Color-magnetic Interaction Research Articles

Study of Hadron Masses with Faddeev-Popov Eigenmode Projection in the Coulomb Gauge

Using SU(3) lattice QCD, we investigate role of spatial gluons for hadron masses in the Coulomb gauge, considering the relation between QCD and the quark model. From the Coulomb-gauge configurations at the quenched level on a 163 × 32 lattice at β = 6.0, we consider the A⃗ = 0 projection, where all the spatial gluon fields are set to zero. In this projection, the inter-quark potential is unchanged. We investigate light hadron masses and find that nucleon and delta baryon masses are almost degenerate. This result suggests that the N-Δ mass difference arises from the color-magnetic interactions, which is consistent with the quark model picture. Next, as a generalization of this projection, we expand spatial gluon fields in terms of Faddeev-Popov eigenmodes and leave only some partial components. We find that the N – Δ and 0++ – 2++ glueball mass splittings are almost reproduced only with 1 % low-lying components. This suggests that low-lying color-magnetic interaction leads to the hadron mass splitting.

Towards the understanding of fully-heavy tetraquark states from various models

We use a color-magnetic interaction model (CMIM), a traditional constituent quark model (CQM) and a multiquark color flux-tube model (MCFTM) to systematically investigate the properties of the states $[Q_1Q_2][\bar{Q}_3\bar{Q}_4]$ ($Q=c,b$). The dynamical investigation indicates that the CMIM can not completely absorb QCD dynamical effects through the effective constituent quark mass and overestimates the color-magnetic interaction in the states under the assumption of the same spatial configurations. The Coulomb interaction plays a critical role in the dynamical model calculations on the heavy hadrons, which induces the fact that none of bound states $[Q_1Q_2][\bar{Q}_3\bar{Q}_4]$ can be found in the dynamical models. The color configuration $\left[[Q_1Q_2]_{\mathbf{6}_c}[\bar{Q}_3\bar{Q}_4]_{\bar{\mathbf{6}}_c}\right]_{\mathbf{1}}$ should be taken seriously in the ground states due to the strong Coulomb attraction between the $[Q_1Q_2]_{\mathbf{6}_c}$ and $[\bar{Q}_3\bar{Q}_4]_{\bar{\mathbf{6}}_c}$. The color configuration $\left[[Q_1Q_2]_{\bar{\mathbf{3}}_c}[\bar{Q}_2\bar{Q}_4]_{\mathbf{3}_c}\right]_{\mathbf{1}}$ is absolutely dominant in the excited states because of the strong Coulomb attraction within the $[Q_1Q_2]_{\bar{\mathbf{3}}_c}$ and $[\bar{Q}_2\bar{Q}_4]_{\mathbf{3}_c}$. The $J/\Psi$-pair resonances recently observed by LHCb are difficult to be accommodated in the CMIM. The broad structure ranging from 6.2 to 6.8 GeV can be described as the ground tetraquark state $[cc][\bar{c}\bar{c}]$ in the various dynamical models. The narrow structure $X(6900)$ can be identified as the excited state $[cc][\bar{c}\bar{c}]$ with $L=1$ ($L=2$) in the CQM (MCFTM).

Spectrum and rearrangement decays of tetraquark states with four different flavors

We have systematically investigated the mass spectrum and rearrangement decay properties of the exotic tetraquark states with four different flavors using a color-magnetic interaction model. Their masses are estimated by assuming that the $X(4140)$ is a $cs\bar{c}\bar{s}$ tetraquark state and their decay widths are obtained by assuming that the Hamiltonian for decay is a constant. According to the adopted method, we find that the most stable states are probably the isoscalar $bs\bar{u}\bar{d}$ and $cs\bar{u}\bar{d}$ with $J^P=0^+$ and $1^+$. The width for most unstable tetraquarks is about tens of MeVs, but that for unstable $cu\bar{s}\bar{d}$ and $cs\bar{u}\bar{d}$ can be around 100 MeV. For the $X(5568)$, our method cannot give consistent mass and width if it is a $bu\bar{s}\bar{d}$ tetraquark state. For the $I(J^P)=0(0^+),0(1^+)$ double-heavy $T_{bc}=bc\bar{u}\bar{d}$ states, their widths can be several MeVs.

Exotic pentaquark states with the qqQQQ¯ configuration

In the framework of the color-magnetic interaction model, we have systematically calculated the mass splittings for the S-wave triply heavy pentaquark states with the configuration $qqQQ\bar{Q}$ $(Q=c,b;q=u,d,s)$. Their masses are estimated and their stabilities are discussed according to possible rearrangement decay patterns. Our results indicate that there may exist several stable or narrow such states. We hope the present study can help experimentalists to search for exotic pentaquarks.

