The $eejj$ Excess Signal at the LHC and Constraints on Leptogenesis

We review the non-supersymmetric (Extended) Left-Right Symmetric Models (LRSM) and low energy $E_6$-based models to investigate if they can explain both the recently detected excess $eejj$ signal at CMS and leptogenesis. The $eejj$ excess can be explained from the decay of the right-handed gauge bosons ($W_R$) with mass $\sim \rm{TeV}$ in certain variants of the LRSM (with $g_{L}\neq g_{R}$). However such scenarios can not accommodate high-scale leptogenesis. Other attempts have been made to explain leptogenesis while keeping the $W_{R}$ mass almost within the reach of the LHC by considering the resonant leptogenesis scenario in the context of the LRSM for relatively large Yukawa couplings. However this may not be feasible due to washout of the lepton asymmetry by certain processes. Therefore we consider three effective low energy subgroups of the superstring inspired $E_{6}$ model having a number of additional exotic fermions which provides a rich phenomenology to be explored. We however find that these three effective low energy subgroups of $E_6$ too cannot explain both the $eejj$ excess signal and leptogenesis simultaneously.

We review the non-supersymmetric (Extended) Left-Right Symmetric Models (LRSM) and low energy E6-based models to investigate if they can explain both the recently detected excess eejj signal at CMS and leptogenesis. The eejj excess can be explained from the decay of the right-handed gauge bosons (WR) with mass ∼ TeV in certain variants of the LRSM (with gL = gR). However such scenarios can not accommodate high-scale leptogenesis. Other attempts have been made to explain leptogenesis while keeping the WR mass almost within the reach of the LHC by considering the resonant leptogenesis scenario in the context of the LRSM for relatively large Yukawa couplings. However this may not be feasible due to washout of the lepton asymmetry by certain processes. Therefore we consider three effective low energy subgroups of the superstring inspired E6 model having a number of additional exotic fermions which provides a rich phenomenology to be explored. We however find that these three effective low energy subgroups of E6 too cannot explain both the eejj excess signal and leptogenesis simultaneously.

I. INTRODUCTION
One of the most popular extensions of the Standard Model (SM) of particle physics is the Left-Right Symmetric Model (LRSM) [1]. The weak interactions of the LRSM are governed by the gauge group SU (2) L × SU (2) R × U (1) B−L where B − L is the difference between baryon and lepton numbers. In such a model, the right-handed gauge bosons (W R ) decay in a manner very similar to their left-handed counterparts except that the left-handed neutrino (ν L ) gets replaced by its right-handed counterpart N R . Now N R may be a Dirac particle, decaying to a "proper-sign" lepton or a Majorana particle which can decay to either sign lepton. It can further decay via a virtual W R emission or via mixing with ν L giving a two lepton two jet signal.
The CMS Collaboration at the LHC at CERN has announced their results for the W R search at a center of mass energy of √ s = 8 TeV and 19.7fb −1 of integrated luminosity. Using the cuts p T > 60 GeV, |η| < 2.5(p T > 40 GeV, |η| < 2.5) for the leading (subleading) electron and selecting events with m ee > 200 GeV a total of 14 events were observed in the energy bin 1.8 TeV < M eejj < 2.2 TeV compared to 4 events expected from the SM background giving a 2.8σ local excess in the pp → ee+2j channel [2]. The excess of eejj events has been explained to be due to W R decay by embedding the LRSM in a class of SO(10) model in Ref. [3] and by considering general flavour mixing in the LRSM in Ref. [4]. Additional tests to study right-handed currents at LHC are proposed in Ref. [5].
