Heavy Diquark Research Articles

Mass and decay width of Tccs from symmetries

We analyze the mass and width of the doubly heavy tetraquark Tccs composed of a heavy diquark and a light-quark cloud with strangeness with assuming that a color antitriplet heavy diquark is a dominant component of the doubly charmed tetraquarks Tcc and Tccs. We construct an effective Lagrangian for masses of heavy hadrons based on the superflavor symmetry between the doubly heavy tetraquarks and the singly heavy baryons by including the terms that simultaneously break the heavy-quark and light-flavor symmetries, and predict the mass of Tccs as M(Tccs)=4047±11 MeV. The comparison of this prediction with future experimental observation will give a clue to understand the color structure of the heavy diquark. We also predict the mass of Ωcc as M(Ωcc)=3706−15+14 MeV. We next calculate the decay width of Tccs, based solely on the light-flavor symmetry, as Γ(Tccs)=42±24 MeV. Published by the American Physical Society 2024

Regge trajectory relation for the universal description of the heavy-heavy systems: Diquarks, mesons, baryons and tetraquarks

By employing the nonlinear Regge trajectory relation M=mR+βx(x+c0x)2/3(x=l,nr), we investigate the heavy-heavy systems, such as the doubly heavy diquarks, the doubly heavy mesons, the heavy-heavy baryons, and the heavy-heavy tetraquarks. The fitted Regge trajectories illustrate that these heavy-heavy systems satisfy the above formula and show the existence of an universal description of the heavy-heavy systems. The universality embodies not only the universal behavior M∼x2/3 but also the universal parameters. The values of cfnr and cfl vary with different heavy-heavy systems, but they are close to one. There is an inequality βnr>βl, and it holds for all the discussed heavy-heavy systems. Moreover, the expression of βx [Eq. (11)] explains its variation with the change of the constituents' masses.

The spectra masses for heavy pentaquark using generalized fractional of the extended Nikiforov-Uvaro method

The Nikiforov-Uvarov method is an efficient technique for solving of heavy diquark systems. It has been used to derive analytic-exact energy eigenvalues and eigenfunctions in fractional forms, which are useful in describing such systems. The potentials employed include the Cornell potential, harmonic potential, and spin-spin interaction; have been updated with respect to previous studies. Mass spectra of heavy pentaquarks were also calculated using this method. Compared to previous studies, the present results exhibit good experimental data agreement and are improved. We deduce that the fractional models contribute greatly to the heavy pentaquark masses.

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.

Mass spectra of doubly heavy tetraquarks in diquark−antidiquark picture* *Supported by the National Natural Science Foundation of China under the No. 12165017.

Inspired by the recent observation of the first doubly charmed tetraquark T cc , we apply the linear Regge relation and mass scaling to study low-lying mass spectra of the doubly heavy tetraquark in a heavy-diquark−light-antidiquark picture. The measured data and other compatible estimates of ground-state masses of doubly heavy baryons are employed to evaluate masses of heavy diquark M QQ (Q = c, b) and the D/D s meson masses are used in mass scaling to determine the hyperfine mass splitting. Our mass computation indicates that all low-lying states of doubly heavy tetraquarks are unstable against strong decays to two heavy-light mesons, except for the ground states of nonstrange bb tetraquarks.

Generalized fractional of the extended Nikiforov–Uvarov method for heavy tetraquark masses spectra

In this paper, the new analytic–exact energy eigenvalues and eigenfunctions are obtained in the fractional forms by using the extended Nikiforov–Uvarov approach in which the heavy diquark systems are described. We have recalculated the mass spectra and fractional radial wave of heavy tetraquarks. The mass spectra are compared to the experimental data. The present results show a good agreement with the experimental data and are improved in comparison with other studies. We conclude that the fractional models play a good role in the heavy tetraquark masses.

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.

Doubly heavy tetraquarks in the chiral quark soliton model

The chiral quark soliton model has been successfully applied to describe the heavy baryon spectrum, both for charm and bottom, leading to the conclusion that the heavy quark has no effect on the soliton. This suggests that replacing a heavy quark by a heavy antidiquark $\overline{Q}\overline{Q}$ in color triplet should give a viable description of heavy tetraquarks. We follow this strategy to compute tetraquark masses. To estimate heavy diquark masses, we use the Cornell potential with appropriately rescaled parameters. The lightest charm tetraquark is 70 MeV above the $D{D}^{*}$ threshold. On the contrary, both nonstrange and strange bottom tetraquarks are bound by approximately 140 and 60 MeV, respectively.

