Early LHC bound on W' boson in the nonuniversal gauge interaction model

We study the phenomenology of the heavy charged gauge boson and obtain the lower bounds on its mass with the early LHC data at 7 TeV center-of-mass energy in the nonuniversal gauge interaction model, in which the electroweak SU(2) gauge group depends upon the fermion family. We found that the direct bound on the mass of the $W'$ boson is compatible to the indirect bound with only the early data of the LHC.

The CERN Large Hadron Collider (LHC) has started to operate with the center-of-mass (CM) energy of 7 TeV. The LHC is a discovery machine of the new physics phenomena beyond the standard model (SM) as well as a probe of the structure of the electroweak symmetry breaking. Discovery of a new particle is a clear evidence of the new physics and the LHC pushes ahead on searching for new particles predicted in various models beyond the SM, e. g. supersymmetric particles, exotic Higgs bosons, the Kaluza-Klein states, and extra gauge bosons etc..
Recently the CMS [1] and ATLAS [2] collaborations has reported the search results for the extra charged gauged boson, W ′ , through the leptonic decay channels with the early data of 36 pb −1 collected in 2010 at the LHC. From the absence of the excess above the SM expectations in the transverse mass distribution of a lepton, the mass bound of W ′ boson is obtained to be about 1.4 TeV, assuming the W ′ boson couplings are same as those of the ordinary W boson. The W ′ boson is predicted in many new physics models such as the left-right symmetric model [3], extra dimensional models [4], Little Higgs models [5] and models with extended gauge symmetry [6,7].
We consider an extension of the SM with a separate SU(2) group which acts only on the third generation while the first two generations couple to the usual SU(2) group [6]. The phenomenology of this model has been intensively studied in the literatures, using the electroweak precision test with Z-pole data and the low-energy data [6,[8][9][10]. The gauge group of this model arises as a theory at an intermediate scale in the path of gauge symmetry breaking of noncommuting extended technicolor models [11]. In this model, the SU(2) gauge coupling constants depend upon the fermion family and are nonuniversal in general. The nonuniversality of the gauge couplings leads to the exotic phenomena in the charged currents and neutral currents interactions although they are suppressed by the high energy scale of new physics. In the charged currents interactions, the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is violated explicitly. In the neutral currents interactions, the flavour-changing neutral current (FCNC) interactions arise at tree level. The unitarity violation of the CKM matrix and the lepton flavor violating processes induced by the FCNC strongly constrain the model parameters [12,13].
The W ′ boson exists in our model, since we have an additional SU(2) gauge symmetry of which mass is of order the new physics scale. In this work, we study the W ′ boson with the early LHC data collected at the first run of the LHC. We obtain constraints on the model parameters of the W ′ mass and the mixing angle between two SU(2) groups from the lack of the signal of W ′ boson at the LHC and will show that the direct bound from the early LHC data is compatible to the indirect bound from the unitarity of the CKM matrix.
We introduce an additional bidoublet scalar field Σ, transforming as (2,2,0), to break the SU (2) l × SU (2) h × U (1) Y gauge symmetry into the SU (2) l+h × U (1) Y , of which vacuum expectation values (VEV) is given by The electroweak symmetry breaking arises at the electroweak scale v by the VEV of the (2,1,1) scalar field Φ, which is corresponding to the SM Higgs boson. We require that the scale u is higher than the electroweak scale v and introduce the small parameter λ ≡ v 2 /u 2 . Note that the third generation fermions do not couple to Φ and they should get masses by other way, e.g introducing higher dimensional operators or another Higgs doublet etc.. The different mechanism of mass generation could be the origin of the heavy masses of the third generation. We do not discuss the details of the Higgs sector in this paper. The Higgs sector of this model has been discussed in Ref. [14]. After the symmetry breaking, the gauge coupling constants are parametrized by in terms of the electromagnetic coupling e, the weak mixing angle θ and the new mixing angle φ between SU (2) l and SU (2) h . We demand that all of the gauge couplings are perturbative so that g 2 (l,h) /4π < 1, which results in 0.03 < sin 2 φ < 0.96.
