Naive Quark Model Research Articles

Instanton effects in twist-3 generalized parton distributions

The instanton vacuum picture is used to study hadronic matrix elements of the twist-3 (dimension-4, spin-1) QCD operators measuring the quark spin density and spin-orbit correlations. The QCD operators are converted to effective operators in the low-energy effective theory emerging after chiral symmetry breaking, in a systematic approach based on the diluteness of the instanton medium and the 1/Nc expansion. The instanton fields induce spin-flavor-dependent “potential” terms in the effective operators, complementing the “kinetic” terms from the quark field momenta. As a result, the effective operators obey the same equation-of-motion relations as the original QCD operators. The spin-orbit correlations are qualitatively different from naive quark model expectations.

S-wave heavy pentaquark production in direct fragmentation of heavy quark

Study of exotic hadrons with configurations beyond the naive quark model has attracted a lot of interests in recent years. Due to their complicated configuration many theoretical models have been designed for describing their structure. Understanding the production mechanism of exotic hadrons could be helpful to find out their inner structure and to test the theory of QCD as well. It is well-known that the dominant production mechanism for conventional heavy hadrons with large transverse momentum is fragmentation so as this mechanism could also be extended to heavy pentaquarks production. This work is a first effort to study the direct fragmentation of heavy quarks into ground state heavy pentaquarks in leading order of perturbative QCD. Considering the picture of compact pentaquark states, through the Suzuki approach we will compute the fragmentation function of heavy quarks into S-wave heavy pentaquarks. The production cross section of heavy pentaquarks through pair annihilation will also be estimated at lowest order of perturbative QCD.

Spin-1 quarkonia in a rotating frame and their spin contents

We propose a new way of studying the spin content of a hadron by looking at its response in a rotating frame. By collecting all responses of quarks and gluons in a rotating frame, we describe the spin-rotation coupling of spin-1 quarkonia and thereby reveal their spin contents in a relativistic formalism. We demonstrate that both the perturbative and non-perturbative contributions in the operator product expansion follow a universal formula that identifies the spin-rotation coupling with unit strength. This allows us to recognize the total spin-1 of the vector and axial vector quarkonia in terms of the total angular momentum of quarks and gluons. Specifically, we find the spin contents of J/ψ, χc1, ϒ(1S), and χb1 are slightly different from the naive quark model picture. For example, the J/ψ is traditionally considered as an S-wave particle, but we find quarks do not carry all of the total spin.

Vector Charmonium-like States at BESIII

BESIII experiment is the only electron positron experiment working in the $\tau$-charm energy region in the world now, and on which the largest sample about Charmonium states has been taken. The Charmonium-like states, which are hadron states beyond the naive quark model are studied with this sample, in the Charmonium plus light hadron, light hadron only and leptonic final states.

The Ds0(2590)+ as the dressed [formula omitted] meson in a coupled-channels calculation

The recent discovery of the Ds0(2590)+ meson by the LHCb Collaboration has stimulated the analysis of meson-meson channels effects in the two-body quark-antiquark meson spectrum. This resonance, assigned to the radial excitation of the pseudoscalar Ds+ meson, has a mass much lower than the predictions of naive quark models, which could indicate a non-negligible D(⁎)K(⁎) coupling which reduces its mass. Based on the importance of nearby meson-meson thresholds in the dynamics of P-wave Ds mesons such as the Ds0⁎(2317)+ and Ds1(2460)+, in this work we perform a coupled-channels calculation including the D(⁎)K(⁎), Ds(⁎)ω and Ds⁎η channels, and study the impact of incorporating those channels in the mass of the bare cs¯. The coupling between two and four-quark sectors is done by means of the P03 mechanism, with all the parameters constrained from previous studies of the heavy meson spectroscopy. The masses, widths and production line shapes of the resulting state are analyzed.

