A Mixing Coupling Scheme for Spectra of Singly Heavy Baryons with Spin-1 Diquarks in P-waves
Duojie Jia, Ji-Hai Pan, Cheng-Qun Pang
备注：
28 pages, 3 figures in total, with one new figure (FIG. 3) and one new section (Section VI) added in this enlarged version(V3). Due to twice extensions (Section V and Section VI added) including two newly added figures(FIG. 2 and FIG. 3), we also changed the title correspondingly
A new scheme of state classification is proposed and applied to analyze masses of the heavy baryons $Ω_{Q}$, $Σ_{Q}$ and $Ξ_{Q}^{\prime}$ in P-waves. The results confirm all excited $Ω_{c}$ and $Ω_{b}$ baryons reported recently by LHCb to be bound states of a P-wave $ss$-diquark and a respective charm or bottom quark, and thereby predict Regge trajectories for more excited $Ω_{c}$ and $Ω_{b}$ baryons. We suggest one excited {$J^{P}=5/2^{-}$} $Ω_{b}$ state to be unseen by LHCb around $6352$ MeV, and predict P-wave masses of all spin-partners of the odd-parity baryons $Σ_{c}(2800)/Ξ_{c}^{\prime}(2942)$ and $Σ_{b}(6097)$/$Ξ_{b}^{\prime }(6227)$. A computation is further given in a relativized potential quark models to explain matched values of spin couplings of all considered baryons, by which a scaling law for these spin couplings is discussed.
The mass spectra of singly charmed and bottom baryons, $Λ_{c/b}(1/2^\pm,3/2^-)$ and $Ξ_{c/b}(1/2^\pm,3/2^-)$, are investigated using a nonrelativistic potential model with a heavy quark and a light diquark. The masses of the scalar and pseudoscalar diquarks are taken from a chiral effective theory. The effect of $U_A(1)$ anomaly induces an inverse hierarchy between the masses of strange and non-strange pseudoscalar diquarks, which leads to a similar inverse mass ordering in $ρ$-mode excitations of singly heavy baryons.
Assuming that vector and scalar diquarks exist in the Quark-Gluon Plasma near the critical temporature $T_c$, baryons can be produced through the processes of quarks and diquarks forming $({1/2})^+$ baryon states. Ratios of different baryons can be estimated through this method, if such kind of QGP with diquarks can exists.
A simple quark-diquark model for the baryons is constructed as a partial solution to the well known missing resonances problem. A complete classification of the baryonic states in the quark-diquark framework is given and the spectrum is calculated through a mass formula built to reproduce the rotational and vibrational Regge trajectories.
The wave functions in the diquark-quark model for baryons are modified to take into account the effect of the different masses of the quarks in diquark formation. A spatial wave function is introduced multiplying each flavour-spin configuration in the quark-diquark model. Futhermore a numerical coefficient is introduced which weighes the contribution of each configuration.
This paper studies the leading chiral corrections to heavy quark-diquark symmetry predictions for doubly heavy baryon semileptonic decay form factors. We derive the coupling between heavy diquarks and weak current in the limit of heavy quark-diquark symmetry, and construct the chiral Lagrangian for doubly heavy baryons coupled to weak current. We evaluate chiral corrections to doubly heavy baryon zero-recoil semileptonic decay for both unquenched and partially quenched QCD. This theory is used to derive chiral extrapolation expressions for measurements of form factors of doubly heavy baryon ze…
A composite Fermion (CF) model of quasi particle has been used to describe a diquark. Considering baryons in quark-diquark configuration,the masses of the heavy light baryons like $Λ_{c}^{+}$, $Σ_{c}^{+}$, $Ξ_{c}^{0}$, $Ω_{c}^{0}$ and $Λ_{b}^{+}$, $Σ_{b}^{+}$, $Ξ_{b}^{0}$, $Ω_{b}^{-}$ have been computed using this CF model of the diquark. The results are found to be in good agreement with the corresponding experimental findings. It has been suggested that the diquark can be well described in the framework of CF model in a gauge invariant way.
A simple quark-diquark model of baryons with direct and exchange interactions is constructed. Spectrum and form factors are calculated and compared with experimental data. Advantages and disadvantages of the model are discussed.
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 $J^P= 1/2 ^ \pm$ are obtained. Some masses are smaller than other theoretic predictions which indicates that these baryons of pentaquark structure could be relatively stable. The results also show that $Λ(2882)$ may be a pentaquark with $J^P=1/2^-$ and $Ξ(3125)$ may be a pentaquark with $J^P=1/2^+$.
