Axial-vector Diquark Research Articles

Chiral-even twist-3 GPDs for the proton in a spectator diquark model

We investigate the chiral-even twist-3 generalized parton distributions (GPDs) of valence quarks in the proton at nonzero skewness ξ, using a spectator model with scalar and axial-vector diquarks. We consider the exponential form factor for the nucleon-quark-diquark vertex and the axial-vector diquark with light-cone transverse polarization. We analyze the dependence of GPDs on the longitudinal momentum fraction x at different ξ, and on the square of the transverse momentum transfer ΔT2 at different x. Our numerical results reveal distinct discontinuities in all twist-3 GPDs except G1 and G˜1. By taking the forward limit, we obtain the twist-3 parton distribution function gT, which encodes the transverse spin distribution of quarks. We also compare the kinetic orbital angular momentum and the spin-orbit correlations of quarks defined by the twist-2 and twist-3 GPDs, respectively. Published by the American Physical Society 2024

Exploring fully heavy scalar tetraquarks [formula omitted

The masses, current couplings and widths of the fully heavy scalar tetraquarks X4Q=QQQ‾Q‾, Q=c,b are calculated by modeling them as four-quark systems composed of axial-vector diquark and antidiquark. The masses m(′) and couplings f(′) of these tetraquarks are computed in the context of the QCD sum rule method by taking into account a nonperturbative term proportional to the gluon condensate 〈αsG2/π〉. Results m=(6570±55)MeV and m′=(18540±50)MeV are used to fix kinematically allowed hidden-flavor decay channels of these states. It turns out that, the processes X4c→J/ψJ/ψ, X4c→ηcηc, and X4c→ηcχc1(1P) are possible decay modes of X4c. The partial widths of these channels are evaluated by means of the couplings gi,i=1,2,3 which describe strong interactions of tetraquark X4c and mesons at relevant vertices. The couplings gi are extracted from the QCD three-point sum rules by extrapolating corresponding form factors gi(Q2) to the mass-shell of a final meson. The mass of the scalar tetraquark X4b is below the ηbηb and ϒ(1S)ϒ(1S) thresholds, therefore it does not fall apart to these bottomonia, but transforms to conventional particles through other mechanisms. Comparing m=(6570±55)MeV and Γ4c=(110±21)MeV with parameters of structures observed by the LHCb, ATLAS and CMS collaborations, we interpret X4c as the resonance X(6600) reported by CMS. Comparisons are made with other theoretical predictions.

Strange cousin of Z c (4020/4025) as a tetraquark state* *Supported by the National Natural Science Foundation of China (12175068)

Motivated by the analogous properties of and , we tentatively assign as the -type hidden-charm tetraquark state with , where A denotes the axialvector diquark states, and explore -type tetraquark states without strange, with strange, and with hidden-strange via QCD sum rules in a consistent manner. We then explore the hadronic coupling constants in the two-body strong decays of tetraquark states without and with strange via QCD sum rules based on rigorous quark-hadron duality and acquire partial and total decay widths. The present calculations support assigning as the -type tetraquark state with , while the predictions for its strange cousin state can be confronted with experimental data in the future.

Nucleon axial form factor at large momentum transfers

Using a Poincaré-covariant quark+diquark Faddeev equation and related symmetry-preserving weak interaction current, we deliver parameter-free predictions for the nucleon axialvector form factor, G_A(Q^2), on the domain 0le x=Q^2/m_N^2le 10, where m_N is the nucleon mass. We also provide a detailed analysis of the flavour separation of the proton G_A into contributions from valence u and d quarks; and with form factors available on such a large Q^2 domain, predictions for the flavour-separated axial-charge light-front transverse spatial density profiles. Our calculated axial charge ratio g_A^d/g_A^u=-0.32(2) is consistent with available experimental data and markedly larger in magnitude than the value typical of nonrelativistic quark models. The value of this ratio is sensitive to the strength of axialvector diquark correlations in the Poincaré-covariant nucleon wave function. Working with a realistic axialvector diquark content, the d and u quark transverse density profiles are similar. Some of these predictions could potentially be tested with new data on threshold pion electroproduction from the proton at large Q^2.