Exclusive f1(1285) meson production for energy ranges available at the GSI-FAIR with HADES and PANDA

We evaluate the cross section for the $p p \to p p f_{1}(1285)$ and $p \bar{p} \to p \bar{p} f_{1}(1285)$ reactions at near threshold energies relevant for the HADES and PANDA experiments at GSI-FAIR. We assume that at energies close to the threshold the $\omega \omega \to f_{1}(1285)$ and $\rho^{0} \rho^{0} \to f_{1}(1285)$ fusion processes are the dominant production mechanisms. The vertex for the $VV \to f_{1}$ coupling is derived from an effective coupling Lagrangian. The $g_{\rho \rho f_1}$ coupling constant is extracted from the decay rate of $f_{1}(1285) \to \rho^{0} \gamma$ using the vector-meson-dominance ansatz. We assume $g_{\omega \omega f_1} = g_{\rho \rho f_1}$, equality of these two coupling constants, based on arguments from the naive quark model and vector-meson dominance. The amplitude for the $VV \to f_{1}$ fusion, supplemented by phenomenological vertex form factors for the process, is given. The differential cross sections at energies close to the threshold are calculated. In order to determine the parameters of the model the $\gamma p \to f_{1}(1285) p$ reaction is discussed in addition and results are compared with the CLAS data. The possibility of a measurement by HADES@GSI is presented and discussed. We performed a Monte Carlo feasibility simulations of the $p p \to p p f_1$ reaction for $\sqrt{s}$ = 3.46 GeV in the $\pi^+ \pi^- \pi^+ \pi^-$ (not shown explicitly) and $\pi^+ \pi^- \pi^+ \pi^- \pi^0$ final states using the PLUTO generator. The latter one is especially promising as a peak in the $\pi^+ \pi^- \eta$ should be observable by HADES.

Coupling Hadron-Hadron Thresholds within a Chiral Quark Model Approach

Heavy hadron spectroscopy was well understood within the naive quark model until the end of the past century. However, in 2003, the X(3872) was discovered, with puzzling properties difficult to understand in the simple naive quark model picture. This state made clear that excited states of heavy mesons should be coupled to two-meson states in order to understand not only the masses but, in some cases, unexpected decay properties. In this work, we will give an overview of a way in which the naive quark model can be complemented with the coupling to two hadron thresholds. This program has been already applied to the heavy meson spectrum with the chiral quark model, and we show some examples where thresholds are of special relevance.

Unquenching the Quark Model in a Nonperturbative Scheme

In recent years, the discovery in quarkonium spectrum of several states not predicted by the naive quark model has awakened a lot of interest. A possible description of such states requires the enlargement of the quark model by introducing quark-antiquark pair creation or continuum coupling effects. The unquenching of the quark models is a way to take these new components into account. In the spirit of the Cornell Model, this is usually done by coupling perturbatively a quark-antiquark state with definite quantum numbers to the meson-meson channel with the closest threshold. In this work we present a method to coupled quark-antiquark states with meson-meson channels, taking into account effectively the nonperturbative coupling to all quark-antiquark states with the same quantum numbers. The method will be applied to the study of the X(3872) resonance and a comparison with the perturbative calculation will be performed.

Heavy mesons in the Quark Model

Since the discovery of theJ/ψ, the quark model was very successful in describing the spectrum and properties of heavy mesons including only q̄ components. However since 2003, with the discovery of theX(3872), many states that can not be accommodated on the naive quark model have been discovered, and they made unavoidable to include higher Fock components on the heavy meson states. We will give an overview of the success of the quark model for heavy mesons and point some of the states that are likely to be more complicated structures such as meson-meson molecules.

Contribution of constituent quark model cbar{s} states to the dynamics of the D_{s0}^*(2317) and D_{s1}(2460) resonances

