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TeV Scale Gauged B-L With Inverse Seesaw Mechanism

We propose a modified version of the TeV scale B-L extension of the standard model, where neutrino masses are generated through the inverse seesaw mechanism. We show that heavy neutrinos associated with this model can be accessible via clean signals at the LHC. The search for the extra gauge boson Z'_{B-L} through the decay into dileptons or two dileptons plus missing energy is studied. We also show that the B-L extra Higgs can be directly probed at the LHC via a clean dilepton and missing energy signal.

The search for new physics at TeV scale is a major goal of the Large Hadron Collider (LHC). Nonvanishing neutrino masses represent a firm observational evidence of new physics beyond the standard model (SM). TeV scale Baryon minus Lepton (B-L) extension of the SM, which is based on the gauge group SU (3) C × SU (2) L × U (1) Y × U (1) B−L , has been recently proposed [1] as the simplest model beyond the SM that provides a viable and testable solution to the neutrino mass mystery of contemporary particle physics. There have been several attempts in the past to extend the gauge symmetry of the SM with U (1) B−L , see for example Ref. [2].
In this model, three SM singlet fermions arise quite naturally due to the anomaly cancellation conditions. These three particles are accounted for right handed neutrinos, and hence a natural explanation for the seesaw mechanism is obtained. In addition, the model also contains an extra gauge boson corresponding to B − L gauge symmetry and an extra SM singlet scalar (heavy Higgs). If the scale of B − L breaking is of order TeV, these new particles will lead to very interesting signatures at the LHC [3][4][5][6]. In general, the scale of B −L symmetry breaking is unknown, ranging from TeV to much higher scales. However, it was proven [7] that in supersymmetric framework, the scale of B-L is nicely correlated with the soft supersymmetry breaking scale, which is TeV. Recently, there has been considerable interest in studying the phenomenological implications of TeV B − L model at colliders [4,6,8].
In TeV scale B − L extension of the SM, the Majorana neutrino Yukawa interaction: λ νR χν c R ν R induces the following masses for the right-handed neutrinos after U (1) B−L symmetry breaking: M νR = λ νR v ′ , where v ′ = χ is the vacuum expectation value (vev) of the B − L symmetry breaking. Below the Electroweak (EW) symmetry breaking, Dirac neutrino masses, m D = λ ν v, are generated. Here v is the vev of the EW symmetry breaking and λ ν are the Dirac neutrino Yukawa couplings. Therefore, the physical light neutrino masses are given by m 2 D /M νR , which can account for the measured experimental results if λ ν < ∼ 10 −6 . Such small couplings may be considered as unnatural fine-tuning. Nevertheless, they induce new interaction terms between the heavy neutrino, weak gauge boson W and Z, and the associated leptons. These couplings play important role in the decay of lightest heavy neutrino at the LHC [5,9]. This signal is one of the striking signatures of TeV scale B − L extension of the SM.
It is very important to note that the above analysis, which led to severe constraints on the neutrino Yukawa couplings, were based on the canonical type-I seesaw mechanism. In this paper, we propose a new modification for our TeV scale B − L model [1], to prohibit type I seesaw and allow another scenario for generating light neutrino masses, namely the inverse seesaw mechanism [10,11]. Our modification is based on the following: (i) The SM singlet Higgs, which breaks the B − L gauge symmetry, has B − L charge = −1. (ii) The SM singlet fermion sector includes two singlet fermions with B − L charges = ±2 with opposite matter parity. In this case, we will show that small neutrino masses can be generated through the inverse seesaw mechanism, without any stringent constraints on the neutrino Yukawa couplings. Therefore, a significant enhancement of the verifiability of TeV scale B − L extension of the SM is obtained. The Lagrangian of the leptonic sector in this model is given by where ing term between the two field strengths is expected. However, in the basis of diagonalizing kinetic terms, , whereg is parameterizing the mixing between the neutral gauge bosons: Z and Z ′ , which is constrained experimentally to be small. Therefore, settingg = 0 is an acceptable approximation. In this case, what is called minimal B − L model is obtained [1,4]. Furthermore, in order to prohibit a possible large mass term M S 1 S 2 in the above Lagrangian, we assume that the SM particles, ν R , χ, and S 2 are even under matter parity, while S 1 is an odd particle. Finally, V (φ, χ) is the most general Higgs potential invariant under these symmetries and can be found in Ref. [1].
