LHC phenomenology of a twoHiggsdoublet neutrino mass model
Abstract
We study the LHC search prospects for a model in which the neutrinos obtain Dirac masses from couplings to a second Higgs doublet with tiny vacuum expectation value. The model contains a charged Higgs boson that decays to with branching fractions controlled by the neutrino masses and mixing angles as measured in neutrino oscillation experiments. The most promising signal is electroweak production of pairs with decays to , where , , and . We find that a cut on the kinematic variable eliminates most of the and pair background. Depending on the neutrino mass spectrum and mixing angles, a 100 (300) GeV charged Higgs could be discovered at the LHC with as little as 8 (24) fb of integrated luminosity at 14 TeV centerofmass energy.
I Introduction
The Standard Model (SM) accounts for almost all experimental high energy physics data; however, the observation of neutrino oscillations requires that the SM be extended to include nonzero neutrino masses. While there are many ways to expand the SM to account for neutrino oscillations, we attempt to do so with the following goals. First, the neutrino mass scale is significantly lower than the mass scales of the other fermions, so we would like the model to account for this without the addition of many tiny parameters. Second, lepton number violation has not yet been observed, so we would like the model to give rise to Dirac neutrino masses, with Majorana masses forbidden. Third, we would like the model to be testable at the CERN Large Hadron Collider (LHC).
Most neutrino mass models give rise to Majorana masses for the SM neutrinos, with many predicting TeVscale new physics accessible at the LHC. In contrast, only a few models for Dirac neutrinos have been proposed. These typically involve a second Higgs doublet with very small vacuum expectation value (vev) that couples only to the lefthanded lepton doublets and the righthanded neutrinos, resulting in neutrino masses of the same order as the very small vev. The original SMlike Higgs doublet couples to all of the quarks and charged leptons in the usual way. Such a Yukawa coupling structure can be obtained by imposing a global symmetry, as proposed in the models of Refs. Ma:2000cc (); Gabriel:2006ns (); however, this does not by itself forbid neutrino Majorana mass terms, which must instead be eliminated by imposing an additional lepton number symmetry. The required Yukawa coupling structure can also be obtained by imposing a global U(1) symmetry; this idea was first proposed in Ref. Fayet:1974fj () as a way of ensuring the (thenassumed) masslessness of the neutrinos in the presence of righthanded neutrino states, and has the virtue of forbidding Majorana mass terms by itself.
In order to generate neutrino masses, the global symmetry used to ensure the desired Yukawa structure has to be broken. Spontaneous breaking leads to a very light scalar which can cause problems with standard bigbang nucleosynthesis Gabriel:2006ns (), as well as having significant effects on the phenomenology of the new Higgs particles Gabriel:2008es (). By instead breaking a global U(1) symmetry explicitly, the model proposed by us in Ref. Davidson:2009ha () generates Dirac neutrino masses while avoiding very light scalars.^{1}^{1}1A similar mechanism was used to explain the topbottom quark mass hierarchy in Ref. Hashimoto:2004xp (). A supersymmetric version of this model was studied in Ref. Marshall:2009bk (), which found spectacular multilepton signals from cascade decays of the supersymmetric partners of the new Higgs bosons and righthanded neutrinos at the LHC.
In this paper we study the LHC detection prospects of the nonsupersymmetric model of Ref. Davidson:2009ha (). This model expands the SM by adding a second Higgs doublet with the same electroweak quantum numbers as the SM Higgs doublet , as well as adding three gaugesinglet righthanded Weyl spinors which will become the righthanded components of the three Dirac neutrinos. The model imposes a global U(1) symmetry under which the second Higgs doublet and the righthanded neutrinos have charge , while all the SM fields have charge zero. This allows Yukawa couplings of the second Higgs doublet only to the righthanded neutrinos and the SM lepton doublet, and forbids Majorana masses for the righthanded neutrinos. It also tightly constrains the form of the Higgs potential. Breaking the U(1) symmetry explicitly using a term in the Higgs potential yields a vev for the second Higgs doublet and consequently gives the neutrinos Dirac masses proportional to . By requiring that , the Dirac neutrino masses are made suitably small without requiring tiny Yukawa couplings.
