LHC Search of New Higgs Boson via Resonant Di-Higgs Production with Decays into
Searching for new Higgs particle beyond the observed light Higgs boson (125GeV) will unambiguously point to new physics beyond the standard model. We study the resonant production of a CP-even heavy Higgs state in the di-Higgs channel via, , at the LHC Run-2 and the high luminosity LHC (HL-LHC). We analyze two types of the decay modes, one with the same signed di-leptons () and the other with tri-leptons (). We perform a full simulation for the signals and backgrounds, and estimate the discovery potential of the heavy Higgs state at the LHC Run-2 and the HL-LHC, in the context of generical two-Higgs-doublet models (2HDM). We analyze the allowed parameter space of the 2HDM which can be effectively probed by the heavy Higgs searches of the LHC, in comparison with the current experimental constraints.
Keywords:Higgs Physics, Beyond Standard Model, LHC
Since the LHC discovery of the light Higgs boson (125GeV) in 2012 ATLAS2012 ()CMS2012 (), both ATLAS and CMS collaborations have much improved the measurements on its mass and couplings which behave fairly standard-model-like Higgs-sum (). But, so far its self-interactions have not yet been tested at the LHC. The cubic Higgs coupling of can be directly probed via the di-Higgs production at hadron colliders h3 (), though it would be much harder. At the LHC(14TeV), the di-Higgs production cross section in the standard model (SM) is small. But, most extensions of the SM contain an enlarged Higgs sector and predict new cubic interaction between a heavier Higgs state and the light Higgs pair . For , the di-Higgs cross section can be significantly enhanced via the resonant production , which simultaneously serves as an important discovery channel of new Higgs boson. Such an extended Higgs sector may include additional new singlets, doublets, or triplets under the SM gauge group , or under an enlarged gauge group with extra SU(2) SU2x (). Among these, the two-Higgs-doublet model (2HDM) 2HDM () is a minimal extension by adding the second Higgs doublet to the SM. It is a necessary ingredient of the minimal supersymmetric SM (MSSM) MSSM () and its next-to-minimal extension (NMSSM) NMSSM (). It is common to impose a discrete symmetry on the 2HDM for preventing the tree-level flavor changing neutral currents. There are at least four kinds of model setup due to the different assignments of fermion Yukawa couplings with each Higgs doublet, namely, Type-I, Type-II, lepton-specific, and flipped. For the current study, we will consider the 2HDM Type-I and Type-II for demonstrations.
The LHC collaborations have searched the resonant heavy Higgs production for a number of di-Higgs decay channels. At the LHC Run-1 with 8 TeV collision energy, the di-Higgs decay final states Aad:2015uka (), Aad:2014yja ()CMSHhh (), Aad:2015xja (), Aad:2015xja () were analyzed. In the channel, ATLAS found an excess of at GeV Aad:2014yja (). The Run-2 of LHC(13 TeV) has searched the resonant di-Higgs production with ATLAS:2016ixk ()CMS:2016pwo (), ATLASRun2bbgg ()CMS:2016vpz (), CMS:2017orf (), CMS:2016rec (), and ATLAS:2016qmt () final states, where the and analyses are updated with 35.9 fb data from CMS. The sensitivity to larger range is also studied for the high luminosity LHC (HL-LHC) with an integrated luminosity of 3000 fb, in the channel LMPHhh () and the channel llc (). There are many recent phenomenological studies on resonant di-Higgs production with the above-mentioned di-Higgs decay channels and for testing different new physics scenarios hh-other ().
In this work, we study the new Higgs boson production via the di-Higgs channel with -decays, . We analyze two kinds of decay products, one with the same signed di-leptons ( ) and the other with tri-leptons ( ). The advantage of these channels is that requiring the same-signed di-leptons or the tri-leptons in the final states can significantly suppress QCD backgrounds. We perform a full analysis of signals and backgrounds by generating the events at parton level, and then use Pythia for hadronization and parton shower, followed by fast Delphes detector simulations. We will study the discovery potential of the heavy Higgs state at the LHC Run-2 and HL-LHC, in the context of the generical 2HDM Type-I and Type-II. We derive the theoretical constraints and the current experimental limits on the 2HDM parameter space. We analyze which part of the 2HDM parameter space can be probed by the new Higgs boson searches at the LHC Run-2 and the HL-LHC. We note that for the LHC discovery of via resonant di-Higgs production, it is valuable to include the channel in addition to other di-Higgs decay modes. This will allow a combined analysis of all di-Higgs decay channel to enhance the discovery reach of the LHC. (In the literature, there are studies of the decay channels for non-resonant di-Higgs production in the SM 4W-SM ().)
