Projected Exclusion Limits on the SM Higgs Projected Exclusion Limits on the SM Higgs Boson Boson

Cross Section by Combining Higgs Channels Cross Section by Combining Higgs Channels at LHCat LHC

Tommaso DorigoTommaso Dorigo (INFN and University of Padova) for the (INFN and University of Padova) for the CMS collaborationCMS collaborationThe CMS experimentThe CMS experimentat the Large Hadron Colliderat the Large Hadron Collider

IntroductionIntroduction

Fig. 1: Fit 2 on electroweak observables as a function of the Higgs mass. The blue band shows the theoretical uncertainty; an alternative (5)

had value and the inclusion of neutrino scattering data produce different curves.

CMS (Compact Muon Solenoid) is a multi-purpose detector, designed to study the 14-TeV proton-proton collisions produced by the Large Hadron Collider (LHC).

The apparatus (see Fig. 3 below, right) is composed by a precision silicon detector tracker and a segmented calorimeter contained within a 4-Tesla solenoid, and surrounded by an almost hermetic system for muon detection.

Electron energies are measured in lead-tungstate crystals, while muon momenta are reconstructed from their inner tracks and outer segments; jet energies are measured by the calorimeters, and the unbalancing in the total transverse energy allows to determine the transverse momentum of escaping neutrinos (see Fig. 4).

After repairs following an incident last September, the LHC is due to start data-taking in November 2009. The latest plan foresees a ten months start-up phase with proton-proton collisions at 7 TeV center-of-mass energy. The present study still considers the Higgs search with CMS in a 14 TeV running scenario. A study of the impact on Higgs searches of lower beam energy at start-up is provided below.

Higgs production and decayHiggs production and decayThe Higgs boson is primarily produced at the LHC by gluon-gluon fusion and vector boson fusion processes. Production cross sections are of a few tens of picobarns in the 120-200 GeV range.

For MH<135 GeV decays to b-quark pairs are the most frequent (see Fig. 5), but are hard to exploit experimentally; in that low-mass region the CMS experiment will primarily search its decay to tau-lepton pairs or photon pairs. For larger masses, the decays to WW(*) or ZZ(*) pairs dominate (the * sign denotes off-shell states). When W or Z bosons decay to electrons or muons, the final state is comparatively clean.

The search for the WW(*) final state of Higgs decay is divided in three distinct sub-searches, depending on the kind of charged leptons identified: the ee, e, and final states are treated separately for the purpose of a combination of the cross-section limits, because they have significantly different signal-to-noise (S/N) levels and their systematic uncertainties are large and not 100% correlated. The eeee, ee, and categories of ZZ(*) candidates can instead be merged together because they are more homogeneous in S/N and their systematics are 100% correlated.

For a combination of HWW(*) and HZZ(*) search results we thus consider four separate channels, each with its own expected signal and background, and relative uncertainties. More details can be found in [3] and [4] (and are summarized in a separate poster[5]).

Combination of HCombination of HWW and HWW and HZZ searchesZZ searches

The combination of the four different counting experiments requires in principle the knowledge of a complete matrix of correlations between the systematic uncertainties affecting signal and background yields in all sub-channels. This has not been done yet, and is the goal of a future iteration of the analysis.

In the simplified treatment given here, we assume a flat prior for the production of the Higgs boson signal, and a full correlation of systematic uncertainties on all signal and background yields si and bi. This reduces the problem to a 1-dimensional integration. The probability density function (PDF) of all relative uncertainties is assumed to be a truncated Gaussian distribution GT(x), null for [-, -1]. One then defines a likelihood function L as a function of a scale parameter r on the signal cross section. If p(n|m) is the probability of observing n events when m are expected, and if we denote as max the largest of the eight uncertainties, we define

where and .

For any given Higgs mass point, the 95% confidence level is then defined as the value of the scale parameter r95 such that

The modified frequentist CLs method is based on comparing the two hypotheses of the observed data being produced by background only (b) or signal plus background (sb), defining an observable quantity Q as a likelihood ratio:

Q is positive if the background hypothesis is better borne by the data, and negative otherwise. One may then integrate from the observed value of Q to infinity the expected PDF of background-only and signal-plus-background experiments, Pb and Psb, to obtain

These are then combined in the CLs ratio CLs = CLsb/CLb: values of the signal rate which return CLs <0.05 are excluded at 95% confidence level. To compute an expected 95% C.L. in the absence of real data we take for Qobs the median value of the PDF dPb/dQ. Then r95 is the value of the expected signal rate which corresponds to CLs(Qobs) = 0.05.

