Exotic Quantum Numbers Research Articles

Charmoniumlike states with the exotic quantum number JPC=3−+

We apply the method of quantum chromodynamics (QCD) sum rules to study the qcq¯c¯ tetraquark states with the exotic quantum number JPC=3−+, and extract the mass of the lowest-lying state to be 4.49−0.41+0.45 GeV. To construct the relevant tetraquark currents we need to explicitly add the covariant derivative operator. Our systematic analysis of these interpolating currents indicates that: (a) this state readily decays into the P-wave [ρJ/ψ]/[ωJ/ψ] channel but not into the [ρχc2]/[ωχc2]/[J/ψf2(1270)] channels, and (b) it readily decays into the [D*D¯2*] channel but not into the P-wave [D*D¯*] channel. Published by the American Physical Society 2024

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 JPC=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 αs 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.

Light single-gluon hybrid states with various exotic quantum numbers

We apply the QCD sum rule method to study the light single-gluon hybrid states with various (exotic) quantum numbers. We construct 24 single-gluon hybrid currents and use 18 of them to calculate the masses of 44 single-gluon hybrid states with the quark-gluon contents q¯qg (q=u/d) and s¯sg. We concentrate on the hybrid states with the exotic quantum number JPC=1−+, whose masses and widths are calculated to be M|q¯qg;1−1−+⟩=1.67−0.17+0.15 GeV, Γ|q¯qg;1−1−+⟩=530−330+540 MeV, M|q¯qg;0+1−+⟩=1.67−0.17+0.15 GeV, Γ|q¯qg;0+1−+⟩=120−110+160 MeV, M|s¯sg;0+1−+⟩=1.84−0.15+0.14 GeV, and Γ|s¯sg;0+1−+⟩=100−80+110 MeV. Our results support the interpretations of the π1(1600) and η1(1855) as the hybrid states |q¯qg;1−1−+⟩ and |s¯sg;0+1−+⟩, respectively. Considering the uncertainties, our results suggest that the π1(1600) and η1(1855) may also be interpreted as the hybrid states |q¯qg;1−1−+⟩ and |q¯qg;0+1−+⟩, respectively. To differentiate these two assignments and to verify whether they are hybrid states or not, we propose to examine the a1(1260)π decay channel in future experiments. Published by the American Physical Society 2024

Light tetraquark states with exotic quantum numbers JPC=2+−

We study the masses of light tetraquark states udu¯d¯, usu¯s¯, and sss¯s¯ with exotic quantum numbers JPC=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 a derivative operator. We calculate the correlation functions up to dimension-ten condensates and extract the 2+− invariant functions via the projector operator. Our results show that the masses of the udu¯d¯, usu¯s¯, and sss¯s¯ tetraquark states with JPC=2+− are about 3.3–3.5, 3.5–3.7, and 3.67 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, b1π, h1π, KK¯*, KK¯1, ΔΔ¯, Σ*Σ¯*, Ξ*Ξ¯*, and ΩΩ¯ channels in the future. Published by the American Physical Society 2024

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 JPC = 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 JPC = 1−+ and five independent currents with JPC = 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 αs, 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.

Why quarkonium hybrid coupling to two S -wave heavy-light mesons is not suppressed

We examine the couplings of quarkonium hybrids to heavy-light meson pairs in the Born-Oppenheimer approximation for QCD. The lowest hybrid multiplets consist of bound states of the Πu and Σu− potentials. We find that the Σu− potential can couple to pairs of S-wave mesons through string breaking, while the Πu potential cannot. From this observation, we derive model-independent selection rules that contradict previous expectations that quarkonium hybrids are forbidden to decay into pairs of S-wave mesons. These Born-Oppenheimer selection rules are consistent with the partial decay widths of the lowest charmonium hybrid with exotic quantum numbers JPC=1−+ recently calculated using lattice QCD. Published by the American Physical Society 2024