The masses of the D^*_{s0}(2317) and D_{s1}(2460) resonances lie below the DK and D^*K thresholds respectively, which contradicts the predictions of naive quark models and points out to non-negligible effects of the D^{(*)}K loops in the dynamics of the even-parity scalar (J^pi =0^+) and axial-vector (J^pi =1^+) cbar{s} systems. Recent lattice QCD studies, incorporating the effects of the D^{(*)}K channels, analyzed these spin-parity sectors and correctly described the D^*_{s0}(2317)-D_{s1}(2460) mass splitting. Motivated by such works, we study the structure of the D_{s0}^*(2317) and D_{s1}(2460) resonances in the framework of an effective field theory consistent with heavy quark spin symmetry, and that incorporates the interplay between D^{(*)}K meson–meson degrees of freedom and bare P-wave cbar{s} states predicted by constituent quark models. We extend the scheme to finite volumes and fit the strength of the coupling between both types of degrees of freedom to the available lattice levels, which we successfully describe. We finally estimate the size of the D^{(*)}K two-meson components in the D^*_{s0}(2317) and D_{s1}(2460) resonances, and we conclude that these states have a predominantly hadronic-molecular structure, and that it should not be tried to accommodate these mesons within cbar{s} constituent quark model patterns.

Form factors of the d*(2380) resonance

In order to explore the possible physical quantities for judging different structures of the newly observed resonance $d^*(2380)$, we study its electromagnetic form factors. In addition to the electric charge monopole $C0$, we calculate its electric quadrupole $E2$, magnetic dipole $M1$, and six-pole $M3$ form factors on the base of the realistic coupled $\Delta\Delta+CC$ channel $d^*$ wave function with both the $S$- and $D$-partial waves. The results show that the magnetic dipole moment and electric quadrupole deformation of $d^*$ are 7.602 and $2.53\times 10^{-2}~\rm{fm}^2$, respectively. The calculated magnetic dipole moment in the naive constituent quark model is also compared with the result of $D_{12}\pi$ picture. By comparing with partial results where the $d^*$ state is considered with a single $\Delta\Delta$ and with a $D_{12}\pi$ structures, we find that in addition to the charge distribution of $d^*(2380)$, the magnetic dipole moment and magnetic radius can be used to discriminate different structures of $d^*$. Moreover, a quite small electric quadrupole deformation indicates that $d^*$ is more inclined to an slightly oblate shape due to our compact hexaquark dominated structure of $d^*(2380)$.

Threshold effects in P -wave bottom-strange mesons

Using a nonrelativistic constituent quark model in which the degrees of freedom are quark-antiquark and meson-meson components, we have recently shown that the $D^{(\ast)}K$ thresholds play an important role in lowering the mass of the physical $D_{s0}^{\ast}(2317)$ and $D_{s1}(2460)$ states. This observation is also supported by other theoretical approaches such as lattice-regularised QCD or chiral unitary theory in coupled channels. Herein, we extend our computation to the lowest $P$-wave $B_{s}$ mesons, taking into account the corresponding $J^{P} = 0^{+}$, $1^{+}$ and $2^{+}$ bottom-strange states predicted by the naive quark model and the $BK$ and $B^{\ast}K$ thresholds. We assume that mixing with $B_{s}^{(\ast)}\eta$ and isospin-violating decays to $B_{s}^{(\ast)}\pi$ are negligible. This computation is important because there is no experimental data in the $b\bar{s}$ sector for the equivalent $j_{q}^{P}=1/2^{+}$ ($D_{s0}^{\ast}(2317)$, $D_{s1}(2460)$) heavy-quark multiplet and, as it has been seen in the $c\bar s$ sector, the naive theoretical result can be wrong by more than $100\,{\rm MeV}$. Our calculation allows to introduce the coupling with the $D$-wave $B^{\ast}K$ channel and to compute the probabilities associated with the different Fock components of the physical state.

The non-perturbative unquenched quark model

In recent years states in the quarkonium spectrum not expected in the naive quark model have appeared and created a lot of interest. In the theoretical side the study of the effect of meson-meson thresholds in the spectrum have been performed in different approximations. In a quark model framework, and in the spirit of the Cornell model, when a meson-meson threshold is included, the coupling to all the quark-antiquark states have to be considered. In practice only the closest states are included perturbatively. In this contribution we will present a framework in which we couple quark-antiquark states with meson-meson states non-perturbatively, taking into account effectively the coupling to all quark-antiquark states. The method will be applied to the study of the X (3872) and a comparison with the perturbative calculation will be performed.