We briefly discuss the relativistic interacting quark-diquark model formalism and its application to the calculation of strange and nonstrange baryon spectra. The results are compared to the existing experimental data.
Recently, some singly bottom baryons have been established experimentally, but none of doubly or triply bottom baryons has been observed. Under the Regge phenomenology, the mass of a ground state unobserved doubly or triply bottom baryon is expressed as a function of masses of the well established light baryons and singly bottom baryons. Then, the values of Regge slopes and Regge intercepts for baryons containing one, two, or three bottom quarks are calculated. After that, masses of the orbitally excited singly, doubly, and triply bottom baryons are estimated. Our predictions may be useful for…
Using a geometric model for the study of the structure of hadrons, we study baryons having one, two and three heavy quarks. The study reveals diquark structure in baryons with one and two heavy quarks but not with three heavy identical quarks.
The baryon structure is investigated in a covariant diquark-quark model. In this approach baryons emerge as relativistic bound states of a constituent quark and a $0^{+}$ or $1^{+}$ diquark. After solving the Bethe-Salpeter Equation for the scalar diquark quark system in ladder approximation we couple various external currents to the constituents of the baryon to probe its internal structure. The quark and the diquarks are assumed to be confined which is implemented by suitable choices for the propagators. This leads to nontrivial vertex functions between the constituents and the external curr…
The relativistic interacting quark-diquark model of baryons, recently developed, is here extended to introduce a spin-isospin transition interaction into the mass operator. The refined version of the model is used to calculate the non strange baryon spectrum. The results are compared to the present experimental data.
We describe the relativistic interacting quark-diquark model formalism and its application to the calculation of strange and nonstrange baryon spectra. The results are compared to the existing experimental data. We also discuss the application of the model to the calculation of other baryon observables, like baryon magnetic moments, open-flavor strong decays and baryon masses with self-energy corrections.
The yield of doubly charmed baryons with excited heavy diquark in $S$ wave and $P$ wave states has been estimated at LHC energies. The observation possibility of such baryons is discussed.
In the framework of the nonrelativistic QCD and a quark-diquark model of baryons we have obtained the fragmentation functions for heavy quark to split into spin-1/2 and spin-3/2 double heavy baryons. It was predicted the production rates as well as the shape of the energy spectra for the $cc-$ and $bc-$baryons in the region of $Z^o$ peak at LEP collider.
The mass spectra of the excited heavy baryons consisting of two light (u,d,s) and one heavy (c,b) quarks are calculated in the heavy-quark--light-diquark approximation within the constituent quark model. The light quarks, forming the diquark, and the light diquark in the baryon are treated completely relativistically. The expansion in v/c up to the second order is used only for the heavy (b and c) quarks. The internal structure of the diquark is taken into account by inserting the diquark-gluon interaction form factor. An overall good agreement of the obtained predictions with available experi…
The baryonic decays of $J/ ψ$ provide a new way to study the internal structure of baryons. We apply a simple diquark model to the calculation of the decay cross-sections for the reactions $J/ ψ\longrightarrow \bar{p}p$, $\bar pN^*(1440)$, $\bar{N}^{\ast}N^{\ast}$, $\barΛΛ$ and $\barΣ^0Σ^0$. The results are different from those given by the ordinary constituent quark model. Hence these reactions may provide a new check of two different pictures for the baryons.
It is shown that the number of independent weak form factors collapses if the heavy diquark exists inside the baryons containing a single heavy quark. The relations between the weak form factors are quite different in the case of light diquark. So a careful analysis on the future data of the weak form factors would clarify that in those baryons the correlation between the heavy quark and a light quark is stronger or weaker than the one between two light quarks.
The mass spectra and wave functions for the doubly heavy baryons are computed under the picture that the two heavy quarks inside a doubly heavy baryon, such as two $c$-quarks in $Ξ_{cc}$, combine into a heavy `diquark core' in color anti-triplet firstly, then the diquark core turns into a color-less doubly heavy baryon via combining the light $q$-quark inside the baryon. Namely both of the combinations, the two heavy quarks inside the baryon into a diquark core in color anti-triplet and the heavy diquark core with the light quark into the baryon, are depicted by relativistic Bethe-Salpeter equ…
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: $m[{Ξ_{cc}^{1/2}}^{+}]\approx m[{Ξ_{cc}^{1/2}}^{++}]=3615\pm 55$ MeV and $m[{Ξ_{cc}^{3/2}}^{+}]\approx m[{Ξ_{cc}^{3/2}}^{++}]=3747\pm 55$ MeV.