The characteristic feature of the model is that the couplings of the charged scalar pair and two neutral scalars and from the second Higgs doublet to leptons and neutrinos are controlled by the neutrino masses and mixing angles. In this paper we take advantage of the distinctive decay of the charged Higgs boson into charged leptons and neutrinos. We focus on electroweak pair production of at the LHC followed by decays to , where can be any combination of oppositesign , , and leptons and denotes missing transverse momentum (carried away by the neutrinos). Because leptons are more difficult to reconstruct experimentally, we concentrate on the final states with , , and . The major backgrounds are diboson production (, , and ) and top quark pair production with both tops decaying leptonically.
To determine whether the signal will be detectable at the LHC, we generated signal and background events using MadGraph/MadEvent version 4 Alwall:2007st () assuming 14 TeV centerofmass energy. We present results both at parton level, and after hadronization with PYTHIA PYTHIA () and fast detector simulation with PGS PGS (). With appropriate cuts, we find that a 5 discovery can be achieved with luminosity in the range 8–75 fb for GeV, depending on the neutrino mixing parameters. For GeV a 5 discovery can be made with luminosity in the range 24–460 fb. The higher luminosity requirements occur when the neutrino parameters are such that decays mostly to , leading to final states not considered in our analysis. We find that the kinematic variable is very effective at separating the signal from the and backgrounds for charged Higgs masses above the mass, and also provides sensitivity to the charged Higgs mass.^{2}^{2}2While we have not made a detailed study of charged Higgs detection prospects at 7 TeV centreofmass energy, we note that the cross section for the most dangerous background is about 2.5 times smaller at 7 TeV. However, the signal cross section is also about 2.5 (4.5) times smaller at this energy for (300) GeV. Furthermore, the LHC is anticipated to collect only about 1 fb of integrated luminosity at 7 TeV. We thus expect detection or even exclusion of the process considered here to be unfeasible in the current 7 TeV LHC run.
This paper is organized as follows. In the next section we review the model and present the charged Higgs decay branching ratios. In Sec. III we describe the signal and background processes, our event generation procedure and selection cuts, and the resulting signal significance. In Sec. IV we summarize our conclusions.
Ii The model
As outlined in the introduction, we start with the field content of the SM and add to it a new scalar SU(2) doublet (the SM Higgs is denoted ) and three righthanded gauge singlets (these are the righthanded neutrinos). We impose a U(1) symmetry under which and the three have charge +1 and all the other fields are uncharged, which leads to the Yukawa coupling structure Davidson:2009ha ()
(1) 
Here is the conjugate Higgs doublet and are the 33 Yukawa matrices for fermion species .
The Higgs doublets can be written explicitly as
(2) 
where will be generated by the usual spontaneous symmetry breaking mechanism of the SM and will be generated by the explicit breaking of the global U(1), described below. Inserting these expressions for into Eq. (1), we obtain the fermion masses and couplings to scalars. In particular, the fourth term in Eq. (1) gives rise to the neutrino mass matrix and interactions:
(3) 
After diagonalizing the mass matrix in the first term, the neutrino mass eigenvalues are given by , where are the eigenvalues of . In this way, the small masses of the three neutrinos can be traced to the small value of .
We obtain the vevs of the scalar doublets from the Higgs potential as follows. The most general gaugeinvariant scalar potential for two Higgs doublets is (see, e.g., Ref. HHG ()),
(4)  
Imposing the global U(1) symmetry eliminates , , , and . The global U(1) symmetry is broken explicitly by reintroducing a small value for . This leaves the Higgs potential Davidson:2009ha (),^{3}^{3}3Note that using a symmetry instead of the global U(1) would allow a nonzero term.
(5)  
Stability of the potential at large field values requires , , and . We want to arise through the usual spontaneous symmetry breaking mechanism, which is achieved when . We do not want the global U(1) to also be broken spontaneously, as that will create a very light pseudoNambuGoldstone boson, which is incompatible with standard bigbang nucleosynthesis; thus we require that the curvature of the potential in the direction at zero field value be positive, i.e., .
