Color-spin Interaction Research Articles

Diquarkyonic matter: Quarks, diquarks, and baryons

In this work, we investigate the color-spin interaction of a quark, a diquark and a baryon with their surrounding baryons and/or quark matter. We extend our previous work by increasing the maximum number of surrounding baryons to 5 and additionally consider all possible diquark probes that are immersed in such surroundings. This is accomplished by classifying all possible flavor and spin states of the resulting multiquark configuration in both the flavor SU(2) and SU(3) symmetric cases. We also discuss the three-body confinement potential and show that this does not contribute to the outcome. Furthermore, we find that a quark becomes more stable than a baryon when the number of surrounding baryons is three or more. Finally, when we consider the internal color-spin factor of a probe, our results show that the effects of the color-spin interaction of a multiquark configuration is consistent with the so-called diquarkyonic configuration.

X(3872) and Tcc : Structures and productions in heavy ion collisions

We argue why the recently observed ${T}_{cc}$ could either be a compact multiquark configuration or a loosely bound molecular configuration composed of charmed mesons, whereas the $X(3872)$ is most likely a molecular configuration. The argument is based on different short range interactions for these tetraquark states coming from the color-color and color-spin interaction in a quark model, and the presence of a common strong $D$-wave mixing at larger distance similar to the deuteron case, which for the molecular configurations leads to large sizes. Such an analogy at large distance allows us to calculate the transverse momentum dependence of the loosely bound molecular configuration of tetraquarks produced in heavy ion collisions using the coalescence model that successfully reproduces the deuteron data using the proton spectra. The ratio of the integrated $X(3872)$ yield obtained from our method to the $\ensuremath{\psi}(2S)$ yield obtained from the statistical hadronization model method is calculated to be $0.806\ifmmode\pm\else\textpm\fi{}0.234$, which is a factor of 2.47 larger than that obtained by using statistical model predictions for both particles and in line with the data from the CMS experiment. As the previously calculated transverse momentum distribution of the ${T}_{cc}$ assuming the structure to be a compact multiquark configuration is markedly different, experimental measurements of the transverse distribution of the tetraquark states will discriminate between their two possible structures.

Algebraic approach to a quarkyoniclike configuration and stable diquarks in dense matter

We study the color-spin interaction energy of a quark, a diquark and a baryon with their surrounding baryons and/or quark matter. This is accomplished by classifying all possible flavor and spin states of the resulting multiquark configuration in both the flavor SU(2) and SU(3) symmetric cases. We find that while the baryon has the lowest interaction energy when there is only a single surrounding baryon, the quark has the lowest interaction energy when the surrounding has more than three baryons or becomes a quark gas. As the short range nucleon-nucleon interactions are dominated by the color-spin interactions, our finding suggests that the baryon modes near other baryons are suppressed due to larger repulsive energy compared to that of a quark and thus provides a quark model basis for the quarkyoniclike phase in dense matter. At the same time, when the internal interactions are taken into account, and the matter density is high so that the color-spin interaction becomes the dominant interaction, the diquark becomes the lowest energy configuration and will thus appear in both the dense baryonic and/or quark matter.

Tribaryons in a constituent quark model

We calculate the matrix elements of the color-spin interaction for all possible multi-quark states of tribaryons in flavor SU(3) broken case. For that purpose, we construct the flavor$\otimes$color$\otimes$spin wave functions of the tribaryons, which are taken to be antisymmetric to satisfy the Pauli exclusion principle. Furthermore, we analyze the diquark structure of the tribaryon configurations using the symmetric and antisymmetric basis set of flavor, color and spin states.

Intrinsic three-body nuclear interaction from a constituent quark model

We study the short distance part of the intrinsic three-nucleon interaction in a constituent quark model with color-spin interaction. For that purpose we first calculate the transformation coefficient between the tribaryon configuration and their corresponding three baryon basis. Using a formula for the intrinsic three-body interaction in terms of a tribaryon configuration, we find that after subtracting the corresponding two-baryon contributions, the intrinsic three-body interaction vanishes in flavor SU(3) symmetric limit for all quantum numbers for the three nucleon states. We further find that the intrinsic three-body interaction also vanishes for flavor-spin type of quark interaction.

Tribaryon configurations and the inevitable three nucleon repulsions at short distance

We decompose the tribaryon configuration in terms of SU(3) flavor and spin state and analyse their color-spin-flavor wave function following Pauli principle. By comparing the color-color and color-spin interactions of compact tribaryon configuration against the lowest three nucleon threshold within a constituent quark model, we show that the three nucleon forces have to be repulsive at short distance for all possible quantum numbers and all values of the SU(3) symmetry breaking parameter. Our work identifies the origin of the repulsive nuclear three body forces including the hyperons at short distance that are called for from phenomenological considerations starting from nuclear matter to the maximum mass of a neutron star.

