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Er-Liang Cui

Publications and source records attributed to Er-Liang Cui.

At least 19 recordsLinked to original sources
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.

hep-ph↗
arXiv2025

A Variance-Based Convergence Criterion in Neural Variational Monte Carlo for Quantum Systems

The optimization of neural wave functions in variational Monte Carlo crucially relies on a robust convergence criterion. While the energy variance is theoretically a definitive measure, its practical application as a primary convergence criterion has been underexplored. In this work, we develop a lightweight, general-purpose solver that utilizes the energy variance as a convergence criterion. We apply it to several systems-including the harmonic oscillator, hydrogen atom, and charmonium hadron-for validating the variance as a reliable diagnostic, and using a empirical threshold $10^{-3}$ as the energy variance convergence values for performing rapid parameter scans to enable preliminary physical verification. To clarify the scope of our approach, we derive an inequality that delineates the limitations of variance-based optimization in nodal systems. Despite these limitations, the energy variance proves to be a highly valuable tool, guiding our solver to efficient and reliable results across a range of quantum problems.

quant-ph↗
arXiv2025

A hybrid nonet with $J^{PC}=1^{-+}$ or a tetraquark 81-plet

Confirming the existence of hybrid states remains challenging due to their experimental indistinguishability from tightly bound tetraquarks and loosely bound molecules. To address this issue, we employ QCD sum rules to systematically investigate the $π_1(1600)$ and $η_1(1855)$ as candidate tetraquark states with exotic quantum numbers $J^{PC} = 1^{-+}$. Within the hybrid framework, an $SU(3)$ flavor nonet is expected, featuring two isoscalar configurations, $q\bar{q}g$ and $s\bar{s}g$, where $q = u/d$. In contrast, the tetraquark scenario predicts an $SU(3)$ flavor 81-plet comprising three isoscalar states: $qq\bar{q}\bar{q}$, $qs\bar{q}\bar{s}$, and $ss\bar{s}\bar{s}$. Our analysis yields a mass of $2.22^{+0.18}_{-0.26}$ GeV for the $ss\bar{s}\bar{s}$ tetraquark state, which is expected to decay predominantly into the $ϕϕ$ and $ηf_1(1420)$ final states. Therefore, experimental scrutiny of their invariant mass spectra is pivotal for distinguishing between hybrid and tetraquark interpretations.

hep-ph↗
arXiv2025

Radiative decays of $P$-wave charmed baryons in the $SU(3)$ flavor $\bf6_F$ representation

We perform a comprehensive investigation of the radiative decays of $P$-wave charmed baryons in the $SU(3)$ flavor $\mathbf{6}_F$ representation, employing the light-cone QCD sum rule approach within the framework of heavy quark effective theory. We analyze their electromagnetic transitions into ground-state charmed baryons via photon emission. When combined with the mass spectra and strong decay properties previously studied in Ref.~\cite{Yang:2021lce}, our results constitute a systematic and complete QCD sum rule analysis of the $P$-wave singly charmed baryons within the framework of heavy quark effective theory. As summarized in Table~\ref{tab:result}, several excited charmed baryons are found to possess suppressed strong decay widths, thereby rendering their radiative decay channels particularly significant for experimental identification and theoretical understanding.

hep-ph↗
arXiv2025

Strong decay properties of P-wave single bottom baryons of the SU(3) flavor antitriplet $\bf\bar 3_F$

We study the $P$-wave bottom baryons of the $SU(3)$ flavor antitriplet and systematically calculate their strong decay properties, including their $D$-wave decays into ground-state bottom baryons with light pseudoscalar mesons and $S$-wave decays into ground-state bottom baryons with light vector mesons. Together with Refs.~\cite{Tan:2023opd,Yang:2019cvw,Yang:2020zrh,Luo:2024jov}, a rather complete investigation has been performed to study their mass spectra and strong/radiative decay properties, through the methods of QCD sum rules and light-cone sum rules within the framework of heavy quark effective theory. Among various possibilities, we identify four $Λ_b$ and four $Ξ_b$ baryons, with limited decay widths and so capable of being observed in experiments. Their masses, mass splittings within the same multiplets, and strong/radiative decay widths are summarized in Table~\ref{tab:decayb3f} for future experimental searching.

