Efi1111
AnlHepPr1128
FermilabPub11189T
plus two jets from a quasiinert Higgs doublet
Abstract
We show that, the result recently reported by the CDF collaboration showing an excess in the invariant mass distribution of jet pairs produced in association with a boson can be explained by a simple extension of the Standard Model (SM) with an additional quasiinert Higgs doublet. The two additional neutral Higgs states and have a mass of about 150 GeV and decay into a pair of jets. pairs are produced from the decay of the heavier charged Higgs boson . Depending on the precise masses of the neutral and charged Higgs bosons, the model is shown to be in agreement with constraints from electroweak precision tests and from flavor physics for a broad range of the Standard Modellike Higgs mass from 100 GeV to several hundreds of GeV. Other possible signals of this model at the Tevatron and the LHC are discussed.
1 Introduction
Recently the CDF collaboration has reported an excess in the dijet invariant mass distribution in events where a boson is produced together with two jets. The boson in this case is required to decay leptonically into electrons or muons. Besides the peak around GeV from diboson production with one hadronically decaying boson, the invariant mass distribution shows an excess in the region GeV GeV. This disagrees with the Standard Model (SM) background at the level and is consistent with a dijet resonance with a mass of GeV [1].
The CDF excess can readily be explained by introducing an additional particle that couples to the first generation of quarks, e.g. using a boson [2, 3, 4, 5, 6, 7, 8, 9]. In this case one has to worry about a potentially large contribution also in the +2jets and +2jets channels, which are only suppressed by electroweak mixing angles and by the branching fraction of the boson into leptons.
Another promising approach is to introduce a second resonance that is produced onshell and decays into a boson and into the dijet resonance. For recent work that implements this and other ideas, see [10, 11, 12, 13, 14, 15, 16, 17]. It is also possible that the excess is due to mismodeling of some of the Standard Model backgrounds, e.g. from single top production [18, 19].
In this paper, we present a simple and renormalizable model that implements the two resonance approach in a compact way. In addition to the Standard Model particle content, just one complex electroweak scalar doublet is introduced. In the next section, we introduce the basic features of the model. In section 3 we discuss constraints from electroweak precision tests and from flavor physics. In section 4 we show that the model can explain the excess reported by CDF, and, in section 5, we discuss possible other signals at the Tevatron and at the LHC. We reserve section 6 for our conclusions and we present an Appendix, in which we analyze the possible consequences of a different mass arrangement for the charged and neutral Higgs bosons of the theory.
2 The model
We consider a simple extension of the Standard Model by including an additional scalar doublet , with the same hypercharge as the SM doublet . Consider the renormalizable scalar potential of and ,
(1)  
where we have assumed that all quartic couplings involving an odd number of or fields are suppressed (see discussion below). All the above parameters are necessarily real except and . We note also that vacuum stability imposes the requirements
(2) 
These conditions are easily fulfilled for the range of parameters relevant to this work.
We assume that and interact with the SM quarks via the Yukawa interaction
(3) 
where denotes the SM quark doublet while and are the SM quark singlets. To avoid experimental constraints from the lepton sector, at this point we choose not to couple to leptons.
We demand that develops a vanishing (or negligible) vacuum expectation value (VEV). In other words is not involved in the electroweak symmetry breaking. The SM gauge symmetry is spontaneously broken by . In order to forbid a VEV for at treelevel it suffices to set the term in the scalar potential to zero. At one loop however, the term will be generated by radiative corrections:
(4) 
where is a cutoff scale that is naturally expected to be around a few TeV. Assuming that the couplings are flavor independent, and of order 0.1, we get a mixing contribution of the order of 1000 GeV. This mixing term would induce a vacuum expectation value of order 10 GeV, leading to too large contributions of to the light quark masses. In order to avoid such a large contribution, a mixing mass smaller than about GeV would be required, what may be obtained in the case of flavor independent couplings by a cancellation between the treelevel and loopinduced contributions, requiring a large fine tuning. It is however possible that only couples to the first generation quarks. In such case, provided that is set to zero at the treelevel by some symmetry, no large fine tuning would be required.
