Abstract
Little Higgs models are an interesting alternative to explain electroweak symmetry breaking without finetuning. Supplemented with a discrete symmetry (Tparity) constraints from electroweak precision data are naturally evaded and also a viable dark matter candidate is obtained. Tparity implies the existence of new (mirror) fermions in addition to the heavy gauge bosons of the little Higgs models. In this paper we consider the effects of the mirror fermions on the phenomenology of the littlest Higgs model with Tparity at the LHC. We study the most promising production channels and decay chains for the new particles. We find that the mirror fermions have a large impact on the magnitude of signal rates and on the new physics signatures. Realistic background estimates are given.
ZHTH 20/06
Phenomenology of Mirror Fermions in the Littlest Higgs Model with TParity
[3.5em] A. Freitas and D. Wyler
Institut für Theoretische Physik, Universität Zürich,
Winterthurerstrasse 190, CH8057 Zürich, Switzerland
1 Introduction
A simple doublet scalar field yields a perfectly appropriate gauge symmetry breaking pattern in the Standard Model (SM). On the other hand, its theoretical shortcomings, such as quadratic divergencies (hierarchy problem) or the triviality of a theory suggest that it is embedded in a larger scheme. On the other hand, electroweak precision data suggests that up to a scale of about 10 TeV, no new strong interaction is present, indicating that indeed some form of a scalar interaction is required, including the possibility that the (Higgs) scalars are composite. A much investigated option to solve the hierarchy problem are supersymmetric theories; but also models with extra dimensions have been considered.
Recently, an alternative known as the little Higgs mechanism [1], has been proposed where the smallness of the electroweak scale is assured by interpreting the Higgs as a (Pseudo) Goldstone particle of a symmetry breakdown at a scale . The new gauge bosons and partners of the top quark with a mass of order cancel the oneloop quadratic corrections to the Higgs mass from Standard Model (SM) particles. A very appealing implementation of the little Higgs concept is the littlest Higgs model [2], which extends the SM by a minimal number of gauge bosons and fermions.
However, even though these new particles are weakly coupled, electroweak precision data requires to be above 5 TeV [3]. On the other hand a scale as low as 1 TeV is required to avoid finetuning of the Higgs mass.
A discrete symmetry, called Tparity [5, 4] circumvents these problems. It forbids all treelevel contributions of the new heavy degrees of freedom to electroweak precision observables. The SM fields are Teven, while the new TeVscale particles are odd. Therefore, the new particles can only be generated in pairs which is reminiscent of Rparity in supersymmetric theories. Besides satisfying the electroweak constraints, Tparity also has the interesting consequence that the lightest Todd particle is stable and, if neutral, a good candidate for cold dark matter.
One of the prime objectives of the next generation of colliders, especially the Large Hadron Collider (LHC), is to unravel the physical mechanism of electroweak symmetry breaking. A first study of the phenomenology of the littlest Higgs model with Tparity (LHT) at the LHC presented in Ref. [6] yielded attractive production rates for the new particles. The collider phenomenology of little Higgs theories with Tparity has some similarities to supersymmetry. In particular, it involves signatures with missing energy originating from the neutral lightest Todd particle (LTP), which escapes detection. On the other hand, little Higgs theories usually do not involve a Todd partner of the gluon, which leads to smaller new physics crosssections at the LHC compared to supersymmetry.
In this paper, the phenomenology of the littlest Higgs model with Tparity is revisited and in particular the important role of the Todd fermions (mirror fermions) is stressed. Backgrounds from SM sources are investigated in order to arrive at realistic estimates for the observability of the new physics signals of the LHT model. After reviewing the LHT model in section 2, the production processes and signatures for various Todd particles are studied in detail in sections 3 and 4. Finally, the conclusions are given in section 5.
2 The model
The littlest Higgs model is based on a coset SU(5)/SO(5), i. e. a global SU(5) symmetry that is explicitly broken down to a SO(5) group, with a subgroup of SO(5) being gauged [2]. The Goldstone modes of the broken SU(5) are implemented in a nonlinear sigma model with a breaking scale . Some of the Goldstone modes only become massive when both gauge subgroups are broken. As a consequence of this simultaneous symmetry breaking oneloop quadratic divergencies to the Higgs mass are naturally avoided and their mass get corrections at most at the twoloop level.
The littlest Higgs model can be supplemented by a discrete called Tparity [5], with SM particles being even (), and nonSM particles odd () under this symmetry. The terms of the nonlinear sigma generate masses of order for the Todd particles. Rather than giving the whole construction of the model we consider, we refer to [6] for a somewhat. detailed description.