To derive the shape of the PDF for the two hypotheses, a large number of pseudo-experiments are performed. In each toy dataset the parameters bi and si are varied according to their systematics, assumed to distribute according to a truncated Gaussian. The errors on expected signal and background counts are taken to be 80% correlated between the WW(*) channels. In this exercise, we assume no correlation between signal and background systematic errors, nor between those of the ZZ(*) and WW(*) channels.

Extraction of Bayesian limitsExtraction of Bayesian limits Extraction of CLExtraction of CLss limits limits

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The exercises described above may be carried out to determine the range of Higgs boson masses that CMS is likely exclude at 95% C.L. in the absence of a signal using the results of [3] and [4], which correspond to a scenario where the luminosity of one inverse femtobarn of proton-proton collisions is collected at the design LHC energy (14 TeV). This also allows to gauge how the simplifying assumptions of the two calculations affect the results.

Figure 6 (right) shows the limit that can be obtained in the 14 TeV scenario (red curves), with Bayesian and Modified Frequentist CLs methods. In general the two methods agree within 10%, which is also a measure of the typical variation in their difference.

Also reported in Fig. 6 is the result of considering a modified scenario (blue curves), in which 1/fb of collisions is collected at the reduced C.M. energy of 10 TeV. The reduction impacts the production of Higgs bosons, particularly in the gluon-fusion process and at large Higgs masses. Backgrounds are in general less affected by the smaller collision energy, except top quark production. Fig. 7 (below, left) shows the ratio of cross sections of signal (for MH=160 GeV) and the main background processes in the WW(*) search; for the ZZ(*) search both signal and the main background from SM diboson production decrease with the effective mass of the ZZ(*) system (Fig. 8, below). Signal and background acceptances also change slightly in going from 14 to 10 TeV, as shown in Fig. 9 (below, right).

Expected cross section limits with 1/fbExpected cross section limits with 1/fb

Fig. 7: Ratio of cross sections at 10 and 14 TeV for signal and backgrounds in the HWW(*) search.

Fig. 8: Ratio of cross sections at 10 and 14 TeV for signal (blue) and SM ZZ(*) background (red) in the HZZ(*) search, as a function of the combined ZZ mass.

A combination of results of the WW(*) and ZZ(*) searches for Higgs boson production will allow the CMS experiment to exclude a range of masses between 140 and 230 GeV, using 1/fb of 14-TeV proton-proton collisions.

About twice more luminosity is required for the same result if the c.m. energy is 10 TeV.

ConclusionsConclusions [1] http://http://lepewwg.web.cern.ch/LEPEWWG/ .[2] arXiv:hep-ex/0903.4001, “Combined CDF and Dzero Upper Limits on Standard Model Higgs Boson Production with up to 4.2/fb of Data”, March 24th, 2009.[3] CMS PAS HIG-08-006, “Search strategy for a Standard Model Higgs boson decaying to two W bosons in the fully leptonic final state”, January 29th, 2009.[4] CMS PAS HIG-08-003, “Search strategy for the Higgs boson in the ZZ(*) decay channel with the CMS experiment”, February 7th, 2009.[5] T.Dorigo, “Search for the SM Higgs boson at CMS”, poster presented at this conference, September 1st, 2009.

Fig. 9: Ratio of kinematic efficiency for SM ZZ(*) (red) and HZZ(*) decays (blue), as a function of the combined mass of the four identified leptons.

ReferencesReferences

Fig. 3: Cut-away view of the CMS detector.

Fig. 4: Transversal section of CMS, showing the characteristic behavior of the different physics objects measured by the detector.

Fig. 6: Predicted limits on the Higgs cross section (in units of the SM expectation) as a function of mass, for 1/fb at 10 or 14 TeV.

The Standard Model (SM) requires the existence of a scalar Higgs boson to break electroweak symmetry and provide mass terms to gauge bosons and fermion fields. The Higgs boson is still undiscovered. Its mass is a priori unknown, but radiative corrections to electroweak observables place indirect constraints on it. The latest fits indicate that MH<157 GeV, as shown in Fig. 1 below[1].

Direct constraints come from experimental searches: those performed at LEP II have determined that MH>114.4 GeV (at 95% of Confidence Level); searches at the Tevatron have so far allowed to exclude the range 160< MH <170 GeV (see Fig. 2), again at 95% C.L.[2].

Fig. 2: Direct Tevatron limits on the ratio between Higgs production cross section and SM expectation (black line) as a function of mass. The pink regions have been excluded at better than 95% C.L. by LEP II and Tevatron.

Fig. 5: Branching ratio of Higgs boson decays as a function of MH.