To explicitly forbid the mixing between the two Higgs doublets, we can impose a parity symmetry under which is odd [20, 21], leading also to a justification of the suppression of the quartic couplings with odd powers of the fields in the scalar potential (Eq. (1)). This is similar to what is obtained in RParity violating models, with replaced by a slepton [11]. However, RParity violating models of this type are strongly constrained by the possible generation of neutrino masses (for a recent analysis, see Ref. [22]), a constraint that is not present in the two Higgs doublet model case.
To allow a coupling of to quarks, we further require that the righthanded up quark is odd under this new parity symmetry, while all the other SM fields are even. A consequence of this is that would not couple to the righthanded up quark and therefore the up quark would remain massless at treelevel. Were this parity symmetry preserved, it would lead to a potential solution of the strong CPproblem, which seems to be disfavored by results from chiral perturbation and lattice gauge theory [23, 24, 25] (see, however, Ref. [26]).
In order to generate a value of the up quark mass of about a few MeV, a soft breakdown of the symmetry, via a nonvanishing term of about 10 GeV, would be necessary.
Assuming this approximate symmetry in the Yukawa Lagrangian of Eq. (3), we can write down the Yukawa couplings that we use for our analysis as
(5) 
Note that the index can only take the values since a coupling of the righthanded up quark to is forbidden by the parity symmetry.
We conclude this section with the Higgs spectrum of the theory:
(6)  
(7)  
(8)  
(9) 
The lone Higgs boson of the Standard Model is of course , whereas , , and are the components of the new scalar doublet.
Using these expressions for the masses of the scalar fields, we can rewrite the condition on the vacuum stability (Eq. (2)) as a condition on the parameter
(10) 
Finally, the pole precision measurement sets the limit
(11) 
There are also bounds coming from the direct searches for the neutral Higgs particles at LEP2, which may increase the above limit in Eq. (11) from to values close to 200 GeV. However, the precise bound on the sum of the neutral Higgs boson masses depends strongly on the decay properties of these particles. In this article, we will be interested in masses for these particles that strongly exceed the precision measurement and LEP2 bounds.
3 Electroweak precision constraints and flavor
We perform the analysis of the ElectroWeak Precision Tests (EWPTs) in the ST plane, with the experimental contours taken from [27]. Since, as we will show in the next section, we have to require a rather large mass splitting between the scalars and the charged Higgs to fit the jets CDF excess, we expect a large positive New Physics (NP) contribution to the T parameter. To calculate the NP effects to S and T, we use the general formula valid for 2HDMs [28, 29], under the assumptions of no mixing between the two Higgs doublets and of negligible VEV of the second doublet . In order to generate a signature consistent with observation, we shall fix the mass of one of the scalars to be close to 150 GeV.
In Fig. 1 we present the values of the and parameters for varying values of the SMlike Higgs mass , from 80 GeV to 900 GeV, and different values of the charged and neutral Higgs bosons masses. Dashed ellipses represent the values of the S and T parameters consistent with electroweak precision tests at 68, 95 and 99 confidence level. Fixing a splitting of 150 GeV between the charged Higgs and the neutral Higgs bosons ( GeV, GeV) and assuming degeneracy between scalar and pseudoscalar masses, a very large mass for the SM Higgs boson , GeV, would be required to obtain consistency with electroweak precision tests at the 2 level (see the blue dotted curve in Fig. 1). A good fit, for moderate values of the SM Higgs boson mass may be obtained by lowering the mass of the charged Higgs: for GeV and GeV, a SM Higgs with mass in the range GeV (and with central value 300 GeV) would be required to be in agreement with EWPTs at the level (see the red dotted curve in Fig. 1).