Inclusive weak-annihilation decays and lifetimes of beauty-charmed baryons

Imbalanced beauty-charmed baryons $ \Xi_{bc}^{+,0} $ are of great significance to the development of heavy flavor physics. In this work, we study the inclusive weak-annihilation decays of $\Xi_{bc}^{+,0}$ and their contributions to the $\Xi_{bc}^{+,0}$ lifetimes. For the calculation of the inclusive $\Xi_{bc}^{+,0}\to X_{cs}$ decay width where $X_{cs}$ stands for the sum of the final states with charm number +1 and strange number -1, we work in the heavy diquark effective theory which provides us with a convenient technical tool to construct the operator product expansion. The $\Xi_{bc}^{+,0}$ is considered to be a superposition of two states with one containing a spin-0 $bc$ diquark and the other one containing a spin-1 $bc$ diquark. It is found that both the $\Xi_{bc}^{+,0}$ lifetimes and the $\Xi_{bc}^{+,0}\to X_{cs}$ branching ratios are very sensitive to the $bc$ spin in $\Xi_{bc}^{+,0}$. The $\Xi_{bc}^{+,0}\to X_{cd}$ results are also presented. As $\Xi_{bc}^+$ has a longer lifetime than $\Xi_{bc}^{0}$ and bigger branching ratios of similar decay channels, the exclusive decays $\Xi_{bc}^+\to D^{(*)+}\Lambda$, $\Xi_{bc}^+\to \Lambda_c^+\bar{K}^{(*)0}$, $\Xi_{bc}^+\to D^{(*)+}K^-p$, and $\Xi_{bc}^+\to D^{0}\bar{K}^{(*)0}p$ are more promising for experimental searches of $\Xi_{bc}^{+,0}$ at the LHC comparing with exclusive decay $\Xi_{b c} ^{0} \to D^0pK^-$.

Inclusive approach to hunt for the beauty-charmed baryons Ξbc

With a distinctive internal structure from all established hadrons, the beauty-charmed baryons $\Xi_{bc}$ can provide us with new points of view to decipher the strong interaction. In this work, we point out that the inclusive $\Xi_{bc} \to \Xi_{cc}^{++}+X$ decay is a golden channel for the experimental discovery of $\Xi_{bc}$ at the LHC. A unique feature of this process is that the $\Xi_{cc}^{++}$ is displaced, which greatly reduces the combinatorial background. A feasibility analysis is performed on the $\Xi_{bc}^+$ search, which is expected to have a longer lifetime than $\Xi_{bc}^0$ and thus a better displacement resolution. The $\Xi_{bc}^+ \to \Xi_{cc}^{++}+X$ branching ratio is calculated within the heavy diquark effective theory. Combining the $\Xi_{bc}$ production rate and the $\Xi_{cc}^{++}$ detection efficiency, we anticipate that hundreds of signal events will be collected during LHCb Run 3.

Strong decays of the low-lying doubly bottom baryons

In this work, we adopt the $^{3}{P}_{0}$ model to investigate the strong decays of the low-lying doubly bottom baryons in the $j\ensuremath{-}j$ coupling scheme systematically. In this scheme, we construct the formulism of the $^{3}{P}_{0}$ model under the spectator assumption, and then the heavy diquark symmetry is preserved automatically. Our results show that some of the $\ensuremath{\lambda}$-mode ${\mathrm{\ensuremath{\Xi}}}_{bb}(1P)$ and ${\mathrm{\ensuremath{\Omega}}}_{bb}(1P)$ states are narrow, which have good potentials to be observed by future experiments. For the low-lying $\ensuremath{\rho}$-mode and $\ensuremath{\rho}\text{\ensuremath{-}}\ensuremath{\lambda}$ hybrid states, the Okubo-Zweig-Iizuka-allowed strong decays are highly suppressed and they should be extremely narrow. Future experiments can test our phenomenological predictions at the quark level.

