Quark-diquark Structure Research Articles

Quark-diquark models and baryonic fluctuations in QCD

We study the baryonic fluctuations of electric charge, baryon number and strangeness, by considering a realization of the Hadron Resonance Gas model in the light flavor sector of QCD. We elaborate on the idea that the susceptibilities can be saturated with excited baryonic states with a quark-diquark structure with a linearly confining interaction identical up to a constant to the quark-antiquark potential, VqD′(r)=Vqq‾′(r). We obtain an overall good agreement with the spectrum obtained with other quark models and with lattice data for the fluctuations.

Weak decays in the light-front quark model with two schemes to deal with the polarization of diquark

Thanks to the remarkable achievements of the LHC, a large database on baryons has been accumulated. There is therefore now the opportunity to precisely study baryons, particularly heavy baryons. By analyzing the data, the quark–diquark structure, which has been the subject of intensive discussions, can be tested. In this work the decay widths of weak transitions are calculated in terms of the light-front quark model. To carry out the calculations, the quark–diquark picture is employed where an axial-vector diquark composed of two light quarks serves as a spectator in the processes concerned. The first step of this work is to construct the vertex functions for and Σb, then the relevant form factors are derived. It is shown that under the heavy quark limit the Isgur–Wise functions for the transition are re-deduced. Indeed, the question of how to properly depict the polarization (ϵμ) of the diquark is slightly tricky. In this work, we apply two schemes to explicitly determine the momentum-dependence of the diquark. The corresponding numerical results are presented which will be testified by future experiments.

Baryonic susceptibilities, quark-diquark models, and quark-hadron duality at finite temperature

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 baryonic fluctuations of electric charge, baryon number and strangeness: $\chi_{BQ}$, $\chi_{BB}$ and $\chi_{BS}$; by considering a realization of the hadron resonance gas model in the light flavor sector of QCD. These results have been obtained by using the baryon spectrum computed within a relativistic quark-diquark model, leading to an overall good agreement with the spectrum obtained with other quark models and with lattice data for the fluctuations.

Quark–Diquark Structure and Masses of Doubly Charmed Baryons

The finite size of doubly heavy diquark gives a positive correction to the masses of baryons calculated in the local diquark approximation. We evaluate this correction for the basic states of doubly charmed baryons to give quite accurate predictions actual for current searches of those baryons at LHCb: $m[{\Xi_{cc}^{1/2}}^{+}]\approx m[{\Xi_{cc}^{1/2}}^{++}]=3615\pm 55$ MeV and $m[{\Xi_{cc}^{3/2}}^{+}]\approx m[{\Xi_{cc}^{3/2}}^{++}]=3747\pm 55$ MeV.

The decay width of stringy hadrons

In this paper we further develop a string model of hadrons by computing their strong decay widths and comparing them to experiment. The main decay mechanism is that of a string splitting into two strings. The corresponding total decay width behaves as Γ=π2ATL where T and L are the tension and length of the string and A is a dimensionless universal constant. We show that this result holds for a bosonic string not only in the critical dimension. The partial width of a given decay mode is given by Γi/Γ=Φiexp⁡(−2πCmsep2/T) where Φi is a phase space factor, msep is the mass of the “quark” and “antiquark” created at the splitting point, and C is a dimensionless coefficient close to unity. Based on the spectra of hadrons we observe that their (modified) Regge trajectories are characterized by a negative intercept. This implies a repulsive Casimir force that gives the string a “zero point length”.We fit the theoretical decay width to experimental data for mesons on the trajectories of ρ, ω, π, η, K⁎, ϕ, D, and Ds⁎, and of the baryons N, Δ, Λ, and Σ. We examine both the linearity in L and the exponential suppression factor. The linearity was found to agree with the data well for mesons but less for baryons. The extracted coefficient for mesons A=0.095±0.015 is indeed quite universal. The exponential suppression was applied to both strong and radiative decays. We discuss the relation with string fragmentation and jet formation. We extract the quark–diquark structure of baryons from their decays. A stringy mechanism for Zweig suppressed decays of quarkonia is proposed and is shown to reproduce the decay width of ϒ states. The dependence of the width on spin and flavor symmetry is discussed. We further apply this model to the decays of glueballs and exotic hadrons.