An alternative way of reducing the required SMlike Higgs boson mass is to assume a splitting between the and masses through a nonvanishing value of ^{1}^{1}1Note however that the constraints coming from flavor physics are in general harder to satisfy in this case, as will be discussed in the following.. In Fig. 1, we show our results once we fix GeV, GeV and the charged mass to GeV (solid blue curve) or GeV (solid red curve). As we can observe from the figure, a more moderate value of the Higgs mass is required in order to be in accordance with EWPTs: the best fit is obtained for GeV (with 2 boundary given by GeV) in the case of a 300 GeV charged Higgs boson, and for GeV (with 2 boundary given by GeV) in the case of GeV. Observe that a heavy SMlike Higgs boson with mass up to 400 GeV will be tested at the LHC through its decay into massive gauge bosons within the next two years [30].
Furthermore flavor adds additional constraints on this model. In the mass eigenbasis, the quark Higgs interaction Lagrangian involving the righthanded up quark is
(12) 
Clearly the GIM mechanism is violated strongly and an assumption about the flavor structure of the Yukawa matrix is needed to avoid large NP effects in flavor violating observables. We choose to make the simplifying assumption, . We shall analyze two possible limits for the rotation matrix, and . Under these assumptions the flavor violating Higgs mediated couplings are
(13) 
For the case , the charged Higgs interactions lead to a new source of flavor violation, beyond the SM one. These flavor violating interactions are governed by the couplings , and depending on the value, treelevel flavor violating processes like can put strong constraints on this scenario. The contribution to the mode due to the charged Higgs, as compared to the Standard Model, is naively suppressed by the factor . Additionally, NP contributions to Kaon mixing appear only at the looplevel. The constraints from Kaon physics are satisfied for values of the Yukawa couplings smaller than about 0.1 and charged Higgs masses larger than 250 GeV, as required to describe the 2jets data within this model.
For the case of , the flavor violating coupling of the c and uquarks to leads to a generically large treelevel contribution to the mixing when the scalar and pseudoscalar masses are nondegenerate. In all generality, we can define the coupling . In Fig. 2, we show the constraint on as a function of the mass splitting . The fit is performed using the experimental values given by HFAG [31]. As Fig. 2 suggests, even a few GeV splitting between and requires that . This bound can be read as a bound on the coupling for the scenario with (). We can conclude that for this scenario to be viable we need and to be almost degenerate in mass.
A comparison of these two flavor scenarios suggests that the flavor constraints on the scenario are weaker and a substantial splitting in the Higgs masses is allowed. With sizable splittings between the Higgs masses and , the electroweak precision tests are consistent with a lighter Standard Modellike Higgs, as is shown in Fig. 2. For the scenario, instead, the flavor constraints typically require a small splitting between the and Higgs masses and hence a heavier Standard Modellike Higgs boson is preferred in this case.
4 production and W+jets Excess
The signal process of interest to us is
where the charged lepton comes from the boson decay. This is the dominant source of production since the charged Higgs is produced resonantly. In addition there are tchannel processes that contribute to the total signal rate. Inverting the hierarchy between the neutral and charged Higgs boson, one could also consider the process
This will have essentially a very similar collider signature and comparable effects in flavor and electroweak measurements.
In addition to the desired signal, our model also contributes to the and channels, through the processes
Since these processes are not mediated by onshell resonances, they are suppressed compared to the channel. The treelevel cross sections for these channels at the Tevatron are listed in Tab. 1.
The mass of the scalar is fixed to GeV in order to reproduce the excess in the dijet invariant mass spectrum. We calculate the cross sections for , and at the Tevatron for two values of the charged Higgs mass, GeV and GeV. Larger splittings between the neutral and charged Higgs states are disfavored by EWPTs. The remaining free parameter is the up quark Yukawa coupling , which is chosen such that the required amount of signal events is obtained. As discussed in the previous section, we shall assume that both and are smaller than and hence they have no impact in the particle production at the Tevatron. We shall briefly discuss on the possible effects of a different coupling arrangement in the conclusions of this article.
