Mass formula based on SU(4)

The quality of the fit of experimental masses by a mass formula based on the two-body Casimir operator of SU(4) is tested and found to be at least as good as that of the Weizsäcker mass formulae, in spite of the fact that this formula is inherently less flexible. The physical basis for, and some ramifications of, this formula are discussed. A simple form for the shell corrections is then added in the formulae, leading to improved fits without modification of the above conclusions.     

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 the SU(3) Mass Formulae

It is found that in the SU(3) broken quark model the SU(3) generators and their time derivatives belong to the SU(3) × SU(3) algebra. Using this algebra and the infinite momentum method the SU(3) mass sum rules are obtained. The possibility is discussed that normal spin-parity nonets and anomalous ones differ in the structure of the mass spectrum.     

Transition between SU(4) and SU(2) Kondo effect

Motivated by experiments in nanoscopic systems, we study a generalized Anderson, which consist of two spin degenerate doublets hybridized to a singlet by the promotion of an electron to two conduction bands, as a function of the energy separation δ$\delta$ between both doublets. For δ=0$\delta =0$ or very large, the model is equivalent to a one-level SU(N$N$) Anderson model, with N=4$N=4$ and 2 respectively. We study the evolution of the spectral density for both doublets (ρ_1σ(ω)${\rho }_{1\sigma }(\omega )$ and ρ_2σ(ω)${\rho }_{2\sigma }(\omega )$) and their width in the Kondo limit as δ$\delta$ is varied, using the non-crossing approximation (NCA). As δ$\delta$ increases, the peak at the Fermi energy in the spectral density (Kondo peak) splits and the density of the doublet of higher energy ρ_2σ(ω)${\rho }_{2\sigma }(\omega )$ shifts above the Ferrmi energy. The Kondo temperature T_K (determined by the half-width at half maximum of the Kondo peak in density of the doublet of lower energy ρ_1σ(ω)${\rho }_{1\sigma }(\omega )$) decreases dramatically. The variation of T_K with δ$\delta$ is reproduced by a simple variational calculation.     

SU(4) weak currents

We suggest SU_L(4) ? U(1) as the gauge symmetry of weak and electromagnetic interactions for quartets of quarks and leptons. We analyze how the (additional) SU_L(4) weak currents (besides the SU_L(2) subgroup) could affect the weak interactions of ordinary particles, the atomic parity violation, the neutral-current neutrino reactions and the decays of the τ heavy lepton and the charmed mesons. The suppression of neutral-current parity violation in atomic experiments can be naturally incorporated in this model while at the same time the success of the Weinberg-Salam model with respect to the inclusive neutral current data is kept. The model has limited freedom and therefore many definite predictions.     

Asymptotically free SU(2) × SU(2) × SU(4) model of unified interaction

An asymptotically free SU(2) × SU(2) × SU(4) model of unified interaction is constructed. The gauge coupling constants are taken equal (in the order of magnitude) to the electromagnetic one. The strong interaction and the quark confinement is provided for by a gluonic mechanism. Some physical consequence of the model are briefly discussed.     

Pseudoscalar Mesons as Goldstone Bosons in Chiral SU(4) ⊗ SU(4) Symmetry

We study the pseudoscalar mesons in the framework of broken chiral SU(4) SU(4) symmetry when the symmetry-breaking Hamiltonian, H_SB, is taken as –(u₀ + cu₈ + du₁₅) and the symmetry of the Hamiltonian is realized in Goldstone-Nambu way. An interesting property of two chimeral SU(4) subgroups and the Goldstone nature of some of the pseudoscalar mesons in certain symmetry limits are exploited to obtain some mass relations and the ratio c/d.     

Instantons in SU(4) gauge theories

A complete set of solutions of SU(4) invariant gauge fields with SO(4) spherical symmetry (euclidian metric in space time) is obtained. It is shown that the solutions fall into two non equivalent classes following a spinor or vector decomposition of the four dimensional representation of SU(4) in SO(4). The energy of the first case and hence the topological quantum number are twice those of the second case.     

Finite transformations of SU(4)

The problem of determining the representation matrices of SU(4) is investigated. A convenient set of parameters is first introduced by writing the general element of the group as a product of exponential functions of the generators, and the generators are expressed as differential operators involving these parameters. Special matrix elements of finite transformations with a SU(3) singlet as the initial state are then obtained by solving the eigenvalue equation of the quadratic Casimir operator of SU(4). The solution has the form of a product of elementary functions and threed _mm ^j functions of SU(2) and is free from summation over intermediate states. By expanding one of thed _mm ^j functions in an appropriate series a sum rule for the special matrix elements of the permutation operator 12343412 is obtained. The discussions are strictly confined to SU(4), but, some of the results given here can be extended to unitary groups of higher dimensions.     