Contact interaction analysis of octet baryon axial-vector and pseudoscalar form factors

Octet baryon axial, induced pseudoscalar, and pseudoscalar form factors are computed using a symmetry-preserving treatment of a vector$\,\times\,$vector contact interaction (SCI), thereby unifying them with an array of other baryon properties and analogous treatments of semileptonic decays of pseudoscalar mesons. The baryons are treated as quark--plus--interacting-diquark bound states, whose structure is obtained by solving a Poincar\'e-covariant Faddeev equation. The approach is marked by algebraic simplicity, involves no free parameters, and since it is symmetry preserving, all consequences of partial conservation of the axial current are manifest. It is found that SCI results are consistent with only small violations of SU$(3)$-flavour symmetry, an outcome which may be understood as a dynamical consequence of emergent hadron mass. The spin-flavour structure of the Poincar\'e-covariant baryon wave functions is expressed in the presence of both flavour-antitriplet scalar diquarks and flavour-sextet axialvector diquarks and plays a key role in determining all form factors. Considering neutral axial currents, SCI predictions for the flavour separation of octet baryon axial charges and, therefrom, values for the associated SU$(3)$ singlet, triplet, and octet axial charges are obtained. The results indicate that at the hadron scale, $\zeta_{\cal H}$, valence degrees-of-freedom carry roughly 50% of an octet baryon's total spin. Since there are no other degrees-of-freedom at $\zeta_{\cal H}$, the remainder may be associated with quark+diquark orbital angular momentum.

Excitation spectra of heavy baryons in diquark models

Abstract The excitation energy spectra of heavy baryons consisting of a heavy quark and two light quarks are investigated using diquark models in order to examine the nature of the diquark as a constituent of single heavy baryons. We consider two diquark models; in Model A the diquark is treated as a point-like particle, while it has a spatial size in Model B. We determine the masses of scalar and axial vector diquarks by the mass difference of the ground-state charmed baryons and the Λc baryon, while the mass of the ud scalar diquark in the Λc baryon is assumed to be 500 MeV as a reference. The parameters of these models are fixed by the 1p excitation energy of Λc. We find that Model A reproduces well the excitation energy spectra of the charmed and bottomed baryons, although the string tension of the confinement potential in Model A should be half of that of the charmonium, while Model B suggests degeneracy of the 2s and 1d states, which is not seen in the Λc spectrum.

Dynamical diquarks in the $${\varvec{\gamma ^{(*)} p\rightarrow N(1535)\frac{1}{2}^-}}$$ transition

The $\gamma^{(\ast)}+p \to N(1535) \tfrac{1}{2}^-$ transition is studied using a symmetry-preserving regularisation of a vector$\,\otimes\,$vector contact interaction (SCI). The framework employs a Poincar\'e-covariant Faddeev equation to describe the initial and final state baryons as quark+di\-quark composites, wherein the diquark correlations are fully dynamical, interacting with the photon as allowed by their quantum numbers and continually engaging in breakup and recombination as required by the Faddeev kernel. The presence of such correlations owes largely to the mechanisms responsible for the emergence of hadron mass; and whereas the nucleon Faddeev amplitude is dominated by scalar and axial-vector diquark correlations, the amplitude of its parity partner, the $N(1535) \tfrac{1}{2}^-$, also contains sizeable pseudoscalar and vector diquark components. It is found that the $\gamma^{(\ast)}+p \to N(1535) \tfrac{1}{2}^-$ helicity amplitudes and related Dirac and Pauli form factors are keenly sensitive to the relative strengths of these diquark components in the baryon amplitudes, indicating that such resonance electrocouplings possess great sensitivity to baryon structural details. Whilst SCI analyses have their limitations, they also have the virtue of algebraic simplicity and a proven ability to reveal insights that can be used to inform more sophisticated studies in frameworks with closer ties to quantum chromodynamics.

Analysis of Zcs (3985) as the axialvector tetraquark state * *Supported by National Natural Science Foundation of China (11775079)

In this study, we choose the scalar and axialvector diquark operators in the color antitriplet as the fundamental building blocks to construct four-quark currents and investigate the diquark-antidiquark type axialvector tetraquark states in the framework of the QCD sum rules. The predicted tetraquark mass is in excellent agreement with the experimental value from the BESIII collaboration, which supports identifying as the cousin of with quantum numbers . We take into account the light flavor mass-breaking effect to estimate the mass spectrum of the diquark-antidiquark type hidden-charm tetraquark states with strangeness according to previous studies.

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.

