Semi-leptonic decays of charmed baryons

We present estimates of semi-leptonic decays of the charmed $\text{1+}\text{2}$ baryons, members of the SU(3) 3¹ and 6 multiplets, into ordinary $\text{1+}\text{2}\text{and}\text{3+}\text{2}$ baryons. We give general expressions for decay rates and the mass M(B⁺?) spectra. We relate the relevant form factors for the $\text{1+}\text{2}\text{→}\text{1+}\text{2}$ transitions to the electromagnetic ones by means of CVC and SU(4). The form factors for $\text{1+}\text{2}\text{→}\text{3+}\text{2}$ transitions are related through SU(4) to those measured in Δ production. We discuss the dependence of the results on the masses of charmed baryons. The $\text{1+}\text{2}\text{→}\text{1+}\text{2}$ and $\text{1+}\text{2}\text{→}\text{3+}\text{2}$ transitions turn out to be dominant for the decays of the multiplets 3¹ and 6, respectively. The partial lifetimes are O(10^?10 ? 10^?14) sec as the masses of the decaying baryons are varied from 2 to 2.9 GeV. Possible ways of getting an idea about the masses of the charmed baryons are given.     

Quarks with charm and colour: A new model of their strong and weak interactions

We discuss the motivation and the consequences of taking the charmed quark to be a $\text{6}$ under colour SU(3). Among the many features of this new quark scheme is that charmed mesons are heavier than charmed baryons.     

Baryon mass splitting by the strong hyperfine interaction and SU(3) breaking

We calculate mass splittings of strange and non-strange baryons in the [56, 0⁺] and the [70, 1^?]. As the most important spin-dependent force we only analyse the hyperfine interaction. The exact treatment of the quark mass breaking shows contributions which have not been considered in similar investigations up to now. Taking $\text{mλ}\text{m}{}_{\mathrm{<mtext>p</mtext>}}\text{? 2}$ and popular values for the slope of the linear potential a, the strong coupling constant α_s and the p-quark mass, we get excellent results for the four mass splittings 〈Σ-Λ〉, $\text{〈Σ}{}^1\text{? Σ〉}$, 〈Δ-N〉 and $\text{〈Ξ}{}^1\text{? Ξ〉}$ in the [56, 0⁺]. The structure of mass spectrum in the [70, 1^?] is well described, too; the strong SU(3) mixing of Σ and Λ states is seen to be due to the quark mass breaking. Predictions for missing Σ states in the [70, 1^?] as as for splittings between charmed baryons can be made.     

Spontaneous symmetry breaking in O(10)

We consider the most general renormalizable O(10) invariant potential for a $\text{45 + 16 +}\text{16}$ representation of Higgs fields. We show that O(10) can be spontaneously broken down to SU(5), SU(4) × U(1) or SU(3) × SU(2) × U(1), this last case being, of course, the most appealing.     

Flavour and superunification

We consider the possibility of a non-trivial embedding of $\text{(}\text{10}\text{+}\text{5}\text{)}\text{SU}\text{(5)}$ families of spin if$\text{1}\text{2}$ left-handed fermions in a combination of irreducible massless supermultiplets of N extended supersymmetry. We demand the whole spectrum of spin $\text{1}\text{2}$ states to be anomaly free with respect to SU(N). This turns out to be a necessary condition for the absence of anomalies at the SU(5) level. We find two classes of models, with spin $\text{1}\text{2}$ fermions in SU(N) representations associated to one- and two-column Young tableaux, respectively, in which each irreducible massless multiplet occurs at most once. These two classes of models lead to a nontrivial family generation due to supersymmetry. For N = 8 extended supersymmetry, they give at most three and five families, respectively. The first class of models is more natural in the way it excludes SU(5) exotics. The same analysis is extended to the massless multiplets that can be obtained from bilinear composite fields of the (preonic) elementary fields of N extended supergravity. We prove that the generation of families requires the repetition of massless multiplets and that ($\text{10 +}\text{5}$) SU(5) families can only be generated in pairs. General properties of multilinear composite operators of the preonic fields are given and the rôle of massive representations to classify towers of operators with definite spin is pointed out.     

