Prospects for the measurement of the Higgs Yukawa couplings to b and c quarks, and muons at CLIC
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Abstract
The investigation of the properties of the Higgs boson, especially a test of the predicted linear dependence of the branching ratios on the mass of the final state is going to be an integral part of the physics program at colliders at the energy frontier for the foreseeable future. The large Higgs boson production cross section at a 3 TeV CLIC machine allows for a precision measurement of the Higgs branching ratios. The cross section times branching ratio of the decays \(\mathrm {H}\to \mathrm {b}\overline {\mathrm {b}}\), \(\mathrm {H}\to \mathrm {c}\overline {\mathrm {c}}\) and H→μ^{+}μ^{−} of a Standard Model Higgs boson with a mass of 120 GeV can be measured with a statistical uncertainty of 0.23 %, 3.1 % and 15 %, respectively, assuming an integrated luminosity of 2 ab^{−1}.
Keywords
Higgs Boson Invariant Mass Distribution Standard Model Higgs Boson Momentum Resolution Hadronic Calorimeter1 Introduction
The Higgs mechanism of the Standard Model predicts the existence of a fundamental spin0 particle. Recently, the ATLAS and CMS experiments at the LHC have observed a particle which is consistent with the predictions for a Standard Model Higgs boson, but its properties remain to be studied [1, 2]. In particular, the Standard Model predicts a linear dependence between the Higgs boson couplings to fermions and their mass. This relation could be altered by the presence of new physics. The detailed exploration of the Higgs sector is thus instrumental to our understanding of the fundamental interactions. The compact linear collider (CLIC) is a proposed e^{+}e^{−} collider with a maximum centreofmomentum energy \(\sqrt{s} = 3~\mathrm{TeV}\), based on a twobeam acceleration scheme [3]. The Higgs boson production cross section with unpolarised beams is 421 fb in the dominant Wfusion channel. This allows for precision measurements of the Yukawa couplings. The beam of the 3 TeV CLIC consists of bunch trains of 312 bunches, which are separated by 0.5 ns. The small beam size and large electric field in the bunches, required to achieve the peak luminosity of 5.9×10^{34} cm^{−2} s^{−1}, lead to a large cross section of real and virtual twophoton processes that are a background to the processes of interest produced in the electronpositron collision. On average, real beamstrahlung photons produce 3.2 γγ→hadrons events per bunch crossing at \(\sqrt{s}=3~\mathrm{TeV}\).
We present simulation studies of the measurements of the branching ratios \(\mathrm {H}\to \mathrm {b}\overline {\mathrm {b}}\), \(\mathrm {H}\to \mathrm {c}\overline {\mathrm {c}}\) [4] and H→μ^{+}μ^{−} [5] at such a machine. These studies of the Higgs branching ratios are part of the benchmarking analyses presented in the CLIC Conceptual Design Report [6]. They are carried out in a Geant4based simulation [7] of the CLIC_SiD [8] detector concept, with full account of Standard Model backgrounds and using a realistic reconstruction in presence of γγ→hadrons background. The latter is reduced partly by removing hits that are out of time with the physics process, partly by advanced offline reconstruction techniques.
2 The CLIC_SiD detector model
The CLIC_SiD detector model in which these studies are carried out is a generalpurpose detector with a 4π coverage and is based on the SiD concept [9] developed for the ILC. It has been adapted [8] to meet the specific detector requirements at CLIC. It is designed for particle flow calorimetry using highly granular calorimeters.
A superconducting solenoid with an inner radius of 2.7 m provides a central magnetic field of 5 T. The calorimeters are placed inside the coil and consist of a 30 layer tungsten–silicon electromagnetic calorimeter with 3.5×3.5 mm^{2} segmentation, followed by a tungsten–scintillator hadronic calorimeter with 75 layers in the barrel region and a steel–scintillator hadronic calorimeter with 60 layers in the endcaps. The readout cell size in the hadronic calorimeters is 30×30 mm^{2}. The iron return yoke outside of the coil is instrumented with nine doubleRPC layers with 30×30 mm^{2} readout cells for muon identification.
The silicononly tracking system consists of five 20×20 μm^{2} pixel layers followed by five strip layers with a pitch of 25 μm, a readout pitch of 50 μm and a length of 92 mm in the barrel region. The tracking system in the endcap consists of four stereostrip disks with similar pitch and a stereo angle of 12^{∘}, complemented by seven pixelated disks in the vertex and farforward region at lower radii with pixel sizes of 20×20 μm^{2}.
The forward region is instrumented with a LumiCal, with coverage down to 40 mrad, and a BeamCal, with coverage down to 10 mrad.
The triggerless readout integrates over 10 ns for all subdetectors except the hadronic calorimeter, which has an integration time of 100 ns to allow for shower development in the tungsten absorber. The silicon detectors allow time stamping of the recorded hits with a precision of a few ns.
3 Analysis framework
The physical processes are produced with the Whizard [10, 11] event generator, taking into account the CLIC beam spectrum, with fragmentation and hadronisation handled by the Pythia [12] package. The branching ratios of a 120 GeV Standard Model Higgs boson are: \(\mathrm{BR}(\mathrm {H}\to \mathrm {b}\overline {\mathrm {b}}) = 6.48\times10^{1}\), \(\mathrm{BR}(\mathrm {H}\to \mathrm {c}\overline {\mathrm {c}}) = 3.27\times 10^{2}\) and BR(H→μ^{+}μ^{−})=2.44×10^{−4} [13]. The events are simulated in the CLIC_SiD detector model using SLIC [14], which is a thin wrapper around Geant4. They are reconstructed by the algorithms in the org.lcsim [15] and slicPandora [16] packages. Unlike in analyses at lowerenergy linear colliders, which use DURHAMstyle jet finders that operate on all particles in the event, it was found that the beamjets of algorithms originally developed for hadron colliders, lead to a crucial improvement of the jetenergy resolution and reduce the effect of the forwardpeaking γγ→hadrons events greatly. In the analysis of Higgs decays to b and c quarks, we use the k _{ t } algorithm [17] as implemented by the FastJet [18, 19] package. The LCFI [20] package is used for flavour tagging. The assumed luminosity of the analyses is 2 ab^{−1}, corresponding to about 4 years of data taking at nominal conditions, assuming 200 days of running per year at an efficiency of 50 %.
3.1 Rejection of γγ→hadrons backgrounds
A 3 TeV CLIC produces 3.2 γγ→hadrons events per bunch crossing on average. The spacing of 0.5 ns between bunches leads to pileup in the subdetectors, which integrate over multiple bunch crossings. Identifying the time of the physics event and reading out only a window of 10 ns for the subdetectors, except for the barrel of the hadronic calorimeter, for which 100 ns are read out, reduces the number of γγ→hadrons events in the data sample by about a factor of 15.
List of processes considered for this analysis with their respective cross section σ and the number of simulated events N _{events}. The cross section takes into account the CLIC luminosity spectrum. Cross sections marked with * include a cut on the invariant mass of the muon pair to lie between 100 and 140 GeV
Process  σ (fb)  Short label 

