Light Diquark Research Articles

λ and ρ Regge trajectories for hidden bottom and charm tetraquarks (Qq)(Q¯q¯′)

We propose the Regge trajectory relations for the heavy tetraquarks (Qq)(Q¯q¯′) (Q=b,c;q,q′=u,d,s) with hidden bottom and charm. By employing the new relations, both the λ-trajectories and the ρ-trajectories for the tetraquarks (Qq)(Q¯q¯′) can be discussed. The masses of the λ-mode excited states and the ρ-mode excited states are estimated, and they agree with other theoretical predictions. We show that the behaviors of the ρ-trajectories are different from those of the λ-trajectories. The ρ-trajectories behave as M∼xρ1/2 (xρ=nr,l) while the λ-trajectories behave as M∼xλ2/3 (xλ=Nr,L). Moreover, the Regge trajectory behaviors for other types of tetraquarks are investigated based on the spinless Salpeter equation. We show that both the λ-trajectories and the ρ-trajectories are concave downward in the (M2,x) plane. The Regge trajectories for the tetraquarks containing the light diquark and/or the light antidiquark also are concave in the (M2,x) plane when the masses of the light constituents are included and the confining potential is linear. Published by the American Physical Society 2024

Two-Body Hadronic Weak Decays of Bottomed Hadrons

The structure of light diquarks plays a crucial role in formation of exotic hadrons beyond the conventional quark model, especially with regard to the line shapes of bottomed hadron decays. We study the two-body hadronic weak decays of bottomed baryons and bottomed mesons to probe the light diquark structure and to pin down the quark–quark correlations in the diquark picture. It is found that the light diquark does not favor a compact structure. For instance, the isoscalar diquark [ud] in Λb0 can be easily split and rearranged to form Σc(*)D¯(*) via the color-suppressed transition. This provides a hint that the hidden charm pentaquark states produced in Λb0 decays could be the Σc(*)D¯(*) hadronic molecular candidates. This quantitative study resolves the apparent conflicts between the production mechanism and the molecular nature of these Pc states observed in experiment.

Regge trajectories for the light diquarks

We attempt to present an unified description of the light meson spectra and the light diquark spectra by applying the Regge trajectory approach. However, we find that the direct application of the linear Regge trajectory formula for the light mesons and baryons fails. To address this issue, we fit the experimental data of light meson spectra and the light diquark spectra obtained by other theoretical approaches. By considering the light quark mass and the parameter C in the Cornell potential, we provide a provisional Regge trajectory formula. We also crudely estimate the masses of the light diquarks (ud), (us), and (ss), and find that they agree with other theoretical results. The diquark Regge trajectory not only becomes a new and very simple approach for estimating the spectra of the light diquarks, but also can explicitly show the behavior of the masses with respect to l or nr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_r$$\\end{document}. Moreover, it is expected that the diquark Regge trajectory can provide a simple method for investigating the ρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho $$\\end{document}-mode excitations of baryons, tetraquarks and pentaquarks containing diquarks.

Regge trajectories for the heavy-light diquarks

We attempt to apply the Regge trajectory approach to the heavy-light diquarks composed of one heavy quark and one light quark. However, we find that the direct application of the usual Regge trajectory formula for the heavy-light mesons and baryons fails. In order to correctly estimate the masses of the heavy-light diquarks, it is needed to consider the light quark mass correction and the parameter C in the Cornell potential within the Regge trajectory formula. By using the modified Regge trajectory formulas, we are able to estimate the masses of the heavy-light diquarks (cu), (cs), (bu) and (bs), which agree with other theoretical results. It is illustrated that the heavy-light diquarks satisfy the universal descriptions irrespective of heavy quark flavors, similar to other heavy-light systems such as the heavy-light mesons, the heavy-light baryons composed of one heavy quark (diquark) and one light diquark (quark), and the heavy-light tetraquarks composed of one heavy diquark (antidiquark) and one light antidiquark (diquark). The diquark Regge trajectory provides a new and very simple approach for estimating the spectra of the heavy-light diquarks.