A classification of compactifying solutions for d =11 supergravity

Supergravity in eleven dimensions is known to have classical solutions of the type (anti-de Sitter space-time) × (7-dimensional Einstein space). We give a list of all homogeneous 7-manifolds which admit an Einstein metric. Known solutions are reviewed, with some emphasis on the SU(3) × SU(2) × U(1) compactifications. Their topology is discussed in detail.The list includes three new solutions, with symmetry groups SU(3) × SU(2), SO(5) and SO(5) × U(1). The first solution has no supersymmetry, while the second and third yield respectively N = 1 and N = 2 supersymmetry in four dimensions. The last two solutions may be extended to solutions with nonzero internal photon curl, breaking all supersymmetry.The existence of a spin structure on homogeneous manifolds $\text{G}\text{H}$ is discussed and related to topological properties of $\text{G}\text{H}$. As an illustration, we treat the coset spaces SU(m + 1) × SU(n + 1)/SU(m) × SU(n) × U(1), which include the spaces with SU(3) × SU(2) × U(1) symmetry.     

Self-consistent solutions for fermions in constant SU(2) gauge potentials

We derive self-consistent solutions for $\text{isospin}\text{-}\text{1}\text{2}$ Dirac particles coupled to constant SU(2) vector potentials. Such solutions can be identified as classical approximations to non-topological fermionic solitons. We discuss the stability of these states under quantum fluctuations.     

SU (4) × SU (4) symmetry breaking and its implications for SU (3) × SU (3) breaking

We investigate models where the SU (4) × SU (4) symmetry breaking Hamiltonian, $\text{H}$_SB, belongs to the (15, 15) and $\text{(10,}\text{10}\text{) + (}\text{10}\text{, 10)}$ representations, and show how they are equivalent to models of SU (3) × SU (3) breaking where $\text{H}$_SB belongs to a mixture of different representations. The results for the ππ scattering lengths in the (15, 15) model are outside the experimental limits, but the $\text{(10,}\text{10}\text{) + (}\text{10}\text{, 10)}$ model yields solutions with a wide range of values for the scattering lengths within the experimental bounds.     

On chiral realizations of confining theories

It is argued that chirality is not necessarily broken in SU(N) colour theories with a chiral flavour symmetry. In this case, massless fermion bound states contributr to anomaly equations, and loop expansions in a 1/N approach are invalid. As a hint to understanding which option is realized by the theory, we investigate it in two dimensions for very small quark masses. The light spectrum shows a rich structure not obtained in a $\text{1}\text{N}$ expansion. Light flavoured baryons and mesons indicate a partial realization of the chiral symmetry.     

Bosonic construction of the Lie algebras of some non-compact groups appearing in supergravity theories and their oscillator-like unitary representations

We give a construction of the Lie algebras of the non-compact groups appearing in four dimensional supergravity theories in terms of boson operators. Our construction parallels very closely their emergence in supergravity and is an extension of the well-known construction of the Lie algebras of the non-compact groups $\text{SP}\text{(2n,}\text{R}$ and $\text{SO}\text{(2n)}{}^1$ from boson operators transforming like a fundamental representation of their maximal compact subgroup U(n). However this extension is non-trivial only for n?4 and stops at n = 8 leading to the Lei algebras of SU(4) × SU(1, 1), SU(1, 1), SU(5, 1), SO(12)¹ and E₇(7). We then give a general construction of an infinite class of unitary irreducible representations of the respective non-compact groups (except for E₇₍₇₎ and SO(12)¹ obtained from the extended construction). We illustrate our construction with the examples of SU(5, 1) and SO(12)¹.     