\(\mathrm{e}^{+}\mathrm{e}^{}\to \mathrm {H}\upnu _{\mathrm{e}} \overline{\upnu }_{\mathrm{e}}\); H→μ^{+}μ^{−}  0.120  H→μ^{+}μ^{−} 
\(\mathrm{e}^{+}\mathrm{e}^{}\to \mathrm {H}\upnu _{\mathrm{e}}\overline{\upnu }_{\mathrm{e}}\); \(\mathrm {H}\to \mathrm {b}\overline {\mathrm {b}}\)  272  \(\mathrm {H}\to \mathrm {b}\overline {\mathrm {b}}\) 
\(\mathrm{e}^{+}\mathrm{e}^{}\to \mathrm {H}\upnu _{\mathrm{e}} \overline{\upnu }_{\mathrm{e}}\); \(\mathrm {H}\to \mathrm {c}\overline {\mathrm {c}}\)  13.7  \(\mathrm {H}\to \mathrm {c}\overline {\mathrm {c}}\) 
\(\mathrm{e}^{+}\mathrm{e}^{}\to \upmu ^{+}\upmu ^{}\upnu \overline{\upnu }\)  132^{∗}  \(\upmu ^{+}\upmu ^{}\upnu \overline{\upnu }\) 
e^{+}e^{−}→μ^{+}μ^{−}e^{+}e^{−}  346^{∗}  μ^{+}μ^{−}e^{+}e^{−} 
e^{+}e^{−}→μ^{+}μ^{−}  12^{∗}  μ^{+}μ^{−} 
e^{+}e^{−}→τ ^{+} τ ^{−}  250^{∗}  τ ^{+} τ ^{−} 
\(\mathrm{e}^{+}\mathrm{e}^{}\to\tau^{+}\tau^{}\upnu \overline{\upnu }\)  125^{∗}  \(\tau^{+}\tau^{}\upnu \overline{\upnu }\) 
\(\mathrm{e}^{+}\mathrm{e}^{}\to \mathrm{q}\overline{\mathrm{q}}\)  3100  \(\mathrm{q}\overline{\mathrm{q}}\) 
\(\mathrm{e}^{+}\mathrm{e}^{}\to \mathrm{q}\overline{\mathrm{q}} \upnu \overline{\upnu }\)  1300  \(\mathrm{q}\overline{\mathrm{q}}\upnu \upnu \) 
\(\mathrm{e}^{+}\mathrm{e}^{}\to\mathrm{q}\overline{\mathrm{q}} \mathrm{e}^{+}\mathrm{e}^{}\)  3300  \(\mathrm{q}\overline{\mathrm{q}} \mathrm{e}^{+}\mathrm{e}^{}\) 
\(\mathrm{e}^{+}\mathrm{e}^{}\to\mathrm{q}\overline{\mathrm{q}}\mathrm{e}\upnu \)  5300  \(\mathrm{q}\overline{\mathrm{q}}\mathrm{e}\upnu \) 
generator level: γγ→μ^{+}μ^{−}  20000^{∗}  γγ→μ^{+}μ^{−} 
In addition to applying readout windows offline, the computation of the cluster time allows to further reduce this background. Assuming ns precision of the calorimeter hit times results in subns precision for the cluster time, which is calculated as a truncated mean of the corresponding hit times. The production time of the reconstructed particle is obtained by correcting the cluster time for its time of flight through the magnetic field. It is required to be consistent with the start of the physics event. Consistency is defined by a time window, whose size depends on the type of particle (hadronic or electromagnetic), its momentum and polar angle θ. For example, in the \(\mathrm {H}\to \mathrm {b}\overline {\mathrm {b}}\) events the fraction of energy from the γγ→hadrons background in reconstructed jets is reduced from 22 % to 6.5 % by removing outoftime particles. At the same time the reconstructed signal energy is reduced by less than 0.2 %.
4 Measurement of Higgs decays to pairs of b and c quarks