The gauge bosons are formed from the gauge bosons of the two SU(2) and U(1) groups, which in the following are indicated by subscripts 1 and 2, respectively:
(Teven)  (1)  
(2)  
with masses from usual electroweak symmetry breaking, and  
(Todd)  (3)  
(4) 
with masses of order generated from the kinetic term of the nonlinear sigma model. After electroweak symmetry breaking, the light gauge bosons mix to form the usual physical states of the SM, , and . Similarly, a small mixing of order is introduced between and through electroweak symmetry breaking. In this work, this mixing and all other terms of order will be consistently neglected. In this case, the masses of the Todd gauge bosons are
(5) 
with . The is always lighter than the other Todd gauge bosons and thus a good candidate for the LTP (lightest Todd particle) and dark matter.
Tparity also requires a doubling of the fermion sector associating to each Teven (SM) fermion a Todd fermion. (mirror fermion). These ’partners’ get masses [7]
(6) 
where the Yukawa couplings can in general depend on the fermion species . The can also generate flavor changing interactions, but this will not be studied in this paper.
The implementation of the mass terms for the mirror fermions also introduces Todd SU(2)singlet fermions, which may receive large masses and do not mix with the SU(2)doublets . Here it is therefore assumed that these extra singlet fermions have large masses and decouple from phenomenology at the LHC.
The top sector requires an additional Teven fermion and one Todd fermion to cancel quadratic divergencies to the Higgs mass. Their masses are
(7) 
The Yukawa couplings are constrained by the top mass , but one has the freedom to choose
(8) 
The decay modes of the Todd gauge bosons and mirror fermions are summarized in Tab. 1 for TeV, degenerate and .
Particle  Mass [GeV]  Width [GeV]  Decay modes  
100%  
100%  
—  —  
50%  
33%  
17%  
50%  
33%  
17%  
1.25  100% 
3 Todd production at LHC
In this section we consider the (pair) production of the various Todd particles at the LHC. Our work completes the previous studies in Ref. [6] and stresses the role of the Todd fermions.
3.1 Heavy gauge bosons
In Ref. [6], the production of heavy Todd gauge bosons was computed including the schannel gauge boson contributions only, Fig. 1 (a–c). It was found that the crosssections can be sizeable, of the order (0.1 pb), for TeV.
However, for perturbative Yukawa couplings
To study this effect of the mirror fermions for heavy gauge boson production, the Feynman rules for the littlest Higgs model with Tparity [8, 6, 9] have been implemented in CompHEP [10]. The package CompHEP was then used to generate numerical results for production crosssections and decay modes of the Todd heavy gauge bosons.
It turns out that the tchannel contributions interfere destructively with the schannel diagrams, as may be expected by unitarity, thus resulting in lower crosssections for gauge boson production, see Fig. 2.
For typical values , the LHC production crosssections are reduced by about one order of magnitude relative to the situation without the tchannel diagrams (). As a consequence, the expected heavy gauge boson crosssections are only several fb for all possible final states , and . The identification of new physics processes of that size at the LHC relies strongly on the presence of leptons in the signature. bosons decay into leptons with a branching ratio of about 20%. Folding in that branching ratio further reduces the signal crosssection. Large backgrounds from SM gauge boson pair production and production make the identification of a signal process with (fb) crosssection practically impossible.
3.2 Mirror quarks
While the mirror quarks effectively lead to a reduction of the Todd gauge boson production at the LHC, the mirror quarks can also be produced directly with large crosssections through gluon exchange, see Fig. 3. In addition, there are also subdominant weak production diagrams.
Due to the strongly interacting production amplitude, the crosssection for mirror quarks is typically larger than for Todd vector bosons, see Fig. 4.
Since for generation and flavorindependent all mirror quarks, except the top partners, have almost degenerate masses, the production crosssections are also independent of the mirror quark flavor.
For sufficiently large masses of the heavy Todd quarks, they decay into Todd vector bosons. This leads to signatures that are similar to supersymmetric theories, where squarks with large production crosssections decay via charginos and neutralinos. However, for a realistic assessment of the discovery potential of the LHC for the Todd quarks, the production rates and relevant SM backgrounds need to be studied in more detail.
In the following the specific scenario with TeV, for all Todd fermion flavors, and will be considered as a concrete example to analyze the discrimination of the mirror fermions signal against SM backgrounds. The relevant Todd particle masses in this scenario are GeV, GeV, GeV for and GeV.
(a)
. Here indicates a (lightflavor) jet, an identified lepton, and stands for missing transverse energy. Since signatures with only hadronic objects in the final state are very challenging to select from the backgrounds, only leptonic decays of the are considered here. The major SM background for the signature comes from production.
Here the signal and background have been calculated with CompHEP, where also offshell effects have been included in the computation of the background. Since the SM background is several orders of magnitude larger than the signal, the signaltobackground ratio needs to be improved with suitable selection cuts. The result is summarized in Tab. 2.
Cut  Signal  Background  S/B 
55 fb  IRdiv.  