To find the values of the vevs in terms of the parameters of the Higgs potential, we apply the minimization conditions,
(6) 
Since we will require , we can ignore and when finding the value of . This yields
(7) 
For , we need to consider , although again we may ignore higher order terms in ; this yields
(8) 
We will choose parameters so that GeV and eV. This requires . We note that because is the only source of breaking of the global U(1) symmetry, its size is technically natural; i.e., radiative corrections to are proportional to itself and are only logarithmically sensitive to the highscale cutoff Davidson:2009ha ().
The mass eigenstates of the charged and CPodd neutral scalars are given by
(9) 
where we define . and are the Goldstone bosons, which do not appear as physical particles in the unitarity gauge. and are the physical charged and CPodd neutral Higgs states and are almost entirely contained in . Neglecting contributions of order and , the masses of and are Davidson:2009ha ()
(10) 
The mass matrix for the CPeven neutral states is almost diagonal, yielding only very tiny mixing of order . Ignoring the mixing, the eigenstates are (SMlike) and , with masses Davidson:2009ha ()
(11) 
After diagonalizing the neutrino mass matrix, Eq. (3) yields the following couplings to the new physical Higgs states:
(12) 
where is the PontecorvoMakiNakagawaSakata (PMNS) matrix, defined according to , where are the neutrino flavor eigenstates.
The PMNS matrix can be parameterized in terms of three mixing angles (with , 23, and 13) and a phase according to (see, e.g., Ref. Fogli:2005cq ()),
(13) 
where and . The 2 experimentallyallowed ranges for the three mixing angles and the neutrino masssquared differences are given in Table 1. The phase and the mass of the lightest neutrino are undetermined, although tritium beta decay experiments set an upper limit on the neutrino masses of about 2 eV Amsler:2008zzb ().
Parameter  Value 

eV  
eV 
Since the decays of and to two neutrinos will be invisible to a collider detector, the decay of most interest is . The charged Higgs can decay into all nine combinations of ; summing over neutrino mass eigenstates, the partial width to a particular charged lepton is Davidson:2009ha ()
(14) 
where we define the expectation value of the neutrino masssquared in a flavor eigenstate by Fukuyama:2008sz ()
(15) 
In what follows we work under the assumption that , i.e., , so that the decays , will be kinematically forbidden. The branching ratios of the charged Higgs are then completely determined by the neutrino masses and mixing:
(16) 
where we used the unitarity of the PMNS matrix to simplify the denominator.
The sign of the larger neutrino mass splitting is unknown (see Table 1). The situation in which is positive, so that is the heaviest neutrino, is called the normal neutrino mass hierarchy, while the situation in which is negative, so that and are heavier, is called the inverted hierarchy. We compute the charged Higgs branching fractions as a function of the lightest neutrino mass for both hierarchies, scanning over the 2 allowed ranges of the neutrino parameters as given in Table 1. Results are shown in Fig. 1.^{4}^{4}4We disagree with the charged Higgs branching fractions to leptons presented in Ref. Gabriel:2008es () for the model of Ref. Gabriel:2006ns (); these decays should have the same relative branching fractions as in our model. The large spread in the branching ratios to and for lightest neutrino masses below about 0.06 eV is due to the current experimental uncertainty in , which controls the relative amount of and in the isolated mass eigenstate .
Limits on the model parameters were discussed in Ref. Davidson:2009ha (). The most significant for our purposes is from searches for leptons plus missing energy at the CERN Large ElectronPositron Collider, which put a lower bound on the charged Higgs mass of 65–85 GeV, depending on the mass of the lightest neutrino. Bigbang nucleosynthesis also puts an upper bound on the neutrino Yukawa couplings of
(17) 
Iii Signal and background at the LHC
In most other twoHiggsdoublet models, the charged Higgs decay rate to a particular charged lepton is proportional to the square of the charged lepton mass (see, e.g., Ref. HHG ()). Such a charged Higgs therefore decays predominantly to , with decays to , below 1%. In our neutrinomass model, however, the charged Higgs decay rate to a particular charged lepton is instead proportional to the square of the mass of the corresponding neutrino flavor eigenstate. As a result, the branching fraction to and/or will always be sizable. In particular, in the normal hierarchy BR(, in the inverted hierarchy BR( and BR(, and for a degenerate neutrino spectrum BR( BR(, as shown in Fig. 1. Considering the high detection efficiency and lower fake rates of and compared to , we study pair production at the LHC mediated by a photon or , followed by decays to or with missing transverse momentum. We consider two scenarios, and 300 GeV, and present results as a function of the lightest neutrino mass for both the normal and inverted hierarchy.
