 2 Mw, where the jets from Higgs decay are completely lost in the QCD background [4]. It is possible that rare decay modes such as H--, ~7 can be used, but it is obviously of importance to extend the Higgs search to the highest possible values at the lower energy e + e- machines.

It might in many ways be considered 'natural' for the Higgs to be roughly degenerate in mass with the weak vector bosons and it is of interest to 'ask whether one could detect such a Higgs at LEP200. A recent study by Kunszt and Stirling [5] has shown that with an integrated luminosity of 10 fb- ~ it would be possible to either detect, or rule out a Higgs with M u = Mz. The Higgs is produced in the reaction e+e - ~ Z H and the analysis of Kunszt and Stifling exploits the different angular distributions of the final state leptons from Z decay in this reaction, to those in the background reaction e + e- --, ZZ, where one Z decays hadronically, the other into leptons. The leptons (e or #) from H Z will have the usual 1 + cosZ0 distribution of single Z decay, since the Higgs is spinless. In Z Z production, however, the Z's are produced in both transverse and longitudinal polarization states. Analysis shows that the angular distribution for this process peaks at cos 0 = 0 rather than at cos 0 = 1. It is concluded that with about 10fb -1 of integrated luminosity it will be possible to establish whether a Higgs with M u = M z exists.

Our study is different in spirit since we make no attempt to exploit any differences in final state topologies of H Z and Z Z events. Instead we use the fact that the Z Z background should be accurately calculable. All the Z parameters will be extremely well determined from LEP and there should be no difficulty in applying perturbation theory. It is therefore possible to ask how much integrated luminosity is required, in order that the signal, if it exists, can be statstically established.

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| '51

| 'C

,O

b

0"5

- - - ' - ~ ~ ~ l I I I I I 160 170 180 190 2 0 0 210 220 2 3 0 2 4 0

V'i" (GeV)

Fig. 1. Tota l cross sections for e+e - ~ Z H and e+e ~ Z Z for M n = 80, 91.1, 100GeV as a function of the centre of mass energy

In Fig. 1 we plot the cross sections for Z M and Z Z

production for various values of MH and x/s. We have included the finite widths of the particles in the calculation. In Sect. 2 we will consider the final state where the Z decays into leptons l + l - ( l = e or /0 and the Higgs decays to jets. In Sect. 3, we consider the final state where the Z ~ v ~ , together with various backgrounds. Finally in Sect. 4 we will consider how one can improve on the Higgs signal if one has an efficient tagging of b quarks, say from a vertex detector. This would be important in establishing the nature of the Higgs particles. For the purpose of this study we work at a centre of mass energy x / s = 2 0 0 G e V and set Mz=91.1 , F z = 2.5GeV, sinZ0w=0.23, a = 1/128. We choose M n = M z since this is the hardest case to distinguish.

Until Sect. 4 we do not consider the four jet final state, which has the largest branching fraction. The reason being that the background for W + W- production is enormous, the cross-section for this being over an order of magnitude larger than Z Z production. Although it may be possible to separate W jets from Z jets, it is likely to be a difficult problem and we do not consider this possibility, b quark tagging, however, can help eliminate the W + W- background.

2 l + l - + 2 jet final state

In this section we consider the final state I + 1- + 2 jets. Here the l+ l - arises from the decay of the Z, and the jets from the decay of the Higgs mainly through its decay to bb. Because of the relatively small branching fraction for Z ~ l + l - this channel suffers from a small cross-section. It is, however, relatively free from

backgrounds apart from that from Z Z production. For M u = M z we can calculate F n ~_ 4.26 MeV and B(H ~jets)

0.96. In order to provide a realistic analysis we have calculated the complete matrix element for the four body final state via Z Z and Z H channels. We also demand that the final state particles satisfy a set of plausible experimental acceptance cuts. We demand that the final state quarks, gluons or leptons are produced with at least 15GeV of energy and with polar angle satisfying [cos 0] < 0.9. We also demand that the quarks or gluons from Higgs decay are separated from each other by at least 45 ~ in angle, and that the leptons are separated from each other and from the partons by at least 30 ~ The result of a calculation for one lepton channel is:

a(no cuts) = 0.0168 pb

a(cuts) = 0.0081 pb.

