arXiv subjects

Ding-Kun Lian

Publications and source records attributed to Ding-Kun Lian.

14 recordsLinked to original sources

arXiv2026

The decay properties of two- and three- gluon glueballs

We previously studied the decay properties of two- and three-gluon glueballs using the Fierz rearrangement method and obtained their relative branching ratios in Ref.~\cite{Tan:2026uue}. In this work, we extend and develop this analysis by providing a more complete treatment of two-gluon glueball decays and by considering the tensor and pseudotensor states with $J^{PC}=2^{++}$ and $2^{-+}$. We also perform an independent QCD sum rule analysis of the $0^{++}$ two-gluon glueball decay. The consistency between the two approaches provides a useful check of the Fierz analysis. Our results support a sizable gluon component in the $f_0(1710)$ and favor the $0^{-+}$ glueball interpretation of the $η(2370)$. For the tensor glueball, the vector--vector ($VV$) decay channels, especially $K^{*}(892)\bar{K}^{*}(892)$, are found to be favorable for experimental searches. We also study three-gluon glueballs with $J^{PC}=0^{++}$ and $1^{+-}$ and identify several potentially favorable three-meson decay channels, including $ππω$ and $K\bar Kϕ$. These results provide possible guidance for future experimental searches for glueball states.

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arXiv2026

Light tetraquark states with $J^{PC}=1^{--}$ from QCD sum rules

We perform a systematic QCD sum rule study of light tetraquark states with $J^{PC}=1^{--}$ in the diquark--antidiquark picture. A complete set of local interpolating currents is constructed and projected onto six flavor-isospin configurations ($q=u/d$): the isoscalar $q q\bar q\bar q$, $q s\bar q\bar s$, and $s s\bar s\bar s$ sectors, the isovector $q q\bar q\bar q$ and $q s\bar q\bar s$ sectors, and the isotensor $q q\bar q\bar q$ sector. The lowest masses in these sectors are derived to be $1.64^{+0.15}_{-0.14}$~GeV, $1.86^{+0.14}_{-0.14}$~GeV, $2.34^{+0.23}_{-0.30}$~GeV, $1.53^{+0.17}_{-0.19}$~GeV, $1.86^{+0.14}_{-0.14}$~GeV, and $2.24^{+0.12}_{-0.14}$~GeV, respectively. We further compare the present $1^{--}$ tetraquark spectrum with previous QCD sum rule results for the $1^{-+}$ tetraquark and hybrid states~\cite{Su:2025bhv}, aiming to provide useful information for distinguishing tetraquark and hybrid configurations in the light hadron spectrum. As an additional improvement, we complete the previously missing isotensor $1^{-+}$ tetraquark entry and obtain its lowest mass to be $M=2.19^{+0.26}_{-0.24}~\mathrm{GeV}$, which is included in the spectral comparison.

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arXiv2026

Subtraction of infrared divergences in light-quark QCD sum rules

In QCD sum rules for light-quark systems, infrared (IR) divergences can appear in the Wilson coefficients of certain condensates. These divergences manifest explicitly in the coordinate-space expressions of the light-quark propagators. We propose an improved method to eliminate these IR divergences at the propagator level and present a subtraction formula that implements this procedure. Compared to the existing methods that rely on the mixing between quark and gluon condensates of the same dimension to eliminate IR divergences, this method is more intuitive and easier to apply in practical QCD sum rule calculations.

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arXiv2026

Interpretation of $Ω(2012)$ as a $Ξ(1530)K$ molecular state

We investigate the mass and strong decay properties of the $Ω(2012)$ resonance using QCD sum rules, assuming it to be an S-wave $Ξ(1530)\bar{K}$ molecular pentaquark state with $I(J^{P})= 0(\frac{3}{2}^{-})$. A unified interpolating current is constructed, and the two-point correlation functions and three-point functions are calculated up to dimension-13 and 10 condensate terms in the OPE series, respectively. The negative-parity contribution is isolated by employing parity-projected sum rules. The two-body strong decays to $Ξ^0 K^-$ and $Ξ^- \bar{K}^0$ are studied via their three-point correlation functions. Our analysis yields a mass of $2.00 \pm 0.15~\mathrm{GeV}$ and a total two-body decay width of $Γ= 0.96^{+0.79}_{-0.41}~\mathrm{MeV}$ for the $Ξ(1530)\bar{K}$ molecular state. The ratio of the two-body decay branching fractions is obtained as $\mathcal{R}^{Ξ^- \bar{K}^0}_{Ξ^0 K^-} = 0.85$. These results are compatible with the experimental data for the $Ω(2012)$ within uncertainties and support its interpretation as a $Ξ(1530)\bar{K}$ molecular pentaquark state.

