Search for a charged Higgs boson decaying to charm and bottom quarks in proton-proton collisions at $\sqrt{s} =$ 8 TeV

A search for charged Higgs boson decaying to a charm and a bottom quark (H$^+\to$ c$\overline{\mathrm{b}}$) is performed using 19.7 fb$^{-1}$ of pp collision data at $\sqrt{s} =$ 8 TeV. The production mechanism investigated in this search is $\mathrm{t\overline{t}}$ pair production in which one top quark decays to a charged Higgs boson and a bottom quark and the other decays to a charged lepton, a neutrino, and a bottom quark. Charged Higgs boson decays to $\mathrm{c\overline{b}}$ are searched for, resulting in a final state containing at least four jets, a charged lepton (muon or electron), and missing transverse momentum. A kinematic fit is performed to identify the pair of jets least likely to be the bottom quarks originating from direct top quark decays and the invariant mass of this pair is used as the final observable in the search. No evidence for the presence of a charged Higgs boson is observed and upper limits at 95% confidence level of 0.8-0.5% are set on the branching fraction $\mathcal{B}$(t $\to$ H$^+$b), assuming $\mathcal{B}$(H$^+\to$ $\mathrm{c\overline{b}}) =$ 1.0 and $\mathcal{B}$(t $\to$ H$^+$b) $+$ $\mathcal{B}$(t $\to$ Wb) = 1.0, for the charged Higgs boson mass range 90-150 GeV.


Introduction
In 2012, a boson with a mass about 125 GeV was discovered at the CERN LHC [1][2][3] with its properties subsequently shown [4][5][6][7] to be consistent with those of the standard model (SM) [8][9][10] Higgs boson [11][12][13][14][15][16]. Although the last missing particle of the SM has been discovered, several questions remain, including the nature of dark matter [17,18], and the origin of neutrino masses [19] inferred from the observation of neutrino oscillations [20]. Several hypotheses beyond the SM have been introduced and tested to answer these questions, and many of them include more than one Higgs doublet. Models with two Higgs doublets, so-called two-Higgsdoublet model (2HDM) [21,22], result in five Higgs bosons: two charged (H ± ) and three neutral (A, H, h). In the 2HDM, the Higgs boson discovered at the LHC can be one of the CP-even neutral bosons (H or h). Unlike the SM, in general 2HDM allows flavour changing neutral current (FCNC) at tree level. To suppress such tree level FCNC, all fermions with the same electric charge are required to couple to one Higgs doublet only [23,24]. The 2HDM is typically categorized into four different types: type-I, type-II, lepton-specific (type-III), and flipped (type-Y, also known as type-IV), depending on the assignment of up/down-type quark and lepton couplings to each Higgs doublet.
We present a search for charged Higgs bosons. Hereafter, we refer to them as H + , but charge conjugate states are always implied. In the 2HDM, the mass of the charged Higgs boson (M H + ) is an unconstrained parameter. Regardless of its mass, H + is expected to have a large coupling to the top quark unless a specific condition is being considered as in Refs. [25,26]. If M H + is smaller than the top quark mass, the so-called light charged Higgs boson scenario, the top quark can decay to a H + and a b quark, t → H + b. The LEP experiments [27] excluded the mass of charged Higgs below 80 (72.5) GeV for type-II (type-I for pseudo-scalar masses above 12 GeV) scenario at 95% confidence level (CL). In the presence of the W boson resonance at a mass of 80.4 GeV, the light charged Higgs boson search range is typically set between the W boson mass and the top quark mass. Previous direct searches for a light H + in decays of a top quark have been performed at hadron collider experiments in following channels: H + → τν [28][29][30][31][32][33], H + → cs [34][35][36][37], and H + → WA [38]. No indication of a H + was observed and the best upper limits on the branching fraction of t → H + b were placed at O(1%). The H + → cb process is the dominant decay channel in the type-Y 2HDM [39][40][41], and this signal could be a signature of models with more than two Higgs doublets [42,43]. The search is performed assuming B(H + → cb) = 1.0 without any other model-dependent assumption.
The search uses tt events with a final state of at least four jets (at least two of which originate from b quarks), a charged lepton (muon or electron), and missing transverse momentum. If a light H + (→ cb) is produced in top quark decays, the tt event would have one more jet to be identified originating from b quark due to the H + decays, as shown in Fig. 1. A kinematic fit is performed to identify the pair of jets least likely to be the b quarks originating from direct top quark decays. The invariant mass of this jet pair is used as the final observable in this search. The signal events are expected to peak at the charged Higgs boson mass. We assume B(t → H + b) + B(t → Wb) = 1.0, which implies a lowering of the branching fraction of top quarks to Wb in presence of H + in top quark decays.