Spectroscopy and decay properties of Σb, Λb baryons in quark–diquark model

Properties of single beauty baryons (Σb, Λb) are studied based on the quark–diquark structure. The confinement potential is assumed as two body color coulomb plus power potential with exponent ν. We find a strong correlation between the choice of the heavy quark mass parameter (mb), strong coupling constant (αs) and the potential exponent (ν) for getting the experimental mass spilt of mΣb*−mΣb=21.2±2.0 MeV. The resultant spectroscopic parameters are used for computing magnetic moments, the electromagnetic radiative decay and strong hadronic decay of Σb, Λb systems. Our predictions on the radiative decay width correspond to Σb*0→Λbγ are in agreement with the QCD sum rule prediction.

Three-body nature of N(*) and Δ(*) resonances from sequential decay chains.

The Nπ^{0}π^{0} decays of positive-parity N^{*} and Δ^{*} resonances at about 2GeV are studied at ELSA by photoproduction of two neutral pions off protons. The data reveal clear evidence for several intermediate resonances: Δ(1232), N(1520)3/2^{-}, and N(1680)5/2^{+}, with spin parities J^{P}=3/2^{+}, 3/2^{-}, and 5/2^{+}. The partial wave analysis (within the Bonn-Gatchina approach) identifies N(1440)1/2^{+} and the N(ππ)_{S wave} (abbreviated as Nσ here) as further isobars and assigns the final states to the formation of nucleon and Δ resonances and to nonresonant contributions. We observe the known Δ(1232)π decays of Δ(1910)1/2^{+}, Δ(1920)3/2^{+}, Δ(1905)5/2^{+}, Δ(1950)7/2^{+}, and of the corresponding spin-parity series in the nucleon sector, N(1880)1/2^{+}, N(1900)3/2^{+}, N(2000)5/2^{+}, and N(1990)7/2^{+}. For the nucleon resonances, these decay modes are reported here for the first time. Further new decay modes proceed via N(1440)1/2^{+}π, N(1520)3/2^{-}π, N(1680)5/2^{+}π, and Nσ. The latter decay modes are observed in the decay of N^{*} resonances and at most weakly in Δ^{*} decays. It is argued that these decay modes provide evidence for a 3-quark nature of N^{*} resonances rather than a quark-diquark structure.

The form factors of the nucleons

There has been much activity in the measurement of the elastic electromagnetic proton and neutron form factors in the last decade, and the quality of the data has been greatly improved by performing double-polarization experiments, in comparison with with previous unpolarized cross section data. Here we will review the experimental data base in view of the new results for the proton and the neutron, obtained at MIT-Bates, JLab and MAMI. The rapid evolution of phenomenological models triggered by these high-precision experiments will be discussed. In particular, the possibility that the proton is non-spherical in its ground state, and that the transverse charge density are model independently defined in the infinite momentum frame. Likewise, flavor decomposition of the nucleon form factors into dressed u and d quark form factors, may give information about the quark-diquark structure of the nucleon. The current proton radius “crisis” will also be discussed.

Σb→ΣcandΩb→Ωcweak decays in the light-front quark model

The successful operation of LHC provides a great opportunity to study the processes where heavy baryons are involved. {In this work we mainly study} the weak transitions of $\Sigma_b\to \Sigma_c$. Assuming the reasonable quark-diquark structure where the two light quarks constitute an axial vector, we calculate the widths of semi-leptonic decay $\Sigma_{b}\to\Sigma_c e\nu_e$ and non-leptonic decay modes $\Sigma_{b}\to\Sigma_c +M$ (light mesons) in terms of the light front quark model. We first construct the vertex function for the concerned baryons and then deduce the form factors which are related to two Isgur-Wise functions for the $\Sigma_{b}\to\Sigma_c$ transition under the heavy quark limit. Our numerical results indicate that $\Gamma(\Sigma_{b}\to\Sigma_c e\nu_e)$ is about $1.38\times10^{10}{\rm s}^{-1}$ and $\Gamma(\Sigma_{b}\to\Sigma_c +M)$ is slightly below $1\times10^{10}{\rm s}^{-1}$ which may be accessed at the LHCb detector. By the flavor SU(3) symmetry we estimate the rates of $\Omega_b\to\Omega_c$. We suggest to measure weak decays of $\Omega_b\to\Omega_c$, because $\Omega_b$ does not decay via strong interaction, the advantage is obvious.