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arXiv2026

Investigations on heavy quarkonium hybrid mesons with exotic quantum numbers $J^{PC}=2^{+-}$

We investigate the heavy quarkonium hybrid mesons with exotic quantum numbers $J^{PC}=2^{+-}$ via QCD sum rule method. We construct the currents with three Lorentz indices and calculate the correlation functions up to dimension six at the leading order of $α_{s}$. The states with $J^{PC}=2^{+-}$ are extracted by constructing the corresponding projection operators. The obtained results indicate that the masses of $2^{+-}$ $\bar{c}Gc$ and $\bar{b}Gb$ hybrid states are about $4.49~\mathrm{GeV}$ and $10.48~\mathrm{GeV}$, respectively. We suggest to search for $\bar{c}Gc$ hybrid meson with $J^{PC}=2^{+-}$ in $J/ψf_{0,1,2}$ and $χ_{c0,1,2} ω$ final states.

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arXiv2026

Predictions of masses for light hybrid baryons

Within the method of parity-projected QCD sum rules, we study the mass spectra of light hybrid baryons with $I(J^{P})=1/2(1/2^{\pm}), 3/2(1/2^{\pm}), 1/2(3/2^{\pm}), 3/2(3/2^{\pm})$ by constructing the local $qqqg$ interpolating currents. We calculate the correlation functions up to dimension eight condensates at the leading order of $α_{s}$. The stable QCD Lapalce sum rules can be established for the positive-parity $N_{1/2^+}, Δ_{3/2^+}, Δ_{1/2^+}$ and negative-parity $N_{1/2^-}, N_{3/2^-}, Δ_{1/2^-}$ channels to extract their mass spectra. The lowest-lying hybrid baryons are predicted to be the positive-parity $N_{1/2^+}$ state around 2.01 GeV. These hybrid baryons mainly decay into conventional baryon plus meson final states. We propose to search for the light hybrid baryons through the $Υ/ψ(3686)$ decays via the three-gluon emission mechanism in BESIII and BelleII experiments. Hopefully our studies of the light hybrid baryons will be useful for understanding the excited baryon spectrum and the behavior of gluonic degrees of freedom in QCD.

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arXiv2025

Light hybrid baryons in QCD sum rules

We have calculated the mass spectra of nucleon and delta hybrid baryons with both positive-parity and negative-parity by using the method of QCD sum rules. We predicte that the lowest-lying hybrid baryons are the negative-parity $N_{1/2^-}$ and $Δ_{1/2^-}$ states, while the positive-parity ones are much heavier. We suggest to search for these light hybrid baryons via the $χ_{cJ}/Υ$ decay processes in the future.

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arXiv2025

Interpreting the $X(2370)$ and $X(2600)$ as light tetraquark states

Inspired by the states $X(2370)$ and $X(2600)$ reported by the BESIII Collaboration, we systematically investigate the mass spectra of light compact tetraquark states with configurations $ud\bar{u}\bar{d}$, $us\bar{u}\bar{s}$, and $ss\bar{s}\bar{s}$ in the $J^{PC}=0^{-+}$ and $2^{-+}$ channels using the QCD sum rules approach. To effectively describe these tetraquark states, we construct appropriate interpolating tetraquark currents featuring three Lorentz indices while avoiding derivative operators. Through meticulous calculations of correlation functions up to dimension 10 condensates, we extract the mass spectra for both $0^{-+}$ and $2^{-+}$ states by employing the projection operator technique. Our results indicate that the masses of light tetraquarks span $1.5-2.5~\text{GeV}$ for $0^{-+}$ states and $2.4-2.7~\text{GeV}$ for $2^{-+}$ states. Notably, our analysis suggests that the $X(2370)$ state could be interpreted as a $0^{-+}$ $us\bar{u}\bar{s}$ or $ss\bar{s}\bar{s}$ tetraquark state, while the $X(2600)$ state is likely to be a $2^{-+}$ $us\bar{u}\bar{s}$ tetraquark. These intriguing findings warrant further detailed investigation in future studies to better understand the nature of these states.