The main background for this search is SM tt, including tt production in association with heavyflavoured jets (ttbb, ttcc). Other considered backgrounds are single top production, multijet, W/Z+jets and diboson production, and tt production in association with an H/Z/W boson.

Event simulation and reconstruction with CMS detector
Background samples of tt, tt+W/Z, and W/Z+jets are simulated at leading order (LO) using the MADGRAPH 5.1 generator [44] with the CTEQ6L1 parton distribution function (PDF) set [45]. The top quark mass is set to 172.5 GeV for simulating these samples. The predicted tt production cross section is calculated with the TOP++ 2.0 program at the next-to-next-toleading order (NNLO) in perturbative quantum chromodynamics (QCD), including soft-gluon resummation at the next-to-next-to-leading-log order (Ref. [46] and references therein), to be σ tt = 252.9 +6.4 −8.6 (scale) ± 11.7 (PDF+α S ) pb, where "scale" and "PDF+α S " refer to the uncertainties coming from the independent variation of the factorization and renormalization scales, and the variations in the PDF set and in the strong coupling constant α S , respectively, following the PDF4LHC prescription with the MSTW2008 68% CL NNLO, CT10 NNLO and NNPDF2.3 5f FFN PDF sets (Refs. [47,48] and references therein, and Refs. [49][50][51]).
The transverse momentum p T distribution of top quarks in simulated tt events is reweighted to match the p T distribution observed in collision data [52]. The simulated W/Z+jets samples are normalized to the NNLO cross section calculated with FEWZ 3.1 [53,54], and tt+W/Z events are normalized to the next-to-leading order (NLO) cross section [55,56]. Single top quark events are generated with the POWHEG v1.0 generator [57][58][59][60] and the CTEQ6M PDF set [45], and are normalized to the production cross section at NLO in QCD computed with HATHOR v2.1 [61,62]. Diboson (WW/WZ/ZZ) and ttH events are generated at LO using PYTHIA v6.4 [63] and normalized to the NLO cross section calculated using MCFM 6.6 [64] and the cross section given in Ref. [65], respectively.
The charged Higgs boson signal events (tt → bH + bW − → bbcb ν) are simulated using the PYTHIA v6.4 and CTEQ6L1 PDF set for M H + = 90, 100, 110, 120, 130, 140, and 150 GeV. These samples are normalized to the SM tt cross section in lepton+jets channel. Consequently, in the assumption of B(H + → cb) = 1.0 and B(t → H + b) + B(t → Wb) = 1.0, a fit using templates of the SM tt and the H + signal determines the branching fraction of t → H + b.
All generated samples are interfaced with PYTHIA v6.4 in order to simulate parton showering and hadronization, and then processed through the full simulation of the CMS detector based on GEANT4 [66]. The underlying event tune Z2* [67,68] is used. To ensure correct simulation of the number of additional interactions per bunch crossing (pileup), simulated events are mixed with multiple inelastic collision events and reweighted according to the distribution of the number of pileup interactions observed in data.
The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections. Additional forward calorimetry complements the coverage provided by the barrel and endcap detectors. Muons are detected in gas-ionization chambers embedded in the steel flux-return yoke outside the solenoid. A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [69].
A particle-flow (PF) algorithm [70] aims to reconstruct and identify particle candidates with an optimized combination of information from various elements of the CMS detector. Muon momenta are obtained from the curvature of muon tracks. The energy of photons is obtained from the ECAL measurement, upon proper calibration of several instrumental effects as described in [71,72]. The energy of electrons is determined from a combination of the electron momentum at the primary interaction vertex (PV) as determined by the tracker, the energy of the corresponding ECAL cluster, and the energy sum of all bremsstrahlung photons spatially compatible with originating from the electron track [73]. The PV is the reconstructed vertex with the largest value of ∑ p 2 T , the sum of squared transverse momenta of the charged particle tracks associated with the vertex. The energy of charged hadrons is determined from a combination of their momentum measured in the tracker and the matching ECAL and HCAL energy deposits. Finally, the neutral hadrons are identified as HCAL energy clusters not linked to any charged hadron trajectory, or as ECAL and HCAL energy excesses with respect to the expected charged hadron energy deposit or photon.
