Search for a light charged Higgs boson in the H$^\pm \to $ cs channel in proton-proton collisions at $\sqrt{s}=$ 13 TeV

A search is conducted for a low-mass charged Higgs boson produced in a top quark decay and subsequently decaying into a charm and a strange quark. The data sample was recorded in proton-proton collisions at $\sqrt{s}=$ 13 TeV by the CMS experiment at the LHC and corresponds to an integrated luminosity of 35.9 fb$^{-1}$. The search is performed in the process of top quark pair production, where one top quark decays to a bottom quark and a charged Higgs boson, and the other to a bottom quark and a W boson. With the W boson decaying to a charged lepton (electron or muon) and a neutrino, the final state comprises an isolated lepton, missing transverse momentum, and at least four jets, of which two are tagged as b jets. To enhance the search sensitivity, one of the jets originating from the charged Higgs boson is required to satisfy a charm tagging selection. No significant excess beyond standard model predictions is found in the dijet invariant mass distribution. An upper limit in the range 1.68-0.25% is set on the branching fraction of the top quark decay to the charged Higgs boson and bottom quark for a charged Higgs boson mass between 80 and 160 GeV.


Introduction
The discovery of the Higgs boson in 2012 by the ATLAS [1] and CMS [2,3] experiments at the CERN LHC has given rise to a wide set of measurements to establish the nature of the discovered particle. The Higgs boson could be the first of many elementary scalars present in nature to be observed in the laboratory. Various extensions of the standard model (SM), such as the two Higgs doublet model (2HDM) [4], including supersymmetry [5][6][7], predict multiple scalars as the remnants of an additional SU(2) L complex doublet introduced to address some known limitations of the SM, such as the origin of dark matter [8,9] and the hierarchy problem [10]. After spontaneous symmetry breaking, out of the eight degrees of freedom of the two Higgs doublets, three are used to make the W and Z bosons massive, leaving five physical scalar particles. Of these, two are neutral Higgs bosons that are CP-even (scalar), one is neutral and CP-odd (pseudoscalar), and the remaining two are charged Higgs bosons (H ± ).
The 2HDM can be classified into different categories depending on the type of interaction of the two doublets with quarks and charged leptons. For example, in the type II 2HDM, leptons and down-type quarks have Yukawa couplings to the first doublet, and up-type quarks couple to the second doublet. The nature of the Yukawa coupling determines the branching fraction B of the charged Higgs boson decays into different final states. We are interested in the search for a low-mass (m H + < m t ) charged Higgs boson in the decay channel H + → cs (and its charge conjugate), whose branching fraction can range up to 100%, depending on the type of Yukawa coupling. The latter is expressed in terms of the parameter tan β = v 2 /v 1 , where v 1 and v 2 are the vacuum expectation values of the two Higgs doublets. In the minimal supersymmetric standard model, this is the dominant decay channel for low values of tan β for most of the mass range considered in this analysis [11,12]. We assume that B(H + → cs ) = 100%.
As illustrated in Fig. 1, in the signal process for H + production, one of the top quarks decays to H + b and the other to W − b, with H − production proceeding by the charge conjugate of this process. The principal SM background to this search consists of tt pair production where both top quarks decay to a W boson and a b quark. In this search, we consider the mode where the W + /H + decays hadronically into a charm and strange antiquark, whereas the W − decays leptonically (in the tt case, this is called the "semileptonic" decay channel); we define two channels depending on whether the lepton produced in the W − decay is a muon or an electron (events with tau leptons are not specifically considered, but can be selected if the tau lepton decays into a muon or an electron). There have been many earlier searches for charged Higgs bosons at LEP, the Tevatron, and the

The CMS detector
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, each composed of a barrel and two endcap sections. The silicon pixel and tracker detectors identify the trajectory of charged particles and accurately measure their transverse momentum p T up to pseudorapidity |η| ≤ 2.5. Forward calorimeters extend the η coverage provided by the barrel and endcap detectors. Segmented calorimeters provide sampling of electromagnetic and hadronic showers up to |η| ≤ 5. Muons are detected in gasionization chambers embedded in the steel flux-return yoke outside the solenoid, in the range of |η| ≤ 2.4.
Events of interest are selected using a two-tiered trigger system [31]. The first level (L1), composed of custom hardware processors, uses information from the calorimeters and muon detectors to select events at a rate of around 100 kHz within a time interval of less than 4 µs. The second level, known as the high-level trigger (HLT), consists of a farm of processors running a version of the full event reconstruction software optimized for fast processing, and reduces the event rate to around 1 kHz before data storage. 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. [32].