Revisit the tetraquark candidates in the J/ψJ/ψ mass spectrum

In this paper, we introduce a relative [Formula: see text]-wave to construct the doubly-charm axialvector diquark operator, then take the doubly-charm axialvector (anti-)diquark operator as the basic constituent to construct the scalar and tensor tetraquark currents to study the scalar, axialvector and tensor fully-charm tetraquark states with the QCD sum rules. We observe that the ground state [Formula: see text]-type tetraquark states and the first radial excited states of the [Formula: see text]-type tetraquark states have almost degenerated masses, where the [Formula: see text] and [Formula: see text] stand for the diquark operators with and without the relative [Formula: see text]-wave, respectively, the broad structure above the [Formula: see text] threshold maybe consist of several diquark–antidiquark-type fully-charm tetraquark states.

Nonrelativistic model of tetraquarks and predictions for their masses from fits to charmed and bottom meson data

We investigate a nonrelativistic model of tetraquarks, which are assumed to be compact and to consist of diquark-antidiquark pairs. We fit, for the first time, basically all currently known values for the measured masses of 45 mesons, including both charmed and bottom mesons, to the model and predict masses of tetraquarks as well as diquarks. In particular, we find masses of four axial-vector diquarks, i.e., $qc$, $cc$, $qb$, and $bb$, where $q = u,d$, and 24 ground-state tetraquarks, including both heavy-light tetraquarks ($qc\overline{qc}$ and $qb\overline{qb}$) and heavy tetraquarks ($cc\overline{cc}$ and $bb\overline{bb}$). In general, our results for the masses of $qb\overline{qb}$, $cc\overline{cc}$, and $bb\overline{bb}$ are largely comparable with other reported results, whereas our results for the masses of $qc\overline{qc}$ are slightly larger than what has been found earlier. Finally, we identify some of the obtained predictions for masses of tetraquarks with masses of experimental tetraquark candidates, and especially, we find that $\psi(4660)$, $Z_b(10610)$, and $Z_b(10650)$ could be described by the model.

Sivers and Boer–Mulders GTMDs in light-front holographic quark–diquark model

We calculate the time reversal odd (T-odd) generalized transverse momentum dependent parton distributions (GTMDs) $F^o_{1,2}$ and $H^o_{1,1}$ in a light-front quark-diquark model based on ADS/QCD. In the limit of zero momentum transfer, these reduce to the Sivers and Boer-Mulders TMDs respectively. We have incorporated both scalar and axial vector diquarks in the model and obtained an overlap representation of the GTMDs using the light-front wave functions (LFWFs). Contribution from the final state interaction is incorporated at the level of one gluon exchange as a phase factor in the LFWF. We show that the final state interaction term can be factored out in this model and this part is the same for both GTMDs. We also present the corresponding Wigner distributions.

Impact of dynamical chiral symmetry breaking and dynamical diquark correlations on proton generalized parton distributions

We calculate the leading-twist, helicity-independent generalized parton distributions (GPDs) of the proton, at finite skewness, in the Nambu--Jona-Lasinio (NJL) model of quantum chomodynamics (QCD). The NJL model reproduces low-energy characteristics of QCD, including dynamical chiral symmetry breaking (DCSB). The proton bound-state amplitude is solved for using the Faddeev equation in a quark-diquark approximation, including both dynamical scalar and axial vector diquarks. GPDs are calculated using a dressed non-local correlator, consistent with DCSB, which is obtained by solving a Bethe-Salpeter equation. The model and approximations used observe Lorentz covariance, and as a consequence the GPDs obey polynomiality sum rules. Extractions of electromagnetic and gravitational form factors are performed. We find a D-term of $-1.08$ when the non-local correlator is properly dressed, and $0.85$ when the bare correlator is used instead, suggesting that within this framework proton stability requires the constituent quarks to be dressed consistently with DCSB. We also find that the anomalous gravitomagnetic vanishes, as required by Poincar\'{e} symmetry.

Study of Spin–Spin Correlations between Quark and a Spin-1/2 Composite System

We study the correlation between the fermion composite system and quark spins by using the light-cone quark–diquark model. We do the calculations for u-quark and d-quark in the fermion system by considering different polarization configurations of both. The contribution from scalar and axial-vector diquarks is taken into account. The overlap representation of light-front wavefunctions is used for the calculations. The spin–spin correlations for u and d quarks are presented in transverse impact-parameter plane and transverse momentum plane as well.

