A Realistic Superunification

It is argued that every quark flavor can be described as a lepton that has been excited by the absorption of a superunified field, which is defined. In this context, a minimal irreducible representation of SUSY SU(5) is constructed exclusively of the chiral modes that correspond to three generations of leptons (or quarks) and their scaler superpartners. The proposed model predicts a new quark–a left-handed (non-strange) version of the strange quark. 1. Quarks as Superunified Excitations of Leptons If one assigns isotopic spins (1.1) I3(e − L ) = −1/2 (1.2) I3(e − R) = 0 and (1.3) I3(ν e − L ) = +1/2, to the light generation of fermions, then the hypercharges of the light quark generation and the strange quark are given by Y=2Q -2I3: (1.4) Y (up) = 2[Q(ν − + (2/3)]− 2I3(ν e− ) = 2[0 + (2/3)]− 2(1/2) = 1/3 (1.5) Y (down) = 2[Q(e−L) + (2/3)]− 2I3(e − L ) = 2(−1 + (2/3))− 2(−1/2) = 1/3 and (1.6) Y (strange) = 2[Q(e−R + (2/3)]− 2I3(e − R) = 2(−1 + (2/3))− 2(0) = −2/3, suggesting that a quark can be interpreted as a lepton that has absorbed an electrical charge of 2/3. It will now be demonstrated that a superunification in the superstring context, and in the context of expressions 1.1 through 1.3 requires the interpretation of quark flavor that is described by expressions 1.4 through 1.6. Because generations of fermions are indistinguishable (because fermions are massless) until supersymmetry is broken, it will be argued that expressions 1.4 through 1.6 also apply to the heavier leptonic generations; and in this context, it will be argued that the heavier quarks can also be described as leptons that have absorbed charges of 2/3. 1 2 J. TOWE Let us consider the herorotic superstring; e.g. let us consider the gravitino state of momentum k that is described by the vector-spinor u. Graviton emission from this gravitino ground state is produced by interaction of the gravitino with a bosonic right-moving (Neveu-Schwarz) prescription, which is tensored with the fermionic left-moving (Ramond) prescription: (1.7) ǫμν [∂τX μ R(0) + 1 2 ψ RkψR(0)]ψ ν L(0)e −ikX Expression 1.7 describes what is known as the graviton vertex operator [J. Bailen, 1994]. The supersymmetric vertex that results from the above-described interaction is as depicted by figure 1, or alternatively by Figure 2. The supersymmetry of the Figure 2 vertex is clearly preserved if the spin-(3/2) field is replaced by a fermion-boson pair of like helicity, as depicted by figure 3. Moreover, if the ingoing fermion in Figure 2 is an electron’s neutrino and if the ingoing boson is a photon, then clearly, the outgoing spin-(2) and spin-(3/2) fields are just the usual graviton and gravitino; i.e. then the interaction is a supergravitational interaction; but if the ingoing boson in Figure 3 is a gluon, and if the ingoing fermion is any lepton, then the outgoing fermion is a quark if and only if the outgoing spin-2 field is a superunified field, which is now defined as a spin-2 field that carries a charge of 2/3, and a color and preserves isotopic spin. To establish this, consider the three possibilities that are depicted by Figures 4, 5 and 6. The ingoing fermions in Figures 4, 5 and 6 are respectively the electron’s neutrino, ν − L , the LH electron, e−L and the RH electron, e − R; while the outgoing fermions are respectively the up, down and strange quarks. Given the assignments of isotopic spin that are indicated by expressions 1.1 through 1.3, the tree-level, superunified interactions depicted by Figures 4, 5 and 6 clearly require the interpretation of quarks that is indicated by expressions 1.4 through 1.6. Moreover, because fermionic generations are indistinguishable (because fermions are massless) previous to the breaking of supersymmetry, the proposed supersymmetric theory permits that the same isotopic spins be assigned to μ−L and τ − L as to e − L ; to ν μ− L and ν τ− L as to ν e− L , and to μ − R and τ − R as to e − R. In this context, one can assign hypercharges to those quarks which, as fermions assume massive status, become the top, bottom and charmed quarks: (1.8) Y (top) = 2[Q(ν − + (2/3)]− 2I3(ν −) = 2[0 + (2/3)]− 2(1/2) = 1/3 (1.9) Y (bottom) = 2[Q(τ− L ) + (2/3)]− 2I3(τ − L ) = 2(−1 + (2/3))− 2(−1/2) = 1/3 and (1.10) Y (charmed) = 2[Q(ν − + (2/3)]− 2I3(ν μ− ) = 2[0 + (2/3)]− 2(1/2) = 1/3 Although this result departs from traditional quark theory [D. Nordstrom, 1992], symmetry appears to permit these assignments of isotopic spin and hypercharge. In the above context, one is also motivated to consider the hypercharge that is generated when μ−L absorbs a superunified field: (1.11) Y (?) = 2[Q(μ−L ) + (2/3)]− 2I3(μ − L ) = 2(−1 + (2/3))− 2(−1/2) = 1/3 Expression 1.11 clearly indicates a quark that is not currently recognized. The strange quark is usually regarded as the generational partner of charmed; but the strange quark cannot be inserted here (the hypercharge of strange is -2/3). Thus, SUPERUNIFICATION 3 expression 1.11 predicts a new quark–a quark that is characterized by the same quantum numbers that associate with the strange quark, except strangeness, which is zero for the predicted quark (the new quark, having an isotopic spin of -1/2, is left-handed). Note that this prediction cures an anomaly that is characteristic of the traditional theory of quark generations. Traditionally the up and top quarks are complemented by left-handed generational partners: the down and bottom quarks; while the charmed quark is, according to traditional theory, complemented only by a right-handed generational partner: the strange quark. The proposed theory cures this anomaly by providing a left-handed (non-strange) version of the strange quark. In the proposed theory, the strange quark is an analogue of the right-handed electron. A second consequence of the proposed interpretation of quarks as superunified excitations of leptons is a SUSY SU(5) model that precisely accommodates three generations of fermions. This model will now be considered. 2. An SUSY SU(5)Model of Three Leptonic Generations In the context proposed by Section 1, a minimal irreducible representation 5⊕10 of SUSY SU(5) can be precisely constituted by the chiral modes that associate with the three leptonic generations and their scaler superpartners. The strictly leptonic realization of the anti-symmetric 10 = [5,2] of SUSY SU(5) can be given by