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arXiv2024

Mixing angle of $K_1(1270/1400)$ and the $K\bar K_1(1400)$ molecular interpretation of $η_1(1855)$

Due to the SU(3) symmetry breaking effect, the axial-vector kaons $K_1(1270)$ and $K_1(1400)$ are established to be mixtures of two P-wave $K_{1A}\left( {^3{P_1}} \right)$ and $K_{1B}\left( {^1{P_1}} \right)$ states. In QCD sum rules, we propose a new construction of the $K_1$ current operators and calculate the two-point correlation functions by including the next-to-leading order four-quark condensates. The mixing angle is determined as $θ= \left( {46.95_{ - 0.23}^{ + 0.25}} \right)^\circ$ by reproducing the masses of $K_1(1270)$ and $K_1(1400)$. We further compose the $K\bar K_1\left( {1270} \right)$ and $K\bar K_1\left( {1400} \right)$ interpolating currents with exotic quantum numbers $J^{PC}=1^{-+}$ to investigate the possible molecular interpretation of the recently observed ${η_1}(1855)$ state. We calculate the correlation functions and perform the QCD sum rule analyses for these two molecular systems. However, the spectral functions are found to be negative in physical regions so that they are not able to provide reliable investigations of the $K\bar K_1$ molecular states.

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arXiv2024

Towards heavy double-gluon hybrid mesons with exotic quantum numbers in QCD sum rules

The double-gluon hybrid meson configuration was recently proposed and investigated within QCD sum rules. In this talk, we discuss the color structures of the double-gluon hybrid meson and construct current operators with exotic quantum numbers $J^{PC}=1^{-+}$ and $2^{+-}$ for two of the structures. In the framework of QCD sum rules, we consider the condensates up to dimension-8 at the leading order of $α_{s}$ for both charmonium and the bottomonium systems. The results indicate that the masses of the $1^{-+}$ and $2^{+-}$ charmonium double-gluon hybrid mesons are approximately $6.1-7.2$ GeV and $6.3-6.4$ GeV, respectively. As for the bottomonium systems, their masses fall within the range of $13.7-14.3$ GeV and $12.6-13.3$ GeV for the $1^{-+}$ and $2^{+-}$ channels, respectively. Additionally, the charmonium hybrids could be produced in the radiative decays of bottomonium mesons in BelleII experiment.

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arXiv2024

Light tetraquark states with exotic quantum numbers $J^{PC}=2^{+-}$

We study the masses of light tetraquark states $ud\bar{u}\bar{d}$ , $us\bar{u}\bar{s}$ and $ss\bar{s}\bar{s}$ with exotic quantum numbers $J^{PC}=2^{+-}$ using the method of QCD sum rules. It is found that there is no tetraquark operator with two Lorentz indices coupling to the $2^{+-}$ quantum numbers. To investigate such tetraquark states, we construct the interpolating tetraquark currents with three Lorentz indices and without derivative operator. We calculate the correlation functions up to dimension 10 condensates, and extract the $2^{+-}$ invariant functions via the projector operator. Our results show that the masses of the $ud\bar{u}\bar{d}$, $us\bar{u}\bar{s}$ and $ss\bar{s}\bar{s}$ tetraquark states with $J^{PC}=2^{+-}$ are about $3.3-3.5 ~\mathrm{GeV}$, $3.5-3.7 ~\mathrm{GeV}$ and $3.67 ~\mathrm{GeV}$, respectively. We further discuss the strong decays of these light tetraquarks into the two-meson and baryon-antibaryon final states, and suggest to search for them in the $ρπ, ωπ, ϕπ$, $b_{1}π$, $h_{1}π$, $K\bar K^\ast, K\bar{K}_{1}$, $Δ\barΔ$, $Σ^{\ast} \bar{Σ}^{\ast}$, $Ξ^{\ast} \bar{Ξ}^{\ast}$, $Ω\bar{Ω}$ channels in the future.