Double-gluon charmonium hybrid states with various exotic quantum numbers

We study the double-gluon charmonium hybrid states with various quantum numbers, each of which is composed of one valence charm quark and one valence charm antiquark as well as two valence gluons. We concentrate on the exotic quantum numbers JPC=0−−/0+−/1−+/2+−/3−+ that the conventional q¯q mesons cannot reach. We apply the QCD sum rule method to calculate their masses to be 7.28−0.43+0.38, 5.19−0.46+0.36, 5.46−0.62+0.41, 4.48−0.31+0.25, and 5.54−0.43+0.35 GeV, respectively. We study their possible decay patterns and propose to search for the JPC=2+−/3−+ states in the D*D¯(*)/Ds*D¯s(*)/Σc*Σ¯c(*)/Ξc*Ξ¯c(′,*) channels. Experimental investigations on these states and decay channels can be useful in classifying the nature of the hybrid state, thus serving as a direct test of QCD in the low energy sector. Published by the American Physical Society 2024

Search for Hybrid Mesons at GlueX

Recent lattice QCD calculations predict a multiplet of hybrid mesons, which are mesons with gluonic degrees of freedom. By mapping out the hybrid meson spectrum, we can gain insight into how the gluon contributes to the properties of bound states in QCD. The π1(1600) is a candidate for the lightest hybrid meson. This state has exotic quantum numbers of JPC = 1−+, which are forbidden for conventional mesons. The GlueX experiment has collected high statistics photoproduction data, which we are using to search for the π1(1600). These proceedings will summarize the search strategy for the π1(1600) at GlueX, including the most recent results in the ωππ, ηπ, and η′π final states.

Light double-gluon hybrid states with the exotic quantum numbers JPC=1−+ and 3−+

We apply the QCD sum rule method to study the double-gluon hybrid states with the quark-gluon contents $\bar q q gg$ ($q=u/d$) and $\bar s s gg$. We construct twenty-eight double-gluon hybrid currents, eleven of which are found to be zero due to some internal symmetries between the two gluons fields. We concentrate on the non-vanishing currents with the exotic quantum numbers $J^{PC} = 1^{-+}$ and $3^{-+}$. Their masses are calculated to be $M_{|\bar q q gg;1^{-+}\rangle} = 4.35^{+0.26}_{-0.30}$ GeV, $M_{|\bar s s gg;1^{-+}\rangle} = 4.49^{+0.25}_{-0.30}$ GeV, $M_{|\bar q q gg;3^{-+}\rangle} = 3.02^{+0.24}_{-0.31}$ GeV, and $M_{|\bar s s gg;3^{-+}\rangle} = 3.16^{+0.22}_{-0.28}$ GeV. The decay behaviors of the $J^{PC} = 3^{-+}$ states are studied, and we propose to search for them in the $\pi a_1(1260)/\rho \omega/\phi \phi$ channels in future particle experiments.

Light double-gluon hybrid states from QCD sum rules

We study the double-gluon hybrid states with the quark-gluon contents $\bar q q gg$ ($q=u/d$) and $\bar s s gg$. We construct twelve double-gluon hybrid currents with various quantum numbers, five of which are found to be zero due to some internal symmetries between the two gluon fields. We use the rest seven currents to perform QCD sum rule analyses. Especially, the masses of the double-gluon hybrid states with the exotic quantum number $J^{PC} = 2^{+-}$ are calculated to be $M_{|\bar q q gg;2^{+-}\rangle} = 2.26^{+0.20}_{-0.25}$ GeV and $M_{|\bar s s gg;2^{+-}\rangle} = 2.38^{+0.19}_{-0.25}$ GeV. Their two- and three-meson decay patterns are also investigated.

Highly excited and exotic fully-strange tetraquark states

Some hadrons have the exotic quantum numbers that the traditional bar{q} q mesons and qqq baryons can not reach, such as J^{PC} = 0^{--}/0^{+-}/1^{-+}/2^{+-}/3^{-+}/4^{+-}, etc. We investigate for the first time the exotic quantum number J^{PC}=4^{+-}, and study the fully-strange tetraquark states with such an exotic quantum number. We systematically construct all the diquark–antidiquark interpolating currents, and apply the method of QCD sum rules to calculate both the diagonal and off-diagonal correlation functions. The obtained results are used to construct three mixing currents that are nearly non-correlated, and we use one of them to extract the mass of the lowest-lying state to be 2.85^{+0.19}_{-0.22} GeV. We apply the Fierz rearrangement to transform this mixing current to be the combination of three meson–meson currents, and the obtained Fierz identity suggests that this state dominantly decays into the P-wave phi (1020) f_2^prime (1525) channel. This fully-strange tetraquark state of J^{PC}=4^{+-} is a purely exotic hadron to be potentially observed in future particle experiments.