[GeV],  [GeV]  Br  

300, 0.06  4.45  97.4%  2.04  0.12  0.11 
250, 0.06  0.587  84 %  3.74  0.12  0.11 
The signal is generated using CalcHEP/CompHEP [32, 33] (and checked independently with MadGraph [34]), and then processed through Pythia [35] for parton showering and hadronization and through PGS for a detector simulation, for which the CDF parameter set is used.
We implement the cuts of the CDF analysis: for the leptons, we require GeV and . In addition, a missing energy greater than GeV is required, and the transverse mass of the lepton+ system is required to be larger than GeV. Jets are reconstructed with a cone size and required to have GeV, and . Further the transverse momentum of the dijet system is required to have GeV. Events with more than two jets are rejected, as well as events with an additional lepton with GeV. We also reject events where the lepton is within a cone around either of the two jets.
To correct the jet energy scale, we also simulate the signal from and production. Then we multiply the jet energy by such that the mass of the hadronically decaying boson is reconstructed at GeV. The same scaling is applied to the signal.
The result of the simulation for diboson background only and for signal plus diboson background is shown in Fig. 3. To match the height of the Wboson peak to data we multiply the treelevel cross sections for and production by a Kfactor of 1.4. For GeV, 17% of the events with , pass the cuts, while for GeV this number drops to 8.7%. A good fit to the dijet invariant mass spectrum is found using 300 signal events, corresponding to a coupling for both GeV and GeV.
In Ref. [10] a different set of cuts was suggested for the CDF analysis that may improve the signal to background ratio by a factor of two. In particular, to be more sensitive to the +resonance structure of the event, they suggest a cut on the sum of lepton and missing transverse momentum, GeV, and require the angular separation between the jets to be . For our model with GeV, these cuts reduce the signal by 32%. Comparing with the results of Ref. [10] we expect a similar increase of the signal to background ratio in our case.
Let us finally comment on the effects of splitting the masses of the neutral Higgs bosons and . Small mass differences have only a minor influence on the signal rate. For large mass differences, 50 GeV, as required for a significant improvement of the fit to precision electroweak data for moderate values of the SM Higgs boson mass, the dominant signal rate is associated with the lightest of these Higgs bosons, while the other one leads to a small or no signal contribution. This is, for instance, the case for the values GeV, GeV, and GeV, used in Fig. 1. Although the charged Higgs may decay to onshell and bosons, the phase space suppression is strong enough to lead to only a very minor increase of the signal in the GeV region. This region can however be populated if also the mass of the charged Higgs is increased (see Appendix).
5 Prospects at Tevatron and LHC
At hadron colliders, the GeV dijet resonance can be produced also in association with a boson or with a photon. In our model, the main production of the signal is through resonant charged Higgs production. Hence, the and signals at the Tevatron, which are only produced in the tchannel, are suppressed by more than an order of magnitude with respect to the 2jets one (c.f. Tab. 1). Assuming a similar signal acceptance, and taking into account the small branching fraction of the boson to lepton pairs, we do not expect the Tevatron to see any relevant excess in the channel [36].
In the photon plus dijet channel at the Tevatron, we expect up to 40 events for a photon with GeV. This channel is dominated by QCD dijet production with an additional photon. A search in this channel has been performed with very mild cuts on the jet energies [37], and our model is consistent with these observations. A more refined analysis with optimized cuts could provide important constraints on this and other models for the +jets CDF excess.
At the LHC, it is possible to search for all of the above signals. In addition, the larger center of mass energy allows for sizable production cross sections also for , and for pair production of scalars. The cross sections at the LHC with TeV are given in Tab. 2.
[GeV],  

300, 0.06  7.72  0.35  0.31  0.026  0.011  0.0010 
250, 0.06  13.7  0.35  0.31  0.034  0.016  0.0023 
One promising signal comes from DrellYan production of pairs, that gives rise to +4jets signals. The main background for this process is production with additional jets. This background can be reduced by explicitly asking for four hard jets, and demanding that the invariant mass of pairs of jets is close to the mass of the resonance. In addition, a veto on b tagged jets may be useful to discriminate between the signal and background.