Tetraquark mixing framework for isoscalar resonances in light mesons

Recently, a tetraquark mixing framework has been proposed for light mesons and applied more or less successfully to the isovector resonances, $a_0(980), a_0(1450)$, as well as to the isodoublet resonances, $K^*_0(800), K^*_0(1430)$. In this work, we present a more extensive view on the mixing framework and extend this to the isoscalar resonances, $f_0 (500)$, $f_0(980)$, $f_0 (1370)$, $f_0(1500)$. Tetraquarks in this framework can have two spin configurations containing either spin-0 diquark or spin-1 diquark and each configuration forms a nonet in flavor space. The two spin configurations are found to mix strongly through the color-spin interactions. Their mixtures, which diagonalize the hyperfine masses, can generate the physical resonances constituting the two nonets, which, in fact, coincide roughly with the experimental observation. We identify that $f_0 (500)$, $f_0(980)$ are the isoscalar members in the light nonet, and $f_0 (1370)$, $f_0(1500)$ are the similar members in the heavy nonet. This means that the spin configuration mixing, as it relates the corresponding members in the two nonets, can generate $f_0 (500), f_0 (1370)$ among the members in light mass, and $f_0(980), f_0(1500)$ in heavy mass. The complication arises because the isoscalar members of each nonet are subject to an additional flavor mixing known as OZI rule so that $f_0 (500), f_0 (980)$, and similarly $f_0 (1370), f_0 (1500)$, are the mixture of two isoscalar members belonging to an octet and a singlet in SU$_f$(3). The tetraquark mixing framework including the flavor mixing is tested for the isoscalar resonances in terms of the mass splitting and the fall-apart decay modes.

Heptaquarks with two heavy antiquarks in a simple chromomagnetic model

We investigate the symmetry property and the stability of the heptaquark containing two identical heavy antiquarks using color-spin interaction. We construct the wave function of the heptaquark from the Pauli exclusion principle in the SU(3) breaking case. The stability of the heptaquark against the strong decay into one baryon and two mesons is discussed in a simple chromomagnetic model. We find that $q^2 s^3 \bar{s}^2$ with $I=0,S=\frac{5}{2}$ is the most stable heptaquark configuration that could be probed by reconstructing the $\Lambda+\phi+\phi$ invariant mass.

Spin-1 diquark contributing to the formation of tetraquarks in light mesons

We apply a mixing framework to the light-meson systems and examine tetraquark possibility in the scalar channel. In the diquark–antidiquark model, a scalar diquark is a compact object when its color and flavor structures are in (bar{mathbf {3}}_c, bar{mathbf {3}}_f). Assuming that all the quarks are in an S-wave, the spin-0 tetraquark formed out of this scalar diquark has only one spin configuration, |J,J_{12},J_{34}rangle =|000rangle , where J is the spin of the tetraquark, J_{12} the diquark spin, J_{34} the antidiquark spin. In this construction of the scalar tetraquark, we notice that another compact diquark with spin-1 in (mathbf {6}_c, bar{mathbf {3}}_f) can be used although it is less compact than the scalar diquark. The spin-0 tetraquark constructed from this vector diquark leads to the spin configuration |J,J_{12},J_{34}rangle =|011rangle . The two configurations, |000rangle and |011rangle , are found to mix strongly through the color–spin interaction. The physical states can be identified with certain mixtures of the two configurations which diagonalize the hyperfine masses of the color–spin interaction. Matching these states to two scalar resonances a_0(980), a_0(1450) or to K^*_0(800), K^*_0(1430) depending on the isospin channel, we find that their mass splittings are qualitatively consistent with the hyperfine mass splittings, which can support their tetraquark structure. To test our mixing scheme further, we also construct the tetraquarks for J=1,J=2 with the spin configurations |111rangle and |211rangle , and we discuss possible candidates in the physical spectrum.

Testing the tetraquark structure for the X resonances in the low-lying region

Assuming four-quark structure for the $X$ resonances in low-lying region, we calculate their masses using the color-spin interaction. In specific, the hyperfine masses of the color-spin interaction are calculated for the possible states in spin-0, spin-1, spin-2 channels. The two states in spin-0 channel as well as the two states in spin-1 channel are diagonalized in order to generate the physical hyperfine masses. By matching the difference in hyperfine masses with the splitting in corresponding hadron masses and using the $X(3872)$ mass as an input, we estimate the masses corresponding to the states $J^{PC}=0^{++}, 1^{+-},2^{++}$. We find the masses of two states in $1^{+-}$ are close to those of $X(3823)$, $X(3900)$, and the mass of the $2^{++}$ state is close to that of $X(3940)$. For them, the discrepancies are about $\sim 10$ MeV. This may suggest that the quantum numbers of the controversial states are $X(3823)=1^{+-}, X(3900)=1^{+-}, X(3940)=2^{++}$. In this work, we use the same inputs parameters, the constituent quark masses and the strength of the color-spin interaction, that have been adopted in the previous work on the $D$ or $B$-meson excited states. There, it was shown that the four-quark structure can be manifested in their excited states. Thus, our results in this work provide a consistent treatment on open- and hidden-charm mesons as far as the four-quark model is concerned.

