Purd-th-92-14 Quark-lepton Symmetry

Quark-lepton symmetric models are a class of gauge theories motivated by the similarities between the quarks and leptons. In these models the gauge group of the standard model is extended to include a “color” group for the leptons. Consequently, the quarks and leptons can then be related by a Z2 discrete quark-lepton symmetry which is spontaneously broken by the vacuum. Models utilizing quarklepton symmetry with acceptable and interesting collider phenomenology have been constructed. The cosmological consequences of these models are also discussed. 1. The minimal quark-lepton symmetric model [1] Historically, there has been a rough correspondence between the hadrons and leptons which is now translated into a quark-lepton “symmetry”. This rough correspondence can be seen in the similarities of the weak interactions for the quarks and leptons. Therefore it maybe interesting to postulate an exact symmetry between quarks and leptons in the context of gauge theories. In the Minimal Standard Model (MSM), the quarks carry color whereas the leptons do not and it is also assumed that there are no right-handed neutrinos. To implement quark-lepton symmetry (hereafter referred to as q-l symmetry), equal numbers of quark and lepton degrees of freedom are needed. To achieve this we will introduce (i) the right-handed neutrino, νR, and (ii) a “color” group for the leptons. This then necessitates extending the MSM gauge group, GSM , to Gql = SU(3)l⊗SU(3)q⊗SU(2)L⊗U(1)X supplemented by a Z2 discrete symmetry between the quarks and leptons. Here SU(3)q is the usual color group and SU(3)l is its leptonic partner. The expanded fermionic generation is defined by the transformation laws QL ∼ (1, 3, 2)(1/3), uR ∼ (1, 3, 1)(4/3), dR ∼ (1, 3, 1)(−2/3), FL ∼ (3, 1, 2)(−1/3), ER ∼ (3, 1, 1)(−4/3), NR ∼ (3, 1, 1)(2/3). Talk given at the DPF92 meeting, Fermilab, November 1992. The Z2 discrete symmetry: FL ↔ QL, ER ↔ uR, NR ↔ dR, Gq ↔ G μ l , C μ ↔ −C can now be defined [where Gμq,l are the gauge bosons of SU(3)q,l and C μ is the gauge boson of U(1)X]. Standard hypercharge is given by Y = X + 13T , where T = diag(−2, 1, 1) is a generator of SU(3)l. Standard leptons are identified with the T = −2 components of the leptonic color triplets, while the T = 1 components are the exotic charge ±1/2 leptons, called liptons. The MSM works very well for energies up to about 100 GeV. In order to spontaneously break SU(3)l and the quark-lepton discrete symmetry, as well as giving mass to the liptons, the Higgs bosons χ1 ∼ (3, 1, 1)(−2/3) and χ2 ∼ (1, 3, 1)(2/3) are introduced with χ1 ↔ χ2. The T = 2 component of χ1 develops a nonzero vacuum expectation value (VEV), while the VEV of χ2 is completely zero. Electroweak symmetry breaking is achieved through the Higgs doublet, φ ∼ (1, 1, 2)(1), with φ ↔ φ(charge conjugate field) under q-l symmetry. The overall symmetry breaking pattern can be summarised as follows: 2 Gql 〈χ1〉 −→ SU(2) ⊗ GSM 〈φ〉 −→ SU(2) ⊗ SU(3)q ⊗ U(1)Q. This minimal Higgs sector results in the tree-level mass relations, Mu = Me and Md = M ν , where Mu,e,d,ν refer to the 3 × 3 fermion mass matrices. These mass relations arise as a consequence of (i) the assumption that q-l symmetry is a symmetry of the Yukawa Lagrangian and (ii) using only one Higgs doublet. If the minimal model is extended to contain two Higgs doublets, then the abovementioned mass relations can be avoided at tree-level but at the expense of predictivity. Alternatively, a certain q-l symmetric model with a non-minimal gauge group has been shown to contain radiative corrections which can yield correct but unpredictive fermion masses[2]. 2. Phenomenological Implications [3] 2.1. Gauge Bosons The low energy gauge group of the q-l model is SU(2) ⊗ SU(3)q ⊗U(1)Q. As a result of the larger symmetry there will be additional gauge bosons, both massive and massless, to that of the MSM. The decomposition of the SU(3)l gauge bosons under the low energy gauge group is: 8 → (1, 1)(0)⊕ (2, 1)(− 1 2 )⊕ (2, 1)( 1 2 )⊕ (3, 1)(0) . The neutral component, the Z ′ boson, can mix with the standard Z boson. The SU(2) doublets of charge ± 1 2 are the massive SU(3)l/SU(2) ′ bosons which can contribute To show that the required pattern of symmetry breaking for the minimal q-l model can be realised, consider the Higgs potential