Low-lying doubly heavy baryons: Regge relation and mass scaling

In framework of heavy-diquark–light-quark endowed with heavy-pair binding, we explore excited baryons QQ^{prime }q containing two heavy quarks (QQ^{prime }=cc,bb,bc) by combining the method of Regge trajectory with the perturbative correction due to the heavy-pair interaction in baryons. Two Regge relations, one linear and the other nonlinear, are constructed semi-classically in the QCD string picture, and a mass scaling relation based on the heavy diquark–heavy antiquark symmetry are employed between the doubly heavy baryons and heavy mesons. We employ the ground-state mass estimates compatible with the observed doubly charmed baryon Xi _{cc} and spectra of the heavy quarkonia to determine the trajectory parameters and the binding energies of the heavy pair, and thereby compute the low-lying masses of the excited baryons Xi _{QQ^{prime }} and Omega _{QQ^{prime }} up to 2S and 1P excitations of the light quark and heavy diquark. The level spacings of heavy diquark excitations are found to be smaller generally than that of the light-quark excitations, in according with the nature of adiabatic expansion between the heavy and light-quark dynamics.

Good and bad diquark properties and spatial correlations in lattice QCD

We study good, bad and not-even-bad diquarks on the lattice in a gauge-invariant formalism in full QCD. We establish their spectral masses with short extrapolations to the physical point, observing agreement with phenomenological expectations. We find that only the good diquark has attractive quark-quark spatial correlations, with spherical shape and size of about 0.6 fm. Our results provide quantitative support for modelling the low-lying baryon spectrum using good light diquark effective degrees of freedom.

Diquark properties from full QCD lattice simulations

We study diquarks on the lattice in the background of a static quark, in a gauge-invariant formalism with quark masses down to almost physical mπ. We determine mass differences between diquark channels as well as diquark-quark mass differences. The lightest and next-to-lightest diquarks have “good” scalar, {overline{3}}_F , {overline{3}}_c , JP = 0+, and “bad” axial vector, 6F, {overline{3}}_c , JP = 1+, quantum numbers, and a bad-good mass difference for ud flavors, 198(4) MeV, in excellent agreement with phenomenological determinations. Quark-quark attraction is found only in the “good” diquark channel. We extract a corresponding diquark size of ∼ 0.6 fm and perform a first exploration of the “good” diquark shape, which is shown to be spherical. Our results provide quantitative support for modeling the low-lying baryon spectrum using good light diquark effective degrees of freedom.

Vector resonance X1(2900) and its structure

The new vector resonance X1(2900) observed recently by LHCb in the D−K+ invariant mass distribution in the decay B+→D+D−K+ is studied to uncover internal structure of this state, and calculate its physical parameters. In the present paper, the resonance X1(2900) is modeled as an exotic vector state, JP=1−, built of the light diquark uTCγ5d and heavy antidiquark c‾γμγ5Cs‾T. The mass and current coupling of X1(2900) are computed using the QCD two-point sum rule approach by taking into account various vacuum condensates up to dimension 10. The width of the resonance X1(2900) is saturated by two decay channels X1→D−K+ and X1→D‾0K0. The strong couplings g1 and g2 corresponding to the vertices X1D−K+ and X1D‾0K0 are evaluated in the context of the QCD light-cone sum rule method and technical tools of the soft-meson approximation. Results for the mass of the resonance X1(2900)m=(2890±122)MeV, and for its full width Γfull=(93±13)MeV are smaller than their experimental values reported by the LHCb collaboration. Nevertheless, by taking into account theoretical and experimental errors of investigations, interpretation of the state X1(2900) as the vector tetraquark does not contradict to the LHCb data. We also point out that analysis of the invariant mass distribution D+K+ in the same decay B+→D+D−K+ may reveal doubly charged four-quark structures [uc][s‾d‾].

Spectrum of singly heavy baryons from a chiral effective theory of diquarks

The mass spectra of singly charmed and bottom baryons, $\Lambda_{c/b}(1/2^\pm,3/2^-)$ and $\Xi_{c/b}(1/2^\pm,3/2^-)$, 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 $\rho$-mode excitations of singly heavy baryons.

Interpretation of the narrow J/ψ p peaks in Λb → J/ψ p K− decay in the compact diquark model

