Sigma Exchange Research Articles

Molecular states from D^{(*)}{bar{D}}^{(*)}/B^{(*)}{bar{B}}^{(*)} and D^{(*)}D^{(*)}/{bar{B}}^{(*)}{bar{B}}^{(*)} interactions

In this work, we preform a systematic investigation about hidden heavy and doubly heavy molecular states from the D^{(*)}{bar{D}}^{(*)}/B^{(*)}{bar{B}}^{(*)} and D^{(*)}D^{(*)}/{bar{B}}^{(*)}{bar{B}}^{(*)} interactions in the quasipotential Bethe–Salpeter equation (qBSE) approach. With the help of Lagrangians with heavy quark and chiral symmetries, interaction potentials are constructed within the one-boson-exchange model in which we include the pi , eta , rho , omega and sigma exchanges, as well as J/psi or varUpsilon exchange. Possible bound states from the interactions considered are searched for as the pole of scattering amplitude. The results suggest that experimentally observed states, Z_c(3900), Z_c(4020), Z_b(10610), and Z_b(10650), can be related to the D{bar{D}}^{*}, D^*{bar{D}}^{*}, B{bar{B}}^{*}, and B^*{bar{B}}^{*} interactions with quantum numbers I^G(J^P)=1^+(1^{+}), respectively. The D{bar{D}}^{*} interaction is also attractive enough to produce a pole with 0^+(0^+) which is related to the X(3872). Within the same theoretical frame, the existence of D{bar{D}} and B{bar{B}} molecular states with 0(0^+) are predicted. The possible D^*{bar{D}}^* molecular states with 0(0^+, 1^+, 2^+) and 1(0^+) and their bottom partners are also suggested by the calculation. In the doubly heavy sector, no bound state is produced from the DD/{bar{B}}{bar{B}} interaction while a bound state is found with 0(1^+) from DD^*/{bar{B}}{bar{B}}^* interaction. The D^*D^*/{bar{B}}^*{bar{B}}^* interaction produces three molecular states with 0(1^+), 0(2^+) and 1(2^+).

Color superconductivity from the chiral quark–meson model

We study the two-flavor color superconductivity of low-temperature quark matter in the vicinity of chiral phase transition in the quark–meson model where the interactions between quarks are generated by pion and sigma exchanges. Starting from the Nambu–Gorkov propagator in real-time formulation we obtain finite temperature (real axis) Eliashberg-type equations for the quark self-energies (gap functions) in terms of the in-medium spectral function of mesons. Exact numerical solutions of the coupled nonlinear integral equations for the real and imaginary parts of the gap function are obtained in the zero temperature limit using a model input spectral function. We find that these components of the gap display a complicated structure with the real part being strongly suppressed above 2Δ0, where Δ0 is its on-shell value. We find Δ0≃40MeV close to the chiral phase transition.

A hidden local symmetry approach to rho-meson photoproduction

We study photoproduction of rho mesons in a model of hidden local symmetry. The rho meson is introduced as a hidden gauge boson and a phenomenological rho meson-nucleon Lagrangian is constructed respecting chiral symmetry. It is shown that the sigma exchange interaction is needed for neutral rho meson photoproduction to reproduce the experimental cross sections. For charged rho meson photoproduction, the model takes into account the rho meson magnetic moments from the three-point vertex in the kinetic terms. We show that the magnetic moment of the charged rho meson has a significant effect on the total cross sections through the rho meson exchange process, which is proportional to the energy of the photon. The t-channel dominance may be used for the study of structures of various unstable particles.

Sigma exchange in the nuclear force and effective field theory

In the phenomenological description of the nuclear interaction a crucial role is traditionally played by the exchange of a scalar I=0 meson, the sigma, of mass 500-600 MeV, which however is not seen clearly in the particle spectrum and which has a very ambiguous status in QCD. I show that a remarkably simple and reasonably controlled combination of ingredients can reproduce the features of this part of the nuclear force. The use of chiral perturbation theory calculations for two pion exchange supplemented by the Omnes function for pion rescattering suffices to reproduce the magnitude and shape of the exchange of a supposed $\sigma$ particle, even though no such particle is present in this calculation. I also show how these ingredients can describe the contact interaction that enters more modern descriptions of the internucleon interaction.