This paper is organized as follows. Sec. 2 will give the 2HDM setup and present the production and decays of the new Higgs boson . We will analyze the relevant theoretical constraints and the current direct/indirect experimental limits on the 2HDM parameter space. We set up the benchmarks for the later collider analysis. In Sec. 3, we will study the new Higgs boson production, , via two kinds of decay modes. For each decay channel, we perform full simulations for three Higgs benchmark scenarios. In Sec. 4, we will analyze the 2HDM parameter space which can be probed by the new Higgs boson searches in the channel at the LHC Run-2 and the HL-LHC. We further present the current theoretical and experimental constraints on the 2HDM parameter space, and combine them with the direct searches of the new Higgs boson in the channel. Finally, we will conclude in Sec. 5.
2 Heavy Higgs Boson H in 2HDM: Decays and Production
In this section, we will first define the model setup of the 2HDM and its parameter space in Sec. 2.1. Then, in Sec. 2.2, we analyze the relevant theoretical constraints and the current direct/indirect experimental limits on the 2HDM parameter space. Finally, in Sec. 2.3, we present the decays and production of the heavy Higgs boson at the LHC. With these, we set up three benchmarks for our LHC studies in the subsequent sections.
2.1 The Model Setup
The 2HDM 2HDM () is a minimal extension of the SM Higgs sector. It is common to impose a discrete symmetry on its Higgs sector, with the Higgs doublets and being odd and even, respectively. The general CP conserving Higgs potential can be written as
where all parameters are real. The potential respects the symmetry except the only mixing mass-term of which provides a soft breaking of .
The vacuum is determined by the potential minimum, with the Higgs vacuum expectation values (VEVs), . Both Higgs fields contribute to the electroweak symmetry breaking, with their VEVs obeying the condition GeV. Defining and , we see that the VEV ratio is described by the parameter . The two Higgs doublets contain eight real components in total,
With the three massless Goldstone bosons eaten by the weak gauge bosons , the physical spectrum consists of five states: two CP-even neutral scalars , one pseudoscalar , and a pair of charged scalars . The CP-even sector involves a generical mass-mixing between , and the mass eigenstates are given by the orthogonal rotation with a mixing angle ,
Given the current LHC data, it is most natural to identify lighter Higgs boson as the observed Higgs boson of mass 125 GeV ATLAS2012 ()CMS2012 (). The heavier state is a brandnew Higgs boson beyond the SM, and can have sizable di-Higgs decays for the mass-range . The current LHC measurements show that the Higgs boson (125GeV) behaves rather SM-like. The favored 2HDM parameter space is then pushed to the region around alignment limit, .
We note that the Higgs potential (1) contains eight parameters in total, including three mass parameters and five dimensionless self-couplings. We can reexpress the eight parameters in terms of four Higgs masses , the combined VEV , the VEV ratio , the mixing angle , and the mixing mass parameter . Imposing the experimental inputs GeV and GeV, we note that the Higgs sector is described by six parameters in total: the VEV ratio , the mixing angle , heavy Higgs masses , and the mass-mixing parameter .
For the later numerical analyses in this section and in Sec. 4, we will consider the 2HDM parameter space in the following ranges,
where all the mass parameters are in the unit of GeV. Here we choose GeV to evade the constraint from the rare -decay measurements.
|Couplings||( )||( )||( )|
The 2HDM Type-I and Type-II are defined according to their different assignments for the Yukawa sector under the symmetry. In the 2HDM Type-I, all the SM fermions are defined as even, thus only the Higgs doublet joins Yukawa interactions and generates all the fermion masses. For the 2HDM Type-II, all the right-handed down-type fermions are assigned as odd, while all other fermions are even. Thus, the 2HDM-II has the Higgs doublets and couple to the up-type and down-type fermions, respectively. Under the assignments, the Yukawa couplings for 2HDM-I and 2HDM-II can be expressed in the form, , , where the dimensionless coefficients only depends on and , as summarized in Table 1. For comparison, we also show the Yukawa couplings of the light Higgs boson , , in the parentheses of this table. The trilinear gauge couplings of take the form , where , while the couplings are given by .