However confirmation of these excess events for the given range of the W R mass has severe implications for * Electronic address: mansi@prl.res.in † Electronic address: chandan@prl.res.in ‡ Electronic address: raghavan@prl.res.in § Electronic address: utpal@prl.res.in the leptogenesis mechanism [6], which offers a very attractive possibility to explain the baryon asymmetry of the universe. The seesaw mechanism [7] which provides a natural solution to the smallness of neutrino masses, offers a mechanism for generating a lepton asymmetry (and hence a B − L asymmetry) before the electroweak phase transition, which then gets converted to the baryon asymmetry of the universe via B + L violating anomalous processes in equilibrium [6,8]. The lepton asymmetry can be generated in two possible ways. One way is via the decay of right-handed Majorana neutrinos (N ) which does not conserve lepton number [6]; another way is via the decay of very heavy Higgs triplet scalars with lepton number violating interactions [9]. In the conventional LRSM, the right-handed neutrinos interact with the SU (2) R gauge bosons. By taking into account the effect of the scattering processes involving such interactions of W R on the primordial lepton asymmetry of the universe, phenomenologically successful high-scale leptogenesis requires M W R to be very heavy for both the cases M N > M W R and M W R > M N [10]. Thus, an observed 1.8 TeV < M W R < 2.2 TeV implies that the decay of right-handed neutrinos can not generate the required lepton asymmetry of the universe. Furthermore, since the W R interactions erase any primordial B − L asymmetry, the observed baryon asymmetry of the universe must be generated at a scale lower than the SU (2) R breaking scale. Attempts have been made to explain the required amount of lepton asymmetry in the context of resonant leptogenesis [11] while pushing the mass of W R to as low as 3 TeV for relatively large Yukawa couplings [12,13]. However in Ref. [14] we have found that the presence of certain lepton number violating processes involving the doubly charged right-handed Higgs triplet in the LRSM which stay in equilibrium close to the electroweak phase transition for M W R in the range of a few TeV will result in washing out of any lepton asymmetry created above the electroweak phase transition. Thus, the W R mass is required to be quite high compared to the CMS signal range to have a successful resonant leptogenesis scenario. Similar arguments hold true even for the extended LRSM models which can be formed by extending the gauge group of the LRSM with additional U (1)'s. Therefore we have considered generalized non-supersymmetric LRSM variants motivated by the low-energy subgroups of superstring inspired E 6 theories. These models are particularly interesting because in addition to having a gauge structure similar to the conventional LRSM, they also have a number of additional exotic fermions, thus providing a rich phenomenology to be explored. To this end, we examine these models to explore if the CMS excess signal can be explained while simultaneously allowing high-scale leptogenesis to generate the observed baryon asymmetry of the universe. The outline of the article is as follows. In section II, we first discuss the particle content and B −L breaking scale of the Left-Right Symmetric Model. Then we argue that the B − L breaking scale will be lower than the SU (2) R breaking scale even in the extended LRSM. We then discuss how the CMS signal (if it is indeed due to W R decay) rules out the possibility of high-scale leptogenesis and also mention certain lepton number violating processes involving the doubly charged right-handed Higgs triplet in (Extended) LRSM which stay in equilibrium close to the electroweak phase transition. These can rule out the possibility of TeV-scale resonant leptogenesis with the W R mass in the few TeV range. In section III, we first discuss the phenomenology of low energy subgroups of E 6 group. Then we show that though one of the subgroups allows high-scale leptogenesis, there does not exist any effective low energy subgroups of E 6 which can explain both the CMS eejj excess as well as leptogenesis 1 . In section IV, we conclude with our results.

II. (EXTENDED) LEFT RIGHT SYMMETRIC MODEL (LRSM) AND CONSTRAINTS FROM LEPTOGENESIS
In the LRSM the leptons and the quarks transform under the gauge group SU The Higgs sector of the LRSM consists of one bi-doublet Φ and two triplet ∆ L,R complex scalar fields with the The left-right symmetry can be spontaneously broken to reproduce the Standard Model and the smallness of the neutrino masses can be taken care of by the see-saw mechanism. The symmetry breaking mechanism follows the scheme Being aware of the above we now turn the table around and ask the question that if the CMS signal is indeed due to the decay of W R corresponding to SU (2) R breaking then can we conclusively say that (one of) the U (1)(s) in the left-right symmetric scheme (and its U (1) extensions) is necessarily U (1) B−L . If so then the next question is at what scale does it get broken. We start with an arbitrary U (1) (where we do not identify the U (1) charge with B − L) in the LRSM gauge group and then generalize the scheme to include more than one U (1). Consider the scheme SU (2) L × SU (2) R × U (1) X , where the charge of the quark doublet under U (1) is assumed to be X Q and that of the lepton pair is assumed to be X l . Under U (1) X the fields transform as Now we consider a scenario where in the first stage the right-handed triplet ∆ R acquires a Vacuum Expectation Value (VEV) which breaks the SU (2) R symmetry to give the righthanded neutrino a Majorana mass and to produce massive W ± R , Z R bosons. The next stage involves breaking the electroweak symmetry at some lower energy where the bi-doublet Higgs and left-handed Higgs triplet get VEVs giving mass to W ± L and Z L gauge bosons 2 . It turns out that in such a scheme X can only be B − L and the combination τ 3 L + τ 3 R + 1 2 1 B−L is the only unbroken generator satisfying the modified Gell-Mann-Nishijima formula The B − L symmetry can be violated either simultaneously or at a scale below the SU (2) R breaking scale.