Weak decays of the double-beauty tetraquark

The spectroscopic parameters and decay channels of the axial-vector tetraquark 213 built of heavy diquark bb and light antidiquark us are explored using QCD sum rule method. Because this state is stable against strong and electromagnetic decays, we consider its semileptonic and nonleptonic decay modes. Partial widths of weak processes TAVb:s¯ → Z0b:s¯ lv¯l and Tb:s¯AV → Z0b:s¯ M are calculated using weak form factors Gi(q2) computed by QCD three-point sum rules: Z0b:s¯ is the scalar tetraquark with quark content bcus¯ and M is a vector meson. The full width and mean lifetime of the tetraquark TAVb:s¯ obtained in this work shed light on features of double-beauty tetraquarks and are useful for their experimental investigations.

Doubly heavy tetraquark resonant states

Spectrum of the doubly heavy tetraquarks, bbq¯q¯, is studied in a constituent quark model. Four-body problem is solved in a variational method where the real scaling technique is used to identify resonant states above the fall-apart decay thresholds. In addition to the two bound states that were reported in the previous study we have found several narrow resonant states above the BB⁎ and B⁎B⁎ thresholds. Their structures are studied and are interpreted by the quark dynamics. A narrow resonance with spin-parity JP=1+ is found to be a mixed state of a compact tetraquark and a B⁎B⁎ scattering state. This is driven by a strong color Coulombic attraction between the bb quarks. Negative-parity excited resonances with JP=0−, 1− and 2− form a triplet under the heavy-quark spin symmetry. It turns out that they share a similar structure to the λ-mode of a singly heavy baryon as a result of the strongly attractive correlation for the doubly heavy diquark.

Mass spectra of one or two heavy quark mesons and diquarks within a nonrelativistic potential model

In this paper, the mass spectra of mesons with one or two heavy quarks and their diquarks partners are estimated within a nonrelativistic framework by solving Schrödinger equation with an effective potential inspired by a symmetry preserving Poincaré covariant vector–vector contact interaction model of quantum chromodynamics. Matrix Numerov method is implemented for this purpose. In our survey of mesons with heavy quarks, we fix the model parameter to the masses of groundstates and then extend our calculations for radial excitations and diquarks. The potential model used in this work gives results which are in good agreement with experimental data and other theoretical calculations.

Semileptonic and nonleptonic decays of the axial-vector tetraquark $$T_{bb;\overline{u} \overline{d}}^{-}$$

The semileptonic and nonleptonic decays of the double-beauty axial-vector tetraquark $T_{bb;\overline{u} \overline{d}}^{-}$ to a state $\widetilde{T}_{bc; \overline{u}\overline{d}}^{0}$ (hereafter $T_{bb}^{-}$ and $\widetilde{T} _{bc}^{0}$, respectively) are investigated in the context of the QCD sum rule method. The final-state tetraquark $\widetilde{T}_{bc}^{0}$ is treated as an axial-vector particle built of a heavy axial-vector diquark $ b^{T}\gamma _{\mu }Cc$ and light scalar antidiquark $\overline{u}C\gamma_{5} \overline{d}^{T}$. Its spectroscopic parameters are calculated using the two-points sum rules by taking into account contributions of quark, gluon and mixed condensates up to dimension $10$. We study the dominant semileptonic $T_{bb}^{-} \to \widetilde{T}_{bc}^{0}l\overline{\nu }_{l}$ and nonleptonic decays $T_{bb}^{-} \to \widetilde{T}_{bc}^{0}M$, where $M$ is one of the pseudoscalar mesons $\pi^{-}, K^{-}, D^{-}$ and $D_s^{-}$. The partial widths of these processes are computed in terms of weak form factors $G_{i}(q^2),\ i=1,2,3,4$, extracted by employing the QCD three-point sum rule approach. Predictions obtained for partial widths of considered decays are used to improve accuracy of theoretical predictions for full width and lifetime of the tetraquark $T_{bb}^{-}$, which are important for experimental exploration of this exotic meson.

Masses of doubly heavy tetraquarks with error bars

In the heavy-quark limit, the two heavy quarks in a doubly heavy baryon or a doubly heavy tetraquark are bound by their color-Coulomb potential into a compact diquark. The doubly heavy hadrons are related by the approximate heavy-quark--diquark symmetry of QCD to the heavy hadrons obtained by replacing the heavy diquark by a heavy antiquark. Effective field theories can be used to expand the masses of singly heavy hadrons and doubly heavy hadrons in inverse powers of the heavy quark masses. The coefficients in the expansions for doubly heavy tetraquarks can be determined from those for heavy mesons, heavy baryons, and doubly heavy baryons using heavy-quark--diquark symmetry. We predict the masses of the ground-state doubly heavy tetraquarks with error bars using as inputs the masses of heavy mesons and heavy baryons measured in experiments and the masses of doubly heavy baryons calculated using lattice QCD. The only doubly heavy tetraquarks predicted to be stable with respect to strong decays are $bb$ tetraquarks with light flavor $\bar u \bar d$, $\bar s \bar u$ and $\bar s \bar d$.