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.

Analysis of the hidden-bottom tetraquark mass spectrum with the QCD sum rules

In this article, we extend our previous work to study the mass spectrum of the ground state hidden-bottom tetraquark states with the QCD sum rules in a systematic way. The predicted hidden-bottom tetraquark masses can be confronted to the experimental data in the future to diagnose the nature of the Z_b states. In calculations, we observe that the scalar diquark states, the axialvector diquark states and the axialvector components of the tensor diquark state are all good diquarks in building the lowest tetraquark states.

Wigner distributions and GTMDs in a proton using light-front quark–diquark model

We investigate the Wigner distributions and generalized transverse momentum-dependent distributions (GTMDs) for u and d quarks in the proton by using light-front quark–diquark model. We consider the contribution of scalar and axial-vector diquark having spin-0 and spin-1 respectively. We take different polarization configurations of quark and proton to calculate the Wigner distributions. The Wigner distributions are studied in the impact-parameter space, momentum space and mixed space for u and d quarks in the proton. We also study the relation of GTMDs with longitudinal momentum fraction carried by the active quark x for different values of ζ (skewness) which is defined as the longitudinal momentum transferred to the proton. Further, we study the GTMDs in the relation with x for zero skewness (ζ=0) at different values of quark transverse momentum p⊥ as well as at different values of total momentum transferred to the proton Δ⊥.

Nucleon quark distribution functions from the Dyson–Schwinger equations

We present results for the nucleon's leading-twist spin-independent valence parton distribution functions obtained from a theoretical framework based on the Dyson–Schwinger equations (DSEs) of QCD that previously gave an excellent description of nucleon electromagnetic form factors. Key dynamical elements selected by experience with the rainbow-ladder truncation of the DSEs are implemented. We utilize nucleon bound state amplitudes from the Poincaré-covariant Faddeev equation that implements the dominant scalar and axial-vector quark–quark correlations. This framework is used to numerically evaluate the first 20 moments of the valence u and d quark distribution functions, from which the x-dependence of the distributions is found to be well constrained. We find good agreement with empirical parameterizations of experimental data and make the prediction that the d/u ratio in the x→1 limit, invariant under scale evolution, takes the value d/u→0.087±0.010. We find that this ratio is rather sensitive to the strength of axial-vector diquark correlations. However, contrary to a naive expectation, our result for the d/u ratio in the x→1 limit does not vanish when only scalar diquark correlations are present, although it is an order-of-magnitude smaller than our d/u result that also includes axial-vector diquarks. The valence quark distribution results are set in a broader context via a simple pion cloud model estimate of sea-quark light-cone momenta and gluon light-cone momentum.

Parton distributions and cos2ϕh asymmetry induced by anomalous photon-quark coupling

In the spectator models of the nucleon with scalar and axial-vector diquarks, we show that the effect of Pauli coupling in photon-quark vertex to the parton distribution functions (PDFs) of nucleon and azimuthal asymmetry in the unpolarized semi-inclusive deep inelastic scattering (SIDIS). This anomalous coupling gives obvious contribution to unpolarized and polarized PDFs, and also leads to a $\cos 2\phi_h$ azimuthal asymmetry proportional to the squared Pauli form factor, due to the helicity flip of the struck quark. After determining the model parameters by fitting PDFs to the global fits, this new distribution for $\cos 2\phi_h$ asymmetry is given numerically. In the framework of transverse momentum dependence (TMD), we find that it is positive and of a few percent in the kinematical regime of HERMES and COMPASS collaborations, in the same order of magnitude with Cahn effect.

Single-spin asymmetries in SIDIS induced by anomalous quark-gluon and quark-photon couplings

We calculate the contribution of the non-perturbative Pauli couplings in the quark-photon and quark-gluon vertices to the single-spin asymmetries (SSAs) in semi-inclusive deep inelastic scattering (SIDIS). We describe the nucleon using the spectator model with scalar and axial-vector diquarks. Both of the new couplings can cause the helicity flip of the struck quark. The helicity flip and the rescattering induced by the non-perturbative gluon exchange between the struck quark and diquark lead to the SSAs. Their azimuthal dependencies are the same as that usually ascribed to the Collins and Sivers effects. Our numerical results, based on the instanton model for the QCD vacuum, show that the non-perturbative quark-gluon and quark-photon interactions have a strong influence on these asymmetries.