Data and simulation
The data used for the analysis were collected with the CMS detector in 2016, in proton-proton (pp) collisions at √ s = 13 TeV, and correspond to an integrated luminosity of 35.9 fb −1 .
As shown in Fig. 1, the charged Higgs boson is assumed to decay into cs or cs only. As a result, in the final state, there will be four jets (two b jets, one c jet, one s jet), one lepton (µ or e; τ is not considered in this analysis), and missing transverse momentum (p miss T ), which is attributed to the neutrino. The SM processes that give the same final states (four jets + one lepton + missing transverse momentum) are considered as background processes for this analysis. Signal and background processes are modeled using simulated samples, generated using the MADGRAPH5 aMC@NLO v2.3.3 [33] and POWHEG v2.0 [34][35][36][37] generators at parton level, with the NNPDF 3.0 [37] parton distribution functions (PDFs), with the order matching that in the matrix element calculations. In all cases, these parton-level events are hadronized using PYTHIA 8.212 [38] with the CUETP8M1 underlying event tune [39] and then passed to GEANT4 [40] for simulation of the CMS detector response. Finally, the events are reconstructed after complete detector simulation using the same reconstruction process as for data.
The SM tt process is an irreducible background, and represents the largest contribution, about 94% of the total expected background in the signal region. The parton-level SM tt events are generated at next-to-leading order (NLO) using POWHEG. The next-to-NLO cross section for tt is calculated to be σ tt = 832 ± 20 29 (scale) ± 35 (PDF + α S ) pb [41]. The top quark mass in the simulated samples is taken to be 172.5 GeV.
The charged Higgs boson signal samples are generated using MADGRAPH5 aMC@NLO at leading order (LO). Only H + samples are generated, and H − production is assumed to be the same. The signal sample is generated for several mass points in the range of 80 to 160 GeV (80, 90, 100, 120, 140, 150, 155, and 160 GeV). The generated cross section for the signal is taken to be 0.21σ tt , where the factor of 0.21 is the branching fraction of W − → − ν (where = µ or e, neglecting the small contribution from potential τ decays) [42].
The single top quark production processes, where a top quark is produced with jets in the s channel, t channel, or tW channel, can also mimic the signal topology. The s-channel single top production samples are generated using MADGRAPH5 aMC@NLO [33] at NLO, while the tchannel and tW-channel samples are generated using POWHEG [43,44] at NLO. The production of W and Z bosons with jets, and vector boson pair production, are also considered as background processes. The inclusive W + jets and Z/γ + jets samples are generated at LO using MADGRAPH5 aMC@NLO with up to four partons included in the matrix element calculations. The MLM technique [45] is used to avoid the double counting of jets from the matrix element calculation and the parton shower. The vector boson pair production samples (WW/WZ/ZZ, collectively referred to as "VV") are generated using PYTHIA at LO. Furthermore, SM events containing only jets produced through the strong interaction, referred to as quantum chromodynamics (QCD) multijet events, can also produce a final state identical to the signal topology, even though these events contain only quarks and gluons at the parton level. QCD multijet events can have reconstructed leptons from, for example, jets misidentified as isolated leptons or decays of bottom and charm hadrons, and p miss T due to the mismeasurement of hadronic activity inside the CMS detector.
The expected yield for each background process is determined from simulation, with the exception of the QCD multijet background, which is estimated from data, as described in Section 5.