The maximum of the absolute values of jet pseudorapidities.

The sum of the remaining LCFI jet flavour tag values, i.e. ctag against u d s bbackground, ctag against bbackground and btag against udsbackground.

R _{ ηϕ }, the distance of jets in the η–ϕ plane.

The sum of jet energies.

The total number of leptons in an event.

The total number of photons in an event.

The acoplanarity of the jets.
5 Measurement of Higgs decays to pairs of muons
The measurement of the rare decay H→μ^{+}μ^{−} requires high luminosity operation and sets stringent limits on the momentum resolution of the tracking detectors. The branching ratio of the decay of a Standard Model Higgs boson to a pair of muons is important as the lower end of the accessible decays and defines the endpoint of the test of the predicted linear dependence of the branching ratios to the mass of the final state particles.
5.1 Event selection
The average muon reconstruction efficiency for polar angles greater than 10^{∘} is 99.6 % without γγ→hadrons background. When adding this background the muon reconstruction efficiency deteriorates to 98.4 % in this region of polar angles. The efficiency for smaller polar angles is limited by the acceptance of the tracking detectors. The events are required to have at least two reconstructed muons, each with a transverse momentum of more than 5 GeV. In case there are more than two muons reconstructed, the two most energetic ones are used, which are referred to as μ_{1} and μ_{2}. In addition, the invariant mass of the two muons M(μμ) is required to be between 105 GeV and 135 GeV. The total reconstruction efficiency of the signal sample is 72 % in the presence of γγ→hadrons background. The inefficiency is dominated by acceptance effects.

The visible energy excluding the two reconstructed muons E _{vis}.

The scalar sum of the transverse momenta of the two muons p _{T}(μ_{1})+p _{T}(μ_{2}).

The helicity angle \(\cos\theta^{*}(\upmu\upmu) = \frac{\mathbf{p}'(\upmu_{1})\cdot\mathbf{p}(\upmu\upmu)}{\mathbf{p}'(\upmu_{1}) \cdot\mathbf{p}(\upmu\upmu)}\), where p′ is the momentum in the rest frame of the dimuon system.

The relativistic velocity of the dimuon system β(μμ), where \(\upbeta= \frac{v}{c}\).

The transverse momentum of the dimuon system p _{T}(μμ).

