Covariant Spectator Quark Model Research Articles

Electromagnetic form factors of the Ω− baryon in the spacelike and timelike regions

We present complete calculations of the electromagnetic form factors of the $\Omega^-$ in the spacelike region and in the timelike region. The four elastic form factors: electric charge ($G_{E0}$), magnetic dipole ($G_{M1}$), electric quadrupole ($G_{E2}$) and magnetic octupole ($G_{M3}$), are estimated within the covariant spectator quark model, in terms of the square momentum transfer $q^2$. The free parameters of the $\Omega^-$ wave function, including a $S$-wave state and two independent $D$-wave states radial wave functions and the admixture coefficients are fixed by the comparison with the lattice QCD data in the spacelike region ($Q^2=-q^2 \le 0$) and with the recent $e^+ e^- \to \Omega^- \bar \Omega^+$ data from CLEO in the timelike region ($q^2 > 0$). The estimates in the timelike region for square momentum transfer $q^2 \ge 4 M_\Omega^2$ are based on large-$q^2$ asymptotic relations ($M_\Omega$ is the $\Omega^-$ mass). We examine also the impact of the large-$Q^2$ correlations between different form factors and analyze the possible solutions. The electric quadrupole and the magnetic octupole moments of the $\Omega^-$, and the $e^+ e^- \to \Omega^- \bar \Omega^+$ integrated cross sections for very large $q^2$ are estimated based on the model results.

Covariant model for Dalitz decays of decuplet baryons to octet baryons

In the last years it became possible to measure in HADES the dilepton decays of several baryons. The baryon dilepton decays provide information about the electromagnetic structure of the baryons in the timelike region. In the present work, we study the $B^\prime \to e^+ e^- B$ decays, where $B^\prime$ is a baryon decuplet member and $B$ is a baryon octet member. Our calculations are based on the covariant spectator quark model, where the contribution of the quark core is complemented with an $SU(3)$ contribution from the pion cloud. The pion cloud contribution prove to be relevant in the range of study. We present predictions for the $\Sigma^0 (1385) \to e^+ e^- \Lambda(1116)$ and $\Sigma^{+}(1385) \to e^+ e^- \Sigma^+(1193)$ decays, which may be tested at HADES in a near future. Predictions for the remaining decuplet baryon Dalitz decays are also presented. We conclude that different orders of magnitudes are expected for the baryon decuplet Dalitz decay widths, according to the quark content of the baryons. We also conclude that the dependence of the transition form factors on the square momentum transfer ($q^2$) is important for some transitions.

Covariant model for the Dalitz decay of the N(1535) resonance

We develop a covariant model for the $\gamma^\ast N \to N(1535)$ transition in the timelike kinematical region, the region where the square momentum transfer $q^2$ is positive. Our starting point is the covariant spectator quark model constrained by data in the spacelike kinematical region ($Q^2 = -q^2 >0$). The model is used to estimate the contributions of valence quarks to the transition form factors, and one obtains a fair description of the Dirac form factor at intermediate and large $Q^2$. For the Pauli form factor there is evidence that beyond the quark-core contributions there are also significant contributions of meson cloud effects. Combining the quark-core model with an effective description of the meson cloud effects, we derive a parametrization of the spacelike data that can be extended covariantly to the timelike region. This extension enabled us to estimate the Dalitz decay widths of the $N(1535)$ resonance, among other observables. Our calculations can help in the interpretation of the present experiments at HADES ($pp$ collisions and others).

$$N^*$$ N ∗ form Factors Based on a Covariant Quark Model

We discuss the results of the covariant spectator quark model for the several $\gamma^\ast N \to N^\ast$ transitions, where $N$ is the nucleon and $N^\ast$ a nucleon excitation. More specifically, we present predictions for the form factors and transition amplitudes associated with the resonances $N(1440)1/2^+$, $N(1535)1/2^-$, $N(1520)3/2^-$, $\Delta(1620)1/2^-$ and $N(1650)1/2^-$. The estimates based on valence quark degrees of freedom are compared with the available data, particularly with the recent Jefferson Lab data at low and large momentum transfer ($Q^2$). In general, the estimates are in good agreement with the empirical data for $Q^2 >2$ GeV$^2$, with a few exceptions. The results are discussed in terms of the role of the valence quarks and the meson cloud excitations for the different resonances $N^\ast$. We also review our results for the resonance $\Delta(1232)3/2^+$ and discuss the relevance of the pion cloud component for the magnetic dipole form factor and the electric and Coulomb quadrupole form factors.

