Chiral Bag Model Research Articles

Historical Introduction to Chiral Quark Models

Chiral symmetry, and its dynamical breaking, has become a cornerstone in the description of the hadron’s phenomenology at low energy. The present manuscript gives a historical survey on how the quark model of hadrons has been implemented along the last decades trying to incorporate, among other important non-perturbative features of quantum chromodynamics (QCD), the dynamical chiral symmetry breaking mechanism. This effort has delivered different models such as the chiral bag model, the cloudy bag model, the chiral quark model or the chiral constituent quark model. Our main aim herein is to provide a brief introduction of the Special Issue “Advances in Chiral Quark Models” in Symmetry and contribute to the clarification of the differences among the above-mentioned models that include the adjective chiral in their nomenclature.

5a-A-5 g_A Problem in the Chiral Bag Model

5a-A-5 g_A Problem in the Chiral Bag Model

Errata: “Condensate-enclosed chiral-bag model of the proton and pp elastic scattering at LHC 13 TeV”

Errata: “Condensate-enclosed chiral-bag model of the proton and <i>pp</i> elastic scattering at LHC 13 TeV”

Condensate-enclosed chiral-bag model of the proton and pp elastic scattering at LHC 13 TeV

Our investigation of high energy [Formula: see text] and [Formula: see text] elastic scattering over the last ten years has led us to consider that the proton has three regions: (i) an outer region consisting of a quark–antiquark [Formula: see text] condensate ground state (also described as quark–antiquark outer cloud), (ii) an inner shell of topological (geometrical) baryonic charge of size [Formula: see text] 0.44 fm, and (iii) a core of size [Formula: see text] 0.2 fm, where the three valence quarks of a proton with baryonic charges are confined. The proton structure that has emerged leads to four main elastic scattering processes in [Formula: see text] scattering. The first process (which gives rise to diffraction scattering) is described by a profile function. The second process involves multiple [Formula: see text]-exchanges. The third process in [Formula: see text] scattering is quark–quark scattering via gluon–gluon interaction. The fourth process — which appears for the first time in our investigation of [Formula: see text] scattering — is a glancing collision at the boundary of a proton with that of the other proton. To describe quantitatively the four processes, their parameters have to be determined. For this purpose, we investigate: (i) [Formula: see text] 7 TeV [Formula: see text] measured by the TOTEM Collaboration and (ii) [Formula: see text] 1.96 TeV [Formula: see text] measured by the D0 Collaboration. Once the parameters are satisfactorily obtained, we calculate [Formula: see text] [Formula: see text] at 7 TeV and compare with the TOTEM data. We also calculate [Formula: see text] [Formula: see text] at 1.96 TeV and compare with the D0 data. We then predict [Formula: see text] elastic [Formula: see text] at 13 TeV which will soon be measured at LHC by the TOTEM Collaboration. This measurement will establish how well we have predicted the 13 TeV [Formula: see text] and determined the structure of the proton.

Recent Status of the Chiral Bag Model

In this note, recent status of the chiral bag model is presented. As it combines the MIT quark bag model and the Skyrme model, the chiral bag model interpolates the two models smoothly as a function of the chiral bag radius R. The correct limit of R→∞ is reproduced by including the higher order terms in the Ω expansion of the cranking method. It resolves the so-called small gA problem in a class of models where the semiclassical method is used.

Nonperturbative proton stability

Proton decay is a generic prediction of GUT models and is therefore an important channel to detect the existence of unification or to set limits on GUT models. Current bounds on the proton lifetime are around ${10}^{33}\text{ }\text{ }\mathrm{years}$, which sets stringent limits on the GUT scale. These limits are obtained under ``reasonable'' assumptions about the size of the hadronic matrix elements. In this paper we present a nonperturbative calculation of the hadronic matrix elements within the chiral bag model of the proton. We argue that there is an exponential suppression of the matrix elements, due to nonperturbative QCD, that stifles proton decay by orders of magnitude---potentially $\mathcal{O}({10}^{\ensuremath{-}10})$. This suppression is present for small quark masses and is due to the chiral symmetry breaking of QCD. Such a suppression has clear implications for GUT models and could resuscitate several scenarios.