2.2 Constraints from Theory and Existing Experiments
Requiring the Higgs potential (1) bounded from below, we have the stability conditions,
The high energy behaviors of scattering amplitudes involving longitudinal weak gauge bosons should obey the perturbative unitarity unitarity1 (). According to the equivalence theorem ET (), such scattering amplitudes are well approximated by the corresponding Goldstone boson scattering amplitudes. The -wave unitarity condition imposes the following constraints on the quartic Higgs couplings,
The existing electroweak precision data will constrain the one-loop contributions induced by the Higgs-gauge couplings via oblique corrections STU (). Around the alignment limit, we can expand the 2HDM contributions to the oblique parameters as follows stu1 (),
where , and the function is given by
where . The leading order contributions to the oblique corrections (7) only involve the masses of new Higgs bosons . This is because the couplings of trilinear vertices involving two new Higgs bosons (--, --, --, and --) either contain the factor or have no -dependence, while the cubic vertices with only one new Higgs boson (--, --, and --) are suppressed by . Besides, the other cubic vertices -- () have couplings proportional to , and lead to the suppression factor after subtracting the corresponding SM contributions.
In Fig. 1(a) we present the 2HDM predictions of by scanning the 2HDM parameter space, where the (red, green, blue) dotted regions correspond to mass GeV, respectively. As a comparison, we also show the 95% C.L. contour from the precision constraints stu2 () in the same plot (with ). In Fig. 1(b), we present the parameter prediction of the 2HDM over the mass-range TeV. We find that in the 2HDM, the oblique contribution to is much larger than , and the and parameters are fairly small in the relevant parameter region, namely, . (For these numerical analyses in Fig. 1, we have used the exact one-loop formulas for the oblique parameters stu1 ().) Hence, Fig. 1 shows that the nontrivial constraint mainly comes from the parameter. Since the current electroweak precision data constrain the parameter to be quite small, especially for small as restricted by the ellipse contour in Fig. 1(a), this requires the mass of to be fairly degenerate with that of or .
Next, we further derive the existing constraints on the 2HDM parameter space by making a global fit for the LHC Run-1 and Run-2 measurements on the light Higgs boson (125GeV). Since this Higgs state (125GeV) is fairly SM-like, the new physics corrections to couplings are tightly constrained and other new Higgs states need to be significantly heavier. So we may regard the global fit bounds as indirect constraints on the 2HDM, in contrast with the constraints from direct searches of new Higgs states.
For the Run-1 Higgs data of the LHC (7+8TeV), we have used the combined analysis of ATLAS and CMS Run1-sum-h (). For the current Higgs data from the Run-2 of the LHC (13TeV), we include the ATLAS measurements on Atlas2-gaga (), Atlas2-4L (), Atlas2-WW (), and Atlas2-bb () channels, and the CMS measurements on CMS2-gaga (), CMS2-ZZ (), CMS2-WW (), CMS2-tautau (), and CMS2-bb () channels. We make use of these Run-1 and Run-2 Higgs data from ATLAS and CMS collaborations, and perform a global fit to derive the current LHC constraints on the 2HDM parameter space. We present the contours (red curves) and contours (blue curves) in the plane for 2HDM-I in Fig. 2(a) and for 2HDM-II in Fig. 2(b). We further incorporate the theoretical requirements from the Higgs stability and perturbative unitarity, and present the combined constraints on the allowed parameter regions marked by red dots (in box shape) at the level and by blue dots (in circle shape) at the level.