hep-ph↗
arXiv2023

Strong decays of the $ϕ(2170)$ as a fully-strange tetraquark state

We study strong decays of the $ϕ(2170)$, along with its possible partner $X(2436)$, as two fully-strange tetraquark states of $J^{PC} = 1^{--}$. We consider seven decay channels: $ϕη$, $ϕη^\prime$, $ϕf_0(980)$, $ϕf_1(1420)$, $h_1(1415) η$, $h_1(1415) η^\prime$, and $h_1(1415) f_1(1420)$. Some of these channels are kinematically possible, and we calculate their relative branching ratios through the Fierz rearrangement. Future experimental measurements on these ratios can be useful in determining the nature of the $ϕ(2170)$ and $X(2436)$. The $ϕ(2170)$ has been observed in the $ϕf_0(980)$, $ϕη$, and $ϕη^\prime$ channels, and we propose to further examine it in the $h_1(1415) η$ channel. Evidences of the $X(2436)$ have been observed in the $ϕf_0(980)$ channel, and we propose to verify whether this structure exists or not in the $ϕη$, $ϕη^\prime$, $h_1(1415) η$, and $h_1(1415) η^\prime$ channels.

hep-ph↗
arXiv2022

Identifying the $Ξ_b(6100)$ as the $P$-wave bottom baryon of $J^P=3/2^-$

We study the $Ξ_b(6100)$ using the methods of QCD sum rules and light-cone sum rules within the framework of heavy quark effective theory. Our results suggest that the $Ξ_b(6100)$ can be well interpreted as the $P$-wave bottom baryon of $J^P=3/2^-$, belonging to the $SU(3)$ flavor $\mathbf{\bar 3}_F$ representation. It has a partner state of $J^P=1/2^-$, labelled as $Ξ_b(1/2^-)$, whose mass and width are predicted to be $m_{Ξ_b(1/2^-)}=6.08^{+0.13}_{-0.11}$~GeV and $Γ_{Ξ_b(1/2^-)}=4^{+29}_{-~4}$~MeV, with the mass splitting $ΔM=m_{Ξ_b(6100)}-m_{Ξ_b(1/2^-)}=9\pm3$~MeV. We propose to search for it in the $Ξ_c({1/2}^-)\to Ξ_b^{\prime}π$ decay channel. Our results also suggest that the $Λ_b(5912)$ and $Λ_b(5920)$ are their partner states with $J^P=1/2^-$ and $3/2^-$ respectively, and moreover, the $Λ_c(2595)$, $Λ_c(2625)$, $Ξ_c(2790)$, and $Ξ_c(2815)$ are their charmed partner states.

hep-ph↗
arXiv2021

Light tetraquark states with the exotic quantum number $J^{PC} = 3^{-+}$

We apply the method of QCD sum rules to study the $s q \bar s \bar q$ tetraquark states with the exotic quantum number $J^{PC} = 3^{-+}$, and extract mass of the lowest-lying state to be $2.33^{+0.19}_{-0.16}$ GeV. To construct the relevant tetraquark currents we need to explicitly add the covariant derivative operator. Our systematical analysis on their relevant interpolating currents indicates that: a) this state well decays into the $P$-wave $ρϕ/ωϕ$ channel but not into the $ρf_2(1525)/ωf_2(1525)/ϕf_2(1270)$ channels, and b) it well decays into the $K^*(892) \bar K_2^*(1430)$ channel but not into the $P$-wave $K^*(892) \bar K^*(892)$ channel.

hep-ph↗
arXiv2020

QCD sum rule studies on the $s s \bar s \bar s$ tetraquark states of $J^{PC} = 0^{-+}$

We apply the method of QCD sum rules to study the $s s \bar s \bar s$ tetraquark states of $J^{PC} = 0^{-+}$. We construct all the relevant $s s \bar s \bar s$ tetraquark currents, and find that there are only two independent ones. We use them to further construct two weakly-correlated mixed currents. One of them leads to reliable QCD sum rule results and the mass is extracted to be $2.51^{+0.15}_{-0.12}$ GeV, suggesting that the $X(2370)$ or the $X(2500)$ can be explained as the $ss\bar s\bar s$ tetraquark state of $J^{PC} = 0^{-+}$. To verify this interpretation, we propose to further study the $ππ/K \bar K$ invariant mass spectra of the $J/ψ\to γππη^\prime/γK \bar K η^\prime$ decays in BESIII to examine whether there exists the $f_0(980)$ resonance.