Method for constructing relativistic three-particle models of the pion-nucleon system

The Bakamjian-Thomas procedure is used to develop a method for constructing relativistic, instant form models of the pion-nucleon system. A limited model space is used to illustrate the method. The model space consists of a single-nucleon subspace, a pion-nucleon subspace, a two-pion-nucleon subspace, and a pion-sigma meson-nucleon subspace. A Poincar\'e invariant mass operator is constructed that includes vertex interactions that couple the various subspaces, as well as renormalization terms. It is shown that the pion-nucleon elastic scattering and production amplitudes can be obtained from the solution of a single, three-dimensional, integral equation of the Lippmann-Schwinger type. The effective pion-nucleon potential that appears in this equation contains contributions from direct and crossed nucleon exchanges along with sigma exchange. The production amplitudes are of the form that arises in isobar models. The elastic scattering and production amplitudes satisfy unitarity. The method developed makes it possible to extend existing coupled-channel models of the pion-nucleon system to include three-particle channels in such a way that the requirements of special relativity and unitarity are satisfied exactly.

Testing the constituent quark model in KN scattering

The kaon–nucleon S, P, D, F, G waves phase shifts have been calculated using a non-relativistic quark potential model and the resonating group method (RGM). The calculation has been performed using quark–quark potential which both includes gluon, pion and sigma exchanges and reproduces as well as possible the meson spectrum. The agreement obtained with the existing experimental phase shifts is quite poor. The results are also compared with a previous calculation based only on gluon exchanges at the quark level.

Meson exchange and nucleon polarizabilities in the quark model

Modifications to the nucleon electric polarizability induced by pion and sigma exchange in the $q\ensuremath{-}q$ potentials are studied by means of sum rule techniques within a nonrelativistic quark model. Contributions from meson exchange interactions are found to be small and in general reduce the quark core polarizability for a number of hybrid and one-boson-exchange $q\ensuremath{-}q$ models. These results can be explained by the constraints that the baryonic spectrum impose on the short-range behavior of the mesonic interactions.

Solution of the Bethe-Salpeter equation for pion-nucleon scattering

A relativistic description of pion-nucleon scattering based on the four-dimensional Bethe-Salpeter equation is presented. The kernel of the equation consists of s- and u-channel nucleon and delta pole diagrams, as well as rho and sigma exchange in the t-channel. The Bethe-Salpeter equation is solved by means of a Wick rotation, and good fits are obtained to the s- and p-wave phase shifts up to 360 MeV pion laboratory energy. The coupling constants determined by the fits are consistent with the commonly accepted values in the literature.