Next we consider the Extended LRSM such as Then also we can argue that the B − L breaking scale is lower than or equal to the SU (2) R breaking scale. The argument goes as follows. We perform an SO(2) rotation on the gauge fields (A X , A Z ) and choose a new basis U (1) X × U (1) Z such that the charge of Φ for one of the two groups, say U (1) X , is zero. At this point we identify U (1) X with B − L. So the transformations of the Higgs fields are given by So this reduces to the standard LRSM scenario if the additional U (1) Z breaks at a scale higher than the SU (2) R breaking scale. This chain of arguments continue for any arbitrary number of U (1) extensions of the LRSM. Thus, B −L gets broken either simultaneously with the SU (2) R or else at a scale lower than the SU (2) R breaking scale in the LRSM or any extension of the LRSM with arbitrary numbers of U (1)'s.
The most stringent constraints on the W R mass for successful high-scale leptogenesis come from the SU (2) R interactions [10]. To have successful leptogenesis in the case M N > M W R the condition that the process goes out of equilibrium translates into the condition with m W R /m N 0.1. Now for the case M W R > M N leptogenesis can happen either at T M N or at T > M W R but at less than B − L breaking scale. For T M N , the condition that the scattering processes that maintain the equilibrium number density for N R go out of equilibrium reduces to For leptogenesis at T > M W R the most relevant scattering process is through N R exchange and the condition for this process to go out of equilibrium gives Thus it follows that if the CMS excess is indeed a W R signal with the mass of the W R in the range 1.8 TeV < M W R < 2.2 TeV then for hierarchical neutrino masses it is not possible to generate the required baryon asymmetry of the universe from high-scale leptogenesis.
The possibility of generating the required lepton asymmetry with a considerably low value of the W R mass has been discussed in the context of the resonant leptogenesis scenario [11]. It has also been pointed out that successful low-scale leptogenesis with a quasi-degenerate right-handed neutrinos mass spectrum requires an absolute lower bound of 18 TeV on the W R mass [12]. Recently it was shown that just the right amount of lepton asymmetry can be produced even for a substantially low value of the W R mass (M W R > 3 TeV) [13] by considering relatively large Yukawa couplings. However there are certain lepton number violating processes which are ignored in the aforementioned analysis. In particular, below the left-right symmetry breaking scale, the lepton number violating scattering processes e ± R W ∓ R → e ∓ R W ± R and e ± R e ± R → W ± R W ± R mediated via doubly charged righthanded Higgs triplet scalars will be very rapid in washing out the lepton asymmetry till the temperature drops below the mass of W R . At a temperature below the W R mass scale the latter process becomes doubly phase space suppressed. However, in spite of being singly Boltzmann suppressed, the former process stays in equilibrium till a temperature near the electroweak phase transition temperature for W R mass in the TeV range and continues to wash out lepton asymmetry [14]. Then the lower limit on M W R for successful resonant leptogenesis will go up beyond the CMS excess range.
Below we consider extensions of the Standard Model motivated by the superstring inspired E 6 model to explore if the CMS excess signals can be compatible with high-scale leptogenesis.

III. E6-SUBGROUPS INVOLVING HEAVY RIGHT-HANDED GAUGE BOSONS
In this section we explore three effective low energy subgroups of the superstring inspired E 6 model which involve additional exotic fermions leading to a rich gauge boson phenomenology. We have already discussed the possibility of producing both the eejj and e / p T jj signals and having sucessful high-scale leptogenesis in the context of low energy subgroups of E 6 in Ref. [15] by involving supersymmetric particles. In this letter we assume that supersymmetry gets broken at a very high scale and that supersymmetric partners do not play any role in the following analysis.
