PHYSICAL REVIEW D VOLUME 40, NUMBER 5 1 SEPTEMBER 1989

Are W pairs a detectable signature for heavy Higgs bosons at the Superconducting Super Collider?

Hans-Uno Bengtsson University of California Los A ngeles, Los A ngeles, California 90024

John Hauptman Ames Laboratory, Iowa State University, Ames, Iowa 50011

Stephan Linn Supercomputer Computations Research Institute, Florida State University, Tallahassee Florida 32306-4052

Aurore Savoy-Navarro* Fermi National Accelerator Laboratory, Batavia, Illinois 60510

(Received 27 March 1989)

Events with high-mass W pairs and corresponding backgrounds have been generated, realistically simulated, and analyzed to isolate the Higgs boson. The signature considered is one produced when one W decays leptonically while the other decays hadronically. Detection efficiencies are calculated for the case of an 800-GeV minimal Higgs boson. For the case of a top quark lighter than the W, the signal is observed with a statistical significance of two standard deviations after one year of simulated Superconducting Super Collider running with a luminosity of cm-* S-I.

INTRODUCTION

The theoretical motivations to search for the Higgs boson(s) light or heavy, have been thoroughly repeated in the past few years. Starting at Snowmass in 1986, several Monte Carlo studies have looked for the best signature to extract the signal of a heavy H 0 at pp colliders.' The gen- eral consensus is that the best chance to find such an ob- ject is the observation of its decays into Z O pairs where both Z O decay leptonically. The other proposed alterna- tive is where the H 0 decays into W pairs, and one of the W s decays leptonically and the other one hadronically. This paper studies this case in great detail, in particular, for a Higgs boson of 800 GeV. It requires that the gen- erated events are submitted to a simulation which repro- duces as realistically as possible the characteristics and properties of a Superconducting Super Collider (SSC) detector of the following type: 4 ~ r solid angle, hermetic, nonmagnetic, including fine-grained calorimeters and transition-radiation detectors. This is in order to make use of the different pieces of information provided by such a detector, and in particular to discriminate ordi- nary QCD jets from the ones produced by the hadronic decay of the W . Such a careful simulation is not neces- sarv in the case of H ~ + Z ~ Z ~ + I + ~ - V V or four l e ~ t o n s . Because experimental limits2 on the top-quark mass are increasing, it is necessary to consider the effect of a top quark with mass greater than the W (100 GeV) because t + Wb would be a large background.

EVENT GENERATION

The PYTHIA Monte Carlo program3 has- been used to generate samples of signal and backgrounds produced by

pp collisions at 6 =40 TeV. The following processes were generated:

The experimental final state studied is one W decaying leptonically and the other allowed to decay hadronically. That is,

W + I v , and W + q q

with I=e or p. The top-quark mass was set to 50 GeV for the processes in Eqs. (1)-(3). The minimum four- momentum transfer of the parton hard scatter was set to 200 GeV in all cases. The cross sections for these pro- cesses are listed in Table I.

PYTHIA version 4.8 includes the processes q q - H O , g g - ~ O , and V V - H O , where V = w',zO. For the latter process, the effective W approximation is used to calculate the total cross section, but the exact matrix ele- ment is employed to generate the correct P, distributions of the Vs. Since the graph V V - H 0 by itself is not gauge invariant but overestimates the cross section for large H O masses, a cut was made on the mass of the HO, M H o < 1200 GeV. This procedure has been shown to yieid results in close agreement with those obtained from simulations based on the full gauge-invariant set of V V - V'V' graphs4 and exact ca l c~ la t ions .~

For the processes qq,gg-ti; a slightly modified ver- sion of PYTHIA was used that contains the massive matrix

1465 @ 1989 The American Physical Society

1466 BENGTSSON, HAUPTMAN, LINN, AND SAVOY-NAVARRO 40

TABLE I. Cross sections for the processes under considera- tion for both cases of top-quark mass for a 800-GeV Higgs bo- son decaying to WW and corresponding backgrounds. All pro- cesses were simulated for q, greater than 200 GeV.

a (pb) o (pb) Process M,,, =50 GeV M,,, = 100 GeV

pp-H"-evqq 0.20 0.34 pp- WW-tevqg 0.36 0.39 pp- Wq (g)+evq(g) 97.4 110.0 pp-tt- ~ ~ b b - e v ~ q - ~ 454.0

SCALE (m) - elements for these processes. A t P, > 200 GeV for a top- 1 2 3 4 5

CJ TRD CALORIMETER

quark mass of 100 G ~ V , the differences between massl~ss and massive matrix elements are, however, negligible. FIG. 1. Cut view of 4.rr nonmagnetic detector.

