Extending the Higgs Boson Reach at the Upgraded Fermilab Tevatron
Tao Han and Ren-Jie Zhang
Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, WI 53706, USA (July, 1998) We study the observability for a Standard Model-like Higgs boson at an upgraded Tevatron via the modes p? → gg → h → W ? W ? → ?νjj and ???ν. We ?nd that with c. m. energy of 2 p ν? TeV and an integrated luminosity of 30 fb?1 the signal may be observable for the mass range of 135 GeV < mh < 180 GeV at a 3 ? 5σ statistical level. We conclude that the upgraded Tevatron ? ? may have the potential to detect a SM-like Higgs boson in the mass range from the LEP2 reach to 180 GeV. 14.80.Bn, 13.85.Qk
arXiv:hep-ph/9807424v2 1 Dec 1998
The Higgs bosons are crucial ingredients in the Standard Model (SM) and its supersymmetric extensions (SUSY). Searching for Higgs bosons has been one of the major motivations in the current and future collider programs since they most faithfully characterize the mechanism for the electroweak gauge symmetry breaking. Experiments at LEP2 will eventually be able to discover a SM-like Higgs boson with a mass about 105 GeV . The LHC should be able to cover the full range of theoretical interest, up to about 1000 GeV . It has been discussed extensively how much the Fermilab Tevatron can do for the Higgs boson search. It appears that the most promising processes continuously going beyond the LEP2 reach would be the electroweak gauge boson-Higgs associated production [3–5] p? → p W h, Zh. The leptonic decays of W, Z provide a good trigger and h → b? may be reconstructible with adeb quate b-tagging. It is now generally believed that for √ an upgraded Tevatron with c. m. energy s = 2 TeV and an integrated luminosity O(10 ? 30) fb?1 a SM-like Higgs boson can be observed up to a mass of about 120 GeV . The Higgs discovery through these channels crucially depends up on the b-tagging e?ciency and the b? mass resolution. It is also limited by statistics for b mh > 120 GeV. It might be possible to extend the mass reach to about 130 GeV via the decay mode h → τ + τ ? . On the other hand, from the theoretical point of view, weakly coupled supersymmetric models generally predict the lightest Higgs boson to have a mass mh < 150 GeV ? . It would be of the greatest theoretical signi?cance for the upgraded Tevatron to extend the Higgs boson coverage over this range. It is important to note that the leading production mechanism for a SM-like Higgs boson at the Tevatron is the gluon-fusion process via heavy quark triangle loops. Although the decay mode h → b? in this case would be b swamped by the QCD background, h → W ? W ? mode (where W ? generically denotes a W boson of either onor o?-mass-shell) will have an increasingly large branching fraction for mh > 130 GeV and may have a chance ? to be observable. In this paper, we study in detail the observability of a SM-like Higgs boson at an upgraded
Tevatron for the modes p? → gg → h → W ? W ? → ?νjj and ???ν, p ν? (1)
where ? = e, ? and j is a light quark jet. In Fig. 1, we show the cross section for gg → h versus mh with p? p √ c. m. energy s = 2 TeV. Along with the inclusive total cross section? (solid curve), we show the W ? W ? (dashes) and Z ? Z ? (dots) channels, as well as their various de? ? cay modes W ? W ? → ?νjj, ???ν and Z ? Z ? → ??ν ν , 4?. ν? The scale on the right-hand side gives the number of events expected for 30 fb?1 . We see that for the mh range of current interest, there may be about 1000 events produced for W ? W ? → ?νjj and about 100 events for W ? W ? → ???ν. This latter channel has been studied at ν? the SSC and LHC energies  and at a 4 TeV Tevatron √ . We ?nd that at s = 2 TeV, after nontrivial optimization for the signal identi?cation for Eq. (1) over the substantial SM backgrounds, it is promising to extend the Higgs boson reach at the upgraded Tevatron with an integrated luminosity of 30 fb?1 to mh ≈ 135 ? 180 GeV at a 3 ? 5σ statistically signi?cant level. W ? W ? → ?νjj : For this mode, we require the ?nal state to have an isolated charged lepton (?), large missing transverse energy (/T ), and two hard jets. The leading SM backgrounds E are p? → W + 2 QCD jets, p? → W W → ?νjj, p p ? ? p? → W Z(γ ) → ?νjj, p? → tt → ?νjjb? p p b. (2)
The background processes are calculated with the full SM matrix elements at tree level.