The process of interest is , with , , and . The relevant backgrounds are with , , or and the neutrinos of any type, and . In spite of the presence of the extra jets that can be vetoed, the process is important because of its exceptionally high cross section at the LHC.
iii.1 Event generation
We simulated the signal and background processes with the partonlevel Monte Carlo MadGraph/MadEvent version 4 Alwall:2007st (). We present both a partonlevel analysis and an analysis including showering, hadronization, and a fast detector simulation using a PYTHIAPGS package designed to be used with MadEvent. PYTHIA (version 6.4.20) PYTHIA () generates initial and finalstate radiation and hadronizes the finalstate quarks and gluons, while PGS (Pretty Good Simulation of High Energy Collisions, version 4) PGS () is a basic detector simulator—we used the default settings for ATLAS. For the signal process we generated 10,000 unweighted events in each of the , , and final states. For both the and backgrounds we generated 100,000 unweighted events in each of the three leptonic final states. We incorporated the final state by doubling the cross sections. For the backgrounds we used the default SM branching fractions from MadGraph/MadEvent, given in Table 2.
Process  Branching fraction 

( or )  0.1068 
( or )  0.0336 
(all 3 neutrinos)  0.2000 
1.0000 
Although MadGraph/MadEvent is a treelevel event generator, we partially incorporated nexttoleading order (NLO) QCD corrections. We did this for two reasons. First, QCD corrections have a significant effect on the signal and background (especially ) cross sections, as well as significantly reducing the QCD scale uncertainty, so that using NLO cross sections lets us obtain more reliable results. Second, for the GeV simulation we will apply a jet veto to reduce the background, which will also affect the signal and background once initialstate radiation is included. While this could be simulated by running the nojet events through PYTHIA, a partonlevel simulation of the and processes provides a more accurate description of jet kinematics. Because these onejet processes make up part of the NLO QCD cross section for the corresponding nojet processes, we must incorporate the NLO cross sections for consistency, as follows.
In the absence of a full NLO Monte Carlo, NLO QCD corrections are usually incorporated by multiplying the leadingorder (LO) cross section—and the cross section corresponding to each simulated event both before and after cuts—by a factor equal to the ratio of the NLO cross section to the treelevel cross section. In our case, however, our jet veto will affect LO events (which have no jet) and NLO events (which can have a finalstate jet) differently. We deal with this by simulating and with the same decay final states as considered in the nojet processes. For simplicity we generate the same number of events with an additional jet at the parton level as were generated for the nojet processes. Because the background already contains two jets at leading order, we do not separately generate events with additional jets for this background. To avoid the collinear and infrared singularities, we apply a minimum cut of 10 GeV on the jet at the eventgeneration level.
The square of the NLO matrix element can be expressed up to order as
(18) 
We used MadGraph/MadEvent to calculate the cross sections corresponding to and . We computed the NLO crosssection for at the LHC using the public FORTRAN code PROSPINO Beenakker:1999xh (); Alves:2005kr () with CTEQ6 parton densities Pumplin:2002vw (), with the renormalization and factorization scales set equal to . We took the NLO cross sections for the SM and background processes from Ref. Campbell:1999ah (). This paper quotes results using both the MRS98 and CTEQ5 parton densities, with results differing by 6%; since we use CTEQ6 for the treelevel MadGraph/MadEvent calculation, we take the results using the CTEQ5 parton densities for consistency. For events with in the final state, only the cross section for is relevant; for events with or in the final state, both the and processes contribute and we add the cross sections at both LO and NLO. We took the cross section from Ref. Bonciani:1998vc (), which includes both NLO and nexttoleading logarithmic corrections. The remaining scale uncertainty is about 5% when the factorization and renormalization scales are varied between and . The relevant cross sections are given in Table 3.