A dynamical theory for the rishon model

We propose a composite model for quarks and leptons based on an exact SU(3)_C × SU(3)_H gauge theory and two fundamental $\text{J=}\text{1}\text{2}$ fermions: a charged T-rishon and a neutral V-rishon. Quarks, leptons and W-bosons are SU(3)_H-singlet composites of rishons. A dynamically broken effective SU(3)_C × SU(2)_L × SU(2)_R × U(1)_B?L gauge theory emerges at the composite level. The theory is “natural”, anomaly free, has no fundamental scalar particles, and describes at least three generations of quarks and leptons.     

“Virtual effects of excited quarks as probes of a possible new hardonic mass scale”

The effects of $\text{spin}\text{-}\text{3}\text{2}$ excited quarks are considered as probes of a possible new hadronic mass-scale Λ. A specific model is developed which describes virtual $\text{spin}\text{-}\text{3}\text{2}$ quarks of mass of O(Λ). Induced effects, which are corrections to the standard SU(2) × U(1) electroweak model, include right-handed charged currents and flavor changing neutral currents. A model-independent classification of all SU(3) × SU(2) × U(1) invariant quark operators of dimension six or less is also presented. Ambiguities in converting this analysis and existing experiments to a definitive lower-bound for Λ are discussed. It is found, depending on the strength of certain Higgs couplings and the underlying global flavor symmetries in the absence of Higgs couplings, that a lower bound as small as Λ > 500 GeV or as large as Λ > 100 TeV is possible.     

Finite size scaling and low mass glueballs

We propose finite lattice effects as a probe of the glueball mass spectrum, and give an analysis of the recent SU(2) Monte Carlo data of Brower, Nauenberg and Schalk in terms of a gas of free glueballs. For L⁴ lattices with L = 4, 5, 6 fits are made to ξ(m = 1/aξ) which indicate a rather large effective number of degrees of freedom (i.e. statistical degeneracy where a spin J counts as 2J + 1) from 5 to 15 states. As the degeneracy is increased, the central glueball mass increases from $\text{m = (1.3±0.2)}\text{κ}$ at degeneracy 5 to about $\text{m = (1.9±0.2)}\text{κ}$ at degeneracy 15, relative to the SU(2) string tension $\text{κ}$.     

An analysis of the Λ (1520) observed in a K− neutron production experiment

The mass, width and branching fractions of the Λ(1520) into $\text{K}\text{N, σπ, Λππ}\text{and}\text{σππ}$ have been determined using a Λ(1520) sample produced in the reaction K^?d→Λ(1520)π^?p_s at K^? -neutron centre-of-mass energies between 1.9 and 2.2 GeV. A Dalitz plot analysis of the Λ⁰π⁺π^? decay mode shows that there is a substantial Σ(1385)π component. The SU(3) octet-singlet mixing angle for the $\text{3}\text{2}{}^{\mathrm{?}}$ baryons calculated from the partial widths for the s-wave σ(1385)π decay of the Λ(1520) and Λ(1690) is found to be consistent with that obtained from the d-wave decays of the singlet and octet members, within experimental limits.     

Irreducible gauge theory of a consolidated Salam-Weinberg model

We derive the Salam-Weinberg model by gauging an internal simple supergroup $\text{SU}\text{(}\text{2}\text{1}\text{)}$. The theory uniquely assigns the correct SU(2)_L ? U(1) eigenvalues for all leptons, fixes θ_W = 30°, generates the W^±_σ, Z⁰_σ and A_σ together with the Higgs-Goldstone $\text{I}{}_{\mathrm{<mtext>L</mtext>}}\text{=}\text{1}\text{2}$ scalar multiplets as gauge fields, and imposes the standard spontaneous breakdown of SU(2)_L ? U(1). The masses of intermediate bosons and fermions are directly generated by $\text{SU}\text{(}\text{2}\text{1}\text{)}$ universality, which also fixes the Higgs field coupling.     