The non-vanishing vacuum expectation value (vev) of χ: | χ | = v ′ / √ 2 is assumed to be of order TeV, consistent with the result of radiative B − L symmetry breaking found in gauged B − L model with supersymmetry [7]. The vev of the Higgs field φ: | φ 0 | = v/ √ 2 breaks the EW symmetry, i.e., v = 246 GeV. After the B − L gauge symmetry breaking, the gauge field Z ′ acquires the following mass: GeV. Now, we turn to neutrino masses in this model. As can be seen from Eq.(1), after B − L and EW symmetry breaking, the neutrino Yukawa interaction terms lead to the following mass terms: where From this Lagrangian, one can easily observe that although the lepton number is broken through the spontaneous B − L symmetry breaking, a remnant symmetry: where L is the lepton number and S is the spin. After this global symmetry is broken at much lower scale, a mass term for S 2 (and possibly for S 1 as well) is generated. Therefore, the Lagrangian of neutrino masses, in the flavor basis, is given by: The possibility of generating small µ s radiatively, in general inverse seesaw model, has been discussed in Ref. [12].
In the basis {ν c L , ν R , S 2 }, the 9 × 9 neutrino mass matrix takes the form: The diagonalization of this mass matrix leads to the following light and heavy neutrino masses respectively: Thus, the light neutrino mass can be of order eV, as required by the oscillation data, for a TeV scale M N , provided µ s is sufficiently small, µ s ≪ M N . In this case, the Yukawa coupling λ ν is no longer restricted to a very small value and it can be of order one. Therefore, the possibility of testing this type of model in LHC is quite feasible. In general, the physical neutrino states are given in terms of ν c L , ν R , and S 2 as follows: For m D ≃ 100 GeV, M N ≃ 1 TeV and µ s ≃ 1 KeV, one finds that and α ∼ sin π/4. Therefore, one of the heavy neutrinos of this model can be accessible via a clean signal at LHC, as will be discussed below.
It is worth mentioning that the light neutrinos ν l have suppressed mixing (of order m D µ s /(M 2 N + m 2 D )) with one type of the heavy neutrinos (say ν H ′ ) and a large mixing (of order m D /M N ) with the other type of heavy neutrinos (ν H ). The mixing between the heavy neutrino ν H and ν ′ H is maximal. The heavy neutrinos ν H and ν ′ H can mediate the lepton flavor processes, like µ → eγ. The µ → eγ decay mediated by these heavy neutrinos have branching ratios [13]: where Γ µ is the total decay width of µ and the loop function I(x) can be found in Ref. [13]. From the present experimental limit: BR(µ → eγ) one finds Thus for (a 3 ) µµ ≃ 0.1, one obtains the following constraint on the off-diagonal element (a 3 ) 12 : It is important to notice that within the inverse seesaw mechanism, the branching ratio of l α → l β γ are significantly enhanced compared to the results in the conventional type I seesaw model. The LHC discovery of Z ′ B−L is considered as a smoking gun for TeV scale B − L extension of the SM. In minimal B − L model, it was shown that Z ′ → l + l − gives the dominant decay channel with BR(Z ′ → l + l − ) ≃ 20%. Therefore, the search for Z ′ can be accessible via a dilepton channel for 600 GeV ≤ M Z ′ ≤ 2 TeV. In our new model of B − L with inverse seesaw, the decay widths of Z ′ into lightest heavy neutrinos ν H and ν H ′ are given by: From Eqs. (8,9), the charges Y νH Thus, for heavy Z ′ B−L (M Z ′ B−L ≫ 2M νH ), the decay channel Z ′ B−L → ν H ν H could be the dominant. In Fig.1 we present the decay branching ratios of Z ′ → ff as a function of M Z ′ for f = l − , ν H , ν l , ν H ′ , q = u, c, d, s, b, and f = t. As can be seen from this figure, the decay Z ′ → l + l − is the dominant if M Z ′ B−L < 2M νH . However, for In this case, one considers the Z ′ B−L decay into two heavy neutrinos. This process could enhance the ν H production cross section, due to the resonant contribution from Z ′ B−L exchange in the s-channel. Then, the ν H mainly decays through the W gauge boson to lepton and neutrino, as shown in Fig.2. As explained in Ref. [5], these decays are very clean with four hard lepton, therefore they are distinctive LHC signals with nearly free background. Note that in this model, the coupling of ν H W l is of order 0.05g 2 , which is not very suppressed as in the minimal B −L model. Therefore, the decay width of ν H → W + l − is not very small, and hence ν H is no longer is a longlived particle. This could be a distinguish difference between the two B − L scenarios [15].
After the breakdown of the B−L and EW symmetry, mixing between φ and χ is generated. The mixing between the neutral scalar components of Higgs multiplets, φ 0 and χ 0 , leads to the following mass eigenstates: SM-like Higgs boson H and heavy Higgs boson H ′ : where the mixing angle θ is defined by The masses of H and H ′ are given by (18) From these expressions, it is clear that λ 3 is the measuring of the mixing between the SM Higgs and the B − L extra Higgs.