GeV,  
GeV,  
,  
23 fb  3.5 pb  
GeV  11 fb  31 fb  0.3 
GeV  8 fb  15 fb  0.5 
Generally, a lower threshold for the transverse energy of the jets needs to be applied. Since the jet originating from the mirror squark decay into is expected to be relatively hard, a rather strong cut of 200 GeV is imposed on the transverse energy of the hardest jet. Furthermore, the jets are required to be in the central region with rapidity and the jets must be separated in solid angle to be identifiable as two individual jets. Due to the large mass of the , which are the stable LTPs in this scenario, the signal is characterized by large missing transverse energy, so that a cut on this variable is very effective to reduce the SM backgrounds. Furthermore, since the boson from the decay is strongly boosted, the final state lepton tends to be relatively hard, so that a cut on the lepton transverse energy is useful.
We have checked that the statistical significance of the signal cannot be improved by varying the values of the cuts in the table. Even after the relatively aggressive cuts in Tab. 2, the signaltobackground ratio is still smaller than one, making a meaningful measurement of the Todd production process difficult, but not impossible. With 30 fb, a statistical significance of nine standard deviations could be achieved, but systematic uncertainties might affect this substantially.
(b)
. With an additional lepton in the final state, this process might be better separable from the SM background than process (a). The main SM backgrounds are , where both top quarks decay leptonically, and , where the two jets originate from initialstate radiation. Note that also for the signal, additional hard jets stemming from initialstate radiation are expected [12].
As before, the signal has been calculated with CompHEP, while the SM background was simulated with MADGRAPH [11]. Again, the SM background is several orders of magnitude larger than the signal, but can be improved with the cuts listed in Tab. 3.
Cut  Signal  Background  S/B  
2.7 fb  
GeV,  
GeV,  
,  
2.2 fb  30 pb  180 fb  
GeV  1.0 fb  88 fb  21 fb  0.01 
GeV  0.7 fb  46 fb  9 fb  0.013 
btag veto  0.5 fb  3.2 fb  7 fb  0.03 
In addition to kinematic cuts, btagging also helps to reduce the background, since only little heavy flavor content is expected in the signal. According to Ref. [13], a btagging efficiency of 90% with an impurity of 25% is assumed. The other selection cuts are similar to the ones used in Tab. 2, with the jet cone size defined as , where is the azimuthal angle between the two jets. It turns out that the signaltobackground ratio remains well below one after application of the selection cuts, and moreover the signal statistics are very low. Therefore this channel does not look promising as a discovery mode for the LHT model at the LHC.
(c)
. Since the boson almost always decays into the (little) Higgs boson , the selection of this signal process needs to make use of the two b jets in the final state. The largest SM background is semileptonic decays.
Again, CompHEP was used to calculate the signal, while the SM background was simulated with MADGRAPH. For the signal selection procedure, it is assumed that the Higgs boson has already been discovered and its mass measured, so that a cut can be applied on the invariant mass of the two bottom jets stemming from the Higgs. This requires a good identification of the b jets among the four or more jets in the event. Thus btagging is mandatory for the signal selection, and it is advantageous to optimize the btagging procedure for a high purity of 98%, at an efficiency of 60% [13]. Applying the cuts in Tab. 4,
Cut  Signal  Background  S/B 
14.0 fb  
GeV,  
GeV,  
,  13.4 fb  128 pb  
GeV  9.8 fb  3.1 pb  
GeV  8.4 fb  1.3 pb  
btag  5.0 fb  770 fb  
5.0 fb  65 fb  0.08 
it is found that the signaltobackground ratio stays well below one after application of the selection cuts, so that this channel is also not suitable for new physics discovery in the LHT model.
(d)
. The final state signature of this process is identical to production. As an example, the semileptonic decay of the top quark pair is considered, leading to the final state .
Signal and background have been computed as above, using btagging with 98% purity and 60% efficiency. The main discrimination to the background is a cut on missing transverse energy, see Tab. 5,
Cut  Signal  Background  S/B 
GeV,  
GeV,  
,  8.2 fb  128 pb  
GeV  1.4 fb  3.2 fb  
btag  0.8 fb  1.9 fb  0.4 
which improves the signaltobackground ratio tremendously. However, the resulting signaltobackground ratio is still below one, and the remaining signal rate is small, so that even without considering systematic uncertainties, only a statistical significance of less than three standard deviations is achievable with 30 fb.
Other decay chains, such as have large SM
background and will not be considered.
Other decay chains, such as have large SM background and will not be considered.
4 Mirror leptons and decay signatures
Mirror leptons, the Todd partners of the leptons, can be produced directly at the LHC through schannel exchange of SM gauge bosons. However, their production crosssections are small, below 1 fb for the scenario with and GeV, i.e. GeV. We therefore do not consider the direct production further.
