Mass spectra and wave functions of the doubly heavy baryons with J~P=1~+ heavy diquark cores

Mass spectra and wave functions of the doubly heavy baryons are computed assuming that the two heavy quarks inside a baryon form a compact heavy 'diquark core' in a color anti-triplet,and bind with the remaining light quark into a colorless baryon.The two reduced two-body problems are described by the relativistic Bethe-Salpeter equations(BSEs) with the relevant QCD inspired kernels.We focus on the doubly heavy baryons with 1~+ heavy diquark cores.After solving BSEs in the instantaneous approximation,we present the mass spectra and the relativistic wave functions of the diquark cores,and of the low-lying baryon states J~P=(1/2)~+ and(3/2)~+ with flavors(ccq)(bcq)and(bbq).A comparison with other approaches is also made.     

Properties of doubly heavy baryons in the relativistic quark model

Mass spectra and semileptonic decay rates of baryons consisting of two heavy (b or c) and one light quark are calculated in the framework of the relativistic quark model. The doubly heavy baryons are treated in the quark-diquark approximation. The ground and excited states of both the diquark and quark-diquark bound systems are considered. The quark-diquark potential is constructed. The light quark is treated completely relativistically, while the expansion in the inverse heavy-quark mass is used. The weak transition amplitudes of heavy diquarks bb and bc going, respectively, to bc and cc are explicitly expressed through the overlap integrals of the diquark wave functions in the whole accessible kinematic range. The relativistic baryon wave functions of the quark-diquark bound system are used for the calculation of the decay matrix elements, the Isgur-Wise function, and decay rates in the heavy-quark limit.     

Baryon properties in the relativistic quark model

Properties of heavy and strange baryons are investigated in the framework of the relativistic quark-diquark picture. It is based on the relativistic quark model of hadrons, which was previously successfully applied for the calculation of meson properties. It is assumed that two quarks in a baryon form a diquark and baryon is considered as the bound quark-diquark system. The relativistic effects and diquark internal structure are consistently taken into account. Calculations are performed up to rather high orbital and radial excitations of heavy and strange baryons. On this basis the Regge trajectories are constructed. The rates of semileptonic decays of heavy baryons are calculated. The obtained results agree well with available experimental data.     

Diquark structure in heavy quark baryons in a geometric model

Using a geometric model to study the structure of hadrons, baryons having one, two and three heavy quarks have been studied here. The study reveals diquark structure in baryons with one and two heavy quarks but not with three heavy identical quarks.     

Quark–Diquark Structure and Masses of Doubly Charmed Baryons

finite size of a doubly heavy diquark yields a positive correction to baryon masses calculated in the local-diquark approximation. Upon evaluating this correction for the ground states of doubly charmed baryons, it became possible to obtain new predictions of importance for current searches of these baryons in LHCb experiments: \(m[\Xi _{cc}^{1/{2^{ + + }}}] \approx m[\Xi _{cc}^{1/{2^{ + + }}}]\) = 3615 ± 55 MeV and \(m[\Xi _{cc}^{3/{2^{ + + }}}] \approx m[\Xi _{cc}^{3/{2^{ + + }}}]\) 3747 ± 55 MeV     

Charmed Baryon in Diquark Model

A diquark model is used to investigate single-charmed baryons.In this model,baryon is composed of two diquarks and an antiquark.Masses of lowest lying states with J~P=1/2~(±) are obtained.Baryons in our results are as heavy as other theoretic predictions and we suggest that the five-quark components should be considered in any three-quark model for studying the charmed baryons.     

Inclusive decays and lifetimes of doubly-charmed baryons

The analysis of singly-charmed hadrons has been extended to the case of doubly-charmed baryons, , and . Doubly-charmed baryons are described as a system containing a heavy cc diquark and a light quark, as in the case of a heavy–light meson. This leads to preasymptotic effects in semileptonic and nonleptonic decays that are essentially proportional to the meson wave function. Interplay between preasymptotic effects in semileptonic and/or nonleptonic decay rates leads to very clear predictions for semileptonic branching ratios and lifetimes of doubly-charmed baryons. Received: 21 January 1999 / Published online: 20 May 1999     

带有两个重夸克的重子谱计算中几个困难问题的研究

由两个重夸克和一个轻夸克组成的重子可以看作是一个两体系统.它的两个重夸克组成一个玻色型的双夸克团.利用B–S方程导出了它的轻夸克和重的双夸克之间的等效相互作用势.在利用这种势计算重子质量的过程中,发现有几个困难问题需要深入探讨.它们是:(1)算符排序,(2)由非相对论展开带来的误差,(3)自旋–自旋耦合,(4)在标量双夸克组成的重子态和矢量双夸克组成的重子态之间的混合.本文详细地讨论并适当地处理了这些问题.     

Quarks and diquarks in a baryon string model

Chew-Frautschi plots are found for baryons containing a quark and a diquark at the extremities of a relativistic string. The quark fields are modelled on free Dirac fields restricted to the ends of the string. Quantum numbers for the diquark field are obtained by adding those for two individual quark fields.The leading trajectory for the quark-diquark configuration is found to be energetically more favourable than the leading trajectories for the linear and Y-shaped baryon configurations considered previously.     