Under one of the maximal subgroups of E 6 given by SU where (u, d, h) : (3, 3, 1) and (h c , d c , u c ) : (3 * , 1, 3 * ) and (1, 3 * , 3) corresponds to the leptons. The exotic quark h carries a charge − 1 3 . The other exotic particles are the charge conjugate of h, a right-handed neutrino N c , two lepton isodoublets (ν E , E), (E c , N c E ) and n. The assignment of the first family is given by where SU ( The SU (2) R doublet is (d c , u c ) as in the LRSM and , : (1, 2, 2, 0), n L : (1, 1, 1, 0). (15) If ν e combines with N c to form the Dirac neutrino then the mass of the W ± R gets constrained from polarized µ + decay [16]. There will also be a charged current mixing matrix for the quarks in the right-handed sector. Using a form similar to the Kobayashi-Maskawa matrix the K L − K S mass difference can constrain the W ± R mass [17][18][19]. In Ref. [20] it was pointed out that a calculation of the mixing matrix for the right-handed quark sector shows that the difference between left and right mixing angles is very small. Kaon decay and neutron electric dipole moment can also give further constraints on the W R mass [19,21]. We have already discussed some of the phenomenological details of the W R decay in connection with the LRSM. Those hold good for this scenario, however one can have more complicated decay modes of W R in the presence of the new exotic fermions.
With the assignment given in Eq. (15), among the five neutral fermions only ν e and N c carry nonzero B − L. Thus the only source of B − L violation is the Majorana mass of N c which also ensures the small neutrino masses. In order to have successful leptogenesis the decay rate of the Majorana neutrino N must satisfy the out-of-equilibrium condition, namely, This translates into the condition that the Majorana mass of N R must be many orders of magnitude greater than the TeV scale. On the other hand, the quantum number assignments of N c as given in Eq. (15)  Another choice for the SU (2) (R) doublet is (h c , u c ), first pointed out in Ref. [22]. The relevant charge equation is given by  1, 1, 0), (18) and Y = Y L + Y R . Here also ν e can pair off with N c to form a Dirac neutrino, but now N c has a trivial transformation under SU (2) R thus allowing high-scale leptogenesis. Two different assignments for N c are possible determining whether ν e is massless or massive. For the case where N c has the assignments B = 0, L = 0 an exactly massless ν e is possible, while in the other case N c is assigned B = 0, L = −1 leading to a tiny mass of ν e via the seesaw mechanism. In this scenario, e is coupled to n via the right-handed charged current, but n being presumably much heavier than the electron, polarized µ + decay cannot constrain the mass of W ± R in contrast to Case 1. Furthermore W ± R does not couple to d and s quarks. Consequently, there is no constraint on the mass of W ± R from the K L − K S mass difference in this case. So this model can allow a much lighter W ± R as compared to Case 1. However in this model D 0 −D 0 mixing can be induced through the W R coupling of the c and u quarks to the exotic leptoquark h [23]. The relevant box diagrams are shown in Fig. 1. The amplitude of this mixing induced by these exotic box diagrams can give constraint on the SU (2) R breaking scale in this model.
So the W R is coupled to h c L and n field, in contrast to the coupling with the d c L and N c in the conventional LRSM. The quantum numbers of W R imply that the usual ud scattering in hadronic colliders can not produce W R . Furthermore 2M W R > M Z forbids the pair production of W R via the decay of the heavy Z . The process which can yield a large cross section for W R production is the associated production of W R and leptoquark h via the process g + u → h + W + R [24]. The relevant diagrams are shown in Fig. 2. The decay modes of the W R can be obtained by using Eq. (19).
To keep our discussion fairly general and model independent we only consider the decay modes (of the new exotic particles) mediated by light and heavy gauge bosons (and ignore the decay modes involving Higgs couplings). Examining all the further decay channels of the exotic particles coming from the decay modes of W R listed above immediately shows that the W R decay can not give rise to the ee + 2j signal in contrast to Case 1. Thus, this scenario has an appealing feature of allowing high-scale leptogenesis. However, a two electron and two jet signal can not be produced from W R decay.