Quark-diquark model description for double charm baryons

We report here the mass spectrum and magnetic moments of ccq(q ∊ u,d,s) systems in the potential model framework by assuming the inter-quark potential as the colour coulomb plus power form with power index ν varying between 0.1 to 2.0. Here the two charm quarks are considered for the diquark states. The conventional one gluon exchange interaction has been employed to get the hyperfine and the fine structure between different states. We have predicted many low-lying states whose experimental verification can exclusively support the quark-diquark structure of the baryons.

SEARCHING FOR THE QUARK–DIQUARK SYSTEMATICS OF BARYONS COMPOSED BY LIGHT QUARKS q = u, d

Supposing quark–diquark structure of baryons, we look for systematics of baryons composed of light quarks (q = u, d). We systematize baryons using the notion of two diquarks: (i) axial–vector state, [Formula: see text], with the spin SD = 1 and isospin ID = 1 and (ii) scalar one, [Formula: see text], with the spin SD = 0 and isospin ID = 0. We consider several schemes for the composed baryons: (1) with different diquark masses, [Formula: see text], (2) with [Formula: see text] and overlapping [Formula: see text] and [Formula: see text] states (resonances), (3) with/without SU(6) constraints for low-lying states (with quark–diquark orbital momenta L = 0). In the high-mass region, the model predicts several baryon resonances at M ~ 2.0–2.9 GeV . Moreover, the model gives us the double pole structure (i.e. two poles with the same Re M but different Im M) in many amplitudes at masses M ≳ 2.0 GeV . We see also that for description of low-lying baryons (with L = 0), the SU(6) constraint is needed.

Inelastic diffractive scattering in nonperturbative QCD

We examine diffractive proton-proton scattering p p -> p X and photo- and electroproduction of \rho^0 mesons \gamma^(*) p -> \rho^0 X, where X denotes a proton or a final state, into which the proton can go by diffractive dissociation. Using a functional integral approach we derive the scattering amplitudes, which are governed by the expectation values of light-like Wegner-Wilson loops, which are then evaluated using the model of the stochastic vacuum. For the proton, we assume a quark-diquark structure. From the scattering amplitudes we calculate total and differential cross sections for high centre of mass energy and small momentum transfer and compare with experiments. Furthermore we calculate isovector form factors for the proton and the pion within the same model.

Spectroscopy of doubly heavy baryons

Spectra of masses are calculated for the families of doubly heavy baryons in the framework of the nonrelativistic quark model with the QCD potential of Buchm\"uller and Tye. We suppose the quark-diquark structure for the wave functions and take into account the spin-dependent splittings. The physical reasons causing the existence of quasistable excited states in the subsystem of heavy diquark are considered for the heavy quarks of identical flavors.

Spectroscopy of doubly heavy baryons

Within a nonrelativistic quark model featuring a QCD-motivated Buchmüller-Tye potential, the mass spectra for the families of doubly heavy baryons are calculated by assuming the quark-diquark structure of the baryon wave functions and by taking into account spin-dependent splitting. Physically motivated evidence that, in the case where heavy quarks have identical flavors, quasistationary excited states may be formed in the heavy-diquark subsystem is analyzed.