Molecular components in P -wave charmed-strange mesons

Results obtained by various experiments show that the $D_{s0}^{\ast}(2317)$ and $D_{s1}(2460)$ mesons are very narrow states located below the $DK$ and $D^{\ast}K$ thresholds, respectively. This is markedly in contrast with the expectations of naive quark models and heavy quark symmetry. Motivated by a recent lattice study which addresses the mass shifts of the $c\bar{s}$ ground states with quantum numbers $J^{P}=0^{+}$ ($D_{s0}^{\ast}(2317)$) and $J^{P}=1^{+}$ ($D_{s1}(2460)$) due to their coupling with $S$-wave $D^{(\ast)}K$ thresholds, we perform a similar analysis within a nonrelativistic constituent quark model in which quark-antiquark and meson-meson degrees of freedom are incorporated. The quark model has been applied to a wide range of hadronic observables and thus the model parameters are completely constrained. The coupling between quark-antiquark and meson-meson Fock components is done using a $^{3}P_{0}$ model in which its only free parameter $\gamma$ has been elucidated performing a global fit to the decay widths of mesons that belong to different quark sectors, from light to heavy. We observe that the coupling of the $0^{+}$ $(1^{+})$ meson sector to the $DK$ $(D^{\ast}K)$ threshold is the key feature to simultaneously lower the masses of the corresponding $D_{s0}^{\ast}(2317)$ and $D_{s1}(2460)$ states predicted by the naive quark model and describe the $D_{s1}(2536)$ meson as the $1^{+}$ state of the $j_{q}^{P}=3/2^{+}$ doublet predicted by heavy quark symmetry, reproducing its strong decay properties. Our calculation allows to introduce the coupling with the $D$-wave $D^{\ast}K$ channel and the computation of the probabilities associated with the different Fock components of the physical state.

Molecular components in D*s0(2317) and Ds1(2460) mesons

Different experiments have confirmed that the D * s 0 (2317) and D s 1 (2460) mesons are very narrow states located, respectively, below the DK and D* K thresholds. This is markedly in contrast with the expectations of naive quark models and heavy quark symmetry. We address the mass shifts of the cs ground states with quantum numbers JP = 0+ (D * s 0 (2317)) and JP = 1+ (D s 1 (2460)) using a nonrelativistic constituent quark model in which quark-antiquark and meson-meson degrees of freedom are incorporated. The quark model has been applied to a wide range of hadronic observables and thus the model parameters are completely constrained. We observe that the coupling of the 0+ (1+ ) meson sector to the DK (D* K ) threshold is a key feature in lowering the masses of the corresponding D * s 0 (2317) and D s 1 (2460) states predicted by the naive quark model, but also in describing the Ds 1 (2536) meson as the 1+ state of the jP q = 3/2+ doublet predicted by heavy quark symmetry and thus reproducing its strong decay properties. Two features of our formalism cannot be address nowadays by other approaches: the coupling of the D -wave D* K threshold in the JP = 1+ cs channel and the computation of the probabilities associated with different Fock components in the physical state.

S-waveKK*interactions in a finite volume and thef1(1285)

Lattice QCD simulations provide a promising way to disentangle different interpretations of hadronic resonances, which might be of particular relevance to understand the nature of the so-called XY Z particles. Recent studies have shown that in addition to the well-established naive quark model picture, the axial-vector meson f1(1285) can also be understood as a dynamically generated state built upon the KK ∗ interaction. In this work, we calculate the energy levels of the KK ∗ system in the f1(1285) channel in finite volume using the chiral unitary approach. We propose to calculate the loop function in the dimensional regularization scheme, which is equivalent to the hybrid approach adopted in previous studies. We also study the inverse problem of extracting the bound state information from synthetic lattice QCD data and comment ′ � �

Tetraneutron in the Chiral Quark Model

The tetraneutron state is studied in the framework of the chiral quark model with tetrahedron configuration. The universal attraction property of σ-meson exchange leads to a strong attraction in the effective potential of the system. It is possible to form a bound state. For comparison, the naive quark model is also employed to carry out the calculation. A weak attraction, which is too weak to bind the system, is obtained.

