Charge quantization in the largest leptoquark-bilepton chiral electroweak scheme

The uniqueness of the hypercharge assignments in the three fermion families leptoquark-bilepton SU(3)C×SU(4)L×U(1)N model is established. Although the gauge group contains an explicit U(1) factor, freedom from triangle anomalies combined with the requirement of nonvanishing charged fermion masses uniquely fix the electric charges of all fermions independently of the neutrinos being massless or not. The electric-charge quantization, family replication, and the existence of three colors are interwoven. PACS numbers: 11.30.Er, 11.30.Hv, 12.15.Cc Typeset using REVTEX 1 So far, the standard model of electroweak and strong interactions [1] has been quite successful in its compatibility with almost all available experimental data [2,3]. It nevertheless leaves some fundamental theoretical questions unexplained. In the standard model, each family of fermions is anomaly-free and this is true as well for grand unified models, supersymmetric extensions, except the supersymmetric preon model [4], technicolor, superstring theories, and most compositeness scenarios where the number of families remains completely unrestricted on theoretical grounds. The chiral anomaly is cancelled between quarks and leptons in each family and the indetermination about the inter-relation between families constitute the so-called flavor question. At present, we know of three families, but the standard model does not explain why this number has to be three, even so the number of neutrino flavors within the electroweak standard model is Nν = 3.00 ± 0.09 and the experimental determination of this number is model dependent [5]. Some very fundamental aspects of the standard model such as the flavor question might be understood by embedding the three-family version in a Yang-Mills theory with the gauge semisimple group G0 ≡ SU(3)C ⊗GW ⊗U(1)L+R just enlarging the SU(2)L weak isospin group to GW = SU(3)L (331 model [6–8]) which is the minimal gauge group that at the leptonic level admits charged fermions and their antiparticles as members of the same multiplet [9]. The key predictions of the G0 alternative models are leptoquark fermions with electric charges ±5/3 and ∓4/3 and bilepton gauge bosons [10] with lepton number L = ±2. The leptoquark fermions are color-triplet particles which possess barion and lepton numbers. Another interesting feature of these leptoquarkbilepton chiral models is that the weak mixing angle of the standard model has an upper limit. Therefore, it is possible to compute an upper bound to the mass scale of the GW = SU(3)L breaking of about 1.7 TeV [11]. Considering the lightest particles of the model as the sector in which a symmetry is manifested, the lepton sector could be the part of the model determining new approximate symmetries. In fact, if right-handed neutrinos are introduced, there arises a more interesting 2 possibility of having νl, l = e, μ, τ , and the charge conjugate fields ν c l , l c in the same multiplet for each family flavor. Model building in that direction, if each family of fermions is treated separately, culminates with the highest symmetry GW = SU(4)L to be considered in the electroweak sector (341 model [12–15]). In the 331 and 341 leptoquark-bilepton models the number of families must be divisible by the number of color degrees of freedom in order to cancel anomalies. This novel method of anomaly cancellation requires that at least one family transforms differently from the others, thus breaking generation universality. To accommodate the replication of three fermion families, the number of families, number of colors, and fractional electric charge values become related [7,16,17]. Having established that connection the flavor question is solved with a relation between the strong and electroweak parts of the model which does not exist in the context of the standard model. In the minimal standard model there is a remarkable failure concerning the connection among family replication and the electric charge quantization [18]. In fact, the charge quantization is realized only within each family [19–23]. Nevertheless, taking the three families together the effect of dequantization occurs [19,20,23,24]. The possibility of charge quantization with three families in the minimal 331 model was shown recently [25]. In the 341 model, the electric charge operator is embedded in the neutral generators of the SU(4)⊗U(1) group Q = Λ3 + ξΛ8 + ζΛ15 + εN (1) with the embedding parameters ξ = −1/√3, ζ = −2√6/3 and N is the new U(1) charge. The neutral generators of SU(4)L are Λ3 = λ3 2 = 1 2 diag(1,−1, 0, 0), Λ8 = λ8 2 = 1 2 √ 3 diag(1, 1,−2, 0), Λ15 = λ15 2 = 1 2 √ 6 diag(1, 1, 1,−3). The model treats the color singlet leptons democratically in each of the three families