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Register a new userPreliminary study of the anti-K N interaction in a chiral constituent quark model
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A preliminary investigation of the anti-K N interaction is performed within a chiral constituent quark model by solving the resonating group method (RGM) equation. The model parameters are taken from our previous work, which gave a satisfactory description of the S-, P-, D-, F-wave KN scattering phase shifts. The channel-coupling between anti-K N, pi Lambda and pi Sigma is considered, and the scattering phase shifts as well as the bound-state problem of anti-K N are dynamically studied. The results show that the S-wave anti-K N interaction in the isospin I=0 channel is attractive, and in the extended chiral SU(3) quark model such an attraction can make for an anti-K N bound state, which appears as a pi Sigma resonance in the coupled-channel calculation, while the chiral SU(3) quark model cannot accommodate the existence of an anti-K N bound state. It seems that the vector meson exchanges are necessary to be introduced in the quark-quark interactions if one tries to explain the Lambda(1405) as an anti-K N bound state or a pi Sigma - anti-K N resonance state.
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The energies of the low-lying isoscalar and isovector ud anti-s anti-s configurations with spin-parity J^P=0^+, 1^+, and 2^+ are calculated in a non-relativistic constituent quark model by use of the variational method. The contributions of various parts of the quark-quark interacting potentials including the s-channel interaction are investigated, and the effect of different forms of confinement potential is examined. The model parameters are determined by the same method as in our previous work, and they still can satisfactorily describe the nucleon-nucleon scattering phase shifts and the hyperon-nucleon cross sections. The parameters of the s-channel interaction are fixed by the masses of K and K^* mesons, for which the size parameter is taken to be two possible values. When it is chosen as the same as baryons, the numerical results show that the masses of all the ud anti-s anti-s configurations are higher than the corresponding meson-meson thresholds. But when the size parameter for the K and K^* mesons is adjusted to be smaller than that for the baryons, the ud anti-s anti-s configuration with I=0 and J^P=1^+ is found to lie lower than the K^*K^* threshold, furthermore, this state has a very small KK^* component and the interaction matrix elements between this state and KK^* is comparatively small, thus its coupling to the KK^* channel will consequently be weak and it might be regarded as a possible tetraquark candidate.
A formalism based on a chiral quark model ($chi$QM) approach complemented with a one-gluon exchange model, to take into account the breakdown of the $SU(6)otimes O(3)$ symmetry, is presented. The configuration mixing of wave functions for nucleon and resonances are derived. % With few adjustable parameters, differential cross-section and polarized beam asymmetry for the $gamma p to eta p$ process are calculated and successfully compared with the data in the centre-of-mass energy range from threshold up to 2 GeV. The known resonances $S_{11}(1535)$, $S_{11}(1650)$, $P_{13}(1720)$, $D_{13}(1520)$, and $F_{15}(1680)$, as well as two new $S_{11}$ and $D_{15}$ resonances are found to be dominant in the reaction mechanism. Besides, connections among the scattering amplitudes of the $chi$QM approach and the helicity amplitudes, as well as decay widths of resonances are established. Possible contributions from the so-called missing resonances are investigated and found to be negligible.
A dynamical coupled-channel study of K* K*bar state with isospin 0 and omega phi state is performed within both the chiral SU(3) quark model and the extended chiral SU(3) quark model by solving a resonating group method (RGM) equation. The model parameters are taken from our previous work, which gave a satisfactory description of the energies of the octet and decuplet baryon ground states, the binding energy of the deuteron, the nucleon-nucleon (NN) scattering phase shifts, and the hyperon-nucleon (YN) cross sections. The results show that the interactions of K* K*bar states are attractive, which consequently result in K* K*bar bound states with the binding energies of about 10-70 MeV, and contrarily, no omega phi bound state is obtained. The channel coupling effect of K* K*bar and omega phi is found to be considerably large, which makes the binding of K* K*bar 5-45 MeV deeper. The plausible interpretation of f_0(1710) and X(1812) being K* K*bar dominated states is briefly discussed.
${bf Background}$ Knowledge of nucleon structure is today ever more of a precision science, with heightened theoretical and experimental activity expected in coming years. At the same time, a persistent gap lingers between theoretical approaches grounded in Euclidean methods (e.g., lattice QCD, Dyson-Schwinger Equations [DSEs]) as opposed to traditional Minkowski field theories (such as light-front constituent quark models). ${bf Purpose}$ Seeking to bridge these complementary worldviews, we explore the potential of a Euclidean constituent quark model (ECQM). This formalism enables us to study the gluonic dressing of the quark-level axial-vector vertex, which we undertake as a test of the framework. ${bf Method}$ To access its indispensable elements with a minimum of inessential detail, we develop our ECQM using the simplified quark $+$ scalar diquark picture of the nucleon. We construct a hyperspherical formalism involving polynomial expansions of diquark propagators to marry our ECQM with the results of Bethe-Salpeter Equation (BSE) analyses, and constrain model parameters by fitting electromagnetic form factor data. ${bf Results}$ From this formalism, we define and compute a new quantity --- the Euclidean density function (EDF) --- an object that characterizes the nucleons various charge distributions as functions of the quarks Euclidean momentum. Applying this technology and incorporating information from BSE analyses, we find the dressing effect on the protons axial-singlet charge to be small in magnitude and consistent with zero. ${bf Conclusions}$ The scalar quark $+$ diquark ECQM is a step toward a realistic quark model in Euclidean space, and urges additional refinements. The small size we obtain for the impact of the dressed vertex on the axial-singlet charge suggests that models without this effect are on firm ground to neglect it.
We evaluate the $sigma$ exchange contribution to the $bar{K}Ntobar{K}N$ scattering within a chiral unitary approach. We show that the chiral transition potentials for $pi pi to K bar{K}$ in the $t$-channel lead to a $sigma$ contribution that vanishes in the $bar{K}$ forward direction and, hence, would produce a null $sigma$ exchange contribution to the $K^-$ optical potential in nuclear matter in a simple impulse approximation. This is a consequence of the fact that the leading order chiral Lagrangian gives an I=0 $pipito Kbar{K}$ amplitude proportional to the squared momentum transfer, $q^2$. This finding poses questions on the meaning or the origin of $sigma$ exchange potentials used in relativistic mean field approaches to the $K^-$ nuclear selfenergy. This elementary $sigma$ exchange potential in $bar{K}Ntobar{K}N$ is compared to the Weinberg-Tomozawa term and is found to be smaller than present theoretical uncertainties but will be relevant in the future when aiming at fitting increasingly more accurate data.
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