We have normalized our signal cross section to include next-to-leading order QCD corrections , and we use the CTEQ4M distribution functions .
hand, for mh ≤ 160 GeV, nearly half of the signal will be cut o? by the m(jj) cuts, making this region of the Higgs mass more di?cult to explore from this mode. We have also examined other mass variables, such as the W -boson transverse mass MT (W ), di-jet-lepton invariant mass m(jj?), and the cluster transverse mass MC , which are de?ned as MT (W ) = MC = (pT ? + ET )2 ? (pT ? + /T )2 , / p (7)
p2 (jj?) + m2 (jj?) + ET . / T
FIG. 1. The Higgs-boson production cross-section via the gluon-fusion process versus mh at the 2 TeV Tevatron. The h → W ? W ? (dashes) and Z ? Z ? (dots) channels and various subsequent decay modes are also depicted.
To roughly simulate the detector e?ects, we use the following energy smearing √ ?Ej /Ej = 0.8/ E j ⊕ 0.05 for jets, √ ?E? /E? = 0.3/ E ? ⊕ 0.01 for leptons, (3) where ⊕ denotes a sum in quadrature. The basic acceptance cuts used here are pT ? > 15 GeV, |η? | < 1.1; pT j > 15 GeV, |ηj | < 3; ET > 15 GeV; ?R(?j) > 0.3, ?R(jj) > 0.7. / (4) For the sake of illustration, we present our study mostly for mh = 140 and 160 GeV and we will generalize the results to the full mh range of interest. The cut e?ciency for the signal is about 35% (60%) for mh ≈ 140 (160) GeV. Since there are only two jets naturally appearing in ? the signal events, the tt background can be e?ectively suppressed by rejecting events with extra hard jets. We therefore impose Jet veto pT j > 15 GeV in |ηj | < 3. (5)
The MT (W ) develops a peak near MW for on-shell W decay. An upper cut on this variable below MW can help remove the background from real W decay as long as mh is less than 160 GeV. The cluster transverse mass MC would be the most characteristic variable for the signal. It peaks near mh and yields a rather sharp end-point above mh . To further improve the signal-to-background ratio S/B, we ?nd the following tighter cuts helpful 100 < m(jj?) < 120 GeV, ET < 30 GeV, 120 < MC < 140 GeV, / 35 < MT (W ) < 55 GeV, 2.4 < ?R(jj) < 3.5; 100 < m(jj?) < 130 GeV, ET < 50 GeV, 130 < MC < 170 GeV, / 40 < MT (W ) < 90 GeV, 2.8 < ?R(jj) < 3.5, for mh = 140 and 160 GeV respectively. We show the results progressively at di?erent stages of the kinematical cuts in Table I. We see that for an integrated luminosity of 30 fb?1 , the signal for mh = 140 GeV is very weak while that for mh ? 160 GeV can reach a 3σ statistical signi?cance. W ? W ? → ???ν : ν? For the pure leptonic channel, we identify the ?nal state signal as two isolated charged leptons and large missing transverse energy. The leading SM background processes are p? → W + W ? → ???ν, p? → ZZ(γ ? ) → ν ν ??, p ν? p ? ? ? p? → tt → ???νb? p? → Z(γ ? ) → τ + τ ? → ???νντ ντ . (9) p ν ? b, p ν? ? We ?rst impose basic acceptance cuts pT ? > 10 GeV, |η? | < 1.1; pT ?′ > 5 GeV, |η?′ | < 2.5; m(??′ ) > 10 GeV, ET > 25 GeV. / (10) The cut e?ciency for the signal is about 70%. We also smear the lepton momenta according to Eq. (3), and veto the hard central jets via Eq. (5) to e?ectively remove ? the tt background. At this level, the largest background comes from the Drell-Yan process for τ + τ ? production. However, this background can be essentially eliminated by removing the back-to-back lepton pair events by requiring φ(??) < 150? . 2 (11) (8)
