Decuplet Resonances Research Articles

Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances

We present the results of a third order calculation of the pion-nucleon scattering amplitude in a chiral effective field theory with pions, nucleons and delta resonances as explicit degrees of freedom. We work in a manifestly Lorentz invariant formulation of baryon chiral perturbation theory using dimensional regularization and the extended on-mass-shell renormalization scheme. In the delta resonance sector, the on mass-shell renormalization is realized as a complex-mass scheme. By fitting the low-energy constants of the effective Lagrangian to the $S$- and $P$-partial waves a satisfactory description of the phase shifts from the analysis of the Roy-Steiner equations is obtained. We predict the phase shifts for the $D$ and $F$ waves and compare them with the results of the analysis of the George Washington University group. The threshold parameters are calculated both in the delta-less and delta-full cases. Based on the determined low-energy constants, we discuss the pion-nucleon sigma term. Additionally, in order to determine the strangeness content of the nucleon, we calculate the octet baryon masses in the presence of decuplet resonances up to next-to-next-to-leading order in SU(3) baryon chiral perturbation theory. The octet baryon sigma terms are predicted as a byproduct of this calculation.

Properties of the ground-state baryons in chiral perturbation theory

We review recent progress in the understanding of low-energy baryon structure by means of chiral perturbation theory. In particular, we discuss the application of this formalism to the description of various properties such as the baryon-octet magnetic moments, the electromagnetic structure of decuplet resonances and the hyperon vector coupling $f_1(0)$. Moreover, we present the results on the chiral extrapolation of recent lattice QCD results on the lowest-lying baryon masses and we predict the corresponding baryonic sigma-terms.

Properties of hyperons in chiral perturbation theory

The development of chiral perturbation theory in hyperon phenomenology has been troubled due to power-counting subtleties and to a possible slow convergence. Furthermore, the presence of baryon-resonances, e.g. the lowest-lying decuplet, complicates the approach, and the inclusion of their effects may become necessary. Recently, we have shown that a fairly good convergence is possible using a renormalization prescription of the loop-divergencies which recovers the power counting, is covariant and consistent with analyticity. Moreover, we have systematically incorporated the decuplet resonances taking care of both power-counting and consistency problems. A model-independent understanding of diferent properties including the magnetic moments of the baryon-octet, the electromagnetic structure of the decuplet resonances and the hyperon vector coupling f 1 ( 0 ) , has been successfully achieved within this approach. We will briefly review these developments and stress the important role they play for an accurate determination of the Cabibbo-Kobayashi-Maskawa matrix element V us from hyperon semileptonic decay data.

Electromagnetic structure of the lowest-lying decuplet resonances in covariant chiral perturbation theory

We present a calculation of the leading SU(3)-breaking $\mathcal{O}({p}^{3})$ corrections to the electromagnetic moments and charge radius of the lowest-lying decuplet resonances in covariant chiral perturbation theory. In particular, the magnetic dipole moment of the members of the decuplet is predicted fixing the only low-energy constant (LEC) present up to this order with the well-measured magnetic dipole moment of the ${\ensuremath{\Omega}}^{\ensuremath{-}}$. We predict ${\ensuremath{\mu}}_{\ensuremath{\Delta}}^{++}=6.04(13)$ and ${\ensuremath{\mu}}_{\ensuremath{\Delta}}^{+}=2.84(2)$, which agree well with the current experimental information. For the electric quadrupole moment and the charge radius, we use state-of-the-art lattice QCD results to determine the corresponding LECs, whereas for the magnetic octupole moment there is no unknown LEC up to the order considered here, and we obtain a pure prediction. We compare our results with those reported in large ${N}_{c}$, lattice QCD, heavy-baryon chiral perturbation theory, and other models.

Leading-order decuplet contributions to the baryon magnetic moments in chiral perturbation theory

We extend an earlier study of the baryon magnetic moments in chiral perturbation theory by the explicit inclusion of the spin-3/2 decuplet resonances. We find that the corrections induced by these heavier degrees of freedom are relatively small in a covariant framework where unphysical spin-1/2 modes are removed. Consequently, implementing the leading SU(3)-breaking corrections given by both the baryon and decuplet contributions, we obtain a description of the baryon-octet magnetic moments that is better than the Coleman–Glashow relations. Finally, we discuss the uncertainties and compare between heavy baryon and covariant approaches.