Object reconstruction
The physics objects of interest are leptons, jets, missing transverse momentum, vertices of pp collisions, and displaced vertices from the decay of bottom or charm hadrons. The particle-flow (PF) algorithm [46] is used to reconstruct these objects by optimally using various subsystems of the CMS detector.
The collision vertices are obtained using reconstructed tracks in the silicon tracker [47]. First, candidate vertices are obtained by clustering tracks using the deterministic annealing algorithm. Subsequently, candidate vertices with at least two tracks are fitted using the adaptive vertex fitter. A primary vertex associated with a hard interaction is expected to be accompanied by a large number of tracks. The reconstructed vertex with the largest value of summed physics-object p 2 T is taken to be the primary pp interaction vertex. The physics objects are the jets, clustered using the jet finding algorithm [48,49] with the tracks assigned to the vertex as inputs, and the associated p miss T , taken as the negative vector sum of the p T of those jets. Further, the reconstructed primary vertex is required to be within 24 cm along the beam axis and within 2 cm in the transverse direction from the nominal pp interaction region.
Muons, being minimum ionizing particles, can traverse a long distance in the CMS detector. The trajectory of the muon is bent due to the presence of a strong magnetic field inside the solenoid and the return magnetic field in the opposite direction outside the solenoid. Muon candidates are identified in the muon detectors and matched to tracks measured in the silicon tracker, resulting in an excellent p T resolution between 1 and 10% for p T values up to 1 TeV [50].
Electrons are reconstructed from the tracks in the tracker and energy deposits in the ECAL [51]. The reconstructed trajectory in the tracker is mapped to the energy deposit in the ECAL to form an electron candidate. The bending direction of the trajectory in the tracker is used to identify the charge of an electron.
Due to color confinement [52], the quarks and gluons produced in pp collisions cannot exist in free states; instead, they produce a cluster of colorless hadrons, most of which subsequently decay to leptons and photons. As mentioned above, jets are clustered from the PF candidates using the anti-k T algorithm [48,49] with a distance parameter of ∆R = √ (∆η) 2 + (∆φ) 2 = 0.4, where φ is the azimuthal angle. Each jet is required to pass dedicated quality criteria to suppress the impact of instrumental noise and misreconstruction. Additional pp interactions within the same or nearby bunch crossings (pileup) can contribute extra tracks and calorimetric energy deposits, increasing the apparent jet momentum. To mitigate this effect, tracks identified to be originating from pileup vertices are discarded and an offset correction is applied to correct for remaining contributions [46]. Jet energy corrections are derived from simulation studies so that the average measured response of jets becomes identical to that of particle-level jets. In situ measurements of the momentum balance in dijet, γ + jet, Z + jet, and multijet events are used to determine any residual differences between the jet energy scale in data and in simulation, and appropriate corrections are applied [53].
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 PF objects in an event. Its magnitude is referred to as p miss T . Neutrinos, being weakly interacting particles with a very low cross section, cannot be directly detected by the CMS detector and thus contribute to p miss T . The reconstruction of p miss T is improved by propagating the jet energy corrections to it.
There are two b jets in the final state as illustrated in Fig. 1, in both the charged Higgs boson signal process and the SM tt background. An accurate identification of b jets substantially reduces the SM backgrounds from other processes, such as Z/γ + jets, VV, or W + jets. The combined secondary vertex (CSV) algorithm [54] is used to tag a b jet. The algorithm combines information on track impact parameters and secondary vertices within a jet into an artificial neural network classifier that provides separation between a b jet and jets of other flavors. As the charged Higgs boson decays to a charm and a strange antiquark, the identification of charm jets is expected to increase the signal significance. A charm tagger has been developed [54], which is based on the CSV method and works similarly to the b tagging procedure.
The p T of jets in the simulated samples is corrected using the jet energy scale (JES) and jet energy resolution (JER) data-to-simulation scale factors [53]. The lepton reconstruction, b, and c tagging efficiencies are different in data and simulated samples; to correct for this, the corresponding data-to-simulation scale factors are applied to the simulated events.

