We propose the enhancement of $Λ_c$ yield in heavy ion collisions at RHIC and LHC as a novel signal for the existence of diquarks in the strongly coupled quark-gluon plasma produced in these collisions as well as in the $Λ_c$. Assuming that stable bound diquarks can exist in the quark-gluon plasma, we argue that the yield of $Λ_c$ would be increased by two-body collisions between $ud$ diquarks and $c$ quarks, in addition to normal three-body collisions among $u$, $d$ and $c$ quarks. A quantitative study of this effect based on the coalescence model shows that including the contribution of diquarks to $Λ_c$ production indeed leads to a substantial enhancement of the $Λ_c/D$ ratio in heavy ion collisions.
We argue that cold quark matter is a color superconductor. The Cooper pairs of QCD are spin-isospin zero, color anti-triplet diquarks. In this contribution we review some of the available information on the quark-quark interaction in QCD. We show that instantons provide a strongly attractive interaction in the scalar diquark channel. In the high density phase, this interaction leads to diquark Bose condensation with a gap on the order of 50 MeV.
We treat baryons as bound states of scalar or axialvector diquarks and a constituent quark which interact through quark exchange. This description results as an approximation to the relativistic Faddeev equation for three quarks which yields an effective Bethe-Salpeter equation. Octet and decuplet masses and fully four-dimensional wave functions have been computed for two cases: assuming an essentially pointlike diquark on the one hand, and a diquark with internal structure on the other hand. Whereas the differences in the mass spectrum are fairly small, the nucleon electromagnetic form factor…
A review of the underlying ideas of the Interacting Quark Diquark Model (IQDM) that asses the baryon spectroscopy in terms of quark diquark degrees of freedom is given, together with a discussion of the missing resonances problem. Some ideas about its generalization the heavy baryon spectroscopy is given.s of freedom is given, together with a discussion of the missing resonances problem. Some ideas about its generalization the heavy baryon spectroscopy is given.The results are compared to the existing experimental data.
We describe baryons as quark-diquark bound states at finite temperature and density within the NJL model for chiral symmetry breaking and restoration in quark matter. Based on a generalized Beth-Uhlenbeck approach to mesons and diquarks we present in a first step the thermodynamics of quark-diquark matter which includes the Mott dissociation of diquarks at finite temperature. In a second step we solve the Bethe-Salpeter equation for the baryon as a quark-diquark bound state in quark-diquark matter. We obtain a stable, bound baryon even beyond the Mott temperature for diquark dissociation since…
The relativistic interacting quark-diquark model, constructed in the framework of point form dynamics, is extended to strange baryons. The strange and nonstrange baryon spectra are calculated and compared with the experimental data.
The excitation energy spectra of heavy baryons consisting of a heavy quark and two light quarks are investigated by using diquark models in order to examine the nature of the diquark as a constituent of single heavy baryons. We consider two diquark models; in model A the diquark is treated as a point-like particle, while it has a spatial size in model B. We determine the masses of scalar and axial vector diquarks by the mass difference of the ground state charmed baryons to the $Λ_{c}$ baryon, while the mass of the $ud$ scalar diquark in the $Λ_{c}$ baryon is assumed to be 500 MeV as a referen…
We present a path-integral hadronization for doubly heavy baryons. The two heavy quarks in the baryon are approximated as a scalar or axial-vector diquark described by a heavy diquark effective theory. The gluon dynamics are represented by a NJL-Model interaction for the heavy diquarks and light quarks, which leads to an effective action of the baryon fields after the quark and diquark fields are integrated out. This effective action for doubly heavy baryon includes the electromagnetic and electroweak interactions, as well as the interaction with light mesons. We also verify the Ward-Takahashi…
The excitation energies of the $Λ_{c}$ and $Λ_{b}$ baryons are investigated in a finite-size diquark potential model, in which the heavy baryons are treated as bound states of a charm quark and a scalar-isoscalar diquark. The diquark is considered as a sizable object. The quark-diquark interaction is calculated as a sum of the quark-quark interaction which is assumed to be half of the quark-antiquark interaction for the color singlet. The potential parameters in the quark-antiquark interaction are fixed so as to reproduce the charmonium spectrum. We find the diquark size to be 1.1 fm for the d…
Nucleon form factors are calculated in a relativistic diquark--quark picture based on the Nambu--Jona-Lasinio model. The nucleon wave function is obtained in a static approximation to the quark exchange interaction between the valence quark and the diquark. We evaluate the valence quark and $0^+$--diquark contribution to the nucleon electromagnetic and weak currents. We find reasonable electric charge radii, magnetic moments as in the additive diquark model, and $g_A \approx 1$. We discuss the dependence on the model parameters.