Recently, the LHCb Collaboration have updated their analysis of the resonant J/ψp mass spectrum in the decay Λb0→J/ψpK−. In the combined Run 1 and Run 2 LHCb data, three peaks are observed, with the former Pc(4450)+ state split into two narrow states, Pc(4440)+ and Pc(4457)+, having the masses M=(4440.3±1.3−4.7+4.1) MeV and M=(4457.3±0.6−1.7+4.1) MeV, and decay widths Γ=(20.6±4.9−10.1+8.7) MeV and Γ=(6.4±2.0−1.9+5.7) MeV, respectively. In addition, a third narrow peak, Pc(4312)+, having the mass M=(4311.9±0.7−0.6+6.8) MeV and decay width Γ=(9.8±2.7−4.5+3.7) MeV is also observed. The LHCb analysis is not sensitive to broad J/ψp contributions like the former Pc(4380)+, implying that there could be more states present in the data. Also the spin-parity, JP, assignments of the states are not yet determined. We interpret these resonances in the compact diquark model as hidden-charm diquark-diquark-antiquark baryons, having the following spin and angular momentum quantum numbers: Pc(4312)+={c¯[cu]s=1[ud]s=0;LP=0,JP=3/2−}, the S-wave state, and the other two as P-wave states, with Pc(4440)+={c¯[cu]s=1[ud]s=0;LP=1,JP=3/2+} and Pc(4457)+={c¯[cu]s=1[ud]s=0;LP=1,JP=5/2+}. The subscripts denote the spins of the diquarks and LP=0,1 is the orbital angular momentum quantum number of the pentaquark. These assignments are in accord with the heavy-quark-symmetry selection rules for Λb-baryon decays, in which the spin S=0 of the light diquark [ud]s=0 is conserved. The masses of observed states can be accommodated in this framework and the two heaviest states have the positive parities as opposed to the molecular-like interpretations. In addition, we predict several more states in the J/ψp mass spectrum, and urge the LHCb Collaboration to search for them in their data.

Heavy quark symmetry and weak decays of thebbaryons in pentaquarks with acc¯component

The discovery of the baryonic states $P_c^+(4380)$ and $P_c^+(4450)$ by the LHCb collaboration has evoked a lot of theoretical interest. These states have the minimal quark content $c \bar{c} u u d$. Interpreted as hidden charm diquark-diquark-antiquark baryons, the assigned spin and angular momentum quantum numbers are $P_c^+(4380)= \{\bar{c} [cu]_{s=1} [ud]_{s=1}; L_{\mathcal{P}}=0, J^{\rm P}=\frac{3}{2}^- \}$ and $P_c^+(4450)= \{\bar{c} [cu]_{s=1} [ud]_{s=0}; L_{\mathcal{P}}=1, J^{\rm P}=\frac{5}{2}^+ \}$, where $s=0,1$ are the spins of the diquarks and $L_{\mathcal{P}}=0,1$ are the orbital angular momentum quantum numbers of the pentaquarks. We point out that heavy quark symmetry allows only the higher mass pentaquark state $P_c^+(4450)$ having $[ud]_{s=0}$ to be produced in $\Lambda_b^0$ decays, whereas the lower mass state $P_c^+(4380)$ having $[ud]_{s=1}$ is disfavored. Pentaquark spectrum is rich enough to accommodate a $J^P=\frac{3}{2}^-$ state, which has the correct light diquark spin $\{\bar{c} [cu]_{s=1} [ud]_{s=0}; L_{\mathcal{P}}=0, J^{\rm P}=\frac{3}{2}^- \}$ to be produced in $\Lambda_b^0$ decays. Assuming that the orbital mass difference between the charmed pentaquarks is similar to the corresponding mass difference in the charmed baryons, we estimate the mass of the lower pentaquark $J^P=3/2^-$ state to be about 4110 MeV and suggest to reanalyze the LHCb data to search for this third state. We present the spectroscopy of the $S$- and $P$-wave pentaquark states having a $c\bar{c}$ pair and three light quarks using an effective Hamiltonian approach. Some of these pentaquarks can be produced in weak decays of the $b$-baryons. Combining heavy quark symmetry and the $SU(3)_F$ symmetry results in strikingly simple relations among the decay amplitudes which are presented here.

Quark confinement potential examined by excitation energy of the Λcand Λbbaryons in a quark–diquark model

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 Lambda_c and Lambda_b in the quark-diquark picture, while the Lambda_c and Lambda_b spectra is reproduced with a half strength of the confinement string tension than for the quarkonium. The finite size effect of the diquark is also examined and it is found that introduction of a finite size diquark would resolve the failure of the spectrum reproduction. The Xi_c excitation energy is also calculated and is found to be smaller than Lambda_c in the quark-diquark model. This is not consistent with the experimental observation.