As in the minimal B − L model [3], the couplings among the SM-like Higgs, H, and the SM fermions and gauge bosons are modified by a factor of cos θ. It is interesting to note that a maximum mixing with θ = π/4 can be obtained if λ 1 v 2 − λ 2 v ′2 = 0, which implies that m H ≃ m H ′ . However, the restriction from precision EW measurements, in particular the fit of the parameters S, T , and U , impose the following constraint on Higgs mixing angle [14]: (19) Therefore, the cross sections of the SM-like Higgs production cross sections and decay branching ratios are slightly changed. Also, the decay widths of H ′ into SM fermions are suppressed by sin 2 θ factor. Due to a large mixing between light and heavy neutrinos in this model, the decay channels and m H ′ > 2m ν H ′ respectively) are relevant and may lead to important effects. The decay widths of these channels are given by where a 2 is the mixing between light and heavy neutrinos as defined in Eq. (7), which is of order 0.04. Thus, for m H ∼ 1 TeV, the decay width Γ(H ′ → ν l ν H ) ∼ 10 −3 . This should be compared with the dominant decay channel: H ′ → W W , which has an order one decay width: (22) The decay branching ratios of H ′ into W + W − , ZZ, ν l ν H , ν H ν H , tt and bb are shown in Fig.3 as function of M H ′ . From this figure, it is clear that the decay of H ′ is dominated by the same channel of the SM-like Higgs. Therefore, these decay channels are experimentally challenged, due to a large background from the SM Higgs decays and can not be considered for probing H ′ at the LHC. Furthermore, the H ′ decay into two heavy neutrinos gives the same signal of two dileptons and missing energy as in Z ′ decay, but with a smaller cross section. Therefore, the H ′ production and decay via H ′ → ν l ν H → l + l − + missing energy, as shown in Fig.4, remains as a distinctive signal at the LHC that is nearly background free.
The total cross section of this process: σ 2l = σ(pp → H ′ → ν l ν H → l − l − + missing energy) can be written as where BR(W + → l + ν l ) ∼ 0.1 and BR(ν H → l − W + ) ∼ O(1), since ν H → l − W + is the dominant decay channel for the heavy neutrino to the SM particles. Finally the cross section σ(pp → H ′ → ν l ν H ) can be approximated as σ(pp → H ′ ) × BR(H ′ → ν l ν H ), where the H ′ production is dominated by gluon-gluon fusion mechanism as shown in Fig.4. In this case, σ(pp → H ′ ) ∼ O(0.01) as emphasized in Ref. [3]. Also from Fig.3, one can notice that BR(H ′ → ν l ν H ) ∼ 10 −3 . Therefore, σ(pp → H ′ → ν l ν H ) ∼ 10 −5 . In this case, the total cross section of the two dilepton signal, which provide indisputable evidence for probing the B − L extra Higgs H ′ , is give by For this value of cross section, the dilepton and missing energy signal can be probed at the LHC as a a clear hint for B − L extra Higgs.
It is worth mentioning that if m H ′ > 2m νR H , then the decay width Γ(H ′ → ν H ν H ) becomes relevant and may be dominant. However, as mentioned above, this process leads to a signals of two dileptons with missing energy similar to the decay of Z ′ → ν H ν H but with a smaller cross section. Therefore, this channel is not the best for probing H ′ at the LHC.
Finally, let us note that the above mentioned two dilptons and missing energy (4l + / E T ) and dilpton plus missing energy (2l + / E T ) final states are mediated by the heavy neutrinos ν H , therefore they are also clean signatures for probing ν H at the LHC.
In conclusion, we have constructed a modified version of minimal TeV scale B−L extension of the SM. In this model, the neutrino masses are generated through the inverse seesaw mechanism therefore, the neutrino Yukawa coupling is no longer constrained to be less than 10 −6 . Thus, the heavy neutrinos associated with this model can be quite feasible at the LHC. We have discussed the main phenomenological features of this class of models. We showed that searching for the Z ′ B−L and heavy neutrinos is accessible via 4l + / E T final state, while searching for the extra Higgs and also heavy neutrino can be accessible through 2l + / E T final state. These final states are very clean signals at LHC, with negligibly small SM background.
Acknowledgments: I would like to thank E. Ma for very useful discussion. This work was partially supported by the Science and Technology Development Fund (STDF) Project ID 437, the ICTP Project ID 30, and the Academy of Scientific Research and Technology.