Jets are reconstructed from all the PF candidates clustered using the anti-k T algorithm [74,75] with a distance parameter of 0.5. The jet momentum is determined as the vectorial sum of all particle momenta in the jet, and corrected for effects of pileup within the same or nearby bunch crossings. Jet energy scale corrections [76,77] are used to account for the nonlinear energy response of the calorimeters and other instrumental effects. Additional selection criteria are applied to each event to remove spurious jet-like features originating from isolated noise patterns in certain HCAL regions. The missing transverse momentum vector p miss T is defined as the projection onto the plane perpendicular to the beam axis of the negative vector sum of the momenta of all reconstructed PF objects in an event. Its magnitude is referred to as p miss T .

Event selection and yields
Candidate signal events are selected using triggers [78] that require a single isolated muon (electron) with p T > 24 (27) GeV and pseudorapidity |η| < 2.1 (2.5). Further selection requirements are made offline. Events with exactly one muon (electron) with p T > 26 (30) GeV and |η| < 2.1 (2.5) are selected. Lepton identification selections, including requirements of a good track quality and close distance with respect to the PV, are imposed on each lepton candidate. Leptons must be isolated, satisfying relative isolation requirement I rel < 0.12 (0.1) for muons (electrons). The I rel is defined as the pileup-corrected scalar p T sum around the lepton candidate's direction at the vertex divided by the lepton candidate p T . The p T sum is calculated from momenta of the reconstructed charged hadrons originating from the PV, neutral hadrons, and photons within a cone of ∆R = √ (∆η) 2 + (∆φ) 2 < 0.4 (0.3) for muons (electrons), where φ is the azimuthal opening angle (in radians). Events with any additional muons (electrons) satisfying p T > 10 (20), |η| < 2.5, and I rel < 0.3, are discarded.
The p miss T is required to be larger than 20 GeV, and at least four jets are required to have p T > 30 GeV within the tracker coverage of |η| < 2.4. To identify jets originating from b quarks, the combined secondary vertex tagging algorithm [79] is used. Selected jets are considered btagged if they satisfy the medium working point requirements of this algorithm. This results in an efficiency of approximately 70% for tagging a b quark jet, and a mistag rate of 1% for light quark and gluon jets. Events with two or more b-tagged jets are selected.
The events selected using the above criteria are dominated by SM tt events (≈92%) based on the background simulation samples. The observed event yields in events with two b-tagged jets are well described by the simulation, however, the events containing three or more b-tagged jets are more difficult to model. In order to estimate the tt component in the three or more btagged jet event sample, we rely on the measurement of the ttbb cross section in Ref. [80]. In this reference, the ttbb cross section is measured to be 0.36 ± 0.08 (stat) ± 0.1 (syst) pb. Comparing with the theoretical expectation of 0.23 ± 0.05 pb, we obtain a ratio between the measured and the expected ttbb production cross section of 1.56 ± 0.66. As the study used dilepton tt events of same generator with current tt simulation sample, in which both top quarks decay to Wb with W → ν, the H + (→ cb) contribution to this extra b quark process is negligible.
The events with only one extra b jet (ttbj) is understood to come from the ttbb process with one b jet missed. Consequently, the ttbb component in the simulated tt sample is estimated by requiring at least one additional jet originated from an extra b quark based on generator information, then rescaled by the ttbb cross section ratio.
The multijet background is estimated following the method used in Ref. [37]. The shapes of the multijet background distributions are obtained from a nonisolated control region defined by 0.15 < I rel < 0.3 and p miss T > 20 GeV, after subtraction of the estimated SM backgrounds. In a QCD enhanced control region (p miss T < 20 GeV), a multiplicative scale factor used for the multijet background normalization is obtained from the nonisolated control region extrapolated to the isolated region. The shape uncertainty is estimated from the multijet background samples obtained using the same method but with shifted nonisolated control regions, 0.2 < I rel < 0.3 (smaller statistics) and reversing I rel selection, 0.12(µ)/0.1(e) < I rel < 0.3 (larger statistics). The normalization uncertainty is estimated by an average difference in the multijet background yields obtained from the shifted nonisolated control regions compared to the nominal multijet background, and its impact on the total SM backgrounds except the tt process (non-tt) is calculated to be 10% or less.
Event yields satisfying the selection criteria in the absence of a signal are summarized in Table 1. The tt event yields are estimated after rescaling the ttbb component. The number of b-tagged jets (b tags) indicated in Table 1 is the number of b tags among the four jets with highest p T in the event, which are used in the tt reconstruction. Signal efficiency satisfying the selection criteria is 4-6% depending on M H + .

