Spin and Resonant States in QCD

I make the case that the nucleon excitations do not exist as isolated higher spin states but are fully absorbed by (K/2,K/2)*[(1/2,0)+ (0,1/2)] multiplets taking their origin from the rotational and vibrational excitations of an underlying quark--diquark string. The \Delta (1232) spectrum presents itself as the exact replica (up to \Delta (1600)) of the nucleon spectrum with the K- clusters being shifted upward by about 200 MeV. QCD inspired arguments support legitimacy of the quark-diquark string. The above K multiplets can be mapped (up to form-factors) onto Lorentz group representation spaces of the type \psi_\mu_1...\mu_K, thus guaranteeing covariant description of resonant states. The quantum \psi_\mu_1...\mu_K states are of multiple spins at rest, and of undetermined spins elsewhere.Comment: Added Ref. M. Kirchbach, D.V. Ahluwlalia, Phys. Lett. B529, 131 (2002) as the source of Figure 1. No further change

Quantum states of indefinite spins: From baryons to massive gravitino

I review theory and phenomenology of (K/2,K/2)*[(1/2,0)+(0,1/2)] states. First I make the case that the observed nucleon and Delta (1232) excitations (up to Delta(1600)) are exhausted by unconstrained (K/2,K/2)*[(1/2,0)+(0,1/2)] states with K=1,3, and 5, which originate from rotational and vibrational excitations of an underlying quark--diquark configuration. Second, I consider the simplest case of K=1 and show that the \gamma^\mu\psi_\mu =0 constraint of the Rarita-Schwinger framework is a short-hand of: - 1/3 (1/m^2 W^2 +3/4)\psi_\mu = \psi_\mu, the covariant definition of the unique invariant subspace of the squared Pauli-Lubanski vector, W^2, that is a parity singlet and of highest spin-3/2 at rest. I suggest to work in the 16 dimensional vector spinor space \Psi= A *\psi rather than keeping Lorentz and spinor indices separated and show that the above second order equation guarantees the covariant description of a has-been spin-3/2 states at rest without invoking further supplementary conditions. In gauging the latter equation minimally and, in calculating the determinant, one obtains a pathology-free energy-momentum dispersion relation, thus avoiding the classical Velo-Zwanziger problem of imaginary energies in the presence of an external electromagnetic field.Comment: Review talk at "Zacatecas Forum in Physics 2002" on theory and phenomenology of (K/2,K/2)*[(1/2,0)+(0,1/2)] state

Lagrangians for invariant sub-spaces of the squared Pauli-Lubanski vector

We present an alternative formalism to the Rarita-Schwinger framework for the description of "has-been" higher spins at rest that avoids the Velo-Zwanziger problem.Comment: 3 pages, Contribution to the X Mexican School on Particles and Fields, 2002; The calculations by the symbolic program Mathematica have been performed by us during the time period Sept. 10, 2002-Febr. 05, 2003 at the computer heritage.reduaz,mx, courtesy D.V.Ahluwali

Linear Wave Equations and Effective Lagrangians for Wigner Supermultiplets

The relevance of the contracted SU(4) group as a symmetry group of the pion nucleon scattering amplitudes in the large $N_c$ limit of QCD raises the problem on the construction of effective Lagrangians for SU(4) supermultiplets. In the present study we suggest effective Lagrangians for selfconjugate representations of SU(4) in exploiting isomorphism between so(6) and ist universal covering su(4). The model can be viewed as an extension of the linear $\sigma$ model with SO(6) symmetry in place of SO(4) and generalizes the concept of the linear wave equations for particles with arbitrary spin. We show that the vector representation of SU(4) reduces on the SO(4) level to a complexified quaternion. Its real part gives rise to the standard linear $\sigma$ model with a hedgehog configuration for the pion field, whereas the imaginary part describes vector meson degrees of freedom via purely transversal $\rho$ mesons for which a helical field configuration is predicted. As a minimal model, baryonic states are suggested to appear as solitons of that quaternion.Comment: 16 pages, LaTe