Negative Parity Resonances Research Articles

The process Ω→γΞ as a possible test of the penguin diagram

It is argued that Ω→γΞ is a convenient process for testing the ΔS=1 penguin diagram. The analysis is based on the standard pole model, including negative parity resonances. Using bag model matrix elements and standard values of the penguin operator coefficients, it is found that the branching ratio for Ω→γΞ is of order 10−5 to 10−4. The weak matrix element for Ω→γΞ estimated by means of soft pion and current algebra techniques is found to be ∼7 times bigger than the corresponding bag model result. This implies a branching ratio close to the experimental upper limit if standard values of the penguin coefficients are used.

The multi-configuration shell model in the continuum and the resonant states in12C

The excitation function of the total cross section in the 11B(p,n) reactions has been analysed in terms of a continuum shell-model formalism developed earlier for the study of the 11B(p, gamma 1) reaction. Overall agreement with experiment has been obtained for 21-5 MeV excitation in 12C. The observed structure is interpreted as due mainly to overlapping negative-parity resonances. The dominant resonance behaviour around 21.5 MeV is attributed to a 3-,T=0 state in 12C.

Effective nuclear forces in the quark model with delta and hidden-color channel coupling

Adiabatic potentials are calculated in a six-quark cluster model corresponding to having NN, ΔΔ and CC (hidden color) channel coupling. Color-dependent quark interactions are used that yield the N and Δ positive- and negative-parity resonances up to 2 GeV. Channel coupling is found to be large (especially with the CC state) and yields an effective NN potential having none of the characteristics of phenomenological potentials extracted from phase shifts.

A coupled-channels treatment of the positive-parity resonances in4He

The coupled-channels formalism, which has been previously applied successfully to interpret the negative-parity resonances in4He, has now been extended to the positiveparity 2ℏω resonances in this system. The 1p-1h approach has been modified to include coupling to the 2p-2h configurations, which also belong to 2ℏω excitations, by using the effective operator formalism. The effect of the Pauli term in thes-wave channel is examined and is found to be important in reproducing the 0+,T=0 resonance energy and width. Resonances with spins up toJπ=3+ have been studied, and the agreement with available data is satisfactory. In particular, from the good fit to the asymmetry coefficientβ(E), one establishes the presence of a 2+,T=0 resonance around 35-MeV excitation in the system.

Resonance scattering with modified continuum states: (II). Application of the unified model with one particle in the continuum to the 12C + n system

Starting from the conventional shell model, different methods for the treatment of the continuum are given. Using the modified continuum states of part I together with the reaction operator formalism, the present approach unifies the numerical features of the R-matrix theory and the physical picture of the shell model. As it treats the bound states and the scattering states in the same basis we calculated both for the 12C + n system as a test case. It is found that the results resemble the experimental data quite well, including for the first time the negative-parity resonances.

A microscopic description of the negative parity resonances in the mass-4 system by the coupled-channels method (II)

The coupled-channels method for the treatment of the continuum is used to study the negative parity excited states of the 4He nucleus in the Tamm-Damcoff approximation. It is shown that the splittings within the SU(4) supermultiplet are well reproduced in this calculation when the spin-dependent forces responsible for the removal of the degeneracy are taken appropriately into account. The location of the T = 0, 1 − resonance and the admixture of spurious c.m. excitation in the intrinsic excitation are discussed. In addition to interpreting the observed spectrum, the available experimental data for the particle channels are well described by the theory.

A microscopic description of the negative parity resonances in the mass-4 system by the coupled-channel method

The negative parity resonances in the mass-4 system have been investigated in the 1p-1h approximation treating the continuum by the coupled-channel method. The observed dipole photo-reaction cross section of 4He as well as the energy dependence of the phase shifts deduced from the p- 3He scattering are well reproduced by the theory.

New Parameters forΔ++Resonances from 2170 to 3490 MeV inπ+pBackward Elastic Scattering

Data obtained in a ${\ensuremath{\pi}}^{+}p$ backward-elastic-scattering experiment from 2 to 6 GeV/c were used to investigate $s$-channel ${\ensuremath{\Delta}}^{++}$ resonances between 2170 and 3490 MeV/${\mathit{c}}^{2}$. Two different models for fitting the energy dependence of ${(\frac{d\ensuremath{\sigma}}{d\ensuremath{\Omega}})}_{180\ifmmode^\circ\else\textdegree\fi{}}$ gave good fits. We present values for the masses, widths, parities, and the product of the spin and elasticity for the $\ensuremath{\Delta}(2420)$, $\ensuremath{\Delta}(2850)$, and $\ensuremath{\Delta}(3230)$ as well as the recently observed negative-parity resonance at \ensuremath{\sim}2200 MeV/${\mathit{c}}^{2}$.