Reconstruction of tt events
Top quark and W boson masses are reconstructed relying on the knowledge of the momenta of their decay products. However, the reconstructed mass is different from the true mass because the measured jet energy is corrected to the energy of a particle-level jet, not to the energy of the initial parton. A correction is derived from the energy shift between a particle-level jet and the matched hard scattering parton within ∆R = 0.3, depending on its matched parton flavour (b, c, or light quarks) in the SM tt simulation sample. This correction is called the top quark specific (TS) correction and is applied as a function of the p T and η of the jet. The application of TS correction in the tt reconstruction have been used in several analyses [34, 36,81]. Using this correction increases the accuracy of the mass reconstruction for top quarks and H + /W boson Table 1: Observed event yields and estimated backgrounds for the µ+jets and e+jets channels satisfying the event selection criteria. The number of b-tagged jets is the number of b tags among the four jets with highest p T in the event. The first and second uncertainty shown corresponds to the statistical and systematic components, respectively. decaying to dijet, resulting in a 7-9% improvement in resolution.
The instrumental mass resolution is further improved using a kinematic fit. The fit is used to fully reconstruct the tt system by assigning selected jets to the hadronic W/H + decays or b quarks in tt decays. The function that is minimized in the fit is as follows: (1) In the first two terms, the momentum with superscript "fit" is the variable to be determined by the fit, and the measured TS-corrected input p T is denoted with the superscript "meas". The first term fits the transverse momentum of the lepton and leading four jets and the second term fits an unclustered energy (UE) in the transverse directions x and y. The unclustered transverse energy vector is obtained from all the observables in the transverse plane by the relation: where the p miss Variation of the lepton, jet, and UE is allowed within the measurement uncertainties, σ i and σ UE , depending on their p T . The longitudinal momentum (p ν z ) of the neutrino is calculated by the leptonic ( ν) W boson mass constraint ([p + p ν ] 2 = M 2 W ) and only real p ν z is taken into account in the fit. During the iterations for minimizing the χ 2 , this p ν z varies to keep the W boson mass constrained. The neutrino momentum vector (p ν,fit x , p ν,fit y , p ν,fit z ) is reconstructed from all the fitted momenta and Eq. 2: p ν,fit x,y = p miss,fit x,y . The last term constrains the hadronic and leptonic top quark candidates to have the true mass of 172.5 GeV. The widths of the W boson (Γ W ) and top quark (Γ t ) in Ref. [19] are used for the resolution in the fit. The χ 2 minimization is performed for each possible combination of the four leading jets to quarks in the tt system, where the b-tagged jets are only assigned to the b quark daughters. In order to suppress combinatorial backgrounds and the irreducible contaminations from initial-and final-state radiation jets, two requirements are imposed: |p jet, meas T − p jet, fit T | < 20 GeV for the jets used in the fit and M k < 200 GeV, in which M k is reconstructed using input jets before the χ 2 fit, for the hadronically decaying top quark. In the jet-quark assignment that minimizes the χ 2 , the two jets not assigned to either b quarks originating directly from top quark decays form a H + → cb candidate.
The reconstructed events are further categorized according to the lepton flavour (µ or e) and the number of b-tagged jets (2 or ≥3). Events containing two b-tagged jets are used to constrain the SM tt background, while events with three or more b-tagged jets are used to search directly the presence of H + → cb decays. In events with two b tags, the fit has only two possible combinations of the jet assignment. However, in events with three or more b tags, one btagged jet is assigned to a leptonically decaying top quark, and two other b-tagged jets are assigned to the hadronically decaying top quark resulting in additional ambiguity. According to simulation, the ambiguity is efficiently resolved by the fit procedure only for H + masses below 120 GeV. At higher masses (130-150 GeV), the ambiguity is resolved by assigning the b jet with the lower p T to the b quark that originates from the t → H + b decay. These choices maximize the search sensitivity over the entire mass range.

Systematic uncertainties
Systematic uncertainties can affect the overall signal and background events, as well as cause distortions in the shape of the dijet mass distribution. Since the H + originates from a top quark decay, a number of systematic uncertainties in the H + signal and SM tt background are correlated. The systematic uncertainties are estimated based on the samples and methods used in Ref. [82]. A summary of the systematic uncertainties is given in Table 2.