Process  Cross section  Source 

( GeV)  295 fb  PROSPINO Beenakker:1999xh (); Alves:2005kr () 
( GeV)  5.32 fb  PROSPINO Beenakker:1999xh (); Alves:2005kr () 
127.8 pb  Ref. Campbell:1999ah ()  
17.2 pb  Ref. Campbell:1999ah ()  
833 pb  Ref. Bonciani:1998vc () 
We find that with our generatorlevel jet cut on , , so the oneloop matrix element must interfere destructively with the LO matrix element. Thus the generated cross section from the LO process must be scaled down in order to incorporate the effects of the oneloop correction. For the partonlevel simulation, the relevant scale factor is determined by solving for in the equation,
(19) 
before cuts are applied, and then using this equation with the same value of to calculate the surviving after the cuts are applied to the LO and onejet MadGraph/MadEvent simulated results.
For the PYTHIAPGS simulation, the simulated events have extra jets produced by PYTHIA and “measured” jet smeared by PGS. To avoid doublecounting, we use the following equation with two constants:
(20) 
where and are the cross sections identified by PGS as having no jets and at least one jet, respectively, with GeV, out of the combined LO and onejet generated samples. The constants and are determined by and using from Eq. (19). Equation (20) with the same values of and is then used after cuts to calculate the surviving .
iii.2 Cuts
We apply four cuts to reduce the background, summarized in Table 4. The first cut checks for the presence of two oppositesign leptons each with GeV and missing transverse momentum of at least 30 GeV. For the partonlevel simulation, we also apply acceptance cuts on the pseudorapidity of both leptons, for electrons and for muons. Second, for the and final states we veto events for which the dilepton invariant mass falls between 80 and 100 GeV, in order to eliminate background from . This will also eliminate the majority of any background from with fake , which we did not simulate. The third cut vetoes events containing a jet with GeV; for the partonlevel simulation, we require that this jet falls in the rapidity range . This eliminates more than 97% of the backgound, but also reduces the signal by about a factor of two. We find that this cut is useful for GeV. For GeV the signal cross section is considerably smaller and the signal events will be better separated from background in our final cut variable, so that we obtain better sensitivity without the jet veto.
Cut name  Explanation 

Basic cuts  Present are a lepton and antilepton, each with GeV, and missing transverse momentum GeV. For the parton level results, we also apply lepton acceptance cuts of and . 
pole veto  To eliminate events that include , we veto events in which the invariant mass of or is between 80 and 100 GeV (not applied to the final state). 
Jet veto  Designed to reduce background, any event with a jet with GeV was rejected. For the parton level results, this veto is only applied when . (Applied only for GeV.) 
cut  To reduce the and backgrounds, we make use of the larger mass of compared to the intermediate bosons in both backgrounds by cutting on (defined in Eq. (21)). For GeV we require GeV and for GeV we require 150 GeV GeV. 
The final cut is on the variable , defined as Lester:1999tx ()
(21) 
where is the square of the transverse mass (ignoring the charged lepton and neutrino masses),
(22) 
In other words, is determined by making a guess for the transverse momenta of the two neutrinos (constrained by the measured total missing transverse momentum) and computing the transverse masses of the two systems; the guess is then varied until the larger of the two reconstructed transverse masses is minimized.
For equalmass intermediate particles each decaying to , the distribution has an upper endpoint at the mass of the intermediate particle. Thus by cutting out events with , all the background should be eliminated (the endpoint is in fact smeared out by the finite width and momentum resolution of the detector). Since the leptons and missing transverse momentum in the process also come from decays of onshell , this background should be eliminated as well. There is also a small contribution to the background from nonresonant processes that can have . Since all signal events will have , we also cut out events with in an effort to reduce the background from these nonresonant processes. For GeV, we find that raising the minimum cut on to 150 GeV reduces the tail of the nonresonant events without reducing the signal too much.