The approach of path integral hadronization, applied to a quark-diquark toy model, is used to derive an effective chiral meson-baryon Lagrangian. In this approach the Goldberger-Treiman relation, found at the quark-meson level, is re-established at the composite hadron level. For illu- strations, electromagnetic low energy characteristics of composite nucleons are estimated.
We treat baryons as bound states of scalar or axialvector diquarks and a constituent quark which interact through quark exchange. We obtain fully four-dimensional wave functions for both octet and decuplet baryons as solutions of the corresponding Bethe-Salpeter equation. Applications currently under investigation are: electromagnetic and strong form factors and strangeness production processes.
The properties of the Theta^{+} and Xi^{--}_{3/2} exotic baryons have been investigated in the framework of diquark- diquark-antiquark system. A model for diquark suggested in an analogy with the quasi-particle in a crystal lattice has been used. The mass of the exotics have been computed. The Decay width of the Theta^{+} has been estimated to be ~ 11 MeV using effective diquark theory. The radius of the Xi^{--}_{3/2} has been extracted as 0.94fm using the experimental value of the frac{Γ_{Θ^{+}}}{Γ_{Ξ^{--}_{3/2}}}. The results obtained are found to be in good agreement with the present experi…
The triply heavy flavour baryons are studied using the Quark-diquark description of the three-body system. The confinement potential for present study of triply heavy flavour baryons is assumed as coulomb plus power potential with power index $ν$. We have solved Schrodinger equation numerically to calculate the masses of triply heavy flavour baryons. The masses and magnetic moments of triply heavy flavour baryons are computed for different power indices, $ν$, starting from 0.4 to 1.0. The predicted masses and magnetic moments are in good agreement with other theoretical predictions.
The perturbative QCD calculation of heavy quark fragmentation into a heavy meson is extended to predict fragmentation into heavy flavor baryons. This is accomplished by implementing the quark-diquark model of the baryons. Several diquark form factors are used to enable the integration over the virtual heavy quark momentum. The resulting spin independent functions for charmed quarks to fragment into charmed baryons with spin 1/2 and 3/2 are compared with recent data. Predictions are made for the spin dependent fragmentation functions as well, particularly for the functions $\hat{g}_1$ in the ca…
We study the response of diquark wave function in Λ-type baryons to strong magnetic fields. It is found that quantum state of J=0 diquark (ud) in the magnetic field changes due to magnetic polarizability, and constituent quarks in (ud) diquark become polarized. The phenomenon influences polarized quark distribution functions Δu(x) and Δd(x), which therefore may be sensitive to the internal electromagnetic fields in hypernuclei. We also speculate, that strange quark polarization in nucleon may originate from the interaction of virtual (ss') quark pairs with the intrinsic magnetic field of nucle…
We use current-current interaction to calculate the fragmentation functions to describe the production of spin-1/2, spin-1/2$'$ and spin-3/2 baryons with massive constituents in a relativistic quark-diquark model. Our results are in their analytic forms and are applicable for singly, doubly and triply heavy baryons. We discuss the production of $Ω_{bbc}$, $Ω_{bcc}$ and $Ω_{ccc}$ baryons in some detail. The results are satisfactorily compared with those obtained for triply heavy baryons calculated in a perturbative regime within reasonable values of the parameters involved.
In a covariant model where constituent quarks and diquarks interact through quark exchange, the Bethe-Salpeter equation in ladder approximation for octet and decuplet baryons is solved. Quark and diquark confinement is thereby effectively parametrised by choosing appropriately modified propagators. Numerical results for the baryon masses are presented. In a second step electromagnetic, weak and pionic currents are coupled to the bound state according to Mandelstam's technique. The arising matrix elements are evaluated in a generalised impulse approximation and observable form factors are extra…
A perturbative QCD calculation of heavy flavor quark fragmentation into heavy flavor baryons is developed along the lines of corresponding heavy meson models. The non-perturbative formation of the baryon is accomplished by implementing the quark-diquark model of the baryons. Diquark color form factors are used to enable the integration over the virtual heavy quark momentum. The resulting spin independent functions for charmed and bottom quarks to fragment into charmed and bottom baryons with spin 1/2 and 3/2 are compared with recent data. Predictions are made for the spin dependent fragmentati…
The magnetic moments, transition magnetic moments and the radiative decay widths of singly charmed baryons are calculated with $ {J^P = \frac{1}{2}}^+$ and $ {J^P = \frac{3}{2}}^+$ in the constitute quark model. Further, the strong decay rates for $ S $, $ P $ and $ D $ wave transitions are also presented. The singly charmed baryon masses used in the calculations were obtained from the hypercentral Constitute Quark Model (hCQM) without and with first order relativistic correction. Obtained results are compared with experimental observation as well as with the other theoretical predictions.