C. Case 3.
A third way of selecting the SU (2) (R) doublet is (h c , d c ) [25] and the relevant charge equation is given by Similar to case 2, in this scenario also W N has nonzero leptonic charge and zero baryonic charge. Note that in this case W N and Z N can induce K 0 −K 0 mixing. Mixing between six quarks (three generations) forming SU (2) N doublets can lead to the tree level Flavor Changing Neutral Current (FCNC) processes shown in Fig. 3 and in such a scenario one can get constraints on the W N mass from the K L − K S mass difference [25]. In the absence of mixing ofd ands with exotich i , one can still have a tree level contribution to the kaon mixing. If opposite T 3N quantum numbers are assigned tod L ands L and if they mix then the diagrams shown in Fig. 3 are still possible [25]. On the other hand if only the exotich i mix and we assign same T 3N tod L ands L then the box diagrams shown in Fig. 4 result [25]. Likewise in the leptonic sector considering SU (2) N doublets even if mixing between the ordinary and exotic fermions is absent, the process µ → eγ can be possible if mixing between the exotic fermions is present [25] as shown in Fig. 5. The coupling of the W N to the fermions reads Following similar arguments as in Case 2, one can not produce W N via the usual Drell-Yan mechanism or from the decay of heavy Z N . The process g + d → h + W N can yield a large cross section for W N production via the diagrams shown in Fig. 6 [26]. Pair production of W N can take place via the process e + e − → W + N W − N [26]. The relevant diagrams are shown in Fig. 7. This process is particularly sensitive to the underlying gauge structure and cancellations between the given amplitudes. Thus it can serve as a probe for the non-abelian SU (2) N gauge theory. The decay modes of the W N can be obtained from Eq. (24) as Like in Case 2, an inspection of all the further decays of the exotic particles for the decay modes of W N listed above tells us that an ee + 2j signal can not be obtained from the decay of W N . Moreover from the assignments of Eq. (21) it follows that N c transforms as a doublet under SU (2) N and hence for low-energy SU (2) N breaking, following the same logic as in Case 1, the possibility of successful leptogenesis is ruled out.

IV. CONCLUSIONS
We have reviewed the non-supersymmetric versions of the (Extended) Left-Right Symmetric Model and the models appearing as the low-energy subgroups of the superstring motivated E 6 group which can have low-scale SU (2) (R) breaking. Our aim was to examine if a signal like the CMS eejj excess can be explained from these models while allowing leptogenesis.
In the LRSM and any extension of it with multiple U(1)'s, for hierarchical neutrino masses (M N 3R M N 2R M N 1R = m N ) the possibility of generating the required baryon asymmetry of the universe from highscale leptogenesis is ruled out if the W R mass lies in the TeV range as indicated by the CMS events. Recently, it was shown that the required lepton asymmetry can be produced even for a substantially low value of the W R mass (M W R > 3 TeV) [13] by considering relatively large Yukawa couplings in the context of resonant leptogenesis. However we have mentioned that certain lepton-number violating scattering processes involv-ing the doubly charged Higgs triplet can wash out the lepton asymmetry below the B − L breaking scale till the electroweak phase transition thus ruling out the possibility of resonant leptogenesis for the mass range of W R as indicated by the CMS excess signal. Therefore we have then considered low energy subgroups of the superstring motivated E 6 group involving new exotic fermions and a low-energy SU (2) (R) gauge sector. Amongst all low energy subgroups considered in the analysis there is only one choice of SU (2) (R) which allows high-scale leptogenesis. However, this particular choice cannot account for the excess signal seen at CMS. So this together with our consideration of high-scale and TeV-scale resonant leptogenesis for the LRSM and its extensions implies that a pre-electroweak phase transition leptogenesis scenario can not generate the baryon asymmetry in the non-supersymmetric models under consideration. Thus one needs to look for post-sphaleron mechanisms to explain the observed baryon asymmetry of the universe. To this end, possibilities like neutron-antineutron oscillations can be explored [27].