However, the mirror leptons may play an important role in the decay signatures. If the mirror fermions are not degenerate, but for instance Todd leptons and Todd quarks have different masses, the experimental signatures can be greatly altered. For example for and , the mirror lepton mass is GeV, and the heavy gauge boson can decay into the mirror leptons, . If this decay channel is open, the branching ratio will be almost 100% for all lepton flavors combined. As a consequence, the Todd quarks can decay through cascades like
(9) 
leading to a signal of oppositesign sameflavor leptons and missing transverse energy, similar to the situation in mSUGRA scenarios in supersymmetry [14]. Here one can make use of the fact that the main SM backgrounds produces uncorrelated leptons, with the same proportion of sameflavor (/) and oppositeflavor () leptons. If then the oppositeflavor events are subtracted from the total sample, the SM backgrounds are effectively removed, while the little Higgs signal is not affected [14]. However, the statistical noise from the backgrounds is not reduced by this method and still affects the extraction of the signal process.
For the signal selection of the decay chain eq. (9), the same cuts as listed in Tab. 3 can be used. Since the decay of one mirror quark already leads to two leptons in the final state, no assumption for the decay of the second mirror quark needs to be made, other than that it leads to the LTP in the final state, which generates missing transverse energy in the signature. This improves the signal statistics compared to the analysis in section 3.2 (b). After application of the cuts in Tab. 3, the signal rate for the process eq. (9) is 21 fb, while the SM backgrounds amount to 10 fb. If in addition the differentleptonflavor subtraction described above is used, the remaining backgrounds are negligible, but introduce some statistical noise. Combining the statistical errors, the new physics signal can be identified in this channel with more than 20 standard deviations with 30 fb luminosity.
Furthermore, the dilepton invariant mass distribution shown in Fig. 5 exhibits a distinct upper endpoint at
(10) 
This feature can be used to extract some information about the Todd particle masses. The spectrum edge can be fitted with a simple triangleshaped fit function, see Fig. 5. Assuming 30 fb luminosity, one obtains
(11) 
which is in good agreement with the input value of the underlying model, 488.5 GeV. Due to the relatively small signal crosssection, the statistical error is quite large. It can be improved by using more luminosity. With a total luminosity of 300 fb, the error is reduced to
(12) 
Still, at this level of precision, systematic errors due to the lepton energy scale uncertainty or due to mistagging can be neglected.
Since eq. (10) depends only mildly on for , the measured endpoint gives a rough estimate of the mass difference between the Todd gauge bosons, . In the case of the scenario studied here, GeV, so that this simplified relation holds within statistical errors.
More information about the mass spectrum of the Todd particle could be obtained by studying invariant mass distributions including the jet originating from the mirror quark decay [14]. However, due to additional jet radiation and ambiguities in the selection of the jet, the kinematic endpoints of these distributions are more smeared out. This fact together with the low signal statistics leads to very large errors for fits to kinematic endpoints of jetlepton distributions.
5 Conclusion
In this paper we have considered the production and decay of the Todd heavy particles at LHC in littlest Higgs models with Tparity. This symmetry implies the presence of heavy mirror particles and that the heavy particles can only be pair produced. In the case of heavy gauge bosons, schannel and tchannel production mechanisms interfere destructively. This reduces the production rate substantially to less than about pb and makes this channel almost impossible to observe.
Similarly, the discovery and measurement of Todd mirror quarks at the LHC is very difficult. We have considered all possible decay chains, but most decay channels are lost in the SM background. Only the channel with a production rate of about 10 fb might be promising, but mandates further study. We discuss to some extent the cuts required to reduce the SM background (see table 2). Although the final state signatures are quite similar to the ones for squark production in the MSSM, the signal rates are typically lower in the LHT models than in the MSSM because there is no partner to the gluon. Recall that in supersymmetric models, the partner of the gluon, the gluino, is typically the primary particle for squark production. This yields larger crosssection and additional hard jets in the final state, which help to discriminate from the background. In LHT models however, the gluon is a has no partner. It should be noted, however, that the somewhat pessimistic results of this section strongly depend on the underlying scenario. For example, by lowering the breaking scale , the production crosssection of Todd quarks at the LHC are greatly enhanced. Fig.4 gives a rough picture of the dependence on ; the actual dependence is more complicated because of the intricate energy dependence of the cuts.
Mirror leptons, are only produced through weak processes, but may play a role in the decay signatures of the heavy quarks if they are lighter than the heavy quarks or gauge bosons. Then the leptonic branching ratio of the neutral gauge boson is close to one, with oppositesign sameflavor leptons. As detailed above, this can be used to effectively suppress the SM background; although some nonnegligible statistical noise remains. Moreover, this decay could also yield information about the spectrum of the Todd particles. Clearly detailed experimental studies along these lines will be required for a more conclusive assessment.
Acknowledgments
This work was supported by the Schweizer Nationalfonds.
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