DETECTOR SIMULATION

The experimental observation of such a signature re- quires a detector capable of lepton ( e , p, and v ) identification as well as jet detection. For a more accu- rate reproduction of nature, a detector simulation used by the DO Collaboration for high-statistics trigger studies is adapted for use here. DO is a 4.ii general-purpose detector comprised of central tracking chambers with no magnetic field, a uranium liquid-argon calorimeter, and a muon spectrometer employing magnetized iron and pro- portional drift tubes. The dimensions of DO have been scaled to be appropriate for an SSC detector and are quite similar to the proposed "SSC nonmagnetic d e t e ~ t o r . " ~ The choice of a nonmagnetic detector was driven by con- cerns about a magnet displacing low-momentum tracks and thus compromising jet energy resolution. The inner radius of the calorimeter is 200 cm and its half-length is 400 cm. The calorimeter is between 12 and 15 absorption lengths thick with a coverage out to 6 units of rapidity. I t has a uniform segmentation of 0.05X0.05 in azimuth and rapidity. Electromagnetic and hadronic showers were simulated using a modified version of the parame- trization which was a fit to test data on DO prototypes.7 Some sensitive regions of the calorimeter have been deadened to simulate supports, cable pathways, and a cryostat. A double cryostat design has been chosen with flanges at 90". This eliminates the large dead area that occurs when three cryostats are used. The beam interac- tion diamond is smeared with a Gaussian of width 20 cm. Figure 1 shows an overview of the detector.

Electron identification relies on calorimeter segmenta- tion to provide information about shower shape. Since electrons are compact in both transverse and longitudinal dimensions, it is possible to define quantities to character- ize a shower. To measure the longitudinal energy distri- bution the ratio p=E,, /E,,,,, is used where E,, is the energy in the first twenty radiation lengths of the calorimeter. Figure 2 shows the p distribution of events with both electrons and jets. A cut at 0.9 accepts 99% of electrons and rejects 89% of the jets. To measure the transverse size of a cluster, the width is defined as R = ~ A + ~ + A ~ ~ where A+ and AT are the energy weighted rms values. The distribution of R is shown in

Fig. 3. A cut at 0.05 retains 99% of the electrons while rejecting 89% of single hadrons and jets. Since both these criteria are correlated the total acceptance is not multiplicative.

An energy cluster, in the context of this analysis, is a collection of calorimeter cells each of which is above a threshold of 1 GeV and within a neighborhood of 0.2 units of 7-4 space. The algorithm employed for this clus- tering makes use of local equivalence relations and is rela- tively insensitive to the connection parameters.8 The ad- vantage of this algorithm over others commonly used is that no a priori cluster size need be assumed so it works equally well for both electrons and jets.

The calorimeter resolution is

a / ~ = 0 . 0 1 + 0 . 2 0 / V ' ~ , (6)

U / E =0.05+0.50/V'z , (7)

where E is in GeV, for electrons and hadrons, respective-

FIG. 2. Distribution of p defined for a cluster of energy in the calorimeter as the ratio of energy in the electromagnetic sec- tion (E,, ) to total cluster energy (E,, , , , 1.

40 ARE W PAIRS A DETECTABLE SIGNATURE FOR HEAVY. . . 1467

FIG. 3. Distribution of R defined as the energy-weighted rms of a cluster, in phase-space units, for both electrons and jets.

ly. The relative response of electrons to hadrons is taken to be 1.1 and constant with energy. Several studies were done with other resolutions and this will be discussed later.

The simulation includes a transition-radiation detector (TRD) with parameters identical to DO (Ref. 9). There are nine T R D chambers instead of three as in DO. T R D information is used only to distinguish between zero or more ionizing tracks. Figure 4 shows the total charge de- posited in the T R D for single electrons and pions which rejects 50% of the pions while accepting 90% of all elec- trons. This rejection factor applys only to isolated tracks. The "trigger" uses the sum of the T R D channels corre- sponding to the cluster of calorimeter cells under con- sideration. This distribution is shown in Fig. 5 where one can see bumps corresponding to one or more particles. Because of multiple hits in the T R D cells associated with the calorimeter energy cluster it is unsed only to detect the presence of a charged particle. Because only events that have high-P, electrons were simulated, it was not necessary to make stringent cuts with the TRD. The

dE/dX (MeV)

FIG. 4. Distribution of ionization energy ( d E / d X ) for single electrons and pions in the TRD.