Baryon decay tests of the form of the charm current

We discuss how semi-leptonic decays of charmed baryons can be used to discriminate between different forms of the charm-changing weak current. Some information can be obtained from the energy and invariant mass distributions of the decay products. More sensitive tests can be made using the polarizations of strange baryons such as Λ, Σ or Ξ in the final state. In principle V±A, pure V and pure A coupling types can all be distinguished. Tests using decays of $\text{3}{}^1$ charmed baryons, such as $\text{C}{}_0{}^{\mathrm{+}}\text{→Λ}{}_0\text{l}{}^{\mathrm{+}}\text{ν}$, are more sensitive than those using decays of $\text{6}$ baryons, such as $\text{C}{}_1{}^{\mathrm{++}}\text{→Σ}{}^{\mathrm{+}}\text{l}{}^{\mathrm{+}}\text{ν}$.     

Chiral fermion generations from higher-dimensional gravity

We discuss a six-dimensional SO(12) gauge theory which can be obtained from pure gravity in 18 dimensions coupled to a Majorana-Weyl spinor, if the ground state is characterized by a noncompact internal space without boundary with small finite volume. The six-dimensional SO(12) theory spontaneously compactifies to a four-dimensional SO(10) theory with local generation group SU(2)_G × U(1)_G. We obtain an even number of chiral fermion generations transforming as ($\text{16, k, ±}\text{1}\text{2}$) under SO(10) × SU(2)_G × U(1)_G. Adding a scalar field to the six-dimensional theory provides us with fields carrying all the quantum numbers needed for a realistic spontaneous symmetry breakdown to SU(3)_c × U(1)_e.m.     

The Wilson-Andrei number for the SU(3) Kondo model

We give asymptotic forms for the high- and low-field magnetic susceptibility for the SU(3) linear dispersion Kondo model for T = 0. The ratio $\text{T}{}_{\mathrm{<mtext>K</mtext>}}\text{T}{}_{\mathrm{<mtext>H</mtext>}}$ is also calculated for the standard SU(2j + 1) Kondo model for general j. From these results the Wilson number W_j, defined by $\text{χ0 =}\text{Wj(gμ)}{}^2\text{j(j + 1)}\text{3kT}{}_{\mathrm{<mtext>K</mtext>}}$ where χ0 is the zero-temperature zero-field susceptibility, which has been calculated by Andrei and Lowenstein for $\text{j =}\text{1}\text{2}$, is deduced for the SU(3) model j = 1.     

A possible description of baryon dynamics in dual and gauge theories

We present an attempt to generalize to baryons a framework recently proposed in order to unify gauge, dual and Regge-Gribov theories of mesons. We find it necessary to depart from the $\text{1}\text{N}{}_{\mathrm{<mtext>colour</mtext>}}$ expansion of quantum chromodynamics (QCD) and to replace it by a more general definition of a “dual” approximation of QCD, based on the zero-width limit. Theoretical and phenomenological consequences of the scheme are derived. For N_colour = 3, the baryon resembles a Y shaped string; three families of new “baryonium” bound states are predicted and rough estimates of intercepts and slopes of the associated Regge trajectories are given. A new type of Zweig-like selection rule is found to hold in leading order and its violations through higher-order topologies are discussed. Duality diagrams for baryons are ambiguous unless implemented with extra lines indicating the flow of certain colour indices. Duality between scattering and annihilation channels is found in B$\text{B}$ scattering and its consequences are discussed. Some justification is given for the quark counting rule for total cross sections. Finally, implications of our scheme for the Regge-Gribov calculus in processes involving baryons are discussed.     

The quark-antiquark potential of SU(2) lattice gauge theory in 2+1 dimensions

Within the framework of a hamiltonian formulation of SU($\text{N}$) lattice gauge theory in two spatial dimensions we develop a weak coupling expansion in the static quark-antiquark sector. For SU(2) the quark-antiquark potential is calculated to fourth order. Moreover we extend the former calculation of the energy gap in the gauge invariant sector to general SU($\text{N}$) and extrapolate to the infinite lattice limit from large lattices. Due to the infrared divergence of the weak coupling expansion on infinite lattices the quark-antiquark potential contains a term diverging logarithmically with the lattice expansion. Hence the expansion has to be interpreted as a pseudo-perturbation expansion in the sense of Symanzik.