NUCLEON IN NUCLEAR MEDIUM

The behavior of a nucleon in nuclear medium is discussed in Chiral Color Dielectric Model. It is assumed that the nucleons in nuclear medium produces a background dielectric field and the quark and dielectric field equations are solved self consistantly in presence of the dielectric field. A nucleon in nuclear medium is then constructed by means of standard procedure followed in chiral bag models. The corrections due to center of mass motion, color magnetic interaction and meson interaction are included. The calculations show that the nucleon becomes bigger in the medium but its mass does not change much. It is found that beyond a certian density, bound solutions in which quarks are bound in self-generated dielectric field are not possible. Thus, the calculations indicate that there is a critical density beyond which the matter consists of deconfined quarks.

Chiral symmetry breaking and vacuum polarization in a bag

We study the effects of a finite quark mass in the hedgehog configuration in the two phase chiral bag model. We discuss the chiral properties, such as the fractional baryon number and the chiral Casimir energy, by using the Debye expansion for the analytical calculation and the Strutinsky's smearing method for the numerical computation. It is shown that the fractional baryon number carried by massive quarks in the vacuum is canceled by that in the meson sector. A finite term of the chiral Casimir energy is obtained with subtraction of the logarithmic divergence term.

Quark droplets with chiral symmetry in the Nambu–Jona-Lasinio model

We discuss the stability of strangelets by considering dynamical chiral symmetry breaking. For quark droplets of finite volume, we formulate the Nambu--Jona-Lasinio model with a basis set of the quark wave functions in the chiral bag model. Chiral symmetry breaking for the finite volume bag is discussed in a mean field approximation. Effects of the pion cloud including the chiral Casimir effect are investigated. Physical quantities of the quark droplets such as masses and radii are obtained for quark droplets of baryon numbers up to five. We also apply our model setting to the nucleon and discuss the stability of the quark droplets against nuclei.

Finite temperature induced fermion number for quarks in a chiral field

We compute the finite temperature correction to the induced fermion number for fermions coupled to a static SU(2) chiral background, using the derivative expansion technique. At zero temperature the induced fermion number is topological, being the winding number of the chiral background. At finite temperature however, higher order terms in the derivative expansion give nontopological corrections to the winding number. We use this result to show that the standard cancellation of the fractional parts of the fermion number inside and outside the bag in an SU(2) x SU(2) hybrid chiral bag model of the nucleon does not occur at nonzero temperature.

Dynamical chiral bag model

We study a dynamical chiral bag model, in which massless fermions are confined within an impenetrable but movable bag coupled to meson fields. The self-consistent motion of the bag is obtained by solving the equations of motion exactly assuming spherical symmetry. When the bag interacts with an external meson wave we find three different kinds of resonances: {\it fermionic}, {\it geometric}, and $\sigma$-resonances. We discuss the phenomenological implications of our results.

CHIRAL BAG MODEL WITH CONSTITUENT QUARKS: TOPOLOGICAL AND NONTOPOLOGICAL SOLUTIONS

We consider a three-phase modification of the hybrid chiral bag model involving the intermediate constituent quark phase along with the asymptotic freedom and hadronization phases. We find self-consistent solutions of the equations of the model in 1+1 dimensions with the fermion vacuum polarization effects taken into account. We study the renormalized total energy of the bag as a function of parameters characterizing the geometry of the bag and its topological (baryon) charge. We show that for a nonzero topological charge, there exists an entire series of configurations that are local minimums of the total energy of the bag and contain all the three phases, whereas in the nontopological case, the bag energy minimum corresponds to zero sizes of the domain of the asymptotic freedom phase.

Hadron Mass and the Properties of Nuclear Matter in the Quark Bag Models**The project supported by National Natural Science Foundation of China (Grant No. 19775072) and the Natural Science Foundation of Guangdong Province of China (Grant No. 970130)

The MIT bag model, chiral bag model and cloudy bag model are revisited. A typical work on the hadron mass calculation by chiral bag model and cloudy bag model is shown in more details with the quark-quark-pi vertex correction and quark self-energy being emphasized. More details are given to review the quark-meson coupling model and its application in nuclear matter. We put forth the Lagrangian of the quark-meson coupling model and studied the possibility of using the model to calculate the hadron mass.

The gluon spin in the chiral bag model

We study the gluon polarization contribution at the quark model renormalization scale to the proton spin, Γ, in the chiral bag model. It is evaluated by taking the expectation value of the forward matrix element of a local gluon operator in the axial gauge A +=0. It is shown that the confining boundary condition for the color electric field plays an important role. When a solution satisfying the boundary condition for the color electric field, which is not the conventionally used but which we favor, is used, the Γ has a positive value for all bag radii and its magnitude is comparable to the quark spin polarization. This results in a significant reduction in the relative fraction of the proton spin carried by the quark spin, which is consistent with the small flavor singlet axial current measured in the EMC experiments.