Isospin splittings of doubly heavy baryons

The SELEX Collaboration has reported a very large isospin splitting of doubly charmed baryons. We show that this effect would imply that the doubly charmed baryons are very compact. One intriguing possibility is that such baryons have a linear geometry Q–q–Q$Q\text{–}q\text{–}Q$ where the light quark q oscillates between the two heavy quarks Q  , analogous to a linear molecule such as carbon dioxide. However, using conventional arguments, the size of a heavy-light hadron is expected to be around 0.5 fm, much larger than the size needed to explain the observed large isospin splitting. Assuming the distance between two heavy quarks is much smaller than that between the light quark and a heavy one, the doubly heavy baryons are related to the heavy mesons via heavy quark–diquark symmetry. Based on this symmetry, we predict the isospin splittings for doubly heavy baryons including Ξ_cc${\Xi }_{cc}$, Ξ_bb${\Xi }_{bb}$ and Ξ_bc${\Xi }_{bc}$. The prediction for the Ξ_cc${\Xi }_{cc}$ is much smaller than the SELEX value. On the other hand, the Ξ_bb${\Xi }_{bb}$ baryons are predicted to have an isospin splitting as large as (6.3±1.7) MeV$(6.3\pm 1.7)\text{MeV}$. An experimental study of doubly bottomed baryons is therefore very important to better understand the structure of baryons with heavy quarks.     

Heavy baryons in the nonperturbative string approach

Physics of Atomic Nuclei - We present some piloting calculations of the short-range correlation coefficients for light and heavy baryons and of the masses of the doubly heavy baryons...     

Spectra of baryons containing two heavy quarks

Doubly heavy baryons, i.e., the baryons containing two heavy quarks are treated in the adiabatic approximation, considering the motion of the light quark as a relativistic motion. The binding energy and mass spectra of doubly heavy baryons are calculated solving the two-center Dirac equation the one-centre Schr?dinger equation for Coulomb plus linear potential. The binding energy of the light quark as a function of the distance between heavy quarks is found. Received: 16 January 2002 / Accepted: 7 February 2002     

Heavy baryons in the relativistic quark model

In the framework of the relativistic quasipotential quark model the mass spectrum of baryons with two heavy quarks is calculated. The quasipotentials for interactions of two quarks and of a quark with a scalar and axial vector diquark are evaluated. The bound state masses of baryons with are computed.     

Discovery potentials of doubly charmed baryons

The existence of doubly heavy flavor baryons has not been well established experimentally so far. In this Letter we systematically investigate the weak decays of the doubly charmed baryons, Ξ~(++)_(cc)and Ξ~+_(cc), which should be helpful for experimental searches for these particles. The long-distance contributions are first studied in the doubly heavy baryon decays, and found to be significantly enhanced. Comparing all the processes, Ξ~(++)_(cc)→Λ~+_cK~-π~+π~+andΞ~+_cπ~+ are the most favorable decay modes for experiments to search for doubly heavy baryons.     

Chiral corrections to the masses of the doubly heavy baryons

We study the masses of the doubly bottom baryons and the charmed-bottom baryons up to ${ \mathcal O }\left({p}^{3}\right)$ in heavy baryon chiral perturbation theory. We determine the unknown low energy constants in the quark model and lattice QCD. We show the numerical results for the masses of the doubly bottom baryons and the charmed-bottom baryons up to ${ \mathcal O }\left({p}^{3}\right)$.     

Fragmentation Production of Θ0c(uuddc-) and Θ+b(uuddb-) Pentaquarks in the Diquark Model

Heavy hadrons have been the focus of attention because of their worthwhile properties. So far the fragmentation function (FF) and total fragmentation probability (F.P) for heavy baryons and mesons have been calculated in quark model and diquark model in leading order of perturbative QCD. After the discovery of pentaquarks, their fragmentation probabilities were estimated based on the known measurementsof c or b quarks into mesons and baryons. In this note we calculate the direct fragmentation function of \( \overline{c}\to {\varTheta}_c^0\left( uudd\overline{c}\right) \) and \( \overline{b}\to {\varTheta}_b^{+}\left( uudd\overline{b}\right) \) processes in leading order of perturbative QCD, employing the diquark model with considerable precision. Consistent with such a process we set up the kinematics of the fragmentation of a heavy antiquark into a pentaquark such that the effect of the Fermi motion of the constituents is ignored. We show that using the diquark model for studying pentaquark can provide reasonably good theoretical results. The findings of this study accord with those in the previous studies.

     

Pair production of doubly heavy diquarks

The differential and total cross sections for the pair production of doubly heavy diquarks are calculated analytically within the diquark model. The cases of electron-positron and quark-antiquark annihilation are considered. The ratios of the total cross sections to the corresponding cross sections for annihilation into two heavy quarks are estimated numerically.     

Discussions on the stability of diquarks

Since the birth of the quark model, the diquark, which is composed of two quarks, has been considered as a substantial structure of a color anti-triplet. This is not only a mathematical simplification for dealing with baryons, but also provides a physical picture where the diquark would behave as a whole object. It is natural to ask whether such a structure is sufficiently stable against external disturbance. The mass spectra of the ground states of the scalar and axial-vector diquarks, which are composed of two-light (L-L), one-light-one-heavy (H-L) and two-heavy (H-H) quarks, respectively, have been calculated in terms of the QCD sum rules. We suggest a criterion as the quantitative standard for the stability of the diquark. It is the gap between the masses of the diquark and √s₀ where s₀ is the threshold of the excited states and continuity, namely the larger the gap is, the more stable the diquark would be. In this work, we calculate the masses of the H-H type to complete the series of the spectra of the ground state diquarks. However, as the criterion being taken, we find that all the gaps for the various diquarks are within a small range. In particular, the gap for the diquark with two heavy quarks, which is believed to be a stable structure, is slightly smaller than that of the other two types of diquarks. Therefore we conclude that because of the large theoretical uncertainty, we cannot use the numerical results obtained with the QCD sum rules to assess the stability of diquarks, but need to invoke other theoretical framework.     

Wave Functions of Doubly Heavy Baryons on the Light Cone

Physics of Atomic Nuclei - Heavy mesons and doubly heavy baryons with the dynamic properties governed by the light quark motion relative to the fixed center of forces are studied within the Heavy...