γ*N→N*(1520) form factors in the timelike regime

The covariant spectator quark model, tested before in a variety of electromagnetic baryon excitations, is applied here to the $\gamma^\ast N \to N^\ast(1520)$ reaction in the timelike regime. The transition form factors are first parametrized in the spacelike region in terms of a valence quark core model together with a parametrization of the meson cloud contribution. The form factor behavior in the timelike region is then predicted, as well as the $N^\ast(1520) \to \gamma N$ decay width and the $N^\ast (1520)$ Dalitz decay, $N^\ast (1520) \to e^+ e^- N$. Our results may help in the interpretation of dielectron production from elementary $pp$ collisions and from the new generation of HADES results using a pion beam. In the $q^2=0$--1 GeV$^2$ range we conclude that the {\it QED approximation} (a $q^2$ independent form factor model) underestimates the electromagnetic coupling of the $N^\ast(1520)$ from 1 up to 2 orders of magnitude. We conclude also that the $N^\ast (1520)$ and the $\Delta(1232)$ Dalitz decay widths are comparable.

A Relativistic Model for the Electromagnetic Structure of Baryons from the 3rd Resonance Region

We present some predictions for the $\gamma^\ast N \to N^\ast$ transition amplitudes, where $N$ is the nucleon, and $N^\ast$ is a nucleon excitation from the third resonance region. First we estimate the transition amplitudes associated with the second radial excitation of the nucleon, interpreted as the $N(1710)$ state, using the covariant spectator quark model. After that, we combine some results from the covariant spectator quark model with the framework of the single quark transition model, to make predictions for the $\gamma^\ast N \to N^\ast$ transition amplitudes, where $N^\ast$ is a member of the $SU(6)$-multiplet $[70,1^-]$. The results for the $\gamma^\ast N \to N(1520)$ and $\gamma^\ast N \to N(1535)$ transition amplitudes are used as input to the calculation of the amplitudes $A_{1/2}$, $A_{3/2}$, associated with the $\gamma^\ast N \to N(1650)$, $\gamma^\ast N \to N(1700)$, $\gamma^\ast N \to \Delta(1620)$, and $\gamma^\ast N \to \Delta(1700)$ transitions. Our estimates are compared with the available data. In order to facilitate the comparison with future experimental data at high $Q^2$, we derived also simple parametrizations for the amplitudes, compatible with the expected falloff at high $Q^2$.

Axial form factors of the octet baryons in a covariant quark model

We study the weak interaction axial form factors of the octet baryons, within the covariant spectator quark model, focusing on the dependence of four-momentum transfer squared, Q^2. In our model the axial form factors G_A(Q^2) (axial-vector form factor) and G_P(Q^2) (induced pseudoscalar form factor), are calculated based on the constituent quark axial form factors and the octet baryon wave functions. The quark axial current is parametrized by the two constituent quark form factors, the axial-vector form factor g_A^q(Q^2), and the induced pseudoscalar form factor g_P^q(Q^2). The baryon wave functions are composed of a dominant S-state and a P-state mixture for the relative angular momentum of the quarks. First, we study in detail the nucleon case. We assume that the quark axial-vector form factor g_A^q(Q^2) has the same function form as that of the quark electromagnetic isovector form factor. The remaining parameters of the model, the P-state mixture and the Q^2-dependence of g_P^q(Q^2), are determined by a fit to the nucleon axial form factor data obtained by lattice QCD simulations with large pion masses. In this lattice QCD regime the meson cloud effects are small, and the physics associated with the valence quarks can be better calibrated. Once the valence quark model is calibrated, we extend the model to the physical regime, and use the low Q^2 experimental data to estimate the meson cloud contributions for G_A(Q^2) and G_P(Q^2). Using the calibrated quark axial form factors, and the generalization of the nucleon wave function for the other octet baryon members, we make predictions for all the possible weak interaction axial form factors G_A(Q^2) and G_P(Q^2) of the octet baryons. The results are compared with the corresponding experimental data for G_A(0), and with the estimates of baryon-meson models based on SU(6) symmetry.

A covariant model for the negative parity resonances of the nucleon

We present a model for the γ*N → N* helicity amplitudes, where N is the nucleon and N* is a negative parity nucleon excitation, member of the SU(6)-multiplet [70, 1-]. The model combines the results from the single quark transition model for the helicity amplitudes with the results of the covariant spectator quark model for the γ*N → N* (1535) and γ*N → N* (1520) transitions. With the knowledge of the amplitudes A1/2 and A3/2 for those transitions we calculate three independent coefficients defined by the single quark transition model and make predictions for the helicity amplitudes associated with the γ*N → N* (1650), γ*N → N* (1700), γ*N → Δ (1620), and γ*N → Δ (1700) transitions. In order to facilitate the comparison with future experimental data at high Q2, we provide also simple parametrizations for the amplitudes, compatible with the expected falloff at high Q2.