Here, as throughout this paper the error on the Monte-Car lo integration is O(1~). For the background process we use the same set of cuts. For the Z decaying into up-like quarks we have:

a(no cuts) = 0.00916 pb

a(cuts) = 0.00497 pb,

whereas for down-like quarks we have:

a(no cuts) = 0.0118 0b

a(cuts) = 0.0064 pb.

Putting this all together, for three down-like channels and two up-like channels we obtain

a s - a(signal) = 0.0081 pb

a n - a(background) = 0.0291 pb

a signal to background ratio of 0.28. It is clear that a large integrated luminosity will be needed to establish this signal. Let us denote this required integrated luminosity 5O. For relatively large numbers of events, the poisson distribution of event probabilities become Gaussian. We ask at what value of 5 ~ is the 95~o upper confidence level for the background event rate equal to the 95~ lower confidence level for background plus signal. In other words at what value of 50 is there a 95~o probability that we will be able to rule out a Higgs of M z = M n at the 95~o confidence level. This provides us with an estimate of the integrated luminosity needed to be sensitive to a Higgs of this mass. This condition is:

( a s + a , ) s o - 1.64x/(a s + a•)so = a , so + 1.64x/~xso

where for an expected means of N events, the standard

deviation is approximately x/N. In a Gaussian distribution 95~ of the probability lies below N + 1.64.~/N or above N - t .64x/N. Thus

x / ~ = 1 . 6 4 ( ~ s + a , ) + x/~B) GS

For one lepton channel we obtain 5O ~ 5400 pb- 1. For two channels we obtain ~ ~ 2700 p b - 1. At this value of

is expected number of background events is 157 whereas if the signal exists we would expect 201 events.

If it is possible to make use of the z +z- decay of the Z with high efficiency, we obtain ~ ~ 1800 pb-1. Although these are higher than the canonical value of ~ ~ 500 pb- 1 such an analysis, based only on event rates would be complementary to that suggested by Kunszt and Stirling.

Finally we should note that to determine this required integrated luminosity, s more accurately one would have to go beyond the analysis given here. One should take into account radiative corrections, as well as perform a full Monte Carlo analysis of the production of the final state jets and leptons, and their detection. It is to be hoped that systematic effects will be small in this channel because there is no strong dependence on the acceptance cuts, and that the errors will be dominated by statistics.

3 vP + 2 jets final state

We now consider the situation where the Z decays to neutrinos. The advantage of this channel is that the signal event rate is higher because of the relatively large branching fraction of Z ~ vg. Thus the signal is of two jets, together with large missing energy. Unfortunately there are other sources of background, as well as that from Z Z production. From W + W- production, there is the possibility that one W decays hadronically, whilst the other decays to Iv, where the I is not detected because it is produced at small polar angle. Although relatively few of the W + W - events will have this topology, the cross-section for W + W- production at x/s = 200GeV is approximately 20pb and so we must consider this background.

Another background, not previously considered is from single W production. For single W- production, the dominant Feynman diagrams are shown in Fig. 2. Here the final state position is preferentially emitted at very small angles and will probably go undetected. If the W- decays hadronically then we will see two jets only. Although the cross-section for this process is smaller (~0.5pb), nearly all the events will have just two jets

~ w -

e +

Ve

e+

Fig. 2. dominant Feynman diagrams for the process e+e e+Ve W-

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observable in the final state and so are a potential background.

There are also backgrounds from two photon events, but these can be largely eliminated by demanding large missing transverse momentum.

We use acceptance cuts as follows: Ejet> 15GeV, [COS0jetl(0.9,0jet_jet)45 ~ We also demand a missing transverse momentum of at least 30 GeV. For the signal we have

a(no cuts) = 0.100 pb

a(cuts) = 0.0562 pb.

For the Z Z background we have

a(no cuts) = 0.320 pb

a(cuts) = 0.157 pb.