Event selection
In the event topology of interest, there are four jets (two b jets, one c jet, and one light-flavor jet), one charged lepton, and p miss T . Various selection requirements are applied to ensure the resulting events have this topology.
The online event selection requires, at the L1 trigger level, either a muon candidate with p T > 22 GeV or electron/photon candidate with p T > 30 GeV (22 GeV if it is isolated); at the HLT level, an isolated muon (electron) with p T > 24 (27) GeV is required. The relative isolation (I rel ) of a lepton is defined as the ratio of the sum of p T for all the other particles within a cone of ∆R = 0.4 around the lepton direction, divided by the lepton p T after correcting for the contribution from pileup [50,55].
In the offline analysis, events that pass the trigger selection and contain a muon (electron) with p T > 26 (30) GeV and |η| < 2.4 (2.5) are selected. To eliminate events where the lepton is found within a jet, the muon is required to have I µ rel < 0.15 and the electron is required to have I e rel < 0.08 (0.07) in the barrel (endcap) regions. No charge requirement is applied to the lepton. The signal event topology has only one lepton, so events having a second muon with p µ T > 15 GeV, |η| < 2.4, and I Jets are selected by requiring p j T > 25 GeV, |η j | < 2.4, neutral hadron energy fraction < 0.99, neutral electromagnetic energy fraction < 0.99, number of constituents > 1, charged hadron energy fraction > 0, charged-hadron multiplicity > 0, and charged-hadron electromagnetic energy fraction < 0.99, as detailed in Ref. [46]; at least four jets are required. The p miss T must exceed 20 GeV. The events are required to have at least two b jets with a selection that has 63% b tagging efficiency [54]. The corresponding probability of a light-flavor (charm) jet being misidentified as a b jet is 1 (12)%, where "light flavor" refers to jets originating from u, d, s, or g. The events are categorized depending on the charm tagging results for the jets, as discussed in Section 6.
To estimate QCD multijet background, a matrix method, also known as an "ABCD" method, is used, which proceeds as follows. First, a normalization is determined from the (low p miss T , isolated) and (low p miss T , anti-isolated) regions; then the QCD background distribution is determined from the (high p miss T , anti-isolated) region. By using the normalization obtained on the distribution, the expected QCD multijet contribution is determined in the signal region (high p miss T , isolated). The low-and high-p miss

Dijet invariant mass distribution
The invariant mass of the system of the two non-b jets (m jj ), assumed to be cs or cs, is used as the final observable. The m jj distribution of the two highest-p T non-b jets is shown in the top row of Fig. 2 for the two leptonic channels. If the two observed non-b jets come from a semileptonic tt decay, then the m jj distribution should have a peak at the W boson mass. The observed mean of the m jj distribution is much higher (around 138 GeV), reflecting the fact that the two non-b jets in each event may not necessarily come from the decay of a W boson.
To identify semileptonic tt events, a kinematic fit (KF) is performed on the reconstructed objects using the top quark kinematic fitter package [56]. The top kinematic fitter takes physics objects such as leptons, jets, p miss T , and their resolutions as input, and gives improved four-vectors of leptons, jets, and a neutrino, along with the overall χ 2 and fit probability for the event, as the output. The x and y components of the neutrino momentum are taken from p miss T , as the missing transverse momentum is attributed to the neutrino, and the z component of the neutrino momentum, p ν z , is determined from the fit. The following kinematic constraints are imposed on the semileptonic tt system: where m inv is the corresponding invariant mass and b had (lep) is the b quark produced by the hadronic (leptonic) top decay. After the fit, p ν z is determined from Eq. (1b). For every event, a χ 2 is constructed and minimized by varying the p T , η, and φ of each object within their resolution. The values of p T , η, and φ are finally selected that minimize the χ 2 and at the same time satisfy Eq. (1). In the output, the top quark kinematic fitter gives exactly four jets (two b jets, one from each of the leptonic and hadronic t decays, and two non-b jets from the hadronic t decay), a lepton, and a neutrino. No cut is placed on χ 2 and events for which the fit does not converge are discarded. Also, the same kinematic requirements (on p T , η, and I rel ) as for the reconstructed objects are applied to the fitted objects. The directions of the kinematically fitted jets and lepton are required to be compatible with those of the reconstructed jets and lepton (∆R < 0.2), respectively. The efficiency of the KF selection for data, simulated tt, and simulated signal events is 43, 47, and 49%, respectively. The m jj distributions after the KF selection are shown in the bottom row of Fig. 2, showing that the mean of the m jj distribution is closer to the W boson mass.   The two non-b jets coming from the hadronic t decay are further used for charm tagging. There are three c tagging working points (loose, medium, and tight) based on the efficiency of a c quark being tagged as a c jet [54]. The corresponding efficiencies are shown in Table 1. The events are divided exclusively into loose, medium, and tight categories, based on whether at least one of the non-b jets passes the loose but neither passes the medium, at least one passes the medium but neither passes the tight, or at least one passes the tight working points of the charm tagging selection requirements shown in Table 1, respectively. The m jj distributions for the exclusive charm categories are shown in Fig. 3 after a background-only maximum likelihood fit to data. From these figures, it can be seen that the expected signal-to-background ratio increases for the charm categories with tighter requirements, so partitioning the events into categories results in an enhanced signal sensitivity. Table 2 shows the corresponding event yields for the different charm categories after the background-only fit to the data reported in Section 8, with statistical and systematic uncertainties as discussed in Section 7.