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arXiv2024

Revisit the heavy quarkonium double-gluon hybrid mesons with exotic quantum numbers

We revisit the masses of heavy quarkonium double-gluon hybrid mesons with exotic quantum numbers $J^{PC}=1^{-+}$ and $2^{+-}$ in the framework of the QCD sum rules. Considering the double-gluon hybrid meson operators in the octet-octet color structure, we have constructed two independent interpolating currents with $J^{PC}=1^{-+}$ and five independent currents with $J^{PC}=2^{+-}$. For the interpolating currents with antisymmetric glueball operator, there exist non-local divergences in one kind of additional Feynman diagrams of the tri-gluon condensate, which will give important contributions to the sum rule stabilities and mass predictions. We use the diagrammatic renormalization to cancel out such divergences. At the leading order of $α_s$, the two-point correlation functions and spectral densities can be expressed in the analytic form of the generalized hypergeometric functions and Meijer's G-functions. After performing the numerical analysis, we predict the masses of the $1^{-+}$ and $2^{+-}$ charmonium double-gluon hybrid mesons to be around $6.1-7.2$ GeV and $6.3-6.4$ GeV, respectively. For the bottomonium systems, their masses are predicted to be $13.7-14.3$ GeV and $12.6-13.3$ GeV for the $1^{-+}$ and $2^{+-}$ channels, respectively. Besides, it is possible to hunt for these charmonium hybrids in the radiative decays of bottomonium mesons in BelleII experiment. Further investigations on these hybrid states in various theoretical and phenomenological methods are also anticipated in the future.

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arXiv2024

Strong decays of $T_{c\bar s0}(2900)^{++/0}$ as a fully open-flavor tetraquark state

We have studied the strong decay properties of the recently observed $T^a_{c\bar s0}(2900)^{++/0}$ by considering it as a $cu\bar{d}\bar{s}/cd\bar{u}\bar{s}$ fully open-flavor tetraquark state with $I(J^P)=1(0^+)$. In the framework of QCD sum rules, we have calculated the three-point correlation functions of the two-body strong decay processes $T^a_{c\bar s0}(2900)^{++}\rightarrow D_s^+π^+$, $D^+K^+, D_s^{\ast +}ρ^+$ and $D_{s1}^+π^+$. The full width of $T^a_{c\bar s0}(2900)^{++/0}$ is obtained as $161.7\pm94.8$ MeV, which is consistent with the experimental observation. We predict the relative branching ratios as $Γ(T\rightarrow D_sπ):Γ(T\rightarrow DK):Γ(T\rightarrow D_s^{\ast} ρ):Γ(T\rightarrow D_{s1}π)\approx1.00:1.10:0.04:0.43$, implying that the main decay modes of $T^a_{c\bar s0}(2900)^{++/0}$ state are $D_sπ$ and $DK$ channels in our calculations. However, the $P$-wave decay mode $D_{s1}π$ is also comparable and important by including the uncertainties. To further identify the nature of $T^a_{c\bar s0}(2900)^{++/0}$, we suggest confirming them in the $DK$ and $D_{s}π$ final states, and measuring the above ratios in future experiments.

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arXiv2023

Predictions of the hybrid mesons with exotic quantum numbers $J^{PC}=2^{+-}$

We study the non-strange and strangeonium light hybrid mesons with $J^{PC}=2^{+-}$ by using the method of QCD sum rules. The local hybrid interpolating currents with three Lorentz indices are constructed to couple to such exotic quantum numbers. We calculate the correlation functions up to dimension eight condensates at the leading order of $α_{s}$. In our results, the masses of the non-strange $b_2$ and $h_2$ hybrids are about $2.65~\mathrm{GeV}$, while that of the strangeonium $h_2^\prime$ hybrid is about $2.72~\mathrm{GeV}$. Such exotic $2^{+-}$ hybrids can be generated through both the two-gluon and three-gluon emission processes in the radiative decays of $χ_{cJ}$. Moreover, these hybrid mesons may be detectable due to their peculiar decay behaviors and small decay widths. Using the high-statistics data samples of $ψ(3686)$ in BESIII and BelleII, it is possible to hunt for such hybrid states through the partial wave analyses in the $b_2\toω/a_1/h_1/a_2π\to4π$, $h_2\toρπ\to3π$ and $h_2\to b_1π\to5π$ processes.

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