Triply charmed dibaryons in the one boson exchange model

The pentaquark states, $P_{c}(4312)$, $P_{c}(4440)$ and $P_{c}(4450)$, can be nicely arranged into a multiplet of seven molecules of $\bar{D}^{(\ast)}\Sigma_{c}^{(\ast)}$ dictated by heavy quark spin symmetry, while the $\Xi_{cc}^{(\ast)}\Sigma_{c}^{(\ast)}$ system can be related to the $\bar{D}^{(\ast)}\Sigma_{c}^{(\ast)}$ system via heavy antiquark diquark symmetry. In this work we employ the one boson exchange model to study the interactions between $\Xi_{cc}^{(\ast)}$ and $\Sigma_{c}^{(\ast)}$ with constraints from the pentaquark system. We show that a multiplet of ten triply charmed dibaryons emerge naturally in the isospin-1/2 sector, while only three appear in the isospin-3/2 sector. In addition, we study their heavy quark flavor partners. Ten triply bottom diybaryons are found in the isospin-1/2 sector, while only nine are likely in the isospin-3/2 sector. Furthermore, the predicted mass splitting between the $0^{+}$ $\Xi_{cc}\Sigma_{c}$ state and its $1^{+}$ counterpart is found to be consistent with the correlation implied by heavy antiquark diquark symmetry recently pointed out in Pan $et$ $al$..

NLO QCD corrections to heavy baryon fragmentation functions through quark-diquark model

At very high transverse momenta, the dominant mechanism for heavy hadron production is fragmentation. In this work, we first use the nonrelativistic quark model to compute the heavy baryon fragmentation functions at lowest order of perturbative QCD and then we apply the approximative quark-diquark model for the same fragmentation process. Diquark model enables one to analyze the two-stage fragmentation of a heavy quark into a heavy diquark followed by the fragmentation of produced diquark into outgoing heavy baryon. An acceptable agreement is found between the results obtained through both approaches. Relying on the diquark model, we extend our computation to next-to-leading order accuracy at perturbative QCD.

Effective field theory for double heavy baryons at strong coupling

We present an effective field theory for doubly heavy baryons that goes beyond the compact heavy diquark approximation. The heavy-quark distance $r$ is only restricted to $m_Q\gg 1/r \gg E_{bin}$, where $m_Q$ is the mass of the heavy quark and $E_{bin}$ the typical binding energy. This means that the size of the heavy diquark can be as large as the typical size of a light hadron. We start from Non-Relativistic QCD, and build the effective field theory at next-to-leading in the $1/m_Q$ expansion. At leading order the effective field theory reduces to the Born-Oppenheimer approximation. The BO potentials are obtained from available lattice QCD data. The spectrum for double charm baryons below threshold is compatible with most of the lattice QCD results. We present for the first time the full spin averaged double bottom baryon spectrum below threshold based on QCD. We also present model-independent formulas for the spin splittings.

Towards a heavy diquark effective theory for weak decays of doubly heavy baryons

We construct a leading-order effective field theory for both scalar and axial-vector heavy diquarks, and consider its power expansion in the heavy diquark limit. By assuming the transition from QCD to diquark effective theory, we derive the most general form for the effective diquark transition currents based on the heavy diquark symmetry. The short-distance coefficients between QCD and heavy diquark effective field theory are also obtained by a tree level matching. With the effective currents in the heavy diquark limit, we perform a reduction of the form factors for semi-leptonic decays of doubly heavy baryons, and find that only one nonperturbative function is remaining. It is shown that this soft function can be related to the Isgur–Wise function in heavy meson transitions. As a phenomenological application, we take a single pole structure for the reduced form factor, and use it to calculate the semi-leptonic decay widths of doubly heavy baryons. The obtained results are consistent with others given in the literature, and can be tested in the future.