Relativistic Constituent Research Articles

Electric transitions of the charmed-strange mesons in a relativistic quark model

In the present work, we adopt a relativistic constituent quark model to depict the charmed strange meson spectroscopy, in which D_{s0}(2317) and D_{s1}(2460) are considered as the 1^3P_0 and 1P_1^prime charmed strange mesons, respectively. By using the wave function obtained from the relativistic quark model, we further investigate the electric transitions between charmed strange mesons. We find the long wave length approximation is reasonable for the charmed strange meson radiative decay by comparing the results with different approximations. The estimated partial widths are all safely under the upper limits of the experimental data. Moreover, we find the branching ratio of D_{s1}(2536) rightarrow D_s^*gamma /D_s gamma are large enough to be detected, which could be searched by further experiments in Belle II and LHCb.

Nuclear structure of bound states of asymmetric dark matter

Models of Asymmetric Dark Matter (ADM) with a sufficiently attractive and long-range force gives rise to stable bound objects, analogous to nuclei in the Standard Model, called nuggets. We study the properties of these nuggets and compute their profiles and binding energies. Our approach, applicable to both elementary and composite fermionic ADM, utilizes relativistic mean field theory, and allows a more systematic computation of nugget properties, over a wider range of sizes and force mediator masses, compared to previous literature. We identify three separate regimes of nugget property behavior corresponding to (1) non-relativistic and (2) relativistic constituents in a Coulomb-like limit, and (3) saturation in an anti-Coulomb limit when the nuggets are large compared to the force range. We provide analytical descriptions for nuggets in each regime. Through numerical calculations, we are able to confirm our analytic descriptions and also obtain smooth transitions for the nugget profiles between all three regimes. We also find that over a wide range of parameter space, the binding energy in the saturation limit is an ${\cal O}(1)$ fraction of the constituent's mass, significantly larger than expectations in the non-relativistic case. In a companion paper, we apply our results to synthesis of ADM nuggets in the early Universe.

Euclidean bridge to the relativistic constituent quark model

${\bf Background}$ Knowledge of nucleon structure is today ever more of a precision science, with heightened theoretical and experimental activity expected in coming years. At the same time, a persistent gap lingers between theoretical approaches grounded in Euclidean methods (e.g., lattice QCD, Dyson-Schwinger Equations [DSEs]) as opposed to traditional Minkowski field theories (such as light-front constituent quark models). ${\bf Purpose}$ Seeking to bridge these complementary worldviews, we explore the potential of a Euclidean constituent quark model (ECQM). This formalism enables us to study the gluonic dressing of the quark-level axial-vector vertex, which we undertake as a test of the framework. ${\bf Method}$ To access its indispensable elements with a minimum of inessential detail, we develop our ECQM using the simplified quark $+$ scalar diquark picture of the nucleon. We construct a hyperspherical formalism involving polynomial expansions of diquark propagators to marry our ECQM with the results of Bethe-Salpeter Equation (BSE) analyses, and constrain model parameters by fitting electromagnetic form factor data. ${\bf Results}$ From this formalism, we define and compute a new quantity --- the Euclidean density function (EDF) --- an object that characterizes the nucleon's various charge distributions as functions of the quark's Euclidean momentum. Applying this technology and incorporating information from BSE analyses, we find the dressing effect on the proton's axial-singlet charge to be small in magnitude and consistent with zero. ${\bf Conclusions}$ The scalar quark $+$ diquark ECQM is a step toward a realistic quark model in Euclidean space, and urges additional refinements. The small size we obtain for the impact of the dressed vertex on the axial-singlet charge suggests that models without this effect are on firm ground to neglect it.

Photo-absorption sum rulesσ−1and further questions about correlations of constituents inside bound hadrons

Within the non-relativistic approach to photo-absorption sum rules for the 3N(4N)-nuclei the new σ −1 sum rules are proposed which are based on general chargesymmetry (CS) consequences for the “CS-conjugated” triton and 3 He and the CS-self-conjugated 4 He . Combining the relativistic constituent quark model of the nucleon and the known spin-,isospin- and the dipole-moment fluctuation sum rules, the relevant moments of the quark coordinate distribution and correlation functions in the ground state of the nucleon are derived and discussed.

Strong three-meson couplings ofJ/ψandηc

We discuss the strong couplings $g_{PPV}$ and $g_{VVP}$ for vector ($V$) and pseudoscalar ($P$) mesons, at least one of which is a charmonium state $J/\psi$ or $\eta_c$. The strong couplings are obtained as residues at the poles of suitable form factors, calculated in a broad range of momentum transfers using a dispersion formulation of the relativistic constituent quark model. The form factors obtained in this approach satisfy all constraints known for these quantities in the heavy-quark limit. Our results suggest sizably higher values for the strong meson couplings than those reported in the literature from QCD sum rules.