We have additional W ′ and Z ′ gauge boson with masses where m 0 = ev/(2 sin θ) is the ordinary W boson mass in the leading order. We find that the W ′ and Z ′ masses are degenerate in this model. The charged current interactions for W ′ boson is given by where U L = (u L , c L , t L ) T , D L = (d L , s L , b L ) T and the couplings are The tree level decay rates of W ′ boson are obtained by the replacements of the couplings and mass of W boson by those of W ′ in the SM decay rates, given by for the first and second generations and for the third generations, where Γ 0 = Γ(W → e − e + ) in the SM. We ignore the final state masses except for the decay involving top quark, since the W ′ mass is more than 600 GeV in this analysis. The branching ratios of W ′ boson are depicted in Fig. 1. Since the W ′ mass is an overall factor for the decay width except for the decay into top quark, the branching ratios depend only on sin 2 φ. Only the W ′ → tb decay shows a small splitting due to the top quark mass effects, one is for m W ′ = 600 GeV and the other for m W ′ = 2 TeV. Such splittings for other fermions are negligible. We see that decays into the third generations are dominant in the small sin 2 φ region. Since the angle φ represents the mixing between SU (2) l and SU (2) h , W ′ boson is almost W h boson and coupled to the third generations in the small φ limit. The mixing is maximal if sin 2 φ → 1, then W ′ is almost W l and decays dominantly into the first and second generations. We consider the single production of W ′ boson in the pp collisions at the LHC. Using about 36 pb −1 data collected at the LHC in 2010, the CMS and the ATLAS groups have searched for W ′ boson through the transverse mass distributions in W ′ → eν/µν decays and determine the upper limit on the cross section from the absence of the W ′ signal in the early LHC data.
We calculate the production cross sections in terms of m W ′ and sin 2 φ in our model by using PYTHIA 6.4 [15]. Our results are shown in Fig. 2 together with the limit from the LHC data at the 95 % C. L., presented as a thick line. Here we use the bound of the CMS collaboration combining the decays into electron and muon [1]. The region above the thick line is excluded. Comparing the cross sections of our model with the limit from the early LHC data, we determine the bound on the W ′ mass with respect to sin 2 φ. For instance, the lower bound of m W ′ is 1.5 TeV when sin 2 φ = 0.3.
In the previous analysis in Ref. [6,8,9] with the LEP and SLC data, the atomic parity violation (APV), the low-energy neutral currents interaction data, the indirect constraints on the model parameters (sin 2 φ, m W ′ ) has been provided. The constraint from the electroweak precision test with the data at the Z-pole is stronger than those of the low-energy experiments.
More detailed phenomenology on this model has been studied to improve the indirect constraints [12,13]. The nonuniversality of the SU(2) couplings derives modifications on both the charged current and the neutral current interactions. For the quark sector, the charged current couplings are measured by elements of the CKM matrix which is unitary. However in this model, the CKM matrix is no more unitary due to the nonuniversality of the gauge coupling. Moreover, additional charged current interactions via the W ′ boson exist in this model. Thus the observed CKM matrix is the combination of the W boson and W ′ boson exchanges. We define the observed CKM matrix in the low-energy four fermion effective Hamiltonian for the semileptonic quark decay and extract V CKM in this model; where the suppression terms ǫ c = λ sin 2 φ + O(λ 2 ) and ǫ ′c = 1/ sin 2 φ + O(λ). The 3 × 3 matrices V U and V D are unitary matrices which diagonalize up-and down-type quarks, V 0 CKM ≡ V U † V D is the CKM matrix defined in the SM, and M ≡ δ 3i δ 3j are defined to express the nonuniversal terms. We simplify the expression to obtain V CKM = V 0 CKM (1 + λ sin 4 φ). In order to measure the unitarity of the CKM matrix, the unitarity violating term ∆ is defined by |V ud | 2 + |V us | 2 + |V ub | 2 = 1 − ∆, which is measured to be ∆ = 0.0009 ± 0.0010 from the nuclear beta decays, kaon decays and B decays [16]. Since we derive ∆ = 2λ sin 4 φ in our model, we have constraints on the parameter space (sin 2 φ, m Z ′ ), which is the stronger limit than those of the electroweak precision test and the low-energy neutral current data [12].
If the SU(2) couplings depend on the fermion family, the neutral currents are not simultaneously diagonalized with the fermion mass marix and the FCNC interactions generically arise in our model. In the lepton sector, the FCNC interactions lead to dangerous lepton flavour violating (LFV) processes at tree level. The LFV processes have not been observed in the experiments so far and is bounde very strongly. Although the FCNC contain additional unidetermined parameters, we can obtain the conservative constraints on the model parameters which are less sensitive to the assumptions on neutrino masses [13].
Finally, we obtain the direct bounds on W ′ masses on (sin 2 φ, m W ′ ) from Fig. 2 and show them together with all the indirect constraints in Fig. 3. We find that the direct bounds from the early LHC data is compatible to the constraints from the CKM unitarity if sin 2 φ > 0.18. Note that both of the production and decay of W ′ boson in of pp → ud → W ± → lν process becomes small in the small sin 2 φ region and the constraints are very weak.
In conclusion, we obtain the direct bound on the mass of the W ′ boson with the early LHC data in the nonuniversal SU (2) l × SU (2) h × U (1) Y model. Since the LHC have already collected more data from the 2011 run than total data collected in 2010, the direct bound with the LHC data will be improved soon.