Exclusive photoproduction of $\Phi$ on proton in the quark–diquark model

We present predictions for exclusive photoproduction of a $\Phi$ meson on proton at large transfer, where we use a quark–diquark structure model for the proton. Extrapolation from our results to lower transfers is comparable in magnitude with available data in that range. This may support the diquark model in its ability to provide, for that process, an appropriate link between diffractive physics at low transfer and the standard semiperturbative approach of hard exclusive processes at very large transfer, in which the proton recovers its three-quark structure.

Odderon and photon exchange in pseudoscalar meson production

We consider exclusive π 0 production in ep-scattering. At high energies odderon and photon exchange contribute. The photon exchange contribution is evaluated exactly using data for the total virtual photon-proton absorption cross section. The odderon exchange contribution is calculated in nonperturbative QCD, using functional integral techniques and the model of the stochastic vacuum. For the proton we assume a quark-diquark structure as suggested by the small odderon amplitude in pp and p p forward scattering. We show that odderon exchange leads to a much larger inelastic than elastic π 0 production cross section. Observing our process at HERA would establish the soft odderon.

Odderon and photon exchange in electroproduction of pseudoscalar mesons

We investigate the reaction \({\rm e}\;{\rm p} \rightarrow{\rm e}\;{\rm PS}\;{\rm X}\) where PS denotes a pseudoscalar meson \(\pi^0\), \(\eta\), \(\eta'\), or \(\eta_c\) and X either a proton or resonance or continuum state into which the proton can go by diffractive excitation. At high energies photon and odderon exchange contribute to the reaction. The photon exchange contribution is evaluated exactly using data for the total virtual photon-proton absorption cross section. The odderon exchange contribution is calculated in nonperturbative QCD, using functional integral techniques and the model of the stochastic vacuum. For the proton we assume a quark-diquark structure as suggested by the small odderon amplitude in pp and \( {\rm p} \bar{{\rm p}}\) forward scattering. We show that odderon exchange leads to a much larger inelastic than elastic PS production cross section. Observation of our reaction at HERA would establish the soft odderon as an exchange object on an equal footing with the soft pomeron and would give us valuable insight into both the nucleon structure and the mechanism of high energy diffractive scattering.

Exclusive photoproduction of

We present predictions for the exclusive photoproduction of $\Phi$-meson on Proton at large tranfer, where we use a quark-diquark structure model for the proton. Extrapolation from our results to lower tranfers is comparable in magnitude with available data in that range. This may support the diquark model in its ability to provide, for that process, an appropriate link between diffractive physics at low transfer and the standard semi-perturbative approach of hard exclusive processes at very large tranfer, where the proton recovers its three-quark structure.

Quark-Quark Correlations in the Nucleon in a Generalized Nambu-Jona-Lasinio Model

We present a relativistic model of the nucleon based upon a quark-diquark structure that emerges from a study of the Nambu-Jona-Lasinio model. Similar calculations, made by other authors, have been carried out after a Wick rotation is performed. These previous calculations have neglected confinement; therefore, the masses of the quarks and diquarks had to be adjusted so that the diquarks and the nucleon were stable, in which case the Wick rotation may be made. In our work, we include a momentum-space model of confinement developed earlier and we are therefore able to carry out the calculation in Minkowski space, after making a number of approximations. We determine the relative admixture of a scalar-isoscalar diquark and an axialvector-isovector diquark dynamically and find that an approximately equal admixture provides a reasonable fit to the nucleon magnetic moments. While the original problem (without approximation) requires the specification of eight scalar functions of two variables, our various approximations allow us to calculate several functions of a single variable. We find that only two of these functions are important. Therefore, we can exhibit a relatively simple relativistic wave function of the nucleon expressed in terms of two wave functions describing the relative motion of the quarks and diquarks.

Nucleon charge root-mean-square radius and the quark-diquark structure

The effect of nucleon's possible quark-diquark structure is added to the usual constituent quark model to calculate nucleon's charge root-mean-square radius. The experimental values of both 1/2=(0.88±0.03) fm for a proton and 1/2=(−0.12±0.01) fm2 for a neutron are reproduced quite well. A few MeV difference between u and d quark masses is also assumed so that the correct mass difference between a proton and a neutron can be obtained at the same time.