A chiral SU(4) × SU(4) gauge theory of weak and electromagnetic interactions

A lepton hadron analogy is considered based on the gauge group SU(4)_L × SU(4)_R × U(1), which is broken entirely spontaneously. The model satisfies the physical requirements of the V-A theory, muon-electron universality, no neutral strangeness changing currents, the Cabibbo structure for the SU(3) currents, and triangle anomalies can be avoided. The contribution of the existing neutral currents to various neutrino processes are calculated.     

Improved QCD vacuum for gauge groups SU(3) and SU(4)

The effective energy for a covariantly constant background field in a pure Yang-Mills theory is calculated to loop order one. For gauge group SU(3) [SU(4)] it is found that the “vacuum” configuration consists of two [three] constant color magnetic fields of equal non-zero magnitude orthogonal to each other in color as well as physical space. We conclude that the structure of the Copenhagen vacuum is more complex than previously expected.     

Adjoint representation admixture to weak nonleptonic decays in SU(4) and SU(8)

In order to remove some of the unsatisfactory features of the GIM model, we consider15-admixture in SU(4). ΔC=±ΔS decays remain unaffected. Lee-Sugawara sum-rule is obtained.15-admixture is extended then to63-admixture in SU(8). The most general Hamiltonian (H _w∼63⊕720⊕1232) in SU(8) is found to give Lee-Sugawara relation and Σ₊ ⁺=0 forS-wave decays of uncharmed baryons. Decay amplitude relations for ΔC=−1, ΔS=0 mode are obtained.     

Multi-component fractional quantum Hall states in graphene: SU(4) versus SU(2)

Because of the spin and Dirac-valley degrees of freedom, graphene allows the observation of one-, two- or four-component fractional quantum Hall effects in different parameter regions. We address the stability of various states in the SU(2) and SU(4) limits. In the SU(4) limit, we predict that new low-energy Goldstone modes determine the stability of the fractional quantum Hall states at 2/5, 3/7, etc; SU(4) skyrmions are not found to be relevant for the low-energy physics. These results are discussed in light of experiments.     

Supersymmetric SU C (4) × SU L (2) × SU R (2) and spontaneous breakdown of symmetries

A supersymmetric version of the left right symmetric partial unification group SU _C (4) × SU _L (2) × SU _R (2) is presented. The spontaneous breakdown of gauge symmetry in a favourable chain of descent has been studied in detail. The mass spectra have been calculated. The method of O’Raifeartaigh has been used to break supersymmetry. The lifting of degeneracy of mass levels between physical multiplets has been shown to occur due to radiative corrections.     

Chiral SU(4) × SU(4) breaking: masses and decay constants of charmed hadrons

The (4, 4*) ⊕ (4*, 4) model of broken chiral SU (4) × SU (4) symmetry has been used to calculate the third-order coupling constants involving charmed and ordinary pseudoscalar mesons. These coupling constants are exploited to derive some interesting new relations among the masses and decay constants of these charmed particles. Using the known masses and decay constants as inputs, we exploit these relations to predict:F _D = −1·41F _π ,F _F = −1·13F _π ,F _D/F_F = 1·25,m(D _s) = 1·43 GeV,m(F _s) = 1·39 GeV andm(K _s) = 1·02 GeV.     

SU(4) Kondo effect in carbon nanotubes

We investigate theoretically the nonequilibrium transport properties of carbon nanotube quantum dots. Owing to the two-dimensional band structure of graphene, a double orbital degeneracy plays the role of a pseudospin, which is entangled with the spin. Quantum fluctuations between these 4 degrees of freedom result in an SU(4) Kondo effect at low temperatures. This exotic Kondo effect manifests as a four-peak splitting in the nonlinear conductance when an axial magnetic field is applied.     

Mass anomalous dimension in SU(2) with six fundamental fermions

We simulate SU(2) gauge theory with six massless fundamental Dirac fermions. We measure the running of the coupling and the mass in the Schrödinger Functional scheme. We observe very slow running of the coupling constant. We measure the mass anomalous dimension γ, and find it is between 0.135 and 1.03 in the range of couplings consistent with the existence of an IR fixed point.