0.0 0.2 0.6 1.0 1.4 1.8 dE/dx (MeV)

FIG. 5. Distribution of ionization energy ( d E / d X ) for T R D cells associated with a cluster in the calorimeter.

T R D would be useful in discriminating against the QCD background. The point where e's and T'S have equal sig- nals corresponds to a P, of about 500 GeV. The useful- ness of this device for electron identification at small an- gles corresponds to a P, approximately ten times lower. Therefore, a T R D of the DO design would only be useful in the central rapidity region. A better set of T R D pa- rameters could be found for SSC energies, even for for- ward detectors, if space permitted. It should be pointed out that segmentation of TRD's is very important. The effect of overlaps is seen by comparing the distributions of Figs. 4 and 5.

EVENT ANALYSIS I (ON LINE)

A convenient, but not necessarily firm, distinction is made between analysis that is done on line to reduce the event rate to that acceptable for data logging and that which is done off line and subjected to sophisticated mul- tiphase analysis. Since lepton identification is relatively easy when compared to jet spectroscopy, a single-W "trigger" will suffice. The difficult task of reconstructing the W which decays to jets will be left to the off-line por- tion of our analysis.

In this section a W-pair trigger will be defined along with estimates of the experimentally achievable resolu- tion for the main parameters of these processes, and the efficiency of each stage of the detection. A single-W trigger is defined as follows.

(a) Search for all clusters in the electromagnetic part of the calorimeter within a range in rapidity 1111 5 3 and with E, > 25 GeV.

(b) Require that most of the energy be contained in the first 20 radiation lengths of the calorimeter ( p 2 0.95).

(c) Require the cluster width to be small ( R < 0.05 ). This criterion is biased toward accepting low rapidity electrons because towers are physically larger.

(d) Ask for the matching of the cluster with an associ- ated track, with more than 400 keV of ionization, in the TRD. The electron candidate with the highest P, is used

1468 BENGTSSON, HAUPTMAN, LINN, AND SAVOY-NAVARRO - 40

FIG. 6. Distribution of transverse mass (M,) for the ev sys- FIG. 7. Distribution of invariant mass (Mjj) for the recon- tem. structed jet-jet system for Ws (solid line) and jets (dashed line).

to reconstruct the W. (el Require the missing E, > 25 GeV. The longitudinal momentum of the neutrino P, (along

the beam axis) is not well defined in pp collisions because large amounts of energy escape detection at small angles. Therefore, the missing E, is used to infer the existence of a neutrino and to reconstruct the e v system decaying from the W. The four-momentum of the electron and the two components of the missing energy together with the W-mass constraint yield a quadratic equation in longitu- dinal neutrino momentum. The solution which yields the smaller value for P, is correct 60% of the time.

Assuming an object with the W mass completely con- strains the kinematics, so the W momentum is deter- mined. The transverse mass of the e v system is shown in Fig. 6. Table I1 shows the efficiency ( E , , ) for identifying the e v system as defined above. All processes with a w decaying leptonically give a value of E,, greater than 75%.

For small values of the Higgs-boson P, the W s are az- imuthally opposite in the detector. A strategy to recog- nize the second W by using constraints from the first W is as follows.

(a) Find all the clusters with E , > 25 GeV, using now the full depth information from the calorimeter.

(b) Use the cluster (jet 1) with the highest E, in the op- posite hemisphere from the leptonically decaying W a n d compute its mass as described below.

(c) Make all possible combinations of jet 1 with all oth- er clusters in the opposite hemisphere. Keep the cluster (jet 2) which combines with jet 1 to have an invariant

mass closest to Mw. If the jet 1 by itself has mass closest, it alone is used.

(d) A cut is made in W mass from 60 to 90 Gev, to eliminate obvious misreconstructions and to reduce the rate.

The above steps could constitute a second level of triggering or a first pass at off-line filtering. The invariant mass is calculated from the tower energies by summing over all the towers included in the W cluster. Then M,. = d ~ - p 2 is calculated where

and Ok and q5, are the polar angles of the kth calorimeter tower.

The mass distributions for the hadronic W decays and single partons are shown in Fig. 7. The low-mass region for W decays is populated by events with neutrinos and particle that are lost in the detector or analysis. The high-mass region for W decays is due to misreconstruc- tion and confusion with fragments from beam jets. I t should also be noted that using the combination of jets with mass closest to the W mass introduces a fictitious bump in the background mass spectrum. The detector simulation and clustering yield a two-jet W-mass resolu- tion of 15 GeV [full width at half maximum (FWHM)]

TABLE 11. Efficiencies at successive stages of analysis and the number of events simulated for each process.

