arXiv subjects
Publications and source records attributed to V. Pascalutsa.
We point out a source of ambiguities in the measurements of the electromagnetic moments of spin-3/2 baryons which rely on relativistic Lagrangian models. An anambiguous relation between the parameters of the spin-3/2 electromagnetic Lagrangian and the electromagnetic moments of the spin-3/2 particle exits in general only for on-shell situation, while the measurements are done on ``virtual'' baryons.
We develop a relativistic covariant and unitary description of the pion-nucleon interaction in a hadron-exchange model. The model is based on the solution of a dimensionally reduced (quasipotential) Bethe-Salpeter equation for the partial-wave off-shell $πN$ scattering amplitudes with the potential consisting of the field-theoretical $s$- and $u$-channel nucleon, Roper, Delta, $D_{13}$, $S_{11}$ exchanges, and the $t$-channel $ρ$ and $σ$ meson exchanges. The contributions of the spin-3/2 Delta and $D_{13}$ resonances are treated within the Rarita-Schwinger formalism and different forms of the $πNΔ$ vertex are investigated. The free parameters of the model are fitted to the $πN$ phase-shift data of the KH80 and SM95 partial-wave analyses in the region up to 600 MeV pion kinetic energy. The resulting on-shell solution provides a good description of the $πN$ scattering lengths, as well as the energy behavior of the S, P, and D partial waves. The sensitivity of the phase shifts on various model-dependent effects is examined.
We study the general non-minimally coupled charged massive spin 3/2 model both for its low energy phenomenological properties and for its unitarity, causality and degrees of freedom behaviour. When the model is viewed as an effective theory, its parameters (after ensuring the correct excitation count) are related to physical characteristics, such as the magnetic moment g factor, by means of low energy theorems. We also provide the corresponding higher spin generalisation. Separately, we consider both low and high energy unitarity, as well as the causality aspects of our models. None (including truncated N=2 supergravity) is free of the minimal model's acausality.
We discuss the nucleon to higher-spin $N$- and $Δ$-resonance transitions by pions and photons. The higher-spin baryons are described by Rarita-Schwinger fields and, as we argue, this imposes a stringent consistency requirement on the form of the couplings. Popular $πNΔ$ and $γNΔ$ couplings are inconsistent from this point of view. We construct examples of consistent interactions with the same nonrelativistic limit as the conventional ones.
Various quasipotential two-body scattering equations are studied at the one-loop level for the case of $t$- and $u$-channel exchange potentials. We find that the quasipotential equations devised to satisfy the one-body limit for the $t$-channel exchange potential can be in large disagreement with the field-theoretical prediction in the case of $u$-channel exchange interactions. Within the spectator model, the description of the $u$-channel case improves if another choice of the spectator particle is made. Since the appropriate choice of the spectator depends strongly on the type of interaction used, one faces a problem when both types of interaction are contained in the potential. Equal-time formulations are presented, which, in the light-heavy particle system corresponding to the mass situation of the $πN$ system, approximate in a reasonable way the field-theoretical result for both types of interactions.
We show how the invariance under the charge conjugation and CPT symmetry, present in the Bethe-Salpeter equation, is lost in the reduction to certain relativistic three-dimensional equations. This in particular leads to the breakdown of the standard Lorentz structure and renormalization procedures for the resulting single-particle propagators. We formulate the equal-time approximation of the Bethe-Salpeter equation in the form which manifestly satisfies the above symmetries, and apply it to the description of the pion-nucleon interaction in a dynamical model based on hadron exchanges. We also consider the one-body limit of various three-dimensional equations for the case of $t$- and $u$-channel one-particle-exchange potential.
Quantization of the free and interacting Rarita-Schwinger field is considered using the Hamiltonian path-integral formulation. The particular interaction we study in detail is the $πN \De$ coupling used in the phenomenology of the pion-nucleon and nucleon-nucleon systems. Within the Dirac constraint analysis, we show that there is an excess of degrees of freedom in the model, as well as the inconsistency related to the Johnson-Sudarshan-Velo-Zwanzinger problem. It is further suggested that couplings invariant under the gauge transformation of the Rarita-Schwinger field are generally free from these inconsistencies. We then construct and briefly analyse some lowest in derivatives gauge-invariant $πN \De$ couplings.
We argue that most of the relativistic 3-D (quasipotential) equations used in hadron physics are inconsistent with the discrete symmetries like charge conjugation and CPT, yielding an incorrect Lorentz structure for the calculated Green's functions. An exception to this is the equal time approximation to the Bethe-Salpeter equation. We present a covariant quasipotential model for the pion-nucleon interaction based on hadronic degrees of freedom and satisfying the full covariance.
We present a unitary relativistic quasi-potential model for describing the low-energy pion-nucleon interaction, based on the equal time Bethe-Salpeter equation. It preserves the covariant structure of a relativistic spin 1/2 particle for the nucleon propagator, to be contrasted to other quasi-potential approximations.
Lagrangian of a massive particle with spin 3/2 is considered in the Rarita-Schwinger formalism. We discuss implications of the contact- and the gauge-transformation on the physical content of free and interacting theories. It is shown that the ``contact-invariance'' is trivial and has no physical relevance. The requirement of the gauge-invariance of the free lagrangian fixes the off-shell lower-spin content of the spin-3/2 field. The gauge-invariance of the interaction lagrangian insures that these lower-spin components are not coupled, and (probably always) leads to theories consistent with local causality.
We present a relativistic calculation of pion scattering, pion photoproduction and Compton scattering on the nucleon in the energy region of the \Del-resonance (upto 450 MeV photon lab energy), in a unified framework which obeys the unitarity constraint. It is found that the recent data on the cross section for nucleon Compton scattering determine accurately the parameters of the electromagnetic nucleon--\Del\ coupling. The calculated pion-photoproduction partial-wave amplitudes agree well with the recent Arndt analysis.