Exclusive decaysJ/ψ→D(s)(*)−ℓ+νℓin a covariant constituent quark model with infrared confinement

We investigate the exclusive semileptonic decays $J/\psi \to D_{(s)}^{(*)-} {\ell}^+ \nu_{\ell}$, where $\ell=e,\mu$, within the Standard Model. The relevant transition form factors are calculated in the framework of a relativistic constituent quark model with built-in infrared confinement. Our calculations predict the branching fractions $\mathcal{B}(J/\psi \to D_{(s)}^{(*)-} {\ell}^+ \nu_{\ell})$ to be of the order of $10^{-10}$ for $D_s^{(*)-}$ and $10^{-11}$ for $D^{(*)-}$. Most of our numerical results are consistent with other theoretical studies. However, some branching fractions are larger than those calculated in QCD sum rules approaches but smaller than those obtained in the covariant light-front quark model by a factor of about $2-3$.

Form factors for BK l+l- decay

The exclusive BV(P)l+l- and BV decays, with a vector (V=K*, , …) or pseudo scalar (P=K, , …) meson in the final state are important for the search for flavour-changing new physics. In this paper we study one of the exclusive rare decays of pseudo scalar B mesons: BKl+l- by using a relativistic constituent quark model, including infrared connement. We calculate the relevant form factors of the (BP) transitions in the full kinematical range of momentum transfer. The calculated form factors are used to evaluate differential decay rates and polarization observables. We present numerical results on these observables using the covariant quark model. This model can be viewed as an effective quantum field theory approach based on an interaction Lagrangian of hadrons interacting with their constituent quarks. Universal and reliable predictions for exclusive processes involving both mesons composed from a quark and antiquark and baryons composed from three quarks result from this approach.

Treatment of broken symmetry in the Faddeev approach to the strange baryon spectra

By solving the Faddeev equations we calculate the mass of the strange baryons in the framework of a relativistic constituent quark model. The Goldstone-boson-exchange quark-quark interaction is derived from $SU(3{)}_{F}$ symmetry, which is explicitly broken as the strange quark is much heavier. This broken symmetry can nicely be accounted for in the Faddeev framework.

Transversity studies with protons and light nuclei

A general formalism to evaluate time-reversal odd transverse momentum dependent parton distributions (T-odd TMDS) is reviewed and applied to the calculation of the leading-twist quantities, i.e., the Sivers and the Boer-Mulders functions. Two different models of the proton structure, namely a non relativistic constituent quark model and the MIT bag model, have been used. The results obtained in both frameworks fulfill the Burkardt sum rule to a large extent. The calculation of nuclear effects in the extraction of neutron single spin asymmetries in semi-inclusive deep inelastic scattering off transversely polarized 3He is also illustrated. In the kinematics of JLab, it is found that the nuclear effects described by an Impulse Approximation approach are under theoretical control.

Covariant model for theγN→N(1535)transition at high momentum transfer

A relativistic constituent quark model is applied to the $\ensuremath{\gamma}N\ensuremath{\rightarrow}N(1535)$ transition. The $N(1535)$ wave function is determined by extending the covariant spectator quark model, previously developed for the nucleon, to the ${S}_{11}$ resonance. The model allows us to calculate the valence quark contributions to the $\ensuremath{\gamma}N\ensuremath{\rightarrow}N(1535)$ transition form factors. Because of the nucleon and $N(1535)$ structure the model is valid only for ${Q}^{2}>2.3\text{ }\text{ }{\mathrm{GeV}}^{2}$. The results are compared with the experimental data for the electromagnetic form factors ${F}_{1}^{*}$ and ${F}_{2}^{*}$ and the helicity amplitudes ${A}_{1/2}$ and ${S}_{1/2}$, at high ${Q}^{2}$.

One-photon decay of the tetraquark stateX(3872)→γ+J/ψin a relativistic constituent quark model with infrared confinement

We further explore the consequences of treating the X(3872) meson as a tetraquark bound state by analyzing its one-photon decay X => \gamma + J/psi in the framework of our approach developed in previous papers which incorporates quark confinement in an effective way. To introduce electromagnetism we gauge a nonlocal effective Lagrangian describing the interaction of the X(3872) meson with its four constituent quarks by using the P-exponential path-independent formalism. We calculate the matrix element of the transition X => \gamma+ J/psi and prove its gauge invariance. We evaluate the X=> \gamma + J/psi decay width and the longitudinal/transverse composition of the J/psi in this decay. For a reasonable value of the size parameter of the X(3872) meson we find consistency with the available experimental data. We also calculate the helicity and multipole amplitudes of the process, and describe how they can be obtained from the covariant transition amplitude by covariant projection.

The pion wave function in covariant light-front dynamics

The structure of the pion wave function in the relativistic constituent quark model is investigated in the explicitly covariant formulation of light-front dynamics. We calculate the two relativistic components of the pion wave function in a simple one-gluon exchange model and investigate various physical observables: decay constant, charge radius, electromagnetic and transition form factors. We discuss the influence of the full relativistic structure of the pion wave function for an overall good description of all these observables, including both low and high momentum scales.