For the W § W - background we must demand that the final state lepton is not observed because it is emitted sufficiently close to the beam direction. If we demand that it be emitted with a polar angle with [cos 01 > 0.95 we have a background cross-section of

aww(lCOS 01 > 0.95) = 0.168 pb

For Icos0l > 0.99 we have:

aww(ICOS 01 > 0.99) = 0.0266 pb.

We have demanded the same acceptance cuts as for Z H and Z Z and, as before, we have calculated the complete matrix element for the four body final state. We have taken M w = 80.6 GeV and Fw = 2.05 GeV.

To estimate the background from single W pro- duction we use the Weizsacker-Williams approximation, applying the same acceptance cuts on the jets. We can cut against this background partially by demanding that the missing particles approximately reconstruct a Z ~ We use the fact that the energy of the W is given by

E w - s + M ~ - ~12

where/y4 is the invariant mass of the missing particles, and M# is the invariant mass of the jet-jet system. Assuming an experimental error of _+10GeV on measuring jet-jet masses, we expect Mjj ~ M w +_ 10. If we demand that N /= M z +_ 10 GeV we get the limits

86.9 < E w < 104.1.

Here E w is determined as the energy of the combined jet-jet system. Using this cut and adding both W + and W- production we obtain an estimated background cross-section from single W production of 0.164 pb. This last cut should not affect either the signal or the ZZ , W + W - background processes.

For this v9 + 2 jet channel, though the signal event rates are larger, the signal to background ratio is far worse. In particular, the background from single W production poses the most serious problem. The background is also extremely sensitive to acceptance cuts, as can be seen, for example, in the calculation of the W + W- background for different polar angle acceptance of the lepton. Thus it will be much harder to perform the

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analysis of Sect. 1, as systematic effects will be more important.

4 b tagging

Since the Higgs particle decays predominantly to b quarks, B ( H ~ b b ) = 0.86, and to c quarks B(H--,,cg)= 0.078, there is the possibility that by tagging on heavy quarks, particularly b quarks, we can improve the Higgs signal. Much of what we say in this section applies to a Higgs of any mass, but we concentrate on MH = Mz. Our previous analysis demonstrates the possibility of observing the Higgs signal as an excess number of events above the background. To really prove these extra events were due to Higgs decays, the existence of excess b quark jets would be an excellent signal that we were, in fact, seeing the Higgs particle.

Tagging on b quarks might also allow us to observe the H Z events, where both the Higgs and the Z decay hadronically. This channel has by far the largest branching fraction, but as mentioned previously, suffers from an overwhelming background from W + W - production. Fortunately since it now seems probable that the top quark is sufficiently heavy, the W can only decay to b quarks through a small Kobayashi-Maskawa mixing angle. Efficient b tagging could remove this background.

At present heavy quark tagging is achieved through looking for the leptons from the semi-leptonic decay of the c or b quark. At best this might achieve an efficiency for detecting b quarks of about 5~ with a purity of 80~o. Present experiments are implementing vertex detectors which are hoped to do much better, b quark tagging may be as good as 90~o efficient at 90~o purity, or 40~o efficient at more than 99~o purity.

Let us first consider the four jet final state. Since it is not clear how good these vertex detectors might be we only give a very crude analysis. We take the following tree level cross sections

a ( W + W - ) = 2Opb, a (ZZ)= l .3pb a (ZH)=0 .544pb

and the following brancing fractions.

B(Z --, bb) = 0.149

B(Z~c~) = 0.116

B(Z ~ hadrons) = 0.677

B(H ---, bb) = 0.863

B(H ~ cg) = 0.078

B(H ~ hadrons) = 0.955

B(W + ~cg) = 1/3

B(W ~ hadrons) = 2/3.

Here we have not included finite width effects or any experimental acceptance cuts. A typical efficiency to detect four jets from W + W- decay will be about 50~o. We also do not consider the background from QCD four jet production as this will be small compared to the W + W- background.