In Fig. 2 we show the distributions for signal and background processes in the channel for and 300 GeV after the other cuts have been applied, for the PYTHIAPGS simulation. Note that the background distribution has a maximum value a little above the mass, so that it can be eliminated with a high enough cut on , as we do for the case of GeV. (The higher endpoint for in the righthand plot in Fig. 2 is due to the absence of the jet veto, resulting in much higher statistics.) The background also falls off dramatically around ; however, due to nonresonant diagrams without onshell intermediate pairs, this background extends to much higher values of . With our simulation statistics, a single event corresponds to a cross section of about 0.1 fb, while a single event corresponds to a cross section of about 0.01 fb.
iii.3 Results
The efficiency of each cut on for the final state is displayed in Tables 5, 6 and 7. Cut efficiencies for are displayed in Tables 8, 9 and 10, and for in Tables 11, 12 and 13. We give efficiencies for both the partonlevel simulation and the simulation including showering, hadronization, and fast detector simulation using the PYTHIAPGS package. All results incorporate NLO corrections as described in Sec. III.1.
GeV  GeV  

Cuts  Parton  PYTHIA/PGS  Parton  PYTHIA/PGS 
Basic cuts  0.62644  0.47860  0.92961  0.72105 
pole veto  0.90754  0.90165  0.97732  0.97724 
Jet veto  0.68433  0.60717  –  – 
cut  0.17075  0.15542  0.47317  0.45945 
Cumulative  0.06643  0.04072  0.42988  0.32375 
Background  Background  

Cuts  Parton  PYTHIA/PGS  Parton  PYTHIA/PGS 
Basic cuts  0.42708  0.33912  0.58407  0.40612 
pole veto  0.74727  0.73255  0.86236  0.85501 
Jet veto  0.63306  0.67299  0.01318  0.02856 
GeV  0.01401  0.01147  0.01205  0.02716 
Cumulative  0.00283  0.00192  0.00008  0.00027 
Background  Background  

Cuts  Parton  PYTHIA/PGS  Parton  PYTHIA/PGS 
Basic cuts  0.42708  0.33912  0.58407  0.40612 
pole veto  0.74727  0.73255  0.86236  0.85501 
150 GeV GeV  0.00260  0.00196  0.00000  0.00000 
Cumulative  0.00083  0.00049  0.00000  0.00000 
GeV  GeV  

Cuts  Parton  PYTHIA/PGS  Parton  PYTHIA/PGS 
Basic cuts  0.51713  0.43680  0.84810  0.69845 
pole veto  0.90869  0.90075  0.97756  0.97696 
Jet veto  0.68310  0.57831  –  – 
cut  0.16875  0.17320  0.47802  0.46847 
Cumulative  0.05417  0.03941  0.39632  0.31966 
Background  Background  

Cuts  Parton  PYTHIA/PGS  Parton  PYTHIA/PGS 
Basic cuts  0.32959  0.28226  0.52593  0.39048 
pole veto  0.73839  0.73098  0.86021  0.85489 
Jet veto  0.62703  0.63204  0.01346  0.02282 
GeV  0.01324  0.01554  0.00657  0.03675 
Cumulative  0.00202  0.00203  0.00004  0.00028 
Background  Background  

Cuts  Parton  PYTHIA/PGS  Parton  PYTHIA/PGS 
Basic cuts  0.32959  0.28226  0.52593  0.39048 
pole veto  0.73839  0.73098  0.86021  0.85489 
150 GeV GeV  0.00288  0.00239  0.00000  0.00000 
Cumulative  0.00070  0.00049  0.00000  0.00000 
GeV  GeV  

Cuts  Parton  PYTHIA/PGS  Parton  PYTHIA/PGS 
Basic cuts  0.56131  0.45743  0.88249  0.70832 
Jet veto  0.68783  0.59528  –  – 
cut  0.16857  0.16121  0.47427  0.46373 
Cumulative  0.06508  0.04390  0.41854  0.32847 
Background  Background  

Cuts  Parton  PYTHIA/PGS  Parton  PYTHIA/PGS 
Basic cuts  0.35835  0.30423  0.55297  0.39556 
Jet veto  0.65590  0.68572  0.01255  0.02592 
GeV  0.00860  0.01207  0.01585  0.03018 
Cumulative  0.00202  0.00252  0.00011  0.00031 
Background  Background  

Cuts  Parton  PYTHIA/PGS  Parton  PYTHIA/PGS 
Basic cuts  0.35835  0.30423  0.55297  0.39556 
150 GeV GeV  0.00057  0.00049  0.00000  0.00000 
Cumulative  0.00021  0.00015  0.00000  0.00000 