Asymmetries of quark sea in nucleon

The effects of in determining the flavor structure of the octet baryons have been investigated in the chiral constituent quark model. The chiral constituent quark model is able to qualitatively generate the requisite amount of quark sea and is also known to provide a satisfactory explanation of the spin and related issues in the nonperturbative regime. The phenomenological implications of the quark sea asymmetries in the nucleon have been investigated to understand the importance of quark sea at lower values of the Bjorken scaling variable. After the first direct evidence for the point-like constituents in the nucleon, identified as the valence quarks with spin-1/2 in the naive constituent quark model (NQM) (1-3), a lot of experiments have been conducted to probe the structure of the in the deep inelastic scattering (DIS) experiments. Surprisingly, the DIS results in the early 80's (4) indicated that the valence quarks of the carry only about 30% of its spin and is referred to as the proton spin crisis in the NQM. These results provided the first evidence for the being composed of three valence quarks surrounded by an indistinct sea of quark-antiquark pairs (henceforth referred to as the sea). In the present day, the study of the composition of hadrons can be said to be primarily the study of the quark sea and gluons and is considered as one of the active areas in hadronic physics. The conventional expectation that the quark sea perhaps can be obtained through the perturbative production of the quark-antiquark pairs by gluons produces nearly equal numbers of ¯ u and ¯ d. Until early 90's a symmetric sea w.r.t. ¯ u and ¯ d was assumed, however, the famous New Muon Collaboration in 1991 (5) established the quark sea asymmetry of the unpolarized quarks in the case of nucleon by measuring ¯ d − ¯ u giving first clear evidence for the nonperturbative origin of the quark sea. This was later confirmed by the Drell-Yan experiments (6) which measured a large quark sea asymmetry ratio ¯ d/¯ u reminding us that the study of the quark sea is intrinsically a nonperturbative phenomena and it is still a big challenge to perform these calculations from the first principles of QCD. The chiral constituent quark model (CQM) (7) can yield an adequate description of the quark sea generation through the chiral fluctuations. The basic idea is based on the possibility that chiral symmetry breaking takes place at a distance scale much smaller than the confinement scale. In this region, the effective degrees of freedom are the valence quarks and the internal Goldstone bosons (GBs) which are coupled to the valence quarks (8-10) allowing a simple and intuitive method to investigate

Polarization effects in the cascade decayΛb→Λ(→pπ−)+J/ψ(→ℓ+ℓ−)in the covariant confined quark model

We calculate the invariant and helicity amplitudes for the nonleptonic decay ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}\ensuremath{\Lambda}+J/\ensuremath{\psi}$, $\ensuremath{\psi}(2S)$ in the covariant confined quark model. We discuss joint angular decay distributions in the cascade decay ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}\ensuremath{\Lambda}(\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{\ensuremath{-}})+J/\ensuremath{\psi}$, $\ensuremath{\psi}(2S)(\ensuremath{\rightarrow}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}})$ and calculate some of the asymmetry parameters that characterize the joint angular decay distribution. We confirm expectations from the naive quark model that the transitions into the ${\ensuremath{\lambda}}_{\ensuremath{\Lambda}}=1/2$ helicity states of the daughter baryon $\ensuremath{\Lambda}$ are strongly suppressed leading to a near maximal negative polarization of the $\ensuremath{\Lambda}$. For the same reason the azimuthal correlation between the two decay planes spanned by ($p{\ensuremath{\pi}}^{\ensuremath{-}}$) and (${\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$) is negligibly small. We provide form factor results for the whole accessible ${q}^{2}$ range. Our results are close to lattice results at minimum recoil and light-cone sum rule results at maximum recoil. A new feature of our analysis is that we include lepton mass effects in the calculation, which allows us to also describe the cascade decay ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}\ensuremath{\Lambda}(\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{\ensuremath{-}})+\ensuremath{\psi}(2S)(\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}})$.

THE STATUS OF MESONIC EXOTICA

Over twenty years ago QCD-inspired models of hadronic states began a rigorous search for meson outside of Naive Quark Model. Here we briefly review the current status of Exotica.