Trigluon Glueballs in QCD Sum Rules

Trigluon glueball might be a gateway to the gluonic meson realm. Here, we briefly report some of our results on this possibility. It was found that the exotic quantum number gluonic states, the oddballs, indeed deserve to pay more attention to, and hopefully the long-searched-for glueball could then be detected.

Partial wave analysis of J/ψ→γηη′

Based on a sample of (10.09$\pm$0.04)$\times$10$^{9}$ $J/\psi$ events collected with the BESIII detector operating at the BEPCII storage ring, a partial wave analysis of the decay $J/\psi \rightarrow \gamma\eta\eta'$ is performed. An isoscalar state with exotic quantum numbers $J^{PC}=1^{-+}$, denoted as $\eta_1(1855)$, has been observed for the first time with statistical significance larger than 19$\sigma$. Its mass and width are measured to be (1855$\pm$9$_{-1}^{+6}$)~MeV/$c^{2}$ and (188$\pm$18$_{-8}^{+3}$)~MeV, respectively. The product branching fraction ${\cal B}(J/\psi$$\rightarrow$$ \gamma\eta_1(1855)$$\rightarrow$$\gamma\eta\eta')$ is measured to be (2.70$\pm 0.41 _{-0.35}^{+0.16}) \times$10$^{-6}$. The first uncertainties are statistical and the second are systematic. In addition, an upper limit on the branching ratio ${\cal B}(f_0(1710)$$\rightarrow$$\eta\eta')$/${\cal B}(f_0(1710)$$\rightarrow$$\pi\pi)$ is determined to be $1.61 \times 10^{-3}$ at 90\% confidence level, which lends support to the hypothesis that the $f_0(1710)$ has a large glueball component.

Observation of an Isoscalar Resonance with Exotic J^{PC}=1^{-+} Quantum Numbers in J/ψ→γηη^{'}.

Using a sample of (10.09±0.04)×10^{9} J/ψ events collected with the BESIII detector operating at the BEPCII storage ring, a partial wave analysis of the decay J/ψ→γηη^{'} is performed. The first observation of an isoscalar state with exotic quantum numbers J^{PC}=1^{-+}, denoted as η_{1}(1855), is reported in the process J/ψ→γη_{1}(1855) with η_{1}(1855)→ηη^{'}. Its mass and width are measured to be (1855±9_{-1}^{+6}) MeV/c^{2} and (188±18_{-8}^{+3}) MeV, respectively, where the first uncertainties are statistical and the second are systematic, and its statistical significance is estimated to be larger than 19σ.

New fermions in the light of the (g − 2)μ

The very precise measurement of the anomalous magnetic moment of the muon, recently released by the Muon g-2 experiment at Fermilab, can serve to set stringent constraints on new particles. If the observed 4σ discrepancy from the Standard Model value is indeed real, it will set a tight margin on the scale of the masses and couplings of these particles. Instead, if the discrepancy is simply a result of additional theoretical and experimental uncertainties to be included, strong constraints can be put on their parameters. In this mini-review, we summarize the impact of the latest muon g-2 measurement on new fermions that are predicted by a wide range of new physics models and with exotic quantum numbers and interactions. We will particularly discuss the case of vector-like leptons, excited leptons, and supersymmetric fermions, as well as spin-3/2 isosinglet fermions, which have been advocated recently.