Chiral hybrid bag model with the boson field inside the bag

The three-phase version of the hybrid chiral bag model, containing the phase of asymptotic freedom, the hadronization phase as well as the intermediate phase of constituent quarks, is proposed. For this model the self-consistent solution, which takes into account the fermion vacuum polarization effects, is found in (1+1)D. Within this solution the total energy of the bag, including the one-loop contribution from the Dirac's sea, is studied as a function of bag geometry under condition of nonvanishing boson condensate density in the interior region. The existence and uniqueness of the ground state bag configuration, which minimizes the total energy and contains all the three phases, are shown.

The proton spin in the chiral bag model: Casimir contributions and Cheshire Cat Principle

The flavor singlet axial charge has been a source of study in the last years due to its relation to the so-called Proton Spin Problem. The relevant flavor singlet axial current is anomalous, i.e., its divergence contains a piece which is the celebrated U A (1) anomaly. This anomaly is intimately associated with the η′ meson, which gets its mass from it. When the gauge degrees of freedom of QCD are confined within a volume as is presently understood, the U A (1) anomaly is known to induce color anomaly leading to “leakage” of the color out of the confined volume (or bag). For consistency of the theory, this anomaly should be canceled by a boundary term. This “color boundary term” inherits part or most of the dynamics of the volume (i.e., QCD). In this paper, we exploit this mapping of the volume to the surface via the color boundary condition to perform a complete analysis of the flavor singlet axial charge in the chiral bag model using the Cheshire Cat Principle. This enables us to obtain the hitherto missing piece in the axial charge associated with the gluon Casimir energies. The result is that the flavor singlet axial charge is small independent of the confinement (bag) size ranging from the skyrmion picture to the MIT bag picture, thereby confirming the (albeit approximate) Cheshire Cat phenomenon.

Fuzzy bag models

We show how hadronic bag models can be generalized to implement effects of a smooth and extended boundary. Our approach is based on fuzzy set theory and can be straightforwardly applied to any type of bag model. We illustrate the underlying ideas by calculating static nucleon properties in a fuzzy chiral bag model.

KNΛ and KNΣ coupling constants from the Chiral Bag Model

The KNΛ and KNΣ coupling constants have been calculated in the framework of the Chiral Bag Model(CBM). We find −3.88 ≤gKNΛ≤−3.67 and 1.15 ≤gKNΣ≤ 1.24 by taking into account pseudoscalar mesons (π, K) and vector mesons (ρ, ω, K*) field effects. Particularly, it is shown that vector mesons make significant contributions to the coupling constants gKNΛ and gKNΣ. Our values are existing within the experimental limits compared to the phenomenological values extracted from the kaon photoproduction and kaon-nucleon scattering experiments. Also, form factors are suggested for the πNN, πNΔ, KNΛ and KNΣ couplings.

A chiral bag model with a soft surface : structure and solutions of the Fuzzy and the modified Fuzzy Bag Model

In the present work we propose a new bag model for hadrons, called the modified fuzzy bag model (MFBM). The distinguishing feature of this model is the suppression of the pion field, as it enters the bag, by means of a scalar potential for the pions, while still preserving chiral symmetry. The mechanism of pion suppression in the MFBM is similar to the mechanism of quark suppression in the fuzzy bag model (FBM). The standard chiral transformation for the pion field suffers a natural alteration in the MFBM, and as a result the model is chiral invariant. We present also a discussion of the FBM and study, in the quark sector, the implications of the soft surface of the bag on the expectation value of the mass operator. In the pion-quark sector, we study the effects of the suppression of the pion field on the form factor for the pion-nucleon interaction, on the pion-nucleon coupling constant $g_{ \pi{\scriptscriptstyle{N}}{\scriptscriptstyle{N}} }$ and on the nucleon axial charge $g_A$ . Calculations of the pion-nucleon form factor exhibit, in particular, an improvement over previous results. The pionic axial current induces, in the MFBM, a nonvanishing and orientation dependent contribution to axial charge. An analysis of the asymptotic behaviour of the axial charge shows that the role of the surface is to increase the difference of the contributions associated to different orientations.

A chiral bag model with a soft surface : structure and solutions of the Fuzzy and the modified Fuzzy Bag Model

A chiral bag model with a soft surface : structure and solutions of the Fuzzy and the modified Fuzzy Bag Model