Axial Properties of Baryon Ground and Resonant States

We report results from a study of axial charges of baryon ground and resonant states with relativistic constituent quark models. In particular, we consider the axial charges of the octet and decuplet baryons N, Σ, Ξ, Δ, Σ*, and Ξ*. The theoretical predictions are compared to experiment, in the case of the N, and to results from other approaches, especially from lattice quantum chromodynamics and chiral perturbation theory. Some remarks are also made regarding the role of axial charges for spontaneous breaking of chiral symmetry.

Relativistic Bose–Einstein condensates: a new system for analogue models of gravity

In this paper we propose to apply the analogy between gravity and condensed matter physics to relativistic Bose—Einstein condensates (RBECs), i.e. condensates composed by relativistic constituents. While such systems are not yet a subject of experimental realization, they do provide us with a very rich analogue model of gravity, characterized by several novel features with respect to their non-relativistic counterpart. Relativistic condensates exhibit two (rather than one) quasi-particle excitations, a massless and a massive one, the latter disappearing in the non-relativistic limit. We show that the metric associated with the massless mode is a generalization of the usual acoustic geometry allowing also for non-conformally flat spatial sections. This is relevant, as it implies that these systems can allow the simulation of a wider variety of geometries. Finally, while in non-RBECs the transition is from Lorentzian to Galilean relativity, these systems represent an emergent gravity toy model where Lorentz symmetry is present (albeit with different limit speeds) at both low and high energies. Hence they could be used as a test field for better understanding the phenomenological implications of such a milder form of Lorentz violation at intermediate energies.

Axial charges of octet and decuplet baryons

We present a study of axial charges of baryon ground and resonant states with relativistic constituent quark models. In particular, the axial charges of octet and decuplet $N$, $\Sigma$, $\Xi$, $\Delta$, $\Sigma^*$, and $\Xi^*$ baryons are considered. The theoretical predictions are compared to existing experimental data and results from other approaches, notably from lattice quantum chromodynamics and chiral perturbation theory. The relevance of axial charges with regard to $\pi$-dressing and spontaneous chiral-symmetry breaking is discussed.

Radiative decays of double heavy baryons in a relativistic constituent three-quark model including hyperfine mixing effects

We study flavor-conserving radiative decays of double-heavy baryons using a manifestly Lorentz covariant constituent three-quark model. Decay rates are calculated and compared to each other in the full theory, keeping masses finite, and also in the heavy quark limit. We discuss in some detail hyperfine mixing effects.

Quark model description of the tetraquark stateX(3872)in a relativistic constituent quark model with infrared confinement

We explore the consequences of treating the X(3872) meson as a tetraquark bound state. As dynamical framework we employ a relativistic constituent quark model which includes infrared confinement in an effective way. We calculate the decay widths of the observed channels X-> Jpsi+2\pi (3\pi) and X-> \bar D0+D0+\pi0 via the intermediate off--shell states X-> Jpsi+\rho(\omega) and X-> \bar D + D*. For reasonable values of the size parameter of the X(3872) we find consistency with the available experimental data. We also discuss the possible impact of the X(3872) in a s-channel dominance description of the Jpsi-dissociation cross section.

Relativistic constituent quark model and experiments at JLab

Within the relativistic-quantum-mechanics version developed by the present authors in their previous studies, the pion electromagnetic form factor is calculated in the region of high momentum transfers reached and planned to be reached in experiments at the Thomas Jefferson Laboratory (JLab). An asymptotic expansion was obtained for the pion form factor for Q 2 → ∞. This expansion describes well existing experimental values and the results of a QCD simulation of future experiments at JLab. It is shown that the region of experiments at JLab is an asymptotic region for the relativistic constituent quark model and that the behavior of the pion form factor, F π (Q 2)Q 2 = const, can be obtained within this model.

Axial charges of the nucleon andN*resonances

The axial charges of the nucleon and the well-established N* resonances are studied within a consistent framework. For the first time the axial charges of the N* resonances are produced for the relativistic constituent quark model. The axial charge of the nucleon is predicted close to experiment, and the ones of N*(1535) and N*(1650), the only cases where such a comparison is possible, agree well with results from quantum chromodynamics on the lattice that have recently become available. The relevance of the magnitudes of the N* axial charges for the low-energy behavior of quantum chromodynamics is discussed.

Relativistic constituent quark model with infrared confinement

We refine the relativistic constituent quark model developed in our previous papers to include the confinement of quarks. It is done, first, by introducing the scale integration in the space of alpha-parameters, and, second, by cutting this scale integration on the upper limit which corresponds to an infrared cutoff. In this manner one removes all possible thresholds presented in the initial quark diagram. The cutoff parameter is taken to be the same for all physical processes. We adjust other model parameters by fitting the calculated quantities of the basic physical processes to available experimental data. As an application, we calculate the electromagnetic form factors of the pion and the transition form factors of the omega and eta Dalitz decays.