We briefly describe our relativistic quark-diquark model, developed within the framework of point form dynamics, which is the relativistic extension of the interacting quark-diquark model. In order to do that we have to show the main properties and quantum numbers of the effective degree of freedom of constituent diquark. Our results for the nonstrange baryon spectrum and for the nucleon electromagnetic form factors are discussed.
The possibility to have diquark configuration in heavy baryons, such as Lambda_c and Lambda_b, is examined by a nonrelativistic potential model with a heavy quark and a light scalar diquark. Assuming that the Lambda_c and Lambda_b baryons are composed of the heavy quark and the point-like scalar-isoscalar ud diquark, we solve the two-body Schrodinger equation with the Coulomb plus linear potential and obtain the energy spectra for the heavy baryons. Contrary to our expectation, it is found that the potential determined by the quarkonium spectra fails to reproduce the excitation spectra of the …
We check a commonly used approximation in which a baryon with a heavy quark is described as a heavy quark-light diquark system. The heavy quark influences the diquark internal motion reducing the average distance between the two light quarks. Besides, we show how the average distance between the heavy quark and any of the light quarks, and that between the heavy quark and the center of mass of the light diquark, are smaller than the distance between the two light quarks, which seems to contradict the heavy quark-light diquark picture. This latter result is in agreement with expectations from Q…
We study the structure of the nuclear force by using a path-integral hadronization approach in a chiral quark-diquark model. After the construction of the chiral quark-diquark model, we hadronize it to obtain a meson-baryon Lagrangian. The effective meson-baryon Lagrangian incorporates chiral symmetry and the composite description of the mesons and baryons. Using the effective meson-baryon Lagrangian we investigate the structure of the nuclear force in the simple case of neglecting the axial-vector diquark. It is shown that the meson-baryon Lagrangian contains two kinds of the nuclear force; t…
Baryons are modeled as bound states of scalar or axialvector diquarks and a constituent quark which interact through quark exchange. This description results as an approximation to the relativistic Faddeev equation for three quarks. The corresponding effective Bethe-Salpeter equation is solved, and fully four-dimensional wave functions for both octet and decuplet baryons are obtained. Confinement of quarks and diquarks is incorporated by modifying their propagators. Results are given for kaon photoproduction which is one of the applications currently under investigation in this model.
We study the baryonic fluctuations from second to eighth order involving electric charge, baryon number and strangeness below the quark-gluon plasma crossover and numerically known from lattice QCD calculations. By considering a particular realization of the Hadron Resonance Gas model, we provide evidence on the dominant role of quark-diquark degrees of freedom to describe excited baryonic resonances. After proving by means of suitable Polyakov loop correlators that the quark-diquark and the quark-antiquark forces coincide, $V_{\bar q q } (r) = V_{\bar q D } (r) + \textrm{const}$, we find that…
From recent study of properties of the lowest spin-parity $1/2^-$ baryons, $N^*(1535)$ and $Δ^*(1620)$, new pictures for the internal structure of the lowest $1/2^-$ baryon octet and decuplet are proposed. While the lowest $1/2^-$ baryon octet may have large diquark-diquark-antiquark component, the lowest $1/2^-$ baryon decuplet is proposed to have large vector-meson-baryon components. Evidence for the "missing" members of the new pictures is pointed out and suggestions are made for detecting these predicted states from forthcoming experiments.
Using an extended version of the Nambu-Jona-Lasinio model we build a simple description of the baryons as diquark-quark bound states. First, a description of the diquarks in a dense and hot medium is presented. Then, we introduce the formalism for the baryons based on the Faddeev equation associated with the so-called `` static approximation'' which finally gives a Bethe-Salpeter equation in the diquarks-quarks channel. By identifying the baryons with the bound states, we can obtain a description of their properties. In particular, we obtain the right mass spectrum for the proton, $Λ$, $Ξ$, an…
In this thesis a model framework for describing baryons as diquark-quark bound states is presented which is formulated in an explicitly covariant manner. The relativistic bound state problem for three quarks is considered. Diquarks are introduced as separable correlations in the two-quark correlation function and thereby baryons are described by a Bethe-Salpeter equation for bound states of quark and diquark which interact by quark exchange. In analogy to the meson spectrum, scalar and axialvector diquarks are considered to be the most important two-quark configurations within baryons. The num…
A quark-diquark model for parity doublet structure of baryons
Research Center for Nuclear Physics (RCNP), Osaka University（大阪大学核物理研究中心）；Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University（名古屋大学小林-益川粒子宇宙起源研究所）；Department of Physics, Nagoya University（名古屋大学物理系）；Advanced Science Research Center, Japan Atomic Energy Agency（日本原子能研究开发机构先进科学研究中心）
Diquark correlations are important in baryons, which can be modeled as quark-diquark bound states. In addition, diquarks could play a role in non-standard hadrons such as tetraquarks and pentaquarks. Here, we obtain properties of these diquarks from the corresponding bound state equation, using a model for the effective quark-quark interaction that has proved successful in the light meson sector. Subsequently, we use the same model to estimate the masses of the lightest diquark-diquark and diquark-antidiquark states.