Using the single quark transition model to predict nucleon resonance amplitudes

We present predictions for the $\gamma^\ast N \to N^\ast$ helicity amplitudes, where $N^\ast$ is a member of the $[70,1^-]$ supermultiplet. We combine the results from the single quark transition model for the helicity amplitudes with the results of the covariant spectator quark model for the $\gamma^\ast N \to N^\ast(1535)$ and $\gamma^\ast N \to N^\ast(1520)$ transitions. The theoretical estimations from the covariant spectator quark model are used to calculate three independent functions $A,B$, and $C$ of $Q^2$, where $Q^2=-q^2$ and $q$ is the momentum transfer. With the knowledge of the functions $A,B$, and $C$ we estimate the helicity amplitudes for the transitions $\gamma^\ast N \to N^\ast(1650)$, $\gamma^\ast N \to N^\ast(1700)$, $\gamma^\ast N \to \Delta(1620)$, and $\gamma^\ast N \to \Delta(1700)$. The analysis is restricted to reactions with proton targets. The predictions for the transition amplitudes are valid for $Q^2 > 2$ GeV$^2$.

γ*N→N*(1520)form factors in the spacelike region

The covariant spectator quark model is applied to the ${\ensuremath{\gamma}}^{*}N\ensuremath{\rightarrow}{N}^{*}(1520)$ reaction in the spacelike region. The spin quark core contributions to the electromagnetic form factors and helicity transition amplitudes are estimated from the covariant structure of the ${N}^{*}(1520)$ wave function calibrated by the experimental data for large squared momentum transfer ${Q}^{2}$. The difference between the model results and the experimental data is then used to parametrize the low ${Q}^{2}$ behavior, where meson cloud effects are assumed to dominate. This parametrization can be very useful for future studies of the reaction, as well as for the extension of the transition form factors to the timelike region.

A covariant model for the γ∗N→N∗(1520) reaction

We apply the covariant spectator quark model to the study of the electromagnetic structure of the $N^\ast(1520)$ state ($J^{P}= \frac{3}{2}^-$), an important resonance from the second resonance region in both spacelike and timelike regimes. The contributions from the valence quark effects are calculated for the $\gamma^\ast N \to N^\ast(1520)$ helicity amplitudes. The results are used to parametrize the meson cloud dominant at low $Q^2$.

What is the role of the meson cloud in theΣ*0→γΛandΣ*→γΣdecays?

We study the effect of the meson cloud dressing in the octet baryon to decuplet baryon electromagnetic transitions. Combining the valence quark contributions from the covariant spectator quark model with those of the meson cloud estimated based on the flavor SU(3) cloudy bag model, we calculate the transition magnetic form factors at $Q^2=0$ ($Q^2=-q^2$ and $q$ the four-momentum transfer), and also the decuplet baryon electromagnetic decay widths. The result for the $\gamma^\ast \Lambda \to \Sigma^{\ast 0}$ decay width is in complete agreement with the data, while that for the $\gamma^\ast \Sigma^+ \to \Sigma^{\ast +}$ is underestimated the data by 1.4 standard deviations. This achievement may be regarded as a significant advance in the present theoretical situation.

Electromagnetic transitions among octet and decuplet baryons in QCD

The magnetic dipole ${G}_{M}({Q}^{2})$, electric quadrupole ${G}_{E}({Q}^{2})$, and Coulomb quadrupole ${G}_{C}({Q}^{2})$ form factors, describing the spin-$3/2$ to spin-$1/2$ electromagnetic transitions, are investigated within the light cone QCD sum rules. The ${Q}^{2}$ dependence of these form factors, as well as ratios of electric quadrupole and Coulomb quadrupole form factors to the magnetic dipole form factors, are studied. We also compare our results on the magnetic dipole form factor with the prediction of the covariant spectator quark model.

Octet to decuplet electromagnetic transition in a relativistic quark model

We study the octet to decuplet baryon electromagnetic transitions using the covariant spectator quark model, and predict the transition magnetic dipole form factors for those involving the strange baryons. Utilizing SU(3) symmetry, the valence quark contributions are supplemented by the pion cloud dressing based on the one estimated in the $\gamma^\ast N \to \Delta$ reaction. Although the valence quark contributions are dominant in general, the pion cloud effects turn out to be very important to describe the experimental data. We also show that, other mesons besides the pion in particular the kaon, may be relevant for some reactions such as $\gamma^\ast \Sigma^+ \to \Sigma^{*+}$, based on our analysis for the radiative decay widths of the strange decuplet baryons.