The polar angle of the dimuon system θ(μμ).
5.2 Invariant mass fit
The number of signal events is determined by an unbinned maximum likelihood fit of the invariant mass distribution of the combined signal and background sample. This sample is randomly selected from all simulated events, according to the assumed integrated luminosity of 2 ab^{−1}. The expected shapes of the signal and background contributions are determined from a fit to the full statistics of the respective sample. The distribution of the invariant mass in the e^{+}e^{−}→H→μ^{+}μ^{−} sample has a tail towards lower masses because of final state radiation. It is described by two half Gaussian distributions, each with an exponential tail. The background is well described by an exponential parametrisation, obtained from a backgroundonly sample.
The BDT selection with the highest signal significance yields a total signal selection efficiency of 21.7 %, corresponding to about 53 selected events in 2 ab^{−1}. The relative statistical uncertainty on the crosssection times branching ratio obtained from the fit of the invariant mass distribution is 26.3 %. This corresponds to a signal significance of approximately 3.8σ. Without addition of the γγ→hadrons background the relative statistical uncertainty on the crosssection times branching ratio improves to 23 %, due to higher signal selection efficiency.
5.3 Study of the momentum resolution
Dependence of the statistical uncertainty of the measurement of cross section times branching ratio for the decay h→μ^{+}μ^{−} on the momentum resolution \(\sigma(\Delta p_{\mathrm{T}})/ p_{\mathrm{T}}^{2}\). The study assumes an integrated luminosity of 2 ab^{−1}. The values do not include the impact of the γγ→hadrons background and the possible reduction of the e^{+}e^{−}→μ^{+}μ^{−} e^{+}e^{−} background using electron tagging in the forward calorimeters
\(\sigma(\Delta p_{\mathrm{T}})/p_{\mathrm{T}}^{2}\)  σ(ΔM(μμ))  Stat. uncertainty 

10^{−3} GeV^{−1}  6.5 GeV  – 
10^{−4} GeV^{−1}  0.70 GeV  34.3 % 
10^{−5} GeV^{−1}  0.068 GeV  18.2 % 
10^{−6} GeV^{−1}  0.022 GeV  16.0 % 
5.4 Forward electron tagging
An independent study [23] of the electron tagging efficiency in the forward calorimeters at a CLIC detector, taking into account the γγ→hadrons background as well as e^{+}e^{−}pair background, confirms the efficiencies we assume here.
6 Results
We have demonstrated the potential of measuring the cross section times branching ratios of a 120 GeV Higgs boson at a 3 TeV CLIC with high precision. For the measurement of Higgs decays to quarks, 0.23 % and 3.1 % statistical uncertainty can be achieved for the decays \(\mathrm {H}\to \mathrm {b}\overline {\mathrm {b}}\) and \(\mathrm {H}\to \mathrm {c}\overline {\mathrm {c}}\), respectively. This includes the effect of background from γγ→hadrons on the flavour tagging. Given the experience of the LEP experiments [24] in the measurements of hadronic Z decays, with systematic uncertainties between 0.3 %–1.2 % for \(R^{0}_{\mathrm {b}}\) and between 1.2 % and 10 % for \(R^{0}_{\mathrm {c}}\), one can assume that a systematic uncertainty of around 1 % is achievable in \(\mathrm {H}\to \mathrm {b}\overline {\mathrm {b}}\) and around 5 % in \(\mathrm {H}\to \mathrm {c}\overline {\mathrm {c}}\).
For the rare decay H→μ^{+}μ^{−}, the cross section times branching ratio can be measured to a precision of about 15 % if the background from e^{+}e^{−}→μ^{+}μ^{−}e^{+}e^{−} can be reduced using tagging of electrons in the LumiCal with an efficiency of 95 %, and the average momentum resolution is not worse than 5×10^{−5}. The effect of background from γγ→hadronshas been taken into account. From the measurements of the branching ratio of Z decays to a pair of muons at the LEP experiments, with systematic uncertainties between 0.1 and 0.4 %, depending on the experiment, one can assume that the systematic uncertainties related to detector effects are of the order of 1 % or less. The expected uncertainty of the peak luminosity is currently being studied but is estimated to be around 1 % or less.
6.1 Extracting the Higgs coupling constants
Statistical uncertainties of the measurements of the cross section times branching fraction, and the sensitivity to the SM b, c and μ Yukawa Higgs coupling constants at a 3 TeV CLIC with an integrated luminosity of 2 ab^{−1}
σB statistical uncertainty (%)  Sensitivity to SM Yukawa deviation (%)  

\(\mathrm {H}\to \mathrm {b}\overline {\mathrm {b}}\)  0.23  4 
\(\mathrm {H}\to \mathrm {c}\overline {\mathrm {c}}\)  3.1  6 
H→μ^{+}μ^{−}  15  7.5 
Notes
Acknowledgements
The authors would like to thank Stephane Poss for generating the event samples and managing the simulation and reconstruction on the grid.
Open Access
This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
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