Possible existence of a dibaryon candidate NΔ(D21)

Inspired by the experimental report by WASA-at-COSY Collaboration, we investigate the possibile existence of the dibaryon candidate $N\Delta$ with quantum numbers $IJ^P=21^+$ ($D_{21}$). The dynamical calculation shows that we cannot obtain the bound $D_{21}$ state in the models which can obtain the experimental $d^{*}$. %although the $D_{21}$ state can bound in the range of parameters in quark models. The low-energy scattering phase shifts of the $N-\Delta$ scattering give the same conclusion. Besides, the mass calculation by using the Gursey-Radicati mass formula and the analysis of the matrix elements of the color magnetic interaction show that the mass of $D_{21}$ is larger than that of $D_{12}$ ($N\Delta$ with $IJ^P=12^+$), which indicate that it is less possible for the $D_{21}$ than the $D_{12}$ to form bound state.

Heavy-flavored tetraquark states with the QQQ¯Q¯ configuration

In the framework of the color-magnetic interaction, we systematically investigate the mass spectrum of the tetraquark states composed of four heavy quarks with the $QQ\bar Q\bar Q$ configuration in this work. We also show their strong decay patterns. Stable or narrow states in the $bb\bar{b}\bar{c}$ and $bc\bar{b}\bar{c}$ systems are found to be possible. We hope the studies shall be helpful to the experimental search for heavy-full exotic tetraquark states.

Exotic tetraquark states with the qqbar{Q}bar{Q} configuration

In this work, we study systematically the mass splittings of the qqbar{Q}bar{Q} (q=u, d, s and Q=c, b) tetraquark states with the color-magnetic interaction by considering color mixing effects and estimate roughly their masses. We find that the color mixing effect is relatively important for the J^P=0^+ states and possible stable tetraquarks exist in the nnbar{Q}bar{Q} (n=u, d) and nsbar{Q}bar{Q} systems either with J=0 or with J=1. Possible decay patterns of the tetraquarks are briefly discussed.

Hidden-charm pentaquarks and their hidden-bottom and Bc -like partner states

In the framework of the color-magnetic interaction, we have systematically studied the mass splittings of the possible hidden-charm pentaquarks $qqqc\overline{c}$ ($q=u$, $d$, $s$) where the three light quarks are in a color-octet state. We find that (i) the LHCb ${P}_{c}$ states fall in the mass region of the studied system, (ii) most pentaquarks should be broad states since their $S$-wave open-charm decays are allowed while the lowest state is the ${J}^{P}={\frac{1}{2}}^{\ensuremath{-}}$ $\mathrm{\ensuremath{\Lambda}}$-like pentaquark with probably the suppressed ${\ensuremath{\eta}}_{c}\mathrm{\ensuremath{\Lambda}}$ decay mode only, and (iii) the ${J}^{P}={\frac{5}{2}}^{\ensuremath{-}}$ states do not decay through the $S$ wave and their widths are not so broad. The masses and widths of the two LHCb ${P}_{c}$ baryons are compatible with such pentaquark states. We also explore the hidden-bottom and ${B}_{c}$-like partners of the hidden-charm states and find the possible existence of the pentaquarks which are lower than the relevant hadronic molecules.

Triply heavy tetraquark states with the $QQ\bar{Q}\bar{q}$ Q Q Q ¯ q ¯ configuration

In the framework of the color-magnetic interaction, we systematically investigate the mass splittings of the $QQ\bar{Q}\bar{q}$ tetraquark states and estimated their rough masses in this work. These systems include the explicitly exotic states $cc\bar{b}\bar{q}$ and $bb\bar{c}\bar{q}$ and the hidden exotic states $cc\bar{c}\bar{q}$, $cb\bar{b}\bar{q}$, $bc\bar{c}\bar{q}$, and $bb\bar{b}\bar{q}$. If a state around the estimated mass region could be observed, its nature as a genuine tetraquark is favored. The strong decay patterns shown here will be helpful to the experimental search for these exotic states.

X(4140) , X(4270) , X(4500) , and X(4700) and their csc¯s¯ tetraquark partners

In the simple color-magnetic interaction model, we investigate possible ground $cs\bar{c}\bar{s}$ tetraquark states in the diquark-antidiquark basis. We use several methods to estimate the mass spectrum and discuss possible assignment for the $X$ states observed in the $J/\psi\phi$ channel. We find that assigning the Belle $X(4350)$ as a $0^{++}$ tetraquark is consistent with the tetraquark interpretation for the $X(4140)$ and $X(4270)$ while the interpretation of the $X(4500)$ and $X(4700)$ needs orbital or radial excitation. There probably exist several tetraquarks around 4.3 GeV that decay into $J/\psi\phi$ or $\eta_c\phi$.