Analysis ofγ*Λ→Σ0transition in QCD

The ${\ensuremath{\gamma}}^{*}\ensuremath{\Lambda}\ensuremath{\rightarrow}{\ensuremath{\Sigma}}^{0}$ transition form factors are investigated within the light-cone QCD sum rules method. Using the most general form of the interpolating current of ${\ensuremath{\Sigma}}^{0}$ baryon and the distribution amplitudes of $\ensuremath{\Lambda}$ baryon we calculate the ${Q}^{2}$ dependence of the electromagnetic form factors. Our results are compared with the predictions of the covariant spectator quark model.

Covariant spectator quark model description of theγ*Λ→Σ0transition

We study the $\gamma^\ast \Lambda \to \Sigma^0$ transition form factors by applying the covariant spectator quark model. Using the parametrization for the baryon core wave functions as well as for the pion cloud dressing obtained in a previous work, we calculate the dependence on the momentum transfer squared, $Q^2$, of the electromagnetic transition form factors. The magnetic form factor is dominated by the valence quark contributions. The final result for the transition magnetic moment, a combination of the quark core and pion cloud effects, turns out to give a value very close to the data. The pion cloud contribution, although small, pulls the final result towards the experimental value The final result, $\mu_{\Lambda\Sigma^0}= -1.486 \mu_N$, is about one and a half standard deviations from the central value in PDG, $\mu_{\Lambda\Sigma^0}= -1.61 \pm 0.08 \mu_N$. Thus, a modest improvement in the statistics of the experiment would permit the confirmation or rejection of the present result. It is also predicted that small but nonzero values for the electric form factor in the finite $Q^2$ region, as a consequence of the pion cloud dressing.

Octet baryon electromagnetic form factors in nuclear medium

We study the octet baryon electromagnetic form factors in nuclear matter using the covariant spectator quark model extended to the nuclear matter regime. The parameters of the model in vacuum are fixed by the study of the octet baryon electromagnetic form factors. In nuclear matter the changes in hadron properties are calculated by including the relevant hadron masses and the modification of the pion–baryon coupling constants calculated in the quark–meson coupling model. In nuclear matter the magnetic form factors of the octet baryons are enhanced in the low Q2 region, while the electric form factors show a more rapid variation with Q2. The results are compared with the modification of the bound proton electromagnetic form factors observed at Jefferson Lab. In addition, the corresponding changes for the bound neutron are predicted.

Shape of theΔbaryon in a covariant spectator quark model

Using a covariant spectator quark model that describes the recent lattice QCD data for the $\ensuremath{\Delta}$ electromagnetic form factors and all available experimental data on $\ensuremath{\gamma}N\ensuremath{\rightarrow}\ensuremath{\Delta}$ transitions, we analyze the charge and magnetic dipole distributions of the $\ensuremath{\Delta}$ baryon and discuss its shape. We conclude that the quadrupole moment of the $\ensuremath{\Delta}$ is a good indicator of the deformation and that the ${\ensuremath{\Delta}}^{+}$ charge distribution has an oblate shape. We also calculate transverse moments and find that they do not lead to unambiguous conclusions about the underlying shape.

Octet baryon electromagnetic form factors in a relativistic quark model

We study the octet baryon electromagnetic properties by applying the covariant spectator quark model, and provide covariant parametrization that can be used to study baryon electromagnetic reactions. While we use the lattice QCD data in the large pion mass regime (small pion cloud effects) to determine the parameters of the model in the valence quark sector, we use the nucleon physical and octet baryon magnetic moment data to parametrize the pion cloud contributions. The valence quark contributions for the octet baryon electromagnetic form factors are estimated by extrapolating the lattice parametrization in the large pion mass regime to the physical regime. As for the pion cloud contributions, we parametrize them in a covariant, phenomenological manner, combined with SU(3) symmetry. We also discuss the impact of the pion cloud effects on the octet baryon electromagnetic form factors and their radii.

Covariant model for theγN→N(1535)transition at high momentum transfer

A relativistic constituent quark model is applied to the $\ensuremath{\gamma}N\ensuremath{\rightarrow}N(1535)$ transition. The $N(1535)$ wave function is determined by extending the covariant spectator quark model, previously developed for the nucleon, to the ${S}_{11}$ resonance. The model allows us to calculate the valence quark contributions to the $\ensuremath{\gamma}N\ensuremath{\rightarrow}N(1535)$ transition form factors. Because of the nucleon and $N(1535)$ structure the model is valid only for ${Q}^{2}>2.3\text{ }\text{ }{\mathrm{GeV}}^{2}$. The results are compared with the experimental data for the electromagnetic form factors ${F}_{1}^{*}$ and ${F}_{2}^{*}$ and the helicity amplitudes ${A}_{1/2}$ and ${S}_{1/2}$, at high ${Q}^{2}$.