Systematic uncertainties
There are various sources of systematic uncertainty, which may arise due to detector calibration effects, uncertainty in the measured reconstruction efficiency, the theoretical modeling of signal events, and other effects.
The uncertainty in the integrated luminosity is 2.5% [57]. Each distribution for simulated events is normalized to the expected number of events in data, using the factor L data σ sim /N sim , where L data is the integrated luminosity of the data sample, N sim is the total number of events in the simulated sample, and σ sim is the cross section for the simulated process considered; the uncertainties in σ sim thus contribute to the uncertainty in each background prediction. The uncertainties in σ sim for tt, single t quark, W + jets, Z/γ + jets, and VV processes are 6.1, 7.0, 4.5, 5.0, and 4.0%, respectively. To account for the uncertainty in the pileup distribution, the total inelastic cross section of 69.2 mb is varied by its uncertainty of 4.7% [58] and the simulated events are reweighted to match the pileup distribution in the data. The systematic uncertainty in the data-to-simulation scale factor for the lepton reconstruction efficiencies is 3.0% for both muons and electrons [50,51].
The systematic uncertainties due to JES and JER data-to-simulation scale factors in the p T of the jets and p miss T are estimated by varying these within their uncertainties [53]. The b and c tag data-to-simulation scale factors are varied within their uncertainties to estimate the corresponding uncertainties, with correlations applied [54].
To estimate the systematic uncertainty in the QCD multijet background estimation, the muon (electron) relative isolation threshold is conservatively changed to 0.17 (0.11) and the corresponding changes in the QCD yields are determined.
It is found that the p T distribution of t quarks in tt events in data is softer compared to that in simulated samples [59]. This is corrected by applying the following weight as a function of p T for SM tt and charged Higgs boson signal samples: The values in the exponent are derived in Ref. [60]. The generator-level p T of the t and t are used to calculate SF. To evaluate the systematic uncertainty due to w t , it is varied to 1 and w 2 t . The SM tt sample was generated with m t = 172.5 GeV. To evaluate the effect of the chosen m t on the m jj distribution, alternate tt samples with m t = 171.5 and 173.5 GeV are considered. To observe the effect of NLO matrix element parton shower matching, additional SM tt samples are generated by changing the default damping parameter h damp value of 1.58m t to 2.24m t and m t [61]. Similarly, SM tt samples where the common nominal value of renormalization and factorization scales is simultaneously changed by factors of 0.5 and 2 are used to evaluate the uncertainties due to these scales [62]. The systematic uncertainties due to t quark mass, parton shower matching, and renormalization and factorization scales are in the ranges 0.2-3.3, 0.7-1.9, and 0.4-1.6%, respectively, depending on the channel and charm tagging category.
The signal extraction procedure is based on a binned maximum likelihood fit of the m jj distributions, as described in Section 6. The systematic uncertainties prior to the fit on the different process yields are listed in Table 3, when they differ from process to process. All systematic uncertainties are incorporated into the fit as nuisance parameters. The statistical uncertainties in the total yield of all backgrounds and the signal samples are also shown in Table 3. However, these are not incorporated in the likelihood. To account for the statistical uncertainty in each bin of m jj , one nuisance parameter per bin is considered for the sum of all backgrounds and charged Higgs boson samples [63]. Table 3: Systematic and statistical uncertainties in the event yield for the different processes in %, prior to the fit to data, for the exclusive charm categories in the muon (electron) channel. The "-" indicates that the corresponding uncertainties are either not considered for the given process, or too small to be measured. The most important sources of uncertainties in terms of impact on the expected limit on B(t → H + b) for m H + = 100 GeV, after the individual charm tagging categories and the muon and electron channels have been combined, as discussed in Section 8, are the lepton selection (3.8%), QCD multijet background estimate (2.4%), tt cross section (1.9%), and b/c tagging (1.9%). The effect of each of the remaining systematic uncertainties on the expected limit is estimated to be less than 0.3%.
The number of events in the background processes and the corresponding uncertainty bands shown in Fig. 3 are obtained using a background-only fit to data. After the fit, the uncertainties (both statistical and systematic) are significantly anticorrelated, resulting in a reduction in the overall uncertainty. Prior to the fit, as shown in Table 3, they are either uncorrelated or positively correlated.