Consider for example the PYTHIAPGS results in the final state, and assume a degenerate neutrino spectrum so that BR(. In this case, for GeV, the cuts reduce the charged Higgs signal cross section in this channel from 32.8 fb to 1.34 fb, while reducing the background from 1570 fb to 3.01 fb and the background from 9500 fb to 2.57 fb. The ratio of signal to background cross sections (S/B) is then 0.24. For GeV, S/B is comparable. These are displayed for all channels for a degenerate neutrino spectrum in Table 14. In all cases S/B is at least 0.22, comfortably larger than the QCD and parton density uncertainties on the and backgrounds; the overall cross sections of these backgrounds can also be normalized experimentally using regions below .
Channel  S/B  Luminosity for 5  

0.24  78 fb  
100 GeV  0.22  88 fb  
0.22  40 fb  
0.25  526 fb  
300 GeV  0.25  540 fb  
0.89  73 fb 
For GeV, the background after cuts depends sensitively on the shape of the background distribution just above . This is controlled by the width and the detector resolution for lepton momenta and missing ; its shape should not suffer from QCD or partondensity uncertainties. For GeV, the shape and normalization of the nonresonant tail of the background is especially important. This background is mostly DrellYan with an additional onshell boson radiated from one of the finalstate leptons; the QCD corrections to such processes are well understood. Given enough statistics, the shape of this background could also be normalized using the region above . Note also that the nonresonant tail of the background is significantly smaller for the final state than for the and final states, leading to a much higher signal purity in this final state for GeV as shown in the last line of Table 14 (for the lower charged Higgs mass this effect is swamped by the resonant contribution).
The integrated luminosity required for a 5 discovery of is displayed in Fig. 3 for GeV and Fig. 4 for GeV, for each channel separately and for all three channels combined. We use the PYTHIAPGS results and compute only the statistical significance. For the normal hierarchy with (300) GeV, we find 5 discovery statistics with a minimum of 9 (56) fb. For the inverted hierarchy, the minimum is 8 (24) fb. For the case of degenerate neutrino masses, 20 (57) fb is needed. For degenerate neutrino masses, the luminosity needed for a 5 discovery in each channel separately is given in Table 14.
Iv Discussion and conclusions
The twoHiggsdoublet model for Dirac neutrino masses studied here provides distinctive leptonic signatures at the LHC due to the characteristic decay pattern of the charged Higgs boson, controlled by the neutrino masses and mixing. We have shown that a simple set of cuts allows discovery of charged Higgs pairs with decays to with relatively modest integrated luminosity. In particular we found that a cut on the kinematic variable provides very effective suppression of pair and backgrounds for charged Higgs masses sufficiently above the mass.
In the inverted neutrino mass hierarchy, the large branching fractions of the charged Higgs to and guarantees a 5 discovery for any allowed neutrino mass and mixing parameter values with only 20 (57) fb for (300) GeV. The discovery potential remains remarkably good at GeV despite the rapidly falling charged Higgs pair production cross section because of the increasing separation of the signal distribution from the background.
In the normal neutrino mass hierarchy, the large uncertainty on the neutrino mixing angle leads to parameter regions in which the charged Higgs decays predominantly to , with a branching fraction to light leptons below 40%, resulting in poor discovery sensitivity in the light lepton channels studied in this paper. Away from these parameter regions, the discovery prospects are only slightly worse than in the inverted hierarchy.