Symmetric Quark Model of Baryon Resonances

The symmetric quark model of baryon resonances is applied to the (56,${0}^{+}$), (70,${1}^{\ensuremath{-}}$), and (20,${1}^{+}$) supermultiplets. Using a systematic $\mathrm{SU}(6)$ analysis, octet dominance, and dominance of two-body contributions to the mass operator, the G\"ursey-Radicati mass formula for the (56,${0}^{+}$) is derived without use of perturbation theory. An equal-spacing relation is derived for the $\mathrm{SU}(6)$-symmetric mass contribution for the (56,${0}^{+}$), (70,${1}^{\ensuremath{-}}$), and (20,${1}^{+}$) in ascending order, with the (20,${1}^{+}$) lying above 2 BeV. A detailed analysis of the (70,${1}^{\ensuremath{-}}$), which yields a quantitative fit for the spin-orbit-split negative-parity resonances, is made, with the result that the magnitude of the octet spin-orbit term is about six times greater than the singlet one. The masses and mixing amplitudes for all the resonances in the (70,${1}^{\ensuremath{-}}$) are calculated, and it is pointed out that because of the large mixings for ${J}^{P}={\frac{1}{2}}^{\ensuremath{-}} \mathrm{and} {\frac{3}{2}}^{\ensuremath{-}}$, the Gell-Mann-Okubo mass formula cannot be expected to hold for these resonances, so that there is no sense in trying to group them into octets and decuplets.

Saturation of current algebra equations with higher baryonic resonances

The saturation of the commutation relations of the chiral $U(3)\ensuremath{\bigotimes}U(3)$ algebra with supermultiplets of $S{U}_{6}$ or $S{U}_{6}\ensuremath{\bigotimes}{O}_{3}$ is considered. The general helicity dependence of the matrix elements of axial charges at $\mathbf{p}=\ensuremath{\infty}$ is calculated. A continuity postulate is introduced to select the physically significant solutions from the multiplicity of solutions of the non-linear set of saturated commutator equations. A linearized approach is developed to derive criteria of "connection" between two supermultiplets with respect to the chiral algebra and to calculate the renormalizatioris (at second order) of the couplings. The possible relevance of the connection criteria and of the compatibility with data of the coupling renormalizations to discriminate among various possibilities of classification of higher resonances is pointed out. Special cases discussed are classifications of negative parity resonances according to the representations and 56 of $S{U}_{6}$ and (20, $L=\mathit{1}$) of $S{U}_{6}\ensuremath{\bigotimes}{O}_{3}$. Only the last one gives consistent predictions.

Dynamical Model for Baryon Resonances

We propose a nonrelativistic three-quark (Q) model of baryons and their resonances with the assumptions of (i) parastatistics which, in constrast to Fermi statistics, allows totally symmetric wave functions, and (ii) operation of Q-Q forces of the factorable type in s and p waves which facilitate an exact solution of the three-body problem. It is found that the s-wave force gives rise to a strong attraction in a spatially symmetric (S) state of L=0, but repulsion in a mixed-symmetric (M) state. This provides a natural dynamical realization of the 56 representation of SU(6) for the familiar octet and decuplet of baryons. The same s-wave force also predicts a set of negative-parity resonances but these are of much too high energy to be of any physical consequence. The p-wave force leads to a set of negative-parity L=1 resonances via strong attraction in M-type spatial states of L=1, thus making up the representation (70,3) of SU(6)×O(3). A p-wave spin-orbit Q-Q force splits these states in a manner which fits in rather well with Dalitz's recent analysis of experimental data for the negative-parity baryonic resonances. Finally, the p-wave force generates a strong attraction in a spatially antisymemtric state (A) of even parity and L=1, giving rise to the representation (20,3) of SU(6)×O(3), of which the lowest states are an octet and a singlet of J P =1/2 + , the central mass of each lying lower than the corresponding lowest mass multiplet of negative parity. This provides a natural explanation of the so-called Roper resonance (at 1450 MeV), and in addition, strongly predicts an even-parity singlet of a mass lower than the Y 0 ∗ (1405). The distinction between Fermi statistics and paraststistics is discussed in the context of the above results, and it is argued that while Fermi statistics could in principle generate negative-parity L=1 resonances (via M functions), it could not possibly account for the 56 of baryons, since with Q-Q forces alone,the A function of L=0 that should go with it has a strongly repulsive kernel.