6 Conclusions
We have presented a simple renormalizable model that can explain the CDF excess in +2jets that was recently observed by the CDF collaboration. Our model is in agreement with all constraints coming from electroweak precision measurements, and depending on the precise values of the new charged and neutral Higgs boson masses, allows a broad range of the Standard Model Higgs mass from 100 GeV to several hundreds of GeV.
The model predicts no significant signal in the +2jets and in the channel, in agreement with current experimental constraints on these channels. At the LHC, the model can be searched for in dijets produced in association with an electroweak gauge boson. In addition, we also expect a sizable production cross section for +jets and +jets at the LHC. These signals might be easier to separate from the notoriously large QCD background.
Given the steadily growing number of models that attempt to explain the CDF excess, it might be worth considering possibilities to discriminate between different models. In principle angular observables should be suitable for this task, since angular distributions typically depend on the spin of intermediate resonances and on the production mode.
More concretely, we expect tchannel models to give a different spectrum (softer and more forward) than in the schannel production considered in this work. Moreover, no resonant feature on the total invariant mass of the system is expected in those models. Considering there is only one leptonic , we can fully reconstruct the event and study the spin of various resonances. In our particular case, the spin of may be studied using the angular distribution in the rest frame of . As stressed before, the relative ratio of rate to the (or + jj) is a very good diagnostic that may distinguish different models.
We finally want to mention that, had we assumed to be the most significant coupling, a relevant signal could still be obtained for large values of this coupling, , via the and channels. We studied this possibility and found that the rate in the former channel is a factor four larger than the latter and therefore the signal characteristics are very similar to the one studied in this article. Similarly to what happens in the model of Ref. [13], such a coupling arrangement leads also to an increase of the topquark forwardbackward asymmetry, but is subject to constraints coming from flavor physics and topquark decays [38]. Further discussion on these possibilities will be studied elsewhere.
Acknowledgements
We thank W. Altmannshofer and R. Culbertson for useful discussions. Work at ANL is supported in part by the U.S. Department of Energy (DOE), Div. of HEP, Contract DEAC0206CH11357. Fermilab is operated by the Fermi Research Alliance, LLC under Contract No DEAC0207CH11359 with the U.S. Department of Energy. P.S. is partially supported by the UIC DOE HEP Contract DEFG0284ER40173. L.T.W. is supported by the DOE Early Career Award under grant DESC0003930. A.M. is supported by the U.S. Department of Energy under Contract No. DEFG0294ER40840.
Appendix
The mass spectrum of the model is strongly constrained by precision constraints. Mass splittings between the scalars larger than the ones considered above are very hard to bring in agreement with these constraints. However, one could also view this model as an effective theory valid up to around the TeV scale, where additional new physics is expected to solve the hierarchy problem. In this case, additional new physics contributions to the electroweak S and T parameters will in general be present. These may partially compensate the contributions from the Higgs doublet, thus making larger mass splittings phenomenologically viable.
Although the data in the invariant mass bins between 180 GeV and 240 GeV lie systematically above the expected background, this excess is not statistically significant, and in addition, is subject to possibly large NLO uncertainties [39]. Consequently, no preference for a model leading to such an excess can be claimed, on the other hand, the data is not in conflict with this possibility. As an example of such a model, in Fig. 4 we show the dijet invariant mass distribution for GeV, GeV and GeV. In this case our model fits well the data up to invariant masses of GeV, while only a small increase of the coupling is required.
References
 [1] T. Aaltonen et al. [ CDF Collaboration ], [arXiv:1104.0699 [hepex]].
 [2] M. R. Buckley, D. Hooper, J. Kopp, E. Neil, [arXiv:1103.6035 [hepph]].
 [3] F. Yu, [arXiv:1104.0243 [hepph]].
 [4] K. Cheung, J. Song, [arXiv:1104.1375 [hepph]].