Exchange Currents in Baryons

This paper reviews calculations of the electromagnetic properties of baryons using the constituent quark model. We start with a short discussion of spontaneous chiral symmetry breaking, which is essential in understanding the transition from QCD to the constituent quark model. We then discuss a chiral version of the constituent quark model, which simulates the symmetries and dynamical content of the underlying field theory in terms of gluon, pion and sigma exchange between constituent quarks. We show that the electromagnetic current charge and current operators, usually approximated by one-body operators (impulse approximation), must be supplemented by appropriate two-body terms (exchange currents). The latter represent the gluon and pion exchange degrees of freedom in the electromagnetic current operator. These exchange currents must be included for reasons of completeness and consistency. Most importantly, however, they are needed in order for the electromagnetic current to be conserved. We also study the effect of scalar exchange currents connected with the confinement and sigma exchange potentials. By including these twobody exchange currents we go beyond the single-quark impulse approximation, which has mainly been used up to now. The inclusion of gluon- pion-, and scalar-exchange currents in the quark potential model is the new point of the present work. We show that for some observables, such as the magnetic moments, charge, and magnetic radii of the proton and charged Δ (1232) states, exchange currents contribute at the level of some 10%. The same holds true for the magnetic moments of the entire baryon octet, with the exception of the Ξ- magnetic moment. On the other hand, the neutron charge radius, the quadrupole moments of the Δ, and the N → Δ transition quadrupole moment, are dominated by pion and gluon exchange contributions to the charge density operator. The inclusion of the pion and gluon exchange currents leads to a neutron charge radius of the correct size and sign. Based on the gluon and pion exchange current diagrams, we derive parameter-free relations between the neutron charge radius, the quadrupole moment of the Δ, and the N → Δ transition quadrupole moment. Neglecting configuration mixing, we find that the neutron charge radius and the N → Δ transition quadrupole moment are simply related as QN→Δ = r2 n√2. The implications of Siegert's theorem for the calculation of the E2 form factor in the N → Δ transition are studied. Finally, we discuss the axial coupling constant of the nucleon. We show that the inclusion of axial pair exchange currents does not significantly alter the NRQM prediction.

KN s-wave phase shifts in a quark model with gluon and boson exchange at the quark level

The kaon-nucleon s-wave phase shifts have been calculated in a quark potential model using the resonating group method (RGM). The interquark potential includes gluon, pion and sigma exchanges. The kaon and nucleon wave functions are expanded as a sum of Gaussian functions and the Hill-Wheeler (HW) equation is solved numerically. The I = 0 phase shifts present too much attraction and in the I = 1 channel too much repulsion is obtained.

Electromagnetic properties of one- and two-baryon systems in the quark potential model

These lectures review calculations of the electromagnetic properties of one- and two-baryon systems using the nonrelativistic quark model. We start with a short discussion of spontaneous chiral symmetry breaking, which is essential in understanding the transition from QCD to the constituent quark model. We then discuss the chiral version of the nonrelativistic quark model which simulates the symmetries and dynamical content of the underlying field theory in terms of gluon, pion, and sigma exchange between constituent quarks. In the second lecture, the electromagnetic properties of the one-baryon system are investigated in this framework. In particular, we focus on the effect of gluon and pion degrees of freedom in the electromagnetic current operators. These must be included in order for the electromagnetic current to be conserved. We also study the effect of scalar exchange currents connected with the confinement and sigma exchange potentials. By including these two-body exchange currents we go beyond the single-quark impulse approximation which has mainly been used up to now. The consistent treatment of gluon-, pion-, and scalar-exchange currents in the quark potential model is the new point of the present work. We show that exchange currents have a large effect on various electromagnetic properties, such as magnetic moments, charge and magnetic radii of the nucleon and Δ(1232). We point out that one cannot extract quantitative information about the quark-quark potential from electromagnetic observables without taking two-body exchange currents into account. In the third lecture, we use the quark potential model to study the electromagnetic properties of the deuteron. We emphasize that a quark-model description leads to short-range modifications of the conventional single-nucleon and two-nucleon currents, due to the quark-exchange currents. These appear as a consequence of the Pauli principle at the quark level.

Bosonization in the presence of confinement: Calculation of the nucleon-nucleon interaction.