The present work has been done on the baryons containing one, two, or three bottom quarks. In this article, the ground-state masses of $Ω_{b}^{-}$, $Ξ_{bb}^{0}$, $Ξ_{bb}^{-}$, $Ω_{bb}^{-}$, and $Ω_{bbb}^{*-}$ baryons are calculated within the framework of Regge phenomenology. Further, the values of Regge slopes and Regge intercepts for singly, doubly, and triply bottom baryons are estimated in both the ($J,M^{2}$) and ($n,M^{2}$) planes to calculate the excited-state masses of these baryons. Here our attempt is to assign a possible spin-parity to recently observed some singly bottom baryons an…
For baryons composed by the light quarks ($q=u,d$) we write spectral integral equation using the notion of two diquarks: (i) axial--vector state, $D^{1}_{1}$, with the spin $S_D=1$ and isospin $I_D=1$ and (ii) scalar one, $D^{0}_{0}$, with the spin $S_D=0$ and isospin $I_D=0$. We present spectral integral equations for the $qD^{0}_{0}$ and $qD^{1}_{1}$ states taking into account quark--diquark confinement interaction.
We construct a chiral Lagrangian for doubly heavy baryons and heavy mesons that is invariant under heavy quark-diquark symmetry at leading order and includes the leading O(1/m_Q) symmetry violating operators. The theory is used to predict the electromagnetic decay width of the J=3/2 member of the ground state doubly heavy baryon doublet. Numerical estimates are provided for doubly charm baryons. We also calculate chiral corrections to doubly heavy baryon masses and strong decay widths of low lying excited doubly heavy baryons.
We give heavy quark-diquark symmetry predictions for doubly heavy baryons and tetraquarks in light of the recent discovery of the $Ξ_{cc}^{++}$ by LHCb. For five excited doubly charm baryons that are predicted to lie below the $Λ_c D$ threshold, we give predictions for their electromagnetic and strong decays using a previously developed chiral Lagrangian with heavy quark-diquark symmetry. Based on the mass of the $Ξ_{cc}^{++}$, the existence of a doubly heavy bottom $I=0$ tetraquark that is stable to the strong and electromagnetic decays has been predicted. If the mass of this state is below 1…
We describe heavy baryons as bound states of a quark and a diquark. For this purpose we derive the Faddeev equation for baryons containing a single heavy quark from a Nambu-Jona-Lasinio type of model which is appropriately extended to include also heavy quarks. The latter are treated in the heavy mass limit. The heavy baryon Faddeev equation is then solved using a static approximation for the exchanged quark.
We argue that there should exist the large combined fluctuations of chiral and diquark condensates along the phase boundary of QCD at moderately high density and relatively low temperature. Such fluctuations might lead to anomalous production of nucleons and its parity partner, which we propose to detect at NICA.
We present a phenomenological ansatz for coupling a heavy quark with two light quarks to form a heavy baryon. The heavy quark is treated in the heavy mass limit, and the light quark dynamics is approximated by propagating scalar and axial vector 'diquarks'. The resulting effective lagrangian, which incorporates heavy quark and chiral symmetry, describes interactions of heavy baryons with Goldstone bosons in the low energy region. As an application, the Isgur--Wise form factors are estimated.
We study the current-induced bottom baryon to charm baryon transitions in the Heavy Quark Symmetry limit as $m_{q}\rightarrow \infty$. Our discussion involves $s$-wave to $s$-wave as well as $s$-wave to $p$-wave transitions. Using a constituent quark model picture for the light diquark system with an underlying $SU(2N_{f})\otimes O(3)$ symmetry and the heavy quark symmetry we arrive at a number of new predictions for the reduced form factors that describe these transitions.
Spin dependent fragmentation functions for heavy flavor quarks to fragment into heavy baryons are calculated in a quark-diquark model. The production of intermediate spin 1/2 and 3/2 excited states is explicity included. The resulting $Λ_b$ production rate and polarization at LEP energies are in agreement with experiment. The $Λ_c$ and $Ξ_c$ functions are also obtained. The spin independent $f_1(z)$ is compared to data. The integrated values for production rates agree with the data.