 [5] L. A. Anchordoqui, H. Goldberg, X. Huang, D. Lust, T. R. Taylor, [arXiv:1104.2302 [hepph]].
 [6] M. Buckley, P. Fileviez Perez, D. Hooper and E. Neil, arXiv:1104.3145 [hepph].
 [7] P. Ko, Y. Omura and C. Yu, arXiv:1104.4066 [hepph].
 [8] P. J. Fox, J. Liu, D. TuckerSmith and N. Weiner, arXiv:1104.4127 [hepph].
 [9] D. W. Jung, P. Ko and J. S. Lee, arXiv:1104.4443 [hepph].
 [10] E. J. Eichten, K. Lane and A. Martin, arXiv:1104.0976 [hepph].
 [11] C. Kilic, S. Thomas, [arXiv:1104.1002 [hepph]].
 [12] X. P. Wang, Y. K. Wang, B. Xiao, J. Xu and S. h. Zhu, arXiv:1104.1161 [hepph].
 [13] A. E. Nelson, T. Okui and T. S. Roy, arXiv:1104.2030 [hepph].
 [14] R. Sato, S. Shirai and K. Yonekura, arXiv:1104.2014 [hepph].
 [15] X. P. Wang, Y. K. Wang, B. Xiao, J. Xu and S. h. Zhu, arXiv:1104.1917 [hepph].
 [16] X. G. He and B. Q. Ma, arXiv:1104.1894 [hepph].
 [17] B. A. Dobrescu and G. Z. Krnjaic, arXiv:1104.2893 [hepph].
 [18] Z. Sullivan and A. Menon, arXiv:1104.3790 [hepph].
 [19] T. Plehn and M. Takeuchi, arXiv:1104.4087 [hepph].
 [20] E. Ma, Phys. Rev. D 73, 077301 (2006).
 [21] L. Lopez Honorez, E. Nezri, J. F. Oliver, M. H. G. Tytgat, JCAP 0702, 028 (2007).
 [22] H. K. Dreiner, M. Hanussek, S. Grab, Phys. Rev. D82, 055027 (2010).
 [23] H. Leutwyler, Nucl. Phys. B 337, 108 (1990).
 [24] C. Aubin et al. [MILC Collaboration], Phys. Rev. D 70, 114501 (2004).
 [25] K. Nakamura et al. [Particle Data Group], J. Phys. G 37, 075021 (2010).
 [26] H. Davoudiasl and A. Soni, Phys. Rev. D 76, 095015 (2007).

[27]
http://gfitter.desy.de/Figures/GOblique/S_vs_T_logo_full.gif
 [28] P. H. Chankowski, M. Krawczyk and J. Zochowski, Eur. Phys. J. C 11, 661 (1999).
 [29] P. H. Chankowski, T. Farris, B. Grzadkowski, J. F. Gunion, J. Kalinowski and M. Krawczyk, Phys. Lett. B 496, 195 (2000).

[30]
ttps://twiki.cern.c
/twiki/bin/view/CMSPublic/PhysicsResultsHIGStandardModelProjections 
[31]
ttp://www.slac.stanford.edu/xorg/
fag/charm/CHARM10/results_mix+cpv.html  [32] A. Pukhov, [hepph/0412191].
 [33] E. Boos et al. [CompHEP Collaboration], Nucl. Instrum. Meth. A 534, 250 (2004).
 [34] J. Alwall, P. Demin, S. de Visscher, R. Frederix, M. Herquet, F. Maltoni, T. Plehn, D. L. Rainwater et al., JHEP 0709, 028 (2007).
 [35] T. Sjostrand, S. Mrenna, P. Z. Skands, JHEP 0605, 026 (2006).
 [36] See e.g. p. 24 of http://theory.fnal.gov/jetp/talks/Viviana.pdf
 [37] CDF Collaboration, CDF Conference Note 10355 (2010).
 [38] G. Zhu, arXiv:1104.3227 [hepph].
 [39] See e.g. p. 33 of http://theory.fnal.gov/jetp/talks/Viviana.pdf