We describe an extended version of the Nambu\char21{}Jona-Lasinio (NJL) model that includes a description of confinement. It is necessary to incorporate some description of confinement in order to discuss the properties of the sigma, rho, and omega mesons in the NJL model. These mesons, in addition to the pion, are the minimum needed to describe the salient features of the nucleon-nucleon interaction. In previous work we considered the relation between the bosonized NJL model and the one-boson-exchange (OBE) model of the nucleon-nucleon force. Most of our attention was given to pion and sigma exchange. We provide a review of that work and extend our discussion to a consideration of rho and omega exchange. We also present a more detailed discussion of the bosonization procedure. Our results depend upon the strength of the confining interaction. Once that is fixed, we obtain good values for the omega-nucleon coupling constant, ${\mathit{G}}_{\mathrm{\ensuremath{\omega}}\mathit{NN}}$, and for the tensor coupling constant ${\mathit{f}}_{\mathrm{\ensuremath{\rho}}}$, in the rho-nucleon interaction. (One limitation of the present version of the model is that the ratio ${\mathit{f}}_{\mathrm{\ensuremath{\rho}}}$/${\mathit{g}}_{\mathrm{\ensuremath{\rho}}}$=3.70, instead of the empirical value of ${\mathit{f}}_{\mathrm{\ensuremath{\rho}}}$/${\mathit{g}}_{\mathrm{\ensuremath{\rho}}}$\ensuremath{\simeq}6.1.) If we consider nucleon-nucleon scattering for relatively small momentum transfer, we obtain good results for the processes of sigma, pion, rho, and omega exchange. Remarkably, the description of pion exchange is very accurate up to ${\mathit{q}}^{2}$\ensuremath{\sim}-2 ${\mathrm{GeV}}^{2}$. That is, the microscopic model reproduces the pion-exchange amplitude of the boson-exchange model over a broad range of momentum transfer when we specify a single parameter than governs the momentum-transfer dependence of the pseudoscalar-isovector form factor of the nucleon. In the other channels (\ensuremath{\sigma},\ensuremath{\rho},\ensuremath{\omega}), the nucleon form factors may be treated in the same manner. However, if we calculate the form factors in our model, we find that they are too ``soft'' to fit the OBE amplitudes away from ${\mathit{q}}^{2}$\ensuremath{\simeq}0. Further work is needed to obtain good fits for the various amplitudes for large momentum transfer, although the OBE amplitudes are well reproduced in the case of scattering at small momentum transfer (\ensuremath{\Vert}${\mathit{q}}^{2}$\ensuremath{\Vert}\ensuremath{\le}0.1 ${\mathrm{GeV}}^{2}$). \textcopyright{} 1996 The American Physical Society.

A consistent study of the the low energy baryon spectrum and the nucleon-nucleon interaction within the chiral quark model

By solving the Schrödinger equation for the three-quark system in the hyperspherical harmonic approach, we have studied the low energy part of the nucleon and Δ spectra using a quark-quark interaction which reproduces the nucleon-nucleon phenomenology. The quark-quark hamiltonian considered includes, besides the usual one-gluon exchange, pion and sigma exchanges generated by the chiral symmetry breaking. The baryonic spectrum obtained is reasonable and the resulting wave function gives consistency to the ansatz used in the two baryon system.

Constituent quark model calculation for a possible JP = 0−, T = 0 dibaryon

There exists experimental evidence that a dibaryon resonance d' with quantum numbers J^P=0^-,T=0 and mass 2065 MeV could be the origin of the narrow peak in the (\pi^+ ,\pi^- ) double charge exchange cross--sections on nuclei. We investigate the six--quark system with these quantum--numbers within the constituent quark model, with linear confinement, effective one--gluon exchange at short range and chiral interactions between quarks (\pi and \sigma exchange). We classify all possible six quark states with J^P=0^-,T=0, and with N=1 and N=3 harmonic oscillator excitations, using different reduction chains. The six--quark Hamiltonian is diagonalized in the basis including the unique N=1 state and the 10 most important states from the N=3 shell. We find, that with most of the possible sets of parameters, the mass of such a "dibaryon" lies above the N(939)+N^\ast(1535) threshold. The only possibility to describe the supposed d'(2065) in the present context is to reduce the confinement strength to very small values, however at the expense of describing the negative parity resonances N^\ast. We also analyze the J^P=0^-,T=2,N=1 six--quark state.

Masses of hadrons and nucleon-nucleon interaction at finite temperature and density in a quantum hadrodynamics model.