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, $D^{1}_{1}$, with the spin $S_D=1$ and isospin $I_D=1$ and (ii) scalar one, $D^{0}_{0}$, with the spin $S_D=0$ and isospin $I_D=0$. We consider several schemes for the composed baryons: (1) with different diquark masses, $M_{D^0_0} \ne M_{D^1_1}$, (2) with $M_{D^0_0} = M_{D^1_1}$ and overlapping $qD^0_0$ and $qD^1_1$ states (resonances), (3) with/without SU(6) constraints for low-lying states (wit…
The parton model relations in conjunction with quark-hadron duality in deep inelastic scattering suggests an asymptotic dominance of quark-diquark type of baryonic excited states with a radial Regge uniformly distributed mass squared spectrum $M_{n}^2 = μ^2 n + M_0^2$. We argue that this points to a lineary quark-diquark confining potential. We analyze the radial ($n$) and angular-momentum ($J$) Regge trajectories for all light-quark states with baryon number one listed in the 2016 edition of the Particle Data Tables. The parameters of the mass squared trajectories are obtained by linear regre…
We study the electroweak properties of ground state octet baryons in a relativistic quark-spectator-diquark model, with light-front formalism applied to take relativistic effects into account. Our model provides a consistent picture of the electroweak properties of the ground state octet baryons in the low momentum transfer region. The Melosh-Wigner rotation is applied as the transformation relation between spinors in the instant form and front form. Numerical results are presented for the magnetic moments, weak transition charges and Sachs form factors. Our results are in good agreement with …
We investigate the quark spin content of the SU(3) baryon octet, decuplet, antitriplet, and sextet in a pion mean-field approach or the chiral quark-soliton model, considering the $1/N_c$ rotational corrections and SU(3) symmetry breaking effects. We compare the present results with those from various theoretical works and lattice QCD.
We present an alternative parameterization of the quark-diquark model of baryons which particularly takes care of the most recent proton electric form-factor data from the E136 experiment at SLAC. In addition to electromagnetic form factors of the nucleon, for which good agreement with data is achieved, we discuss the weak axial vector form factor of the nucleon as well as electromagnetic form factors of $Λ$ and $Σ$ hyperons. Technical advance in calculating the pertinent analytic expressions within perturbative quantum chromodynamics is gained by formulating the wave function of the quark-diq…
We investigate a model in which tiny neutrino masses are generated at the two-loop level by using scalar leptoquark and diquark multiplets. The diquark can be singly produced at the LHC, and it can decay into a pair of leptoquarks through the lepton number violating interaction. Subsequent decays of the two leptoquarks can provide a clear signature of the lepton number violation, namely two QCD jets and a pair of same-signed charged leptons without missing energy. We show that the signal process is not suppressed while neutrino masses are appropriately suppressed.
We study B meson decays to two charmless baryons in the diquark model, including strong and electroweak penguins as well as the tree operators. It is shown that penguin operators can enhance $\bar{B} \to \Bb_s \bar{\Bb}$ considerably, but affect $\bar{B} \to \Bb_1 \bar{\Bb}_2$ only slightly, where $\Bb_{(1,2)}$ and $\Bb_s$ are non-strange and strange baryons, respectively. The $γ$ dependence of the decay rates due to tree-penguin interference is illustrated. In principle, some of the $\Bb_s \bar{\Bb}$ modes could dominate over $\Bb_1 \bar{\Bb}_2$ for $γ> 90^\circ$, but in general the effect is…
In the paper, we study the production of pentaquark $\bar{c}q qqq$ from singly bottom baryon. The tensor representations of pentaquark $\bar{c}q qqq$ are completed at first. Under the light quark symmetry analysis, we decompose the singly charmed pentaquarks into $6$, $15$ and $15'$ multiple states, and deduce the representations of these states. Then we construct the production Hamiltonian of the multiple states in proper order. For completeness, we systematically study the production channels of pentaquark states, including the possible production amplitudes and cross section relations betwe…
We enumerated ground and excited state masses of singly heavy bottom-strange baryons using the Hypercentral Constituent Quark Model (hCQM). The screening potential is used with color-Coulomb potential, as the confining potential. We determine the possible $J^P$ values to recently observed excited states like, $Ξ_b(6100)$, $Ξ_b(6227)$, $Ξ_b(6327)$, $Ξ_b(6333)$ and four $Ω_b(6316,6330,6340,6350)$ states. The Regge trajectories are plotted in $(J, M^2)$ plane to assign the $J^P$ values and quantum numbers to recently observed states. Using the calculated spectroscopic data, properties such as mag…
We investigate the meson, baryon and anti-baryon productions in πp and Kp collisions in terms of a constituent cascade model which includes charm flavour. The constituent diquark in an incident baryon has a tendency to get a large momentum fraction, resulting in considerable difference of subenergies for particle productions from quark-diquark and quark-antiquark chains in a meson-baryon collision. As a consequence, the leading particle effects on D meson productions are expected to be quite different in π+ and π- beams at present accelerator energies.