Connected parts of decuplet electromagnetic properties

We determine the electromagnetic properties of decuplet resonances using chiral perturbation theory at next-to-leading order. Utilizing a partially quenched charge matrix, we isolate and remove the quark disconnected contractions. This allows us to compare the physical meson loop contributions to the connected contributions, of which the latter are currently calculated using lattice QCD. Finally we determine linear combinations of decuplet resonance and hyperon electromagnetic properties that are exactly independent of disconnected contractions in the isospin limit.

Non-leptonic hyperon decays in chiral perturbation theory

The non-leptonic hyperon decays are analyzed up to one-loop order including all counterterms in the framework of heavy baryon chiral perturbation theory. We use the exchange of the spin-\(\frac{3}{2}\) decuplet resonances as an indication of which low-energy constants contribute significantly to these investigated processes. We choose four independent decay amplitudes that are not related by isospin relations in order to perform a fit for the pertinent low-energy constants and find a satisfactory fit both for s- and p-waves. The chiral corrections to the lowest order forms for the s-waves are moderate whereas there are significant modifications of the p-wave amplitudes.

Non-leptonic hyperon decays in chiral perturbation theory

The non-leptonic hyperon decays are analyzed up to one-loop order including all counterterms in the framework of heavy baryon chiral perturbation theory. We use the exchange of the spin-3/2 decuplet resonances as an indication of which low-energy constants contribute significantly to these investigated processes . We choose four independent decay amplitudes that are not related by isospin relations in order to perform a fit for the pertinent low-energy constants and find a satisfactory fit both for s- and p-waves. The chiral corrections to the lowest order forms for the s-waves are moderate whereas there are significant modifications of the p-wave amplitudes.

Quark-Model Predictions for Reactions with Hyperon Beams

Quark-model predictions are discussed for Primakoff excitation of hyperon resonances, total hyperon-nucleon cross sections, and diffractive excitation. The $U$-spin selection rule forbidding electromagnetic excitation of negatively charged decuplet resonances is shown to hold even in the presence of large SU(3)-symmetry breaking. A new model for diffractive excitation is presented which suggests the existence of new hyperon resonances, not yet discovered, which would be observed in diffractive excitation but only weakly coupled to two-body formation and decay channels. The SU(3) partners of the Roper resonance $N(1470)$ might be such states and be found with hyperon beams.

Decay Rates of the Decuplet Resonances from O(3, 1)⊗SU(3) Dynamics. Definite SU(3) Symmetry Breaking

The simplest dynamical group including SU(3), O(3, 1)\ensuremath{\bigotimes} SU(3), is used to describe the decay widths of the ${j}^{P}={\frac{3}{2}}^{+}$ decuplet resonances. SU(3) breaking comes in naturally (and uniquely) through the mass differences in the multiplet. The only two parameters of the theory have been fixed in an independent fit of the $I=\frac{3}{2}$ baryon decay rates for different spins. The agreement with experiment is excellent.

Electromagnetic mass differences and coupling-constant ratios in the strong coupling group SU(3) × SU(2) × T24

Assuming that the SU(3), SU(2) contents of the infinite unitary irreducible representation of SU(3) × SU(2) × T 24 are 8 1 2 , 10 3 2 , 10 3 2 , 27 1 2 , 27 3 2 , … etc. as given by Goebel, we obtain relations between the various matrix elements of the generators of the group. The method employed here is that due to Singh and Udgaonkar, based on the equivalence of the static strong coupling theory and the bootstrap conditions of the static pion nucleon scattering. As an application we have calculated electromagnetic mass differences of octet baryons and decuplet resonances and their ratios. Various coupling and magnetic moments relations are predicted, in particular we have obtained the decay width of N ∗ → N + γ in terms of proton magnetic moment. The results of these calculations are in reasonable agreement with experiment.

Octet enhancement and the reciprocal bootstrap

Perturbations of the masses of baryon and meson-baryon resonances due to the breaking of an internal symmetry group are studied in the static model. For particular assignments of particles to representations of SU(2) we show that the bootstrap condition for the baryon implies the enhancement of perturbations which transform like isotopic vectors. In the case of SU(3) we use the reciprocal bootstrap for the octet baryons and decuplet resonances and demonstrate the relationship between it and octet enhancement. These results show in a simple way the manner in which the bootstrap equations make definite predictions about the transformation properties of mass perturbations.