Results
After applying all selection requirements, the expected number of background events agrees with the data within the uncertainties. The absence of a charged Higgs boson signal in the data is characterized by setting exclusion limits on the branching fraction B(t → H + b). An asymptotic 95% CL limit on B(t → H + b) is calculated using the CL s method [64,65] with likelihood ratios [66]: where the likelihood is defined as In this equation, x = B(t → H + b) is the parameter of interest, the first product over j designates the three charm tagging categories, and i runs over the bins of the m jj distributions shown in Fig. 3. For a given mass bin i and charm tagging category j, n ij is the observed number of events in that bin and charm tagging category, and N ij (Θ) is the expected number of events. The last term is the product over the individual nuisance parameters k of the probability density function p( Θ k |Θ k ), where Θ k is the value of the nuisance parameter. The estimatorsx and Θ correspond to the global maximum of the likelihood defined in Eq. 4. The expected number of events N ij (Θ) is given by, in the presence of signal: and in the absence: where N tt →H + W − ij (Θ) and N tt →W ± W ∓ ij (Θ) are the number of events from the simulated signal process and the SM tt process, respectively. Both are normalized to the expected tt cross sections, as described in Section 3. The factor of 2 in Eq. 5 is derived from the assumption that the event yield and B(t → H − b ) for H − are the same as those of H + .
The exclusion limits on B(t → H + b) as a function of charged Higgs boson mass using the m jj distribution and combining different exclusive event categories based on charm tagging are shown in Fig. 4 and in Tables 4 and 5. Among the individual categories, the expected limits from the exclusive medium category are most stringent, followed by those from the exclusive loose and tight categories. By construction, the exclusion limits on B(t → H − b ) are the same as those on B(t → H + b).

Summary
A search for a light charged Higgs boson produced by top quark decay has been performed in the muon + jets and electron + jets channels at √ s = 13 TeV, using a data sample corresponding to an integrated luminosity of 35.9 fb −1 . The observed and predicted number of events from standard model processes are in agreement within the uncertainties. An exclusion limit at 95% confidence level on the branching fraction B(t → H + b) has been computed by assuming B(H + → cs ) = 100%. The observed exclusion limits are in the range, for a charged Higgs boson mass between 80 and 160 GeV, 2.44-0.32, 2.77-0.26, and 1.68-0.25% for the muon + jets, electron + jets, and the combination of the two channels, respectively. These are the first results from the LHC at √ s = 13 TeV for the above final states, and represent an improvement by a factor of approximately 4 over the previous results at √ s = 8 TeV.

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 centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses.  [20] ATLAS Collaboration, "Search for charged Higgs bosons decaying via H ± → τ ± ν in fully hadronic final states using pp collision data at √ s = 8 TeV with the ATLAS detector", JHEP 03 (2015) 088, doi:10.1007/JHEP03(2015)088, arXiv:1412.6663.