Fig. 2 shows that the current LHC global fit of (125GeV) shifts the viable parameter space somewhat towards region for 2HDM-I, while it pushes the allowed parameter range significantly to side for 2HDM-II. The reasons are the following. We note that the current LHC data give tight constraints on the signal strengths F+ and (VBF+). For 2HDM-I, we find that fitting the combined Run-1 data Run1-sum-h () gives quite symmetric bounds around . The asymmetry of the bounds in Fig. 2(a) mainly arises from the ATLAS Run-2 data for channel Atlas2-gaga (), which favor F+ and thus a reduced coupling. ATLAS Run-2 measurement on channel Atlas2-gaga () also somewhat favors F+, but with larger error bars. Hence, the net effect is to reduce coupling, leading to for 2HDM-I (cf. Table 1), i.e., the region is favored in Fig. 2(a). On the other hand, for 2HDM-II, we find that fitting the combined Run-1 data Run1-sum-h () prefers an enhanced coupling, mainly because and channels favor F+. Including the Run-2 measurements, we find that the ATLAS data for Atlas2-gaga () and the CMS data for CMS2-gaga () play the major role to require F+ and thus an enhanced coupling. From Table 1, we find that these lead to for 2HDM-II, i.e., the region is favored in Fig. 2(b).
Finally, for this study, we will consider the upper bounds from the existing LHC Run-1 and Run-2 searches on a heavier Higgs state with decays in various channels. These will put additional constraints on the 2HDM parameter space through various couplings. The LHC Run-1 searches include from CMS CMSHhh (), the combined searches of , , , from ATLAS Aad:2015xja (), from ATLAS ATLASHVV (), and the combined searches of from CMS CMSHVV (). The LHC Run-2 searches include from ATLAS HWWlvlvATLAS13 (), from ATLAS HZZ4lATLAS13 ()HZZ2l2vATLAS13 (), from ATLAS tataATLAS () and from CMS tataCMS (), and from CMS CMS:2017orf (). With these, we summarize in Table 2 the current upper limits (95% C.L.) from the LHC Run-1 and Run-2 direct searches on the production cross sections of the heavier Higgs boson in various decay channels, where the numbers do not contain the decay branching fractions of the final states , , and .
In Fig. 3, we present the current experimental constraints on the 2HDM parameter space in the plane of . The parameter region with blue dots (circle shape) satisfy the theoretical conditions, the electroweak precision limits (), and the LHC bounds () from the Higgs global fit of (125GeV) data. The red dots (square shape) present the parameter region obeying the existing LHC direct search limits () on the heavier Higgs boson in combination with the theoretical constraints. The electroweak precision tests mainly bound the oblique parameter as shown in Fig. 1, and prefer the masses and to be fairly degenerate for GeV. The present LHC global Higgs fit prefers (125GeV) to be quite SM-like, and favors the 2HDM parameter space around the alignment limit (cf. Fig. 2). Fig. 3 shows that the allowed region of (with blue dots) in 2HDM-I is more shifted to as in plot-(a), while the region with blue dots in 2HDM-II is largely excluded on the side, as in plot-(b). These features are consistent with Fig. 2. The current LHC direct search limits on the heavier Higgs state are reflected by the red dotted regions in Fig. 3. They are comparable to the bounds imposed by the LHC (125GeV) global fit (combined with the electroweak precision limits) for 2HDM-I, but they are significantly weaker for the case of 2HDM-II.
2.3 H Production in Di-Higgs Channel and Benchmarks
For the present study, we focus on the productions and decays of the heavy Higgs state . We have summarized the Yukawa couplings for 2HDM-I and 2HDM-II in Table 1. The gauge couplings of take the form , (), which differs from the SM Higgs-gauge coupling by a factor . With these, we determine the vertex by rescaling SM contributions inside the loop accordingly. The ratios of the decay widths with respect to the SM results are given as follows,
Around the alignment limit the decay width is suppressed by , while for down-type fermions the partial width is enhanced by a factor .
The main production mechanism of the neutral Higgs boson at the LHC is the gluon fusion production . In the 2HDM-I, all Yukawa couplings rescale in the same way with respect to the SM values. So the gluon fusion production is still dominated by the top-loop, and the cross section is rescaled by a factor . In the 2HDM-II, the Yukawa couplings of the down-type quarks have a different form from the corresponding up-type quarks. For , the bottom-loop in the gluon fusion process may have visible contribution and thus will be included. For the present study, we consider the four-flavor scheme, and the relevant -related production process is the bottom-pair associated production , which may be sizable.