Sources of systematic uncertainties are grouped into several categories: jet corrections, b tagging effects, tt modeling, and normalizations. Uncertainties due to jet energy corrections, Table 2: Summary of the relative systematic uncertainties in the event yields for the H + signal (M H + = 120 GeV), simulated SM backgrounds (separated into tt and non-tt components), and the data-driven multijet events. The uncertainties apply to both µ+jets and e+jets events, and in the case where the uncertainties in the two channels differ, a range is given. Uncertainties on the shape of templates are marked with an asterisk.  flavour-dependent uncertainties, and uncertainties due to jet energy resolution corrections are estimated by varying the correction factors by ±1 standard deviation (s.d.). The efficiency difference from data to the simulation (scale factor) in heavy quark tagging (b/c jets) and mistagging for light-flavoured jets is also varied by ±1 s.d. separately and the corresponding changes are estimated. Similarly, the following quantities are also varied by ±1 s.d.: normalization of the tt cross section in the simulation, integrated luminosity [83] of the data sample, and lepton scale factors including the single-lepton trigger, identification, and relative isolation. The uncertainty due to pileup is estimated by varying the total inelastic cross section used in the simulation by ±5% [80].
To account for the uncertainties in the modeling of SM tt events, we consider the uncertainty in reweighting the shape of the top quark p T distribution in the tt events to match the simulation to data, NLO production versus LO production with 0-3 partons (POWHEG versus MADGRAPH), matching thresholds used for interfacing the matrix-elements calculations of the MADGRAPH generator to the PYTHIA parton showers (ME-PS), renormalization and factorization scales, and the uncertainty in the top quark mass of 172.5 ± 1.0 GeV. The uncertainty in the ttbb rescaling ratio is estimated to be 50%, combining the ttbb cross section uncertainties (42%) and a few percent of the inefficiency of counting b jets in generator level. The ttbb rescaling uncertainties listed in Table 2 are the impact of rescaling on the selected tt events.
The systematic uncertainty in the SM tt modeling is estimated using simulation samples in which the corresponding systematic sources are varied. In order to estimate the tt modeling uncertainties in the simulated H + signal events, the p T distribution of the top quarks from SM tt events is used. The ratio of the p T distribution with each parameter shifted to the nominal value is calculated, then is used to reweight the top quark p T distributions in the H + signal simulation to mimic the systematic sample. By using this method the modeling uncertainties for H + signal events are estimated as listed in Table 2. In addition, as the H + events are generated using PYTHIA, the difference in tt generation estimated by the top quark p T distributions of PYTHIA and MADGRAPH, is then used as an additional systematic uncertainty. Figure 2 shows the dijet mass distributions together with the expected SM processes and H + signal after the fit procedure in µ+jets and e+jets events with two b tags and at least three b tags, which are used for the H + search with M H + of 90-120 and 130-150 GeV. A binned maximum likelihood fit is performed simultaneously to all the observed dijet mass distributions, using the signal and background templates extracted from the simulation or from the data. The background templates are composed of the dominant SM tt and non-tt contributions. No significant excess is seen above the expected SM background. The upper limits at 95% CL on the branching fraction B(t → H + b) are calculated using the statistical tools in ROOSTAT [84] and the CL s criterion [85,86] with a profile likelihood ratio as a test statistic [87] and using an asymptotic formulae [88]. The expected branching fraction limit is calculated using an Asimov dataset with a null hypothesis. Systematic uncertainties are treated as nuisance parameters and profiled in the fit following a log-normal distribution for the normalization uncertainties and using distorted templates for shape systematic uncertainties. With the assumptions of B(H + → cb) = 1.0 and B(t → H + b) + B(t → Wb) = 1.0, the expected and observed limits as a function of M H + are shown in Fig. 3. The expected limits without systematic uncertainties are also shown to illustrate that the analysis sensitivity is largely limited by the present level of our knowledge of the systematic uncertainties. The biggest impact on the expected limit comes from the ttbb production rescaling uncertainty.

Summary
A search for charged Higgs boson decaying to a charm and a bottom quark (H + → cb) is performed for the first time. The search uses tt events with a final state containing at least four jets, a charged lepton (muon or electron), and missing transverse momentum. The search is based on the analysis of proton-proton collision data recorded at √ s = 8 TeV, corresponding to an integrated luminosity of 19.7 fb −1 . A kinematic fit is performed to identify the pair of jets least likely to be the b quarks originating from direct top quark decays and the invariant mass of this pair is used as the final observable in the search. No evidence for the presence of a charged Higgs boson is observed and upper limits at 95% confidence level of 0.8-0.5% are set on the branching fraction B(t → H + b), assuming B(H + → cb) = 1.0 and B(t → H + b) + B(t → Wb) = 1.0, for the charged Higgs boson mass range 90-150 GeV.

Acknowledgments
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centres and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: [6] ATLAS Collaboration, "Measurements of the Higgs boson production and decay rates and coupling strengths using pp collision data at √ s = 7 and 8 TeV in the ATLAS experiment", Eur. Phys. J. C 76 (2016) 6, doi:10.1140/epjc/s10052-015-3769-y, arXiv:1507.04548.