X(5568)and its partner states

Stimulated by the recent observation of the $X(5568)$, we study the $X(5568)$ and its partners under the tetraquark scenario. In the framework of the color-magnetic interaction, we estimate the masses of the partner states of the $X(5568)$ and discuss their decay pattern, which provide valuable information on the future experimental search of these states.

Phenomenological QCD equation of state for massive neutron stars

We construct an equation of state for massive neutron stars based on quantum chromodynamics phenomenology. Our primary purpose is to delineate the relevant ingredients of equations of state that simultaneously have the required stiffness and satisfy constraints from thermodynamics and causality. These ingredients are: (i) a repulsive density-density interaction, universal for all flavors; (ii) the color-magnetic interaction active from low to high densities; (iii) confining effects, which become increasingly important as the baryon density decreases; (iv) non-perturbative gluons, which are not very sensitive to changes of the quark density. We use the following "3-window" description: At baryon densities below about twice normal nuclear density, 2n_0, we use the Akmal-Pandharipande-Ravenhall (APR) equation of state, and at high densities, > (4-7)n_0, we use the three-flavor Nambu-Jona-Lasinio (NJL) model supplemented by vector and diquark interactions. In the transition density region, we smoothly interpolate the hadronic and quark equations of state in the chemical potential-pressure plane. Requiring that the equation of state approach APR at low densities, we find that the quark pressure in non-confining models can be larger than the hadronic pressure, unlike in conventional equations of state. We show that consistent equations of state of stiffness sufficient to allow massive neutron stars are reasonably tightly constrained, suggesting that gluon dynamics remains non-perturbative even at baryon densities ~10n_0.

From Ω- to Ωb, doubly heavy baryons and exotics

I discuss accurate theoretical predictions for masses of baryons containing the b quark. I point out an approximate effective supersymmetry between heavy quark baryons and mesons and provide predictions for the magnetic moments of Λc and Λb. Proper treatment of the color-magnetic hyperfine interaction in QCD is crucial for obtaining these results. Closely related methods are then applied to doubly-heavy hadrons: the recently observed exotic [Formula: see text] mesons and QQq baryons. Predictions are given for the masses and decay modes of additional [Formula: see text] mesons and of QQq baryons: Ξcc(ccq), Ξbb(bbq) and Ξbc(bcq), which might soon be seen experimentally, as indicated by the large number of Bc mesons observed by LHCb.

Hidden-charm tetraquarks and chargedZcstates

Experimentally several charged axial-vector hidden-charm states were reported. Within the framework of the color-magnetic interaction, we have systematically considered the mass spectrum of the hidden-charm and hidden-bottom tetraquark states. It is impossible to accommodate all of the three charged states ${Z}_{c}(3900)$, ${Z}_{c}(4025)$, and ${Z}_{c}(4200)$ within the axial-vector tetraquark spectrum simultaneously. Not all of these three states are tetraquark candidates. Moreover, the eigenvector of the chromomagnetic interaction contains valuable information of the decay pattern of the tetraquark states. The dominant decay mode of the lowest axial-vector tetraquark state is $J/\ensuremath{\psi}\ensuremath{\pi}$ while its ${D}^{*}\overline{D}$ and ${\overline{D}}^{*}{D}^{*}$ modes are strongly suppressed, which is in contrast with the fact that the dominant decay mode of ${Z}_{c}(3900)$ and ${Z}_{c}(4025)$ is $\overline{D}{D}^{*}$ and ${\overline{D}}^{*}{D}^{*}$, respectively. We emphasize that all the available experimental information indicates that ${Z}_{c}(4200)$ is a very promising candidate of the lowest axial-vector hidden-charm tetraquark state.

New States with Heavy Quarks

We discuss several highly accurate theoretical predictions for masses of baryons containing the b quark which have been recently confirmed by experimental data. Proper treatment of the color-magnetic hyperfine interaction in QCD is crucial for obtaining these results. Several predictions are given for additional properties of heavy baryons. We also discuss the two charged exotic resonances Z b with quantum numbers of a ( b u ) tetraquark, very recently reported by Belle in the channel [ϒ( nS )π + , n = 1, 2, 3]. Among possible implications are deeply bound I = 0 counterparts of the Z b -s and existence of a Σ b + Σ b − dibaryon, a beauteron .