We can deduce the coupling of the cubic scalar vertex from the Higgs potential,
where we expand the formula around the alignment limit in the second line. For the mass-range , the tree-level decay width of is
The di-Higgs decay width is also suppressed by in the alignment limit, but it may receive enhancement from other mass-parameters and in the Higgs potential.
To set viable benchmarks for searching the new Higgs boson via resonant di-Higgs production in channel, we will implement the theory constraints and the current experimental bounds on the 2HDM parameter space, as we have analyzed in Sec. 2.2. The requirements of vacuum stability and perturbative unitarity strongly favor the small region llc (). This means that the bottom-pair associated production is subdominant, especially for the experimental searches aiming at gluon fusion production without making extra -tagging. According to the analysis in Sec. 3, we generate events for in the four-flavor scheme. With the selection cuts aiming at gluon fusion production, in particular the -veto which helps to suppress the top-related backgrounds, we find contribution unimportant for the current study. Hence, in the following we will focus on the gluon fusion production,
where the NLO QCD corrections in the 2HDM are assumed to be the same as in the SM which are already included in .
In Fig. 4, we present the allowed cross sections of as a function of the heavy Higgs mass at the LHC(14TeV) for the 2HDM-I [plot-(a)] and 2HDM-II [plot-(b)]. We note that the existing constraints in Fig. 3 will set upper bounds on the resonant production cross sections at the on-going LHC Run-2 and the HL-LHC. In Fig. 4, we plot the red dots (square shape) to show the viable parameter region allowed by the LHC limits () of the existing direct searches combined with the theoretical requirements. For comparison, the blue dots (circle shape) represent the parameter space obeying the theoretical requirements, the indirect electroweak precision limits (), and the LHC bounds () from the global fit of (125GeV). Inspecting Fig. 4, we see that the allowed production cross sections in the 2HDM-I and 2HDM-II are not much different over the wide mass range of GeV. But, the distribution of the blue dots for 2HDM-II [plot-(b)] is relatively sparser than that for 2HDM-I [plot-(a)], due to the stronger constraints on the 2HDM-II by the current LHC global fit of (125GeV) (cf. Fig. 3).
Based upon our analyses of the existing indirect and direct experimental bounds on the 2HDM (combined with theoretical constraints), we will systematically study the direct probe of the heavy Higgs boson via channel at the LHC(14TeV) in the following Section 3. For this, we set up three benchmark scenarios for the mass and the cross section as follows,
which will be denoted by (H300, H400, H500) for short.
3 Analyzing Signals and Backgrounds at the LHC
In this section, we perform systematical Monte Carlo analysis for the heavy neutral Higgs signal and the main backgrounds at the LHC (14TeV). We set up the signal process model by FeynRules Alloul:2013bka () with and vertices. We generate the events by MadGraph5 package Alwall:2014hca () at parton level, and then process them by Pythia Sjostrand:2006za () for hadronization and parton shower. Finally, we use Delphes 3 deFavereau:2013fsa () for detector simulations.
We study two major decay channels of the final state : (i). with same-sign di-leptons (SS2L); (ii). with tri-leptons (3L). For boson, its branching fractions of leptonic decays are 10.8%, 10.6%, and 11.3%, respectively, while its hadronic decay has branching fraction 67.6 Agashe:2014kda (). For this analysis, we include the detected and from decays as well. These two decay channels of have branching fractions about 9.6% and 9.2%, respectively. Although they are quite small (less than 10%), we note that requiring the detection of the same-signed di-leptons or the tri-leptons in the final state can significantly reduce the QCD backgrounds and enhance the signal sensitivity.
3.1 Final State Identification
To analyze the signal sensitivity, we apply the ATLAS procedure to identify the final states in both SS2L and 3L decay channels. Jets, leptons, and transverse missing energy are selected by the following cuts,
Electrons with are rejected in order to remove the transition region of electromagnetic calorimeter of ATLAS. After the trigger, we require the leading lepton passing the trigger requirement GeV. The -taging algorithm based on of jet is implemented in Delphes ATL-PHYS-PUB-2015-022 ().