We parameterise the b tagging in terms of two

parameters, the efficiency for detecting b quarks, eb, and the probability that a c quark is misidentified as a b quark, ec- A related quantity is the purity, p, of a sample which originally contained equal numbers of b and c quarks where

eb p -

We first demand that there be at least one b jet in our four jet sample. The background from W + W - events is then

~ww{B2(W--,cs)(1 - ( 1 - ~c) 2) + 2B(W-,cs)B(W-- ,ud)~2.

In a similar manner we can calculate the Z H signal and the Z Z background in terms of eb. It is clear that unless e~ is small there will be a large contamination from W + W - events. If e~ is as large as 4~o, for example then the background from W + W- is larger than the signal would be even with 100~o efficiency for tagging on b quarks, e~ must also be well determined to keep this background under control. Whilst the signal is relatively insensitive to ec, the W + W - background is, to a good approximation, linearly dependent on e~. To show what is possible, however, we give some examples. If we could achieve eb = 0.6 and a purity of 99~, this gives ec = 0.0061, and we would obtain

alb(ZH ) = 0.283 pb

1 b(ZZ) = 0.202 pb

alb(WW) = 0.054 pb.

Here the suffix lb denotes we have demanded at least one b quark in the event. This gives a signal to background ratio of 1.1. It is also important, however, to know ~b very well. A 50~o uncertainty in eb leads to roughly a 50~o uncertainty in these expected cross- sections. If in order to achieve a purity of 99~o we have to go to b tagging efficiencies as low as 0.1, then e~ = 0.001 and we would have

alb(ZH ) = 0.073 pb

alb(ZZ) = 0.049 pb

alb(WW) = 0.009 pb

a signal to background ratio of 1.26. The conclusion is that if we can achieve a high rejection of charm events (e~ ~0.01eb), then as long as eb, ec are reasonably well determined, it should be possible to see this signal at reasonable event rates, and with signal to background ratios better than 1.0. Any uncertainties in these quantities, however, will lead to sizeable systematic effects.

A better method might be to demand at least two b quarks in our events. A sizeable number of the Z H and Z Z events have either two or four b quarks in the final state, and so good signals should be possible. The W W background is now much less severe, and it is not necessary to demand such high purities. For example if e b = 0.9 with a purity of 90~ can be achieved, then we have ec=O.1, i.e. a tenth of all charm events are misidentified as b. Even then there would be no problem with the W + W - background. The cross sections for at

least two b quarks in the event would be

azb(ZH ) = 0.279 pb

o-2b(ZZ ) = 0.198 pb

o ' 2 b ( W W ) = 0.022 pb

a signal to background ratio of 1.27. Even if to achieve a purity of 90% we need eb = 0.2, giving ec = 0.022, we would still have

ffzb(ZH) --- 0.024 pb

a2b(ZZ ) = 0.014 pb

a2b(WW ) = 0.001 pb

a signal to background ratio of 1.6. Demanding two b quarks in the event makes the cross-sections much less sensitive to ec. They are still sensitive, however, to how well eb is determined, particularly for low values of eb. At higher values they are less sensitive. For example, if %=0.9 with an error of +0.1, then this leads to an uncertainty of 0(20%) on the Z H signal and the Z Z background cross sections. If e = 0.1, then even a 0.05 uncertainty in this quantity can lead to Z H and Z Z cross sections varying by factors of two or three. Since we are not so worried about contamination, we should be able to work at relatively high values of eb, and it should be possible to isolate the Higgs.

By demanding at least three b quarks, then there is no contamination whatsoever from W + W- events. The cross-sections, however, will be smaller, and eb will need to be moderately high to achieve a signal. Again at eb = 0.9 at 90% purity we achieve

o-3b(ZH ) = 0.075 pb

a3b(ZZ) = 0.034 pb

a good signal to background ratio of 2.2. As long as the purity is larger than about 90% the Z Z background is not larger than about 0.04 pb, even for eb = 1.0. Even at e b = 0.6 and 90% purity we have

o-3b(ZH ) = 0.036 pb

a3b(ZZ) = 0.016 pb

a signal to background ratio of 2.25. Thus, with large integrated luminosities the Higgs should show up clearly.