hep-ph↗
arXiv2020

Excited $Ω_b$ baryons and fine structure of strong interaction

The heavy baryon system bounded by the strong interaction has a rich internal structure, so its mass spectra can have the fine structure similar to the line spectra of atom bounded by the electromagnetic interaction. We systematically study the internal structure of $P$-wave $Ω_b$ baryons and calculate their $D$-wave decay properties. The present study, together with our previous studies on their mass spectra and $S$-wave decay properties, suggest that all the four excited $Ω_b$ baryons recently discovered by LHCb can be well explained as $P$-wave $Ω_b$ baryons, and their beautiful fine structure is directly related to the rich internal structure of $P$-wave $Ω_b$ baryons.

hep-ph↗
arXiv2020

Decay properties of $P$-wave heavy baryons accompanied by vector mesons within light-cone sum rules

We use the method of light-cone sum rules to study decay properties of $P$-wave bottom baryons belonging to the $SU(3)$ flavor $\mathbf{6}_F$ representation. In Ref.~\cite{Cui:2019dzj} we have studied their mass spectrum and pionic decays, and found that the $Σ_{b}(6097)$ and $Ξ_{b}(6227)$ can be well interpreted as $P$-wave bottom baryons of $J^P = 3/2^-$. In this paper we further study their decays into ground-state bottom baryons and vector mesons. We propose to search for a new state $Ξ_b({5/2}^-)$, that is the $J^P = 5/2^-$ partner state of the $Ξ_{b}(6227)$, in the $Ξ_b({5/2}^-) \to Ξ_b^{*}ρ\to Ξ_b^{*}ππ$ decay process. Its mass is $12 \pm 5$~MeV larger than that of the $Ξ_{b}(6227)$.

hep-ph↗
arXiv2019

Identifying the $Ξ_{b}(6227)$ and $Σ_{b}(6097)$ as $P$-wave bottom baryons of $J^P = 3/2^-$

We use the method of QCD sum rules within the framework of heavy quark effective theory to study the mass spectrum of the $Σ_{b}(6097)^{\pm}$ and $Ξ_{b}(6227)^{-}$, and use the method of light-cone sum rules still within the heavy quark effective theory to study their decay properties. Our results suggest that they can be well interpreted as $P$-wave bottom baryons with the spin-parity $J^P = 3/2^-$. They belong to the baryon doublet $[\mathbf{6}_F, 2, 1, λ]$, where the total and spin angular momenta of the light degree of freedom are $j_l = 2$ and $s_l = 1$, and the orbital angular momentum is between the bottom quark and the two-light-quark system ($λ$-type). This doublet contains six bottom baryons, and we predict masses (mass differences) and decay widths of the other four states to be $M_{Ω_b(3/2^-)} = 6.46 \pm 0.12 {~\rm GeV}$, $Γ_{Ω_b(3/2^-)} = 58{^{+65}_{-33}} {~\rm MeV}$, $M_{Σ_b(5/2^-)}-M_{Σ_b(3/2^-)}= 13 \pm 5 {~\rm MeV}$, $M_{Ξ_b^{\prime}(5/2^-)}-M_{Ξ_b^{\prime}(3/2^-)} = 12 \pm 5 {~\rm MeV}$, and $M_{Ω_b(5/2^-)}-M_{Ω_b(3/2^-)} = 11 \pm 5 {~\rm MeV}$. We propose to search for them in further LHCb experiments.

hep-ph↗
arXiv2019

QCD sum rule studies on the $s s \bar s \bar s$ tetraquark states with $J^{PC} = 1^{+-}$

We apply the method of QCD sum rules to study the structure $X$ newly observed by the BESIII Collaboration in the $ϕη^\prime$ mass spectrum in 2.0-2.1 GeV region in the $J/ψ\rightarrow ϕηη^\prime$ decay. We construct all the $s s \bar s \bar s$ tetraquark currents with $J^{PC} = 1^{+-}$, and use them to perform QCD sum rule analyses. One current leads to reliable QCD sum rule results and the mass is extracted to be $2.00^{+0.10}_{-0.09}$ GeV, suggesting that the structure $X$ can be interpreted as an $s s \bar s \bar s$ tetraquark state with $J^{PC} = 1^{+-}$. The $Y(2175)$ can be interpreted as its $s s \bar s \bar s$ partner having $J^{PC} = 1^{--}$, and we propose to search for the other two partners, the $s s \bar s \bar s$ tetraquark states with $J^{PC} = 1^{++}$ and $1^{-+}$, in the $η^\prime f_0(980)$, $η^\prime K \bar K$, and $η^\prime K \bar K^*$ mass spectra.

hep-ph↗
arXiv2017

Understanding the internal structures of the $X(4140)$, $X(4274)$, $X(4500)$ and $X(4700)$