The QCD background in (2) has the largest rate. The di-jet in the signal is from a W decay, while that in the QCD background tends to be soft and collinear. We thus impose the cuts on the di-jet: 65 < m(jj) < 95 GeV, φ(jj) > 140? ; 70 < m(jj) < 90 GeV, φ(jj) > 160? ,
for mh = 140 and 160 GeV respectively, where m(jj) is the invariant mass of the di-jet and φ(jj) the opening angle of the two jets in the transverse plane. For mh ≥ 160 GeV, the m(jj) distribution has a unique peak because both W bosons are on shell, so the m(jj) cuts in Eq. (6) would not signi?cantly harm the signal. On the other
The W ? W ? mass cannot be accurately reconstructed due to the two undetectable neutrinos. However, both the transverse mass MT and the cluster transverse mass MC , de?ned as MT = 2 MC = p2 (??) + m2 (??), T p2 (??) + m2 (??) + ET , / T (12)
yield a broad peak near mh . We note that these transverse mass variables are very important for the signal identi?cation and for controlling the systematic error.
some angular variables implement the information for decay lepton spin correlations and are powerful in discriminating against the backgrounds. With some further selective cuts on the angular distributions, we ?nd that the S/B can be improved to about 8% and 21%, with the signal rates 2.6 and 3.3 fb for mh = 140 and 160 GeV, respectively. We show in Fig. 2(b) the event rate distributions for the SM background (solid) and signal plus background (dashes) for mh = 160 GeV. The statistical error bars on the background are also indicated.
FIG. 2. The cluster transverse mass distributions for ???ν ν? mode (a) for the signal mh = 140, 160 and 180 GeV and the leading SM backgrounds with cuts (10) and (11). With further selective cuts, we show the event rates in (b) for SM background (solid) and background plus signal (dashes) for mh = 160 GeV. The statistical error bars are also indicated on the background curve in (b).
FIG. 3. The integrated luminosity needed to reach 3σ and 5σ statistical signi?cance versus mh . The dotted and dashed lines correspond to the ?νjj and ???ν modes respectively. The ν? solid lines are the (quadratically) combined results.
In Fig. 2(a), we show the MC distributions for the ???ν signal with mh = 140, 160 and 180 GeV along with ν? the leading backgrounds after the cuts in (10) and (11). Although the mass peaks in MC are hopeful for signal identi?cation, they are rather broad. We may have to rely on the knowledge of the SM background distribution. We hope that with the rather large statistics of the data sample, one may obtain good ?t for the normalization of the background shape outside the signal region in Fig. 2(a), so that the deviation from the predicted background can be identi?ed as signal. Some additional useful cuts are m(??) < 80 GeV (70 for mh ≤ 140 GeV),
ET < mh /2, mh /2 < MC < mh . /
The results at di?erent stages of kinematical cuts are shown in Table II. Due to the absence of the large QCD background in (2), this pure leptonic mode seems to be statistically more promising than the ?νjj mode. One may expect a more than 3σ (4σ) e?ect for mh = 140 (160) GeV with 30 fb?1 . It was pointed out in  that 3