Dibaryons with two strange quarks and total spin zero in a constituent quark model

We investigate the symmetry property and construct the wave function of the dibaryon states containing two strange quarks with S=0 in both the flavor SU(3) symmetric and breaking cases. We discuss how the color $\otimes$ isospin $\otimes$ spin states of dibaryon in the symmetry broking case of flavor SU(3) can be extracted from the fully antisymmetric states in flavor SU(3). The stability of the dibaryon against the strong decay into two baryons are then discussed, by using the variational method within a constituent quark model with a confining and color-spin interactions. To compare our results with that from lattice QCD in flavor SU(3) limit, we search for the stable H-dibaryon in a wide range of $\pi$ meson mass. We find that with the given potential, there is no compact six quark dibaryon state in the SU(3) flavor symmetry broken case with realistic quark masses as well as in flavor SU(3) symmetric case in a wide range of quark masses.

Four-quark structure of the excited states of heavy mesons

We propose a four-quark structure for some of the excited states of heavy mesons containing a single charm or bottom quark. The four-quark wave functions are constructed based on a diquark-antidiquark form under the constraint that they form an antitriplet $\bar{\bf{3}}_f$ in $\mbox{SU(3)}_f$, which seems to be realized in some of the excited states listed in Particle Data Group. Depending on the structure of antidiquark, we construct two possible models for its wave functions: Model I) the antidiquark is symmetric in flavor ($\bar{\bf{6}}_f$) and antisymmetric in color ($\bf{3}_c$) and Model II) the antidiquark is antisymmetric in flavor ($\bf{3}_f$) and symmetric in color ($\bar{\bf{6}}_c$). To test phenomenological relevance of these wave functions, we calculate the mass differences among the excited states of spin $J=0,1,2$ using color-spin interactions. The four-quark wave functions based on Model~I is found to reproduce the observed mass of the excited states of heavy mesons. Also, our four-quark model provides an interesting phenomenology relating to the decay widths of the excited states. To further pursue the possibility of the four-quark structure, we make a few predictions for open charm and open bottom states that may be discovered in future experiments. Most of them are expected to have broad widths, which would make them difficult to be identified experimentally. However, one resonance with $J=1$ containing bottom and strange quarks is expected to appear as a sharp peak with its mass around $B^{\bar s}_{1N} \sim 5753$~MeV. Confirmation of the existence of such states in future experiments will shed light on our understanding of the structure of heavy meson excited states.

Stable multiquark states with heavy quarks in a diquark model

Based on the color–spin interaction in diquarks, we argue why some multiquark configurations could be stable against strong decay when heavy quarks are included. After showing the stability of previously discussed states we identify new possible stable states. These are the $T^{0}_{cb}(ud\bar{c}\bar{b})$ tetraquark, the $\varTheta _{bs}(udus\bar{b})$ pentaquark and the H c (udusuc) dibaryon, and so forth.

Charmed exotics in heavy ion collisions

Based on the color–spin interaction in diquarks, we argue that charmed multiquark hadrons are likely to exist. Because of the appreciable number of charm quarks produced in central nucleus–nucleus collisions at ultrarelativistic energies, the production of charmed multiquark hadrons is expected to be enhanced in these collisions. Using both the quark coalescence model and the statistical hadronization model, we estimate the yield of charmed tetraquark mesons, Tcc, and pentaquark baryons, Θcs, in heavy ion collisions at RHIC and LHC. We further discuss the decay modes of these charmed exotic hadrons in order to facilitate their detections in experiments.

Negative parity pentaquarks in largeNcQCD and quark model

Recently, the $1/{N}_{c}$ expansion has been applied to the study of exotic baryons containing both quarks and antiquarks. We extend this approach to exotic states with mixed-symmetric spin-flavor symmetry, which correspond in the quark model to negative parity pentaquarks, and discuss the large ${N}_{c}$ predictions for their mass spectrum. The heavy exotics $\overline{Q}{q}^{4}$ transform as $\mathbf{3},\overline{\mathbf{6}},\mathbf{15}$ and ${\mathbf{15}}^{\ensuremath{'}}$ under SU(3), while the light states $\overline{q}{q}^{4}$ include the exotic multiplets $\overline{\mathbf{10}},\mathbf{27},\mathbf{35}$. We give mass relations among these multiplets in the $1/{N}_{c}$ expansion. In the quark model, the mass splittings between these states are given by color-spin interactions. Using the observation of an anticharmed exotic by the H1 Collaboration, we give predictions for the masses of other expected heavy pentaquarks.