4 FIG. 2: The LHC discovery reach for (a) model (I) and (b) model (II). The required luminosity is the same for both e $^{+}$e − and µ $^{+}$µ − resonances in model (I). The required luminosity for the e $^{+}$e − (solid line) resonance is about an order of magnitude smaller than that for the µ $^{+}$µ − (dashed line) resonance in model (II). There are two sources of lepton flavor violation. One comes from explicit interactions linking N c through S 1 , 2 ; the other through the mismatch of lepton and slepton mass matrices (which is common to all supersymmetric models). Since we choose x$_{e}$ = x$_{µ}$ = x$_{τ}$ , the latter ap- plies only to the µ − τ sector, whereas the former applies to all leptons, but for one-loop processes such as µ → eγ , they are negligible because of the smallness of neutrino masses. The muon anomalous magnetic moment ( a$_{µ}$ ) does not violate lepton flavor, so it has a contribution from Z ′ $_{X}$, i.e. [26] x$_{S}$ = 3 accomplishes three objectives. (i) The conven- tional R parity survives as an exact discrete symmetry, desirable for having the LSP as a good dark-matter can- didate. (ii) Realistic neutrino masses and mixing are ob- tained. (iii) An exact residual Z 3 symmetry, i.e. baryon triality B 3 , emerges which makes the proton absolutely stable. The neutral gauge boson of this new U (1)$_{X}$ has large couplings to leptons over quarks: three or nine times larger than in the case of B − L . Using present Tevatron bounds with g$_{X}$ = 0 . 1, we find M$_{Z}$ ′ X to be greater than 830 GeV in model (I), and 940 GeV in model (II). The indirect bounds from LEP2 are 1 . 4 TeV in model (I), and 2 . 3 TeV in model (II). It should be accessible at the LHC, possibly at a very early stage. To have a background-free signal of 10 dilepton events at the LHC, the Z ′ X with M$_{Z}$ ′ X = 1 . 5 TeV in model (I) may be discovered for an integrated luminosity of only about 1 fb − $^{1}$. In model (II), because of the flavor-dependent charges, the event rate of the e $^{+}$e − resonance is predicted to be nine times that of µ $^{+}$µ $^{−}$. This work was supported by U. S. Department of En- ergy Grants No. DE-AC02-98CH10886 (HL) and No. DE-FG03-94ER40837 (EM). for both models (I) and (II). Using the Tevatron bounds on M$_{Z}$ ′ X with g$_{X}$ = 0 . 1, we find this to be at most of order 10 − $^{11}$, which is negligible compared to the present experimental accuracy. On the other hand, since we are considering a supersymmetric model, there are one-loop contributions to a$_{µ}$ from the neutralinos and charginos, which may account for the possible deviation in its mea- surement at the Brookhaven Alternating Gradient Syn- chrotron [27]. We have proposed a new U (1) gauge symmetry B − x$_{i}$L , with x$_{e,µ,τ}$ = ( − 3 , 3 , 3) [model (I)] or (9 , − 3 , − 3) [model (II)], in the context of supersymmetry with three neutral singlets N c $_{e,µ,τ}$. The spontaneous breaking of this U (1)$_{X}$ by the addition of singlets S 1 , 2 with L = ± 2 and Conclusion One-loop charged lepton processes Δ a$_{µ}$ = 3 g 2 X 4 π 2 m 2 µ M 2 Z ′ X (18) [1] S. Weinberg, Phys. Rev. D 26 , 287 (1982). [2] E. Ma, Phys. Lett. B 433 , 74 (1998). [3] E. Ma and U. Sarkar, Phys. Lett. B 439 , 95 (1998). [4] E. Ma and D. P. Roy, Phys. Rev. D 58 , 095005 (1998). [5] X. J. Bi, X. G. He, E. Ma and J. Zhang, arXiv:0910.0771 [hep-ph]. [6] E. Salvioni, A. Strumia, G. Villadoro and F. Zwirner, arXiv:0911.1450 [hep-ph]. (a) (b)