The reconstructed objects in the final state have to be well separated spatially to prevent the potential double-counting. We implement the following criteria criteria (): (i). any electron overlapped with a muon with is removed; (ii). for any electron pair with , the electron with lower is removed; (iii). any jet within is removed; (iv). any muon within is removed.
3.2 Analysis of Same-Signed Di-lepton Decay Channel
With the identification of the final state particles as in Sec. 3.1, our analysis of the same-signed di-leptons (SS2L) channel further requires the sub-leading lepton obeying GeV to reduce the fake backgrounds (as will be described in the following) and
The jets arising from the off-shell boson decays could be soft and the requirement of provides an optimal significance. The above defines the basic event selection for the SS2L channel.
The main prompt backgrounds that contribute to the same-signed di-leptons include , (with , (with , ), , (with , (with , (with and (with and . The background processes with a pair of top quarks (namely, , , and ) can be efficiently rejected by -veto. With the basic event selection and -veto, the background becomes negligible. The diboson backgrounds, , , and , can be suppressed by requiring exactly two same-signed leptons as in Eq.(16). Hence, we can safely ignore and backgrounds given their small cross sections, and only include channel for the background estimate.
|& Backgrounds||(before PreS)||(after PreS)|
|24.1 PhysRevLett.107.152003 ()||0.39|
|54.6 Campbell2012 ()||1.61|
|12.6 1310.1132 ()||0.185|
|921 PhysRevD.60.113006 ()||15.0|
|(semi-leptonic)||433500 https://twiki.cern.ch/twiki/bin/view/LHCPhysics/TtbarNNLO ()||2.28|
For the SS2L channel, backgrounds with fake leptons from jets or charge misidentifications (QmisID) can also be significant. Jet faking leptons mainly come from +jets final state and semi-leptonic mode of final state (which both have large cross sections). For the samples of fake electrons, we assign a weight to each event in the following way. (i). We generate jets background (including two or more jets) and the background (in the semi-leptonic decay mode). (ii). For each selected event of lepton+jets, we loop over all possible jets that could fake an electron with a probability as a function of jet ATL-PHYS-PUB-2013-004 (). (iii). We sum over all fake rates and divide it by two to account for the same sign fakes with the selected leptons. (iv). We randomly choose one jet to be the fake electron according to the fraction of fake rates, and rescale the jet’s energy to its 40% as that of the fake electron ATL-PHYS-PUB-2013-004 (). Since fake electrons are usually soft, we find that the selection cut GeV helps to significantly suppress these backgrounds and makes them comparable to other prompt backgrounds. With the upgrade Level-0,1 Muon Trigger for ATLAS detector ATL-PHYS-PUB-2016-026 (), the contribution of fake muons with GeV is small and can also be safely ignored. The QmisID mainly comes from the +jets and the pure leptonic mode of , with one charge misidentified lepton. Pseudo-events are generated in a way similar to that for the fake electrons, with a weight 0.0026 assigned to each event ATL-PHYS-PUB-2016-026 (). These backgrounds can be significantly suppressed by -veto, i.e., GeV. With these, we find that the contribution due to QmisID is negligible.
After all pre-selection cuts, including the basic event selection, -veto, and -veto, we obtain as shown in the last column of Table 3. We will make further optimization to increase the significance. In Fig. 5, we present the distributions of kinematic variables after all pre-selections, each of which has its own advantage to help the discrimination of signals from backgrounds. Some variables are insensitive to the heavy Higgs mass . The invariant mass of the closest pair of jets, , well represents the mass scale of boson. The invariant mass of the leading lepton and the two closest jets, , reflects the mass scale of the light Higgs boson (125GeV). To represent , one obvious choice is the sum of the selected leptons, jets and transverse missing energy. For larger Higgs mass , the intermediate bosons become more boosted. The distance between the two leptons and their closest jets, , tend to be smaller, while their corresponding invariant masses, , are larger. In summary, has stronger power of separating the signal from backgrounds for the higher case, while all invariant-masses and play a better role for the case of lower .