Process € 6 . ~ E W W Events

pp-+HO-evqq 0.86 0.46 0.125 2000 pp-, WW-evqq 0.58 0.29 0.089 1 200 pp- Wq(g)-+evq(g) 0.80 0.15 0.012 59 000 pp -tT- W W ~ ~ - - + ~ V ~ ~ X 0.72 0.19 0.017 7000

40 - ARE W PAIRS A DETECTABLE SIGNATURE FOR HEAVY . . . 1469

for the 800-GeV Higgs-boson decays. A smaller mass in- terval could reduce the rate further. I t was found that this value is completely dominated by the process of clus- tering. That is, increasing the sampling term in the reso- lution from 0.20 to 0.30 for the E M calorimeter and from 0.50 to 0.75 in the hadronic calorimeter did not change the width significantly. The efficiency after this stage ( E , , is given in Table 11. The remaining events constitute an event sample which can then be subjected to a more sophisticated analysis as will be described below.

EVENT ANALYSIS 11 (OFF LINE)

The magnitude and shape of energy depositions in the calorimeter can be used to characterize W decays. The first characteristic is the mass which alone is not enough to distinguish the signal from the Q C D background. The W s produced by Higgs-boson decay have longitudinal polarization and therefore a sin2@* distribution. This produces two symmetric jets in the calorimeter. Continu- um W pairs are produced with transverse polarization with decay distributions which are peaked in the forward direction. a ( l+cos28*) distribution. which results in highly asymmetric decays. The parton recoiling against a single W will fragment to produce one or more jets which have a continuum mass distribution seen in Fig. 7. Most of these events are asymmetric but have a rather large rate. These properties can be used to further distinguish Higgs-boson decays from background.

T o use the shape of the energy distribution as a discriminant, it is necessary to form a statistical hy- pothesis of what characterizes the W decay distributions. The hypothesis must be obtained from a Monte Carlo simulation of W decays. By the time SSC is operational, there should be a substantial amount of information about the hadronic decays of W s from CERN LEP 200 and Fermilab Tevatron experiments. The test functions for this study were obtained from the same version of PYTHIA but were simulated in a less realistic detector." In addition, the jet pattern recognition algorithm that was used was different.

A W decay to quarks is characterized in a calorimeter by two concentrations of energy separated in angle by roughly a = M w /Pw. This angular separation depends on the quark decay angle ( Q * ) in the W frame, and reduces to M w /Pw for a 90" decay to massless quarks. A pattern of these energy concentrations is formed which is energy independent and has minimum variance about the mean by the following procedure.

(i) In the ( T , + ) coordinates of the calorimeter towers, translate to the center of energy (qo,40) of the pattern.

(ii) A thrust algorithm in two dimensions is used to define an axis, ' $ = ( s y , s 4 ) , which is aligned with the sem- imajor axis of the energy distribution in the calorimeter.

(iii) Rotate in (v,#) to align the positive 3 axis towards the higher-energy concentration.

(iv) For each tower energy E,, the variable si is defined to be the distance along the '$ axis from the center of en- ergy (qo,4') scaled by Pw /Mw:

(v) The density of tower energies in s is accumulated and normalized to form the quantity

in s bins of As ~ 0 . 0 5 . (vi) The two-dimensional distribution ( ( 1 /E )dE /ds )

as a function of cose* is formed. Heavy quarks ( b and t ) are removed since they will

contribute too much variance to ( ( 1 /E )dE /ds ) . For a 90" decay to massless quarks, this quantity will have two equal-density peaks at s = + 1 and - 1, and for an asym- metric W decay the forward decaying quark will have a higher energy density at smaller s while the backward de- caying quark will have lower density at larger, but more negative s. This is kinematically just like TO- decay. Slices in c o d * are shown in Fig. 8. On an event-by-event basis the ( ( 1 / E )dE /ds ) pattern and its variance are compared to each cose* hypothesis by computing x2 and a best fit can be found. The distribution of X* is shown in Fig. 9.

Other parameters characteristic of W decays are the elongation of the calorimeter energy pattern along the $ axis, and the relative widths of the energy concentrations at positive and negative s. This elongation may be mea- sured by E, / E l , where

and

where ei is the vector from (70, 4') to the ith tower locat- ed at (v i ,$ , ) of magnitude Ei. This distribution is shown in Fig. 10.

Another characteristic of the W+qP energy pattern is the ratio of relative widths of the + s and -s energy con- centrations ( u + /(r - ), where, for positive ei .'&

w , 1 0.9 < cos 0 < 1.0

FIG. 8. Distributions of ( ( 1 / E )dE /dS ) for different values of cose.