A chiral effective theory of quarks and diquarks is formulated and applied to exotic tetraquarks and pentaquarks. The effective theory is similar to the chiral quark effective theory with the addition of diquark degrees of freedom and couplings to quarks. Chiral symmetry through generalized Goldberger-Treiman relations, fixes the mass splitting between the even and odd parity diquarks to be about 600 MeV. We provide an estimate of the parameters of the effective theory from both the random instanton model and known data on the low lying scalar nonet. We assess the static properties of the exot…
Fluctuations of conserved charges such as baryon number, electric charge and strangeness may provide a test for completeness of states in lattice QCD for three light flavors. We elaborate on the idea that the corresponding susceptibilities can be saturated with excited baryonic states with an underlying quark-diquark structure with a linearly confining interaction. Using Polyakov-loop correlators we show that in the static limit, the quark-diquark potential coincides with the quark-antiquark potential in marked agreement with recent lattice studies. We thus study in a quark-diquark model the b…
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-…
We introduce an improved mass formula for the nucleon and delta resonances and show how it emerges from AdS/QCD in a straightforward extension of the 'metric soft wall' gravity dual. The resulting spectrum depends on just one adjustable parameter, characterizing confinement-induced IR deformations of the anti-de Sitter (AdS) metric, and on the fraction of 'good' (i.e. maximally attractive) diquarks in the baryon's quark model wave function. Despite its simplicity, the predicted spectrum describes the masses of all 48 observed light-quark baryon states and their linear trajectory structure with…
The baryon octet and decuplet masses and Bethe-Salpeter vertex and wave functions are calculated in the ladder approximation to the quark exchange between a scalar or axialvector diquark and a constituent quark. These functions reflecting full Lorentz covariance are given in terms of an expansion in Gegenbauer polynomials. In the rest frame of the baryon, a complete partial wave decomposition of the Bethe-Salpeter wave function is performed. The confinement of quarks and diquarks is implemented via a parametrisation of the corresponding propagators. We also discuss some aspects of the momentum…
Lattice data on QCD thermodynamics, especially recent study of high order susceptibilities by UK-Bielefeld collaboration, have provided valuable information about matter properties around and above the critical temperature $T_c$. In this work we tried to understand what physical picture would explain these numerical data. We found two scenarios which will do it: (i) a quark quasiparticle gas, with the effective mass which is strongly $decreasing$ near the phase boundary into the QGP phase; or (ii) a picture including baryons at $T>T_c$, with the mass rapidly $increasing$ across the phase bound…
Chiral effective theory of scalar and vector diquarks is formulated according to the linear sigma model. The main application is to describe the ground and excited states of singly heavy baryons with a charm or bottom quark. Applying the potential quark model between the diquark and the heavy quark ($Q=c, b$), we construct a heavy-quark--diquark model. The spectra of the positive- and negative-parity states of $Λ_Q$, $Σ_Q$, $Ξ^{(')}_Q$ and $Ω_Q$ are obtained. The masses and interaction parameters of the effective theory are fixed partly from the lattice QCD data and also from fitting low-lying…
We study the nucleon and diquarks in a non-local Nambu-Jona-Lasinio model. For certain parameters the model exhibits quark confinement, in the form of a propagator without real poles. After truncation of the two-body channels to the scalar and axial-vector diquarks, a relativistic Faddeev equation for nucleon bound states is solved in the covariant diquark-quark picture. The dependence of the nucleon mass on diquark masses is studied in detail. We find parameters that lead to a simultaneous reasonable description of pions and nucleons. Both the diquarks contribute attractively to the nucleon m…
We study the formation of baryons as composed of quarks and diquarks in hot and dense hadronic matter in a Nambu--Jona-Lasinio (NJL)--type model. We first solve the Dyson-Schwinger equation for the diquark propagator and then use this to solve the Dyson-Schwinger equation for the baryon propagator. We find that stable baryon resonances exist only in the phase of broken chiral symmetry. In the chirally symmetric phase, we do not find a pole in the baryon propagator. In the color-superconducting phase, there is a pole, but is has a large decay width. The diquark does not need to be stable in ord…