Prospects for observing the lowest-lying odd-parityΣcandΣbbaryons

There exist candidates for the negative-parity states $\Lambda_{c,b}(1/2^-, 3/2^-)$ consisting of an isospin-zero, spin-zero light diquark $[ud]$ with one unit of orbital angular momentum with respect to a $c,b$ quark. However, there exists only one candidate for the orbital excitations of the $\Sigma_c(1/2^+)$ and $\Sigma_c^*(3/2^+)$, and none for the orbital excitations of $\Sigma_b(1/2^+)$ or $\Sigma_b^*(3/2^+)$. We extend a previous discussion of odd-parity $\Lambda_{c,b}$ states and explore some patterns of the odd-parity $\Sigma_{c,b}$ baryons consisting of a light isospin-one nonstrange diquark $(uu,ud,dd)$ in a state of $L=1$ with respect to the spin-1/2 heavy quark $(c,b)$.

DecaysΞb→Λbπand diquark correlations in hyperons

The decays $\Xi_b \to \Lambda_b \pi$ are strangeness changing weak transitions involving only the light diquark in the baryon. Thus these decays can test the properties of such diquarks, in particular the suggestions existing in the literature of enhanced correlations in $J^P=0^+$ light diquarks. We revisit the estimates of the rates of these decays and point out that with the enhanced correlation their branching fraction can reach a few percent and may become visible in the measurements of differences of the lifetimes of $b$ baryons.

Heavy Diquark Effective Theory and Supersymmetry of Hadrons Containing a Single Heavy Quark

A new supersymmetry is proposed for hadrons containing a single heavy quark.This supersymmetry is based on a new approximation to those hadrons, which wewould consider as a further step beyond the spectator light diquark model ofbaryons. The heavy diquark effective theory is constructed by the techniquesintroduced in a different context by Georgi and Wise [1] and by Carone [2]. This theory can be incorporated into a supersymmetric theory together withHeavy Quark Effective Theory, and leads to a common universal Isgur-Wisefunction for mesons and baryons.

Calculation of1/mb2corrections to⟨Λb(v,s)|b¯γλγ5b|Λb(v,s)⟩for polarizedΛbin the Bethe-Salpeter equation approach

The heavy baryon \Lambda_{Q} (Q=b or c) can be regarded as composed of a heavy quark and a scalar light diquark which has good spin and isospin quantum numbers. In this picture we establish the Bethe-Salpeter (BS) equation for \Lambda_{Q} to second order in the 1/m_{Q} expansion. With the kernel containing both the scalar confinement and the one-gluon-exchange terms we solve the BS equation numerically. The value of the spin-dependant form factor for the matrix element <\Lambda_{b}{(v,s)}|\bar{b}\gamma^{\lambda}\gamma_{5}b|\Lambda_{b}(v,s)>, \epsilon_{b}, which is non-zero at order 1/m^{2}_{b}, is obtained numerically from our model.

Spectroscopy and Regge trajectories of heavy baryons in the relativistic quark-diquark picture

Mass spectra of heavy baryons are calculated in the heavy-quark--light-diquark picture in the framework of the QCD-motivated relativistic quark model. The dynamics of light quarks in the diquark as well as the dynamics of the heavy quark and light diquark in the baryon are treated completely relativistically without application of nonrelativistic v/c and heavy quark 1/m_Q expansions. Such approach allows us to get predictions for the heavy baryon masses for rather high orbital and radial excitations. On this basis the Regge trajectories of heavy baryons for orbital and radial excitations are constructed, and their linearity, parallelism, and equidistance are verified. The relations between the slopes and intercepts of heavy baryons are considered and a comparison of the slopes of Regge trajectories for heavy baryons and heavy-light mesons is performed. All available experimental data on heavy baryons fit nicely to the constructed Regge trajectories. The possible assignment of the quantum numbers to the observed excited charmed baryons is discussed.

Test of the heavy quark–light diquark approximation for baryons with a heavy quark

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 QCD sum rules and lattice QCD calculations. Our results also show that the diquark approximations produces larger masses than the ones obtained in a full calculation.

The new [formula omitted] multiplet, heavy baryon mass predictions, meson–baryon universality and effective supersymmetry in hadron spectrum

The recent measurement by CDF M(Σb)−M(Λb)=192 MeV is in striking agreement with our theoretical prediction M(Σb)−M(Λb)=194 MeV. In addition, the measured splitting M(Σb∗)−M(Σb)=21 MeV agrees well with the predicted splitting of 22 MeV. We point out the connection between these predictions and an effective supersymmetry between mesons and baryons related by replacing a light antiquark by a light diquark. We discuss the theoretical framework behind these predictions and use it to provide additional predictions for the masses of spin-12 and spin-32 baryons containing heavy quarks, as well as for magnetic moments of Λb and Λc.

Masses of excited heavy baryons in the relativistic quark–diquark picture

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 experimental data is found.