1470 BENGTSSON, HAUPTMAN, LINN, AND SAVOY-NAVARRO 40

FIG. 9. Distribution of X* shape for Ws (solid line) and jets (dashed line).

(and similarly for a - for negative values of the dot prod- uct).

Also useful is the sum of the rms deviations of e ( s + +s- ), where

for positive e, .$ and similarly for s -. All these quantities depend on cosO* and are highly

correlated. For example, if events with mass near M w are selected out by a mass cut, then necessarily this sam- ple is enriched in events with substantial transverse momentum with respect to the W laboratory direction, and this usually means two, or more, jets each with about a P, of M w / 2 . Hence E I / E I l is small, and it is not too difficult to match the shape of the ( ( 1 / E )dE Ids ) distri-

FIG. 10. Distribution of E , / E I for Ws (solid line) and jets (dashed line).

Signal Background

Mww(GeV)

FIG. 11. Distribution of the invariant mass ( M w w ) of the reconstructed WW system for both Higgs boson (solid line) and background (dashed line). The signal has been scaled by a fac- tor of fifteen with respect to the background.

bution for some value of cosO*. As a result, subsequent cuts on cosO* and x2 for the shape fit are less effective.

The probability that a W or a QCD jet will pass the W selection cuts is called cww. The QCD jet rejection fac- tor is then the ratio

One set of cuts which results in a W acceptance (or efficiency) of about 10% and a rejection against single QCD jets (relative to Ws) of 100 is

Further and more stringent cuts lower the efficiency of the Higgs-boson events ensemble and increase the rejec- tion against non- W QCD background. A figure of merit for this problem, by which different algorithms and methods may be compared is

a signal dbackground '

(24)

This quantity is the common quantity often used to esti- mate the significance of a signal over background. Figure 11 gives the d a / d M w w distributions for the Higgs-boson events and W+jet events after all cuts.

CONCLUSIONS

This study attempted for the first time to fully simulate a realistic SSC detector and carry out a complete analysis

40 ARE W PAIRS A DETECTABLE SIGNATURE FOR HEAVY . . . 1471

from triggering to the off-line stages of analysis. The number of events at any stage of the experiment is given by N = a L c . Assuming one year of SSC running ( lo7 sec) yields an integrated luminosity of & = lo4 pb-'. I t fol- lows from Tables I1 and I11 that for M,,, =50 GeV that the stat~stical significance of the Higgs signal is about two standard deviations above the background (WW continu- um and W t j e t ) . For M,,,= 100 GeV the significance is one standard deviation. he signal to background for each case is 3.0% and 1.5%, respectively. While prob- ably not a viable discovery mode for the heavy Higgs bo- son, this decay channel may be used to confirm the background-free but rare modes with more than one visi- ble lepton. Recent results from UA2 (Ref. 10) suggest that this is possible. The heavy-top-quark result should be considered a worst case because no attempt was made to identify events with additional leptons. I t may be pos- sible to use leptons with microvertex detection and track- ing to identify some fraction of the top events.

Most of the hardware characteristics of the simulated detector are adequate for high-mass particle spectroscopy using leptons, missing transverse energy, and jets. The electromagnetic energy resolution of the calorimeter was limited by energy-dependent effects and not sampling fluctuations. Since electron resolution was not a significant factor in reconstruction of the leptonically de- caying W, the sampling fraction of the calorimeter could

be reduced to better match the hadron calorimeter and reduce energy-dependent systematic effects. The missing-transverse-energy resolution of the detector in this study was adequate; however, until detailed engineer- ing studies are done, it will not be known if the assump- tions of the simulation are correct. The assumptions about hadronic energy resolution were conservative by todays standards. The effect of a noncompensating calorimeter was observed by slight shifts in the mass spectrum. Jet energy resolution is not limited by intrinsic calorimeter resolution but the abilitv to cluster the had- ronization fragments in the presence of the underlying event. The effect of multiple interactions per bunch crossing has been shown elsewhere to further worsen this effect." Previous studies" have indicated that a more finely segmented calorimeter could aid the off-line analysis in discriminating between the hadronic decays of the Wand single jets; this analysis deserves further study.

With the upgrade of the CERN SpP and its detectors as well as C D F and DO running at the Fermilab Teva- tron, more detailed understanding will be gained before the larger machines are commissioned.

ACKNOWLEDGMENTS

This work was supported in part by U.S. Department of Energy Contracts Nos. DE-AT03-88ER40384, W- 7405-ENG-82, and DE-FC05-85ER2500.

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