Finally, we turn to our earlier work and consider the final states / + / - + 2 j e t , v~+2jet . Since these cross- sections are small we need relatively high efficiency if we are to tag on b quarks. For l+l - + 2 jet, if we demand at least one b quark, the cross section for one lepton channel is

Crzn{B(H - bb)(1 - (t - eb) 2) + B(H ~ c6)(1 -- (1 - e c ) 2 ) }

�9 B ( Z - - , t + t - )

for the signal Z H cross section, and

~zz{2B(Z~ bb)(1 - (1 - eb) 2) + 2B(Z ~ cg)(1 - ( 1 - ~c)2) }

�9 B ( Z ~ I + I -)

for the Z Z background. If we set e b = 0.9 at a purity of 90%, then we have ec = 0.1 and

~(ZH) = 0.016 pb

~r(ZZ) -- 0.015 pb.

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Once we have folded in acceptance cuts (efficiency of 50%), it is clear that for high efficiencies we lose

relatively little of the Higgs signal, whilst improving the signal to background ratios from about 0.3 tol.0. If the efficiency eb was much lower, however, the event rate would become too small.

Finally in the vg + 2 jet channel, b tagging will help remove the backgrounds from W + W - and single W events. In both cases we gain a factor of ~c/3 in reducing these backgrounds, whereas for high efficiencies, the Higgs cross-section is hardly affected. As with the l + l -q~ case the Z Z signal is reduced to the level of that for ZH. Thus efficient b quark tagging could allow us to use this channel.

5 Conclusions

With sufficient integrated luminosity it should be possible to detect a Higgs with MH ,,~ Mz at LEP200. By just counting events in l + l- + 2 jet final states an integrated luminosity of 3fb ~ should suffice to statistically establish or rule out an excess due to the Higgs particle. Because of backgrounds from W + W - , and in particular single W production, it is unlikely that the v9 + 2 jet final state can be used, despite its larger cross-section.

Even if such an excess of events is established it would be of great importance to confirm they are due to Higgs production. One possible method is that proposed by Kleiss and Stirling, where the different angular distribut- ion of the final state leptons from the Z H events could be distinguished from those from Z Z events. Another pos- sibility is by tagging on b quarks, since the Higgs decays predominantly into bb. By tagging on a single b quark one can obtain signal to background ratios of about 1.0, but only if the contamination from charm is small. This will probably only be achieved at relatively low efficien- cies, where it is then important to know the efficiency well.

By tagging on at least two b quarks the charm contamination from W + W - events becomes much less of a problem and such high purities are not necessary. At large efficiencies for b tagging signal to background ratios are again about 1.0, but the fact we can work at large efficiencies makes us less sensitive to errors in our knowledge of that efficiency.

Tagging on more than two b quarks will necessarily demand high efficiencies if we are to preserve a reasonable signal, but signal to background ratios of more than 2.0 can be achieved. Tagging on b quarks at a high efficiency can also improve the 1 + l- + 2jets channel and may allow us to use the v~ + 2 jet channel.

It is clear that with large integrated luminosities, and a combined analysis using event rates, angular dis- tributions and b tagging we can observe a Higgs, even if it is degenerate in mass with the Z boson at LEP200. Since the Higgs is responsible for the masses of the weak vector bosons, it may well be natural to expect M n ~_ Mz. We have shown that it is possible to observe such a Higgs, and believe that such a search should be given serious consideration.

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Acknowledgements. I would like to thank Roger Phillips for many fruitful discussions and encouragement. I would also like to thank Dick Roberts, Elena Papageorgiu, Robin Marshall, Norman McCubbin, Chris Damerell and David Saxon.

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4. See e.g.S. Jensen: Proc. 1988 Snowmass Workshop on Physics in the 1990's, Singapore: World Scientific 1989

5. Z. Kunszt, W.J. Stirling: Phys. Lett. B242 (t990) 507 6. See e.g.H. Dijkstra et al.: Nucl. Instrum. Methods A277 (1989)

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