In Fig. 3, we show the integrated luminosities needed to reach 3σ and 5σ signi?cance versus mh . The dotted curves are for the ?νjj mode and the dashed for ???ν. ν? We consider that these two modes have rather di?erent systematic errors, so that we can combine the results for them quadratically. This is shown by the solid curves. We see that with an integrated luminosity of 30 fb?1 , one may be able to reach at least a 3σ signal for 135 GeV < mh < 180 GeV. Taking into account the ? ? previous studies [3,5,6], we conclude that the upgraded √ Tevatron with s = 2 TeV and 30 fb?1 may have the potential to detect the SM-like Higgs boson in the mass range from the LEP2 reach to 180 GeV. On the other hand, if there is only about 10 fb?1 data available, the sensitivity to the Higgs boson search via the modes of Eq. (1) would be very limited. A higher luminosity is strongly called for in this regard. Finally, a few remarks are in order. (a) In our analyses, we have not considered the W → τ ντ mode. Including this decay channel would increase the signal rate by a factor of 3/2 (9/4) for ?νjj (???ν) mode. But ν? the signal identi?cation would be more challenging. The ? ? ? other modes such as Z ? Z ? → ??jj, ??ν ν and 4?, although smaller, may also be helpful to improve the signal observability. (b) Our results presented here are valid not
only for the SM Higgs boson, but also for SM-like ones such as the lightest Higgs boson in SUSY at the decoupling limit. If there is an enhancement from new physics for Γ(h → gg) × BR(h → W W, ZZ) over the SM expectation, the signal of Eq. (1) would be more viable. If BR(h → b? is suppressed, such as in certain parameter b) region in SUSY, then the signal under discussion may complement the W h, Zh (h → b? channels at a lower b) mh region. Our results summarized in Fig. 3 based on the partonlevel simulation are clearly encouraging to signi?cantly extend the reach for the Higgs boson search at the upgraded Tevatron. The more comprehensive results with full Monte Carlo simulations in a realistic environment will be reported elsewhere . Acknowledgments: We would like to thank V. Barger, E. Berger, R. Demina, M. Drees, T. Kamon, S. Mrenna, J.-M. Qian, S. Willenbrock and J. Womersley for helpful comments. T.H. would like to thank the Aspen Center for Physics for its hospitality during the ?nal stage of the project. This work was supported in part by a DOE grant No. DE-FG02-95ER40896 and in part by the Wisconsin Alumni Research Foundation.
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σ [fb] mh [GeV] signal background W jj WW WZ tt S/B √ S/ B (30 fb?1 )
Basic Cuts in (4) 140 160 23 49 6.5 × 105 1.3 × 103 66 0.4 -
Cuts in (6) 140 160 8.8 21 6.1 × 103 2.1 × 103 5.5 × 102 2.4 × 102 20 7.0 0.1 0.1% 0.9% 0.6 2.4
Cuts in (8) 140 160 2.2 15 1.4 × 102 5.5 × 102 17 55 0.3 1.3 0.0 1.4% 2.5% 1.0 3.3
TABLE I. h → W ? W ? → ?νjj signal and background cross sections (in fb) for mh = 140 and 160 GeV, after di?erent stages ? of kinematical cuts. A jet-veto cut in Eq. (5) has been implemented for the tt background.
σ [fb] mh [GeV] signal background WW ZZ(γ ? ) Z(γ ? ) tt S/B √ S/ B (30 fb?1 )
Basic Cuts in (10) 140 160 7.3 10 2.7 × 102 24 3.9 × 102 0.2 1.1% 1.5% 1.5 2.1
φ(??) < 150? 140 160 7.0 9.9 2.4 × 102 18 0.0 0.1 2.7% 3.9% 2.4 3.4
Cuts in (13) 140 160 6.3 9.1 1.1 × 102 1.4 × 102 1.8 1.8 0.0 0.0 5.6% 6.4% 3.3 4.2
Re?ned Cuts 140 160 2.6 3.3 32 16 0.3 0.1 0.0 0.0 8.0% 21% 2.5 4.5
TABLE II. h → W ? W ? → ???ν signal and background cross sections (in fb) for mh = 140 and 160 GeV, after di?erent ν? stages of kinematical cuts. The last column corresponds to the re?nement of mass cuts and various angular distribution cuts. ? A jet-veto cut in Eq. (5) has been implemented for the tt background.