We investigate the newly observed $X(4500)$ and $X(4700)$ based on the diquark-antidiquark configuration within the framework of QCD sum rules. Both of them may be interpreted as the $D$-wave $cs\bar{c}\bar{s}$ tetraquark states of $J^P = 0^+$, but with opposite color structures, which is remarkably similar to the result obtained in Ref.~\cite{Chen:2010ze} that the $X(4140)$ and $X(4274)$ can be both interpreted as the $S$-wave $cs\bar{c}\bar{s}$ tetraquark states of $J^P = 1^+$, also with opposite color structures. However, the extracted masses and these suggested assignments to these $X$ states do depend on these running quark masses where $m_s (2 \mbox{ GeV}) = 95 \pm 5$ MeV and $m_c (m_c) = 1.23 \pm 0.09$ GeV. As a byproduct, the masses of the hidden-bottom partner states of the $X(4500)$ and $X(4700)$ are extracted to be both around 10.64 GeV, which can be searched for in the $Υϕ$ invariant mass distribution.

hep-ph↗
arXiv2016

QCD sum rule study of hidden-charm pentaquarks

We study the mass spectra of hidden-charm pentaquarks having spin $J = {1\over2}/{3\over2}/{5\over2}$ and quark contents $uud c \bar c$. We systematically construct all the relevant local hidden-charm pentaquark currents, and select some of them to perform QCD sum rule analyses. We find that the $P_c(4380)$ and $P_c(4450)$ can be identified as hidden-charm pentaquark states composed of an anti-charmed meson and a charmed baryon. Besides them, we also find a) the lowest-lying hidden-charm pentaquark state of $J^P = 1/2^-$ has the mass $4.33^{+0.17}_{-0.13}$ GeV, while the one of $J^P = 1/2^+$ is significantly higher, that is around $4.7-4.9$ GeV; b) the lowest-lying hidden-charm pentaquark state of $J^P = 3/2^-$ has the mass $4.37^{+0.18}_{-0.13}$ GeV, consistent with the $P_c(4380)$ of $J^P = 3/2^-$, while the one of $J^P = 3/2^+$ is also significantly higher, that is above $4.6$ GeV; c) the hidden-charm pentaquark state of $J^P = 5/2^-$ has a mass around $4.5-4.6$ GeV, slightly larger than the $P_c(4450)$ of $J^P = 5/2^+$.

hep-ph↗
arXiv2015

$a_1(1420)$ resonance as a tetraquark state and its isospin partner

We systematically construct tetraquark currents of $I^GJ^{PC}=1^-1^{++}$ and classify them into types $\mathbf{A}$ (antisymmetric), $\mathbf{S}$ (symmetric) and $\mathbf{M}$ (mixed), based on flavor symmetries of diquarks and antidiquarks composing the tetra quark currents. We use tetraquark currents of type $\mathbf{M}$ to perform QCD sum rule analyses, and find a tetraquark current $η^M_{5μ}$ with quark contents $q s\bar q \bar s$($q=u$ or $d$) leading to a mass of $1.44 \pm 0.08$ GeV consistent with the $a_1(1420)$ state recently observed by the COMPASS collaboration. Our results support tetraquark explanations for both $a_1(1420)$ and $f_1(1420)$, assuming that they are isospin partners. We also study their possible decay patterns. As tetraquark candidates, the possible decay modes of $a_1(1420)$ are $S$-wave $a_1(1420) \rightarrow K^*(892)K$ and $P$-wave $a_1(1420)\rightarrow f_0(980) π$ while the possible decay patterns of $f_1(1420)$ are $S$-wave $f_1(1420) \rightarrow K^*(892)K$ and $P$-wave $f_1(1420) \rightarrow a_0(980) π$. We speculate that $a_1(1420)$ is partly responsible for the large isospin violation in the $η(1405)\to f_0(980)π_0$ decay mode which is reported by BESIII collaboration in the $J/ψ\toγ3π$ process.

hep-ph↗
arXiv2015

K-pi interaction in finite volume and the K* resonance

We evaluate energy levels of the K-pi system in the K* channel in finite volume using chiral unitary theory. We use these energy levels to obtain K-pi phase shifts, and then obtain the K* mass and its decay width. We investigate their dependence on the pion mass and compare this with Lattice QCD calculations. We also compare our method with the standard Luscher approach, and solve the inverse problem to obtain the K-pi phase shifts from these "synthetic" lattice data.

hep-lat↗