Possible structure of the newly found exotic state η1(1855)

Recently, a hadronic state named $\eta_1(1855)$, about 1.86 GeV, was observed in the BESIII experiment. This finding has a peculiar interest due to its exotic quantum number $J^{PC}=1^{-+}$. In this paper, we examine the tetraquark interpretation for the structure of $\eta_1(1855)$ in the configurations of $[1_c]_{\bar{s}s}\otimes[1_c]_{\bar{q}q}$ and $[1_c]_{\bar{s}q}\otimes[1_c]_{\bar{s}q}$, and perform a mass spectrum calculation in the framework of QCD sum rules. The results show that the observed $\eta_1(1855)$ could be embedded into the $[1_c]_{\bar{s}s}\otimes[1_c]_{\bar{q}q}$ configuration. The possible tetraquark and hybrid decay modes are analyzed, which are critical in decoding its inner structure. In the same way, we evaluate as well the $\bar{s}s\bar{s}s$ molecular state with $1^{-+}$ quantum number and find that there might exist two such ground states.

S - and P -wave fully strange tetraquark states from QCD sum rules

We apply the QCD sum rule method to systematically study the $S$- and $P$-wave fully-strange tetraquark states within the diquark-antidiquark picture. We systematically construct their interpolating currents by explicitly adding the covariant derivative operator. Our results suggest that the $f_0(2100)$, $X(2063)$, and $f_2(2010)$ may be explained as the $S$-wave $s s \bar s \bar s$ tetraquark states with the quantum numbers $J^{PC} = 0^{++}$, $1^{+-}$, and $2^{++}$, respectively. Our results also suggest that both the $X(2370)$ and $X(2500)$ may be explained as the $P$-wave $s s \bar s \bar s$ tetraquark states of $J^{PC} = 0^{-+}$, and both the $\phi(2170)$ and $X(2400)$ may be explained as the $P$-wave $s s \bar s \bar s$ tetraquark states of $J^{PC} = 1^{--}$. The masses of the $s s \bar s \bar s$ tetraquark states with the exotic quantum number $J^{PC} = 1^{-+}$ are extracted from two non-correlated currents to be $2.45^{+0.20}_{-0.25}$ GeV and $2.49^{+0.21}_{-0.25}$ GeV.

Masses of vector and pseudovector hybrid mesons in a chiral symmetric model

We enlarge the chiral model, the so-called extended Linear Sigma Model (eLSM), by including the low-lying hybrid nonet with exotic quantum numbers J^{PC}=1^{-+}JPC=1−+ and the nonet of their chiral partners with J^{PC}=1^{+-}JPC=1+− to a global U(3)_r \times U(3)_lU(3)r×U(3)l chiral symmetry. We use the assignment of the \pi_1^{hyb}= \pi_1(1600)π1hyb=π1(1600) as input to determine the unknown parameters. Then, we compute the lightest vector and pseudovector hybrid masses that could guide ongoing and upcoming experiments in searching for hybrids.

QCD Axial Anomaly Enhances the ηη′ Decay of the Hybrid Candidate η 1(1855)

We study the hybrid mesons with the exotic quantum number I G J PC = 0+1−+ and investigate their decays into the η η′, a 1(1260) π, f 1(1285) η, f 1(1420) η, , , and channels. It is found that the QCD axial anomaly enhances the decay width of the η η′ channel although this mode is strongly suppressed by the small p-wave phase space. Our results support the interpretation of the η 1(1855) recently observed by BESIII as the hybrid meson of I G J PC = 0+1−+. The QCD axial anomaly ensures the η η′ decay mode to be a characteristic signal of the hybrid nature of the η 1(1855).

New hadron configuration: The double-gluon hybrid state

This is the first study on the double-gluon hybrid, which consists of one valence quark and one valence antiquark together with two valence gluons. We concentrate on the one with the exotic quantum number $J^{PC} = 2^{+-}$ that conventional $\bar q q$ mesons can not reach. We apply QCD sum rule method to evaluate its mass to be $2.26^{+0.20}_{-0.25}$ GeV, and study its possible decay patterns. Especially, its three-meson decay patterns are generally not suppressed severely compared to two-meson decay patterns, so the $S$-wave three-meson decay channels $f_1\omega\pi/f_1\rho\pi$ can be useful in identifying its nature, which is of particular importance to the direct test of QCD in the low energy sector.