The effective masses and the screening masses of hadrons at finite temperature and density for the quantum hadrodynamics two (QHD-II) model have been investigated under the one-loop approximation. The nucleon-nucleon interaction through pion, sigma, omega, and rho mesons exchange in hot nuclear matter is given. We have found that the potential well of the nucleon-nucleon interaction becomes shallow as the temperature and/or density increases. At a critical temperature and/or a critical density, the potential well disappears.

Spin-orbit force in a quark model based nucleon-nucleon potential.

The spin-orbit interaction coming from the scalar meson-exchange potential between quarks is included in a quark cluster model for the nucleon-nucleon interaction. Its influence on the triplet [ital P]-wave scattering phase shifts and on the baryon spectrum is analyzed. We require that the deuteron binding energy is simultaneously reproduced. Our results indicate that a considerable part of the nucleon-nucleon spin-orbit force can be explained by gluon and sigma exchange between quarks while improving the description of the excited baryon spectrum.

Exchange currents and nucleon magnetic moments

We investigate the effect of gluon and pion exchange currents on the magnetic moments of the nucleon using the constituent quark model. We also study the effect of scalar exchange currents connected with the confinement and sigma exchange potentials. We conclude that although individual exchange currents are quite large, the total exchange current contribution is relatively small, due to a cancellation of gluon, pion, and scalar exchange currents.

Low-energy nucleon-nucleon scattering in a relativised quark model.

Low-energy nucleon-nucleon phase shifts are calculated in resonating group formalism using a Dirac basis for quarks with gluon, pion, and sigma exchange quark-quark interactions. Nucleon polarization as well as quark interchange are included for the short-distance behavior. Reasonable agreement with experiment is obtained.

Effective interaction for relativistic mean-field theories of nuclear structure.

We construct an effective interaction, which when treated in a relativistic Hartree-Fock approximation, reproduces rather accurately the nucleon self-energy in nuclear matter and the Migdal parameters obtained via relativistic Brueckner-Hartree-Fock calculations. This effective interaction is constructed by adding Born terms, describing the exchange of pseudoparticles, to the Born terms of the Dirac-Hartree-Fock analysis. The pseudoparticles have relatively large masses and either real or imaginary coupling constants. (For example, exchange of a pseudo-sigma with an imaginary coupling constant has the effect of reducing the scalar attraction arising from sigma exchange while exchange of a pseudo-omega with an imaginary coupling constant has the effect of reducing the repulsion arising from omega exchange. The terms beyond the Born term in the case of pion exchange are well simulated by pseudo-sigma exchange with a real coupling constant.) The effective interaction constructed here may be used for calculations of the properties of finite nuclei in a relativistic Hartree-Fock approximation.

Dynamical theory for theP-wave pion-nucleon interaction

We present a dynamical theory of low energy $P$-wave $\ensuremath{\pi}N$ interaction. The theory is an extension of the Chew-Low theory, with three additional features, namely, (1) inclusion of the full nucleon recoil effect, (2) inclusion of the $Z$ graphs, and (3) inclusion of $P11$ channel inelasticity. The second feature is new in a $P$-wave theory based on the Low expansion. We are able to fit the $P33$ and the $P11$ phase shifts in the energy region $0<{T}_{\ensuremath{\pi}}<250$ MeV quite well. In particular, we show that it is possible to explain the change of sign of the $P11$ phase shift, ${T}_{\ensuremath{\pi}}\ensuremath{\sim}150$ MeV, in terms of the strong inelasticity present in the channel. For the $P13$ and $P31$ channels, where the phase shifts are the smallest, we do reasonably well at threshold, but not so well as the energy increases. We have also examined the structure of the off-mass-shell amplitudes in the $P11$ and $P33$ channels. Only the $P33$ channel amplitude is found to be factorable. A major result of our work is that the $P33$ form factor is very hard. If one used a monopole form, the form factor mass should be $10{m}_{\ensuremath{\pi}}$ or larger.NUCLEAR REACTIONS Pion-nucleon interaction, $Z$-graph term, sigma exchange term, $P33$ resonance, form factor of $P33$ amplitude, $P11$ inelasticity, nonstatic kinematics.