QCD Sum Rule Method Research Articles

Mass spectra of strange double charm pentaquarks with strangeness S=−1

The observation of the Tcs¯(2900) indicates the potential existence of strange double charm pentaquarks based on the heavy antidiquark symmetry. We systematically study the mass spectra of strange double charm pentaquarks with strangeness S=−1 in both molecular and compact structures for quantum numbers JP=1/2−, 3/2−, 5/2−. By constructing the interpolating currents, the mass spectra can be extracted from the two-point correlation functions in the framework of QCD sum rule method. In the molecular picture, we find that the Ξc′+D*+, Ξc*+D*+, Ξcc*++K¯*0, and Ωcc*+ρ+ may form molecular strange double charm pentaquarks. In both pictures, the masses of the JP=1/2−,3/2− pentaquarks locate within the 4.2–4.6 GeV and 4.2–4.5 GeV regions, respectively. As all of them are above the thresholds of their strong decay channels, they behave as a broad state, making them challenging to be detected experimentally. On the other hand, the strange double charm pentaquark with JP=5/2− lies below its strong decay channel, which may be a very narrow state and easy to identify experimentally. The best observed channel is its semileptonic decay to double charm baryon. As the result, we strongly suggest experiments to search for JP=5/2− strange double charm pentaquarks first. Published by the American Physical Society 2024

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

Parameters of the tensor tetraquark [formula omitted]

The mass and width of the tensor tetraquark T=bbc‾c‾ with spin-parity JP=2+ are calculated in the context of the QCD sum rule method. The tetraquark T is modeled as a diquark-antidiquark state built of components bTCγμb and c‾γνCc‾T with C being the charge conjugation matrix. The mass m=(12.795±0.095)GeV of the exotic tensor meson T is found by means of the two-point sum rule approach. Its full width Γ is evaluated by considering processes T→Bc−Bc−, Bc−Bc⁎−, and Bc⁎−Bc⁎−. Partial widths of these decays are computed by means of the three-point sum rule approach which is used to determine the strong couplings at relevant tetraquark-meson-meson vertices. Predictions obtained for the width ΓT=55.5−9.9+10.6MeV, as well as the mass of the tetraquark T can be useful in investigations of fully heavy four-quark mesons.

Semileptonic Ωb→Ωcℓν¯ℓ transition in full QCD

We investigate the semileptonic decay of Ωb→Ωcℓν¯ℓ in three lepton channels. To this end, we use the QCD sum rule method in three point framework to calculate the form factors defining the matrix elements of these transitions. Having calculated the form factors as building blocks, we calculate the decay widths and branching fractions of the exclusive decays in all lepton channels and compare the results with other theoretical predictions. The obtained results for branching ratios and ratio of branching fractions at different leptonic channels may help experimental groups in their search for these weak decays. Comparison of the obtained results with possible future experimental data can be useful to check the order of consistency between the standard model theory predictions and data on the heavy baryon decays. Published by the American Physical Society 2024

Electromagnetic properties of vector doubly charmed tetraquark states

We conduct a systematic study of the electromagnetic properties of multiquark systems with undetermined internal structures. Motivated by the recent observation of the Tcc+ state, we apply the light-cone version of the QCD sum rule method to extract the magnetic dipole moments of several possible doubly charmed vector tetraquark states. When analyzing the magnetic dipole moment of these states, they are modeled to have the diquark-antidiquark configurations. The magnetic dipole moments for the members are extracted as μTccu¯d¯=1.17−0.32+0.44μN, μTccu¯s¯=1.35−0.37+0.50μN, μTccd¯s¯=−2.69−0.75+1.02μN, μTccu¯u¯=1.33−0.40+0.56μN, μTccd¯d¯=1.41−0.43+0.57μN, and μTccs¯s¯=1.44−0.41+0.53μN. Comparing the results obtained for the magnetic dipole moments of the Tccu¯d¯ state with the Tccu¯s¯ state, the U symmetry is seen to be broken at about 15%, while, for the Tccd¯d¯ and Tccs¯s¯ states, this symmetry is minimally broken. The obtained results may be useful to determine the true nature of these new interesting states. Published by the American Physical Society 2024

Further prediction on the possible double-peak structure of the X17 particle

The [Formula: see text] particle, discovered by [A. J. Krasznahorkay et al., Phys. Rev. Lett. 116, 042501 (2016), doi:10.1103/PhysRevLett.116.042501] at ATOMKI, was recently confirmed in the [Formula: see text] invariant mass spectra by [K. U. Abraamyan, C. Austin, M. I. Baznat, K. K. Gudima, M. A. Kozhin, S. G. Reznikov and A. S. Sorin, arXiv:2311.18632] at JINR. We notice with surprise and interest that the [Formula: see text] seems to have a double-peak structure. This is in a possible coincidence with our QCD sum rule study of [H.-X. Chen, arXiv:2006.01018], where we interpreted the [Formula: see text] as a tetraquark state composed of four bare quarks ([Formula: see text]), and claimed that “A unique feature of this tetraquark assignment is that we predict two almost degenerate states with significantly different widths”. These two different tetraquark states are described by two different chiral