Hadronic Interactions from SU(2) Lattice QCD

We study hadronic interactions from Bethe-Salpeter amplitudes in quenched two-color lattice QCD, concentrating on the interactions of two scalar diquarks (uCγ5d) in S-wave scattering states. Between two identical scalar diquarks, we observe repulsive force in short-range region. By defining and evaluating the "quark-exchange part" in the interaction, which is induced by quark-exchange diagrams, or equivalently, by introducing Pauli blocking among some of quarks, we find that the repulsive force in short-distance region arises purely from the "quark-exchange part" and that it disappears when quark-exchange diagrams are omitted. It is qualitatively consistent with the constituent-quark model picture that the origin of short-range repulsion is a color-magnetic interaction among quarks. We also find a novel long-ranged attractive force, which enters in any flavor channels of two scalar diquarks and whose interaction range and strength are quark-mass independent.

Spin contribution to light baryons in different large-Nlimits

We investigate the spin contribution to light baryon ground states in three inequivalent large-$N$ limits: 't Hooft, QCD antisymmetric and QCD symmetric. Our framework is a constituent quark model with a relativistic Hamiltonian containing a stringlike confinement and a one-gluon exchange term. Two spin-dependent potentials are considered and treated as perturbations: the color magnetic interaction stemming from the one-gluon exchange process and the chiral boson exchange interaction. We analytically prove that the spin contributions scale like $S(S+1)/n_q$, where $S$ is the total spin and $n_q$ is the number of quark, in agreement with diagrammatic methods. Both potentials yield also $S$-independent contributions which scale at most as O$(n_q)$.

Hadron-hadron interaction from SU(2) lattice QCD

We evaluate interhadron interactions in two-color lattice QCD from Bethe-Salpeter amplitudes on the Euclidean lattice. The simulations are performed in quenched SU(2) QCD with the plaquette gauge action at $\ensuremath{\beta}=2.45$ and the Wilson quark action. We concentrate on $S$-wave scattering states of two scalar diquarks. Evaluating different flavor combinations with various quark masses, we try to find out the ingredients in hadronic interactions. Between two scalar diquarks ($uC{\ensuremath{\gamma}}_{5}d$, the lightest baryon in SU(2) system), we observe repulsion in short-range region, even though present quark masses are not very light. We define and evaluate the quark-exchange part in the interaction, which is induced by adding quark-exchange diagrams, or equivalently, by introducing Pauli-blocking among some of quarks. The repulsive force in short-distance region arises only from the quark-exchange part and disappears when quark-exchange diagrams are omitted. We find that the strength of repulsion grows in light quark-mass regime, and its quark-mass dependence is similar to or slightly stronger than that of the color-magnetic interaction by one-gluon-exchange (OGE) processes. It is qualitatively consistent with the constituent-quark-model picture that a color-magnetic interaction among quarks is the origin of repulsion. We also find a universal long-range attractive force, which enters in any flavor channels of two scalar diquarks and whose interaction range and strength are quark-mass independent. The weak quark-mass dependence of interaction ranges in each component implies that meson-exchange contributions are small and subdominant, and the other contributions, e.g., flavor-exchange processes, color-Coulomb, or color-magnetic interactions, are considered to be predominant, in the quark-mass range we evaluated.

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.

Λ(1405)resonance in baryon-meson scattering with a bound state embedded in the continuum

We investigate $\ensuremath{\Lambda}(1405)$ as a resonance in a coupled-channels baryon-meson ($\ensuremath{\Sigma}\ensuremath{\pi}\text{\ensuremath{-}}N\overline{K}\text{\ensuremath{-}}\ensuremath{\Lambda}\ensuremath{\eta}$) scattering with a `bound state embedded in the continuum' (BSEC). For this purpose, we solve the Lippmann-Schwinger equation including a BSEC with the semirelativistic kinematics in the momentum space. This BSEC is introduced by hand, as a state not originated from a simple baryon-meson system. We assume it comes from the three-quark state. There appears a resonance in the $\ensuremath{\Sigma}\ensuremath{\pi}$ scattering below the $N\overline{K}$ threshold without introducing a BSEC when the $N\overline{K}$ channel has a strong attraction, just like the chiral unitary approach. Even if the baryon-meson interaction is weakened by using a lower-momentum cut-off parameter, a resonance also appears around 1405 MeV when a BSEC is introduced. The corresponding peak also has a large width, and the $N\overline{K}$ scattering length is well reproduced. The interaction whose channel dependence is the same as the one originated from the color-magnetic interaction, where no $N\overline{K}$ attraction exists, also gives a broad peak with help of a BSEC. In order to reproduce the observed $N\overline{K}$ scattering length, the calculation including a BSEC seems to be preferable. Our calculation gives an appropriate $N\overline{K}$ scattering length when the BSEC contribution to the resonance is roughly half that of the $N\overline{K}$ channel.