As more stringent experimental limits are placed on the neutrino parameters from neutrino oscillation experiments and direct searches for the kinematic neutrino mass in beta decay, the predictions for the charged Higgs branching ratios in this model will tighten. For example, one goal of the currentlyrunning T2K longbaseline neutrino oscillation experiment in Japan is to improve the measurement accuracy of by an order of magnitude Zito:2008zza (), which would reduce the 2 spread in the charged Higgs branching ratios to and at low lightestneutrino mass from the current 30% to about 10%. Sensitivity to the neutrino mass hierarchy relies on detection of a nonzero , a major goal of T2K and the longerbaseline U.S.based experiment NOA currently under construction NOvATDR (). The ratios of the signal rates in the three channels considered here would allow the normal, inverted, and degenerate neutrino spectra to be differentiated, providing a key test of the connection of the model to the neutrino sector.
Measurement of the charged Higgs branching fractions will also provide some sensitivity to the mass of the lightest neutrino. For a lightest neutrino mass between about 0.01 and 0.1 eV, the charged Higgs branching ratios vary dramatically with the value of the lightest neutrino mass (Fig. 1); once the measurement of from neutrino oscillations has improved, measurement of the ratio of the and modes will provide sensitivity to the lightest neutrino mass in this range. This is nicely complementary to the prospects for direct kinematic neutrino mass determination from the tritium beta decay experiment KATRIN, which is designed to be sensitive down to neutrino masses of about 0.2 eV Valerius:2005aw ()—i.e., at the lower end of the degenerate part of the spectrum—and is scheduled to begin commissioning in 2012 KatrinTalk (). We note that, because the neutrinos in this model are Dirac particles, neutrinoless double beta decay experiments will have no signal and will thus not be sensitive to the neutrino mass scale.
The mass of the charged Higgs is also accessible at the LHC through the signal event kinematics. In particular, the signal distribution is flat up to an endpoint at the charged Higgs mass, as shown in Fig. 2. A fit to this distribution on top of the background should provide a measurement of the charged Higgs mass. This would allow a valuable crosscheck of the charged Higgs pair production cross section together with the visible branching fractions as predicted by the neutrino parameters. The pair production cross section is sensitive to the isospin of the charged Higgs through its coupling to the boson, allowing the twodoublet nature of the model to be established Davidson:2009ha ().
We finally comment on the applicability of our results to two other neutrino mass models that contain a charged Higgs boson. First, the model of Ref. Gabriel:2006ns () contains a charged Higgs with partial widths to leptons and LHC production cross section identical to those in our model. The charged Higgs in the model differs from ours in that it can also decay to , where the neutral scalar is extremely light due to the spontaneous breaking of the symmetry. This competing mode dominates unless is not much heavier than and the neutrino Yukawa couplings are Gabriel:2008es () (this parameter region is forbidden by standard bigbang nucleosynthesis, but the model already requires nonstandard cosmology due to the very light scalar ). For this parameter range, then, our results should carry over directly. For smaller Yukawa couplings or a heavier , the decays to leptons used in our analysis are suppressed, resulting in a smaller signal on top of the same background.
Second, neutrino masses of Majorana type can be generated by the socalled Type II seesaw mechanism type2seesaw (), in which an SU(2)triplet Higgs field with very small vev is coupled to a pair of SM lepton doublets. LHC phenomenology for this Higgstriplet model was studied in Ref. Perez:2008ha (), which considered signatures from and (and the conjugate process) at the LHC. While the decay branching fractions of in this model are identical to those of the charged Higgs in our Higgsdoublet model, the LHC production cross section for in the triplet model is about 2.7 times smaller than for in the doublet model Davidson:2009ha (), due to the different isospin of which modifies its coupling to the boson. The signals studied here would thus have a S/B of less than 10% for most channels, potentially leading to problems with background systematics. For sufficiently high charged Higgs mass, though, the channel would still have a decent S/B (33% for GeV and a degenerate neutrino spectrum); the reduced cross section in the triplet model would however require an integrated luminosity close to 300 fb for discovery. In any case, searches for the doublycharged scalar would yield an earlier discovery of the triplet model.
Acknowledgements.
This work was supported by the Natural Sciences and Engineering Research Council of Canada.References
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