We discuss the emergence of a low-energy effective theory with quarks, mesons, diquarks and baryons at vanishing and finite baryon density from first principle QCD. The present work also includes an overview on diquarks at vanishing and finite density, and elucidates the physics of transitional changes from baryonic matter to quark matter including diquarks. This set-up is discussed within the functional renormalisation group approach with dynamical hadronisation. In this framework it is detailed how mesons, diquarks, and baryons emerge dynamically from the renormalisation flow of the QCD effe…
Using a confining, symmetry-preserving regularisation of a vector$\times$vector contact interaction, we compute the spectra of ground-state pseudoscalar and vector $(f\bar g)$ mesons, scalar and axial-vector $(fg)$ diquarks, and $J^P=1/2^+, 3/2^+$ $(fgh)$ baryons, where $f,g,h \in \{u,d,s,c,b\}$. The diquark correlations are essentially dynamical and play a key role in formulating and solving the three-valence-quark baryon problems. The baryon spectrum obtained from this largely-algebraic approach reproduces the 22 known experimental masses with an accuracy of $2.9(2.4)$%. It also possesses th…
We examine the nucleon's electromagnetic form factors in a Poincare-covariant Faddeev framework. The three-quark core contributions to the form factors are obtained by employing a quark-diquark approximation. We implement the self-consistent solution for the quark-photon vertex from its inhomogeneous Bethe-Salpeter equation. We find that the resulting transverse parts which add to the Ball-Chiu vertex have no significant impact on nucleon magnetic moments. The current-quark mass evolution of the form factors agrees with results from lattice QCD.
Quark-hadron matter at finite temperature and density is studied using a two-flavor, color SU(2) (P)NJL model. The hadronic effective Lagrangian, derived by bosonization of the quark fields and renormalized using the Eguchi method, emerges in the form of an extended linear sigma model with meson and diquark-baryon fields. Chiral and diquark condensates are studied as functions of temperature and baryon density. Masses of mesons and diquark-baryons are calculated with and without the Polyakov loop effect. We investigate the equation of state of quark-hadron matter by taking into account the con…
We present results of numerical simulations of the 3+1d Nambu - Jona-Lasinio model with a non-zero baryon chemical potential mu, with particular emphasis on the superfluid diquark condensate and associated susceptibilities. The results, when extrapolated to the zero diquark source limit, are consistent with the existence of a non-zero BCS condensate at high baryon density. The nature of the infinite volume and zero temperature limits are discussed.
For very heavy quarks, the two heavy quarks in a doubly heavy baryon are expected to form a pointlike, heavy diquark in an antitriplet color configuration. In this limit the dynamics of the light degrees of freedom `factorize' from the dynamics of the heavy diquark system, and a superflavor symmetry emerges which relates the properties of doubly heavy baryons to heavy mesons. The charm quark may not be heavy enough for the $cc$ diquark in a $Ξ_{cc}$ to be regarded as pointlike. However, there are indications from the results of a nonrelativistic constituent quark model that many of the consequ…
We calculate masses of light and heavy mesons as well as baryons of negative parity containing $u,d,s,c$ and $b$ quarks. It is an extension of our previous work where we had studied the positive parity baryons. We adopt a quark-diquark picture of baryons where the diquarks are non-pointlike with a finite spatial extension. The mathematical foundation for this analysis is implemented through a symmetry-preserving Schwinger-Dyson equations treatment of a vector-vector contact interaction, which preserves key features of quantum chromodynamics, such as confinement, chiral symmetry breaking, axial…
A hybrid model for baryons based on a dynamical interplay between relativistic three--quark bound states and soliton configurations of mesons is constructed. The Bethe-Salpeter equation for diquarks and the Faddeev equation for diquark-quark bound states in the background of a soliton is solved. The results show that baryons are very much like hybrids containing both, solitonic meson clouds and three--quark correlations.
Diquarks may play an important role in hadron spectroscopy, baryon decays and color superconductivity. We investigate the existence of diquark correlations in lattice QCD by considering systematically all the lowest energy diquark channels in a color gauge-invariant setup. We measure mass differences between the various channels and show that the positive parity scalar diquark is the lightest. Quark-quark correlations inside the diquark are clearly seen in this channel, and yield a diquark size of order 1 fm.
We discuss the light baryon spectrum obtained from a recent quark-diquark calculation, implementing non-pointlike diquarks that are self-consistently calculated from their Bethe-Salpeter equations. We examine the orbital angular momentum content in the baryons' rest frame and highlight the fact that baryons carry all possible values of L compatible with their spin, without the restriction P=(-1)^L which is only valid nonrelativistically. We furthermore investigate the meaning of complex conjugate eigenvalues of Bethe-Salpeter equations, their possible connection with 'anomalous' states, and we…
We derive covariant baryon wave functions for arbitrary Lorentz boosts. Modeling baryons as quark-diquark systems, we reduce their manifestly covariant Bethe-Salpeter equation to a covariant 3-dimensional form by projecting on the relative quark-diquark energy. Guided by a phenomenological multigluon exchange representation of a covariant confining kernel, we derive for practical applications explicit solutions for harmonic confinement and for the MIT Bag Model. We briefly comment on the interplay of boosts and center-of-mass corrections in relativistic quark models.
We adopt the heavy baryon chiral perturbation theory (HBChPT) to calculate the scattering lengths of $ϕB_{cc}^{(*)}$ up to $\mathcal{O}(p^3)$, where $ϕ$ is the pseudoscalar mesons. The recoil effect and the mass splitting between the spin-$1\over 2$ and spin-$3\over 2$ doubly charmed baryons are included. In order to give the numerical results, we construct the chiral Lagrangians with heavy diquark-antiquark (HDA) symmetry in a formally covariant approach. Then, we relate the low energy constants (LECs) of the doubly charmed baryons to those of $D^{(*)}$ mesons. The LECs for the $ϕD^{(*)}$ sca…
It is shown that the instanton-induced interaction in qq pairs, iterated in t-channel, leads to a meson-exchange interactions between quarks. In this way one can achieve a simultaneous understanding of low-lying mesons, baryons and the nuclear force. The discussion is general and does not necessarily rely on the instanton-induced interaction. Any nonperturbative gluonic interaction between quarks, which is a source of the dynamical chiral symmetry breaking and explains the $π$ - $ρ$ mass splitting, will imply an effective meson exchange picture in baryons. Due to the (anti)screening there is a…
We describe a calculation of the spectrum of flavour-SU(3) octet and decuplet baryons, their parity partners, and the radial excitations of these systems, made using a symmetry-preserving treatment of a vector-vector contact interaction as the foundation for the relevant few-body equations. Dynamical chiral symmetry breaking generates nonpointlike diquarks within these baryons and hence, using the contact interaction, flavour-antitriplet scalar, pseudoscalar and vector, and flavour-sextet axial-vector quark-quark correlations can all play an active role. The model yields reasonable masses for …
We give an estimate of $Ξ_{cc}^{++}$ production rate and transverse momentum spectra in relativistic heavy ion collisions. We use Boltzmann transport equations to describe the dynamical evolution of charm quarks and diquarks inside quark-gluon plasma. In-medium formation and dissociation rates of charm diquarks are calculated from potential non-relativistic QCD for the diquark sector. We solve the transport equations by Monte Carlo simulations. For $2.76$ TeV Pb-Pb collisions with $0-10\%$ centrality, the number of $Ξ_{cc}^{++}$ produced in the transverse momentum range $0-5$ GeV and rapidity …
The $γ^{(\ast)}+p \to N(1535) \tfrac{1}{2}^-$ transition is studied using a symmetry-preserving regularisation of a vector$\,\otimes\,$vector contact interaction (SCI). The framework employs a Poincaré-covariant Faddeev equation to describe the initial and final state baryons as quark+di\-quark composites, wherein the diquark correlations are fully dynamical, interacting with the photon as allowed by their quantum numbers and continually engaging in breakup and recombination as required by the Faddeev kernel. The presence of such correlations owes largely to the mechanisms responsible for the …
Octet baryon axial, induced pseudoscalar, and pseudoscalar form factors are computed using a symmetry-preserving treatment of a vector$\,\times\,$vector contact interaction (SCI), thereby unifying them with an array of other baryon properties and analogous treatments of semileptonic decays of pseudoscalar mesons. The baryons are treated as quark--plus--interacting-diquark bound states, whose structure is obtained by solving a Poincaré-covariant Faddeev equation. The approach is marked by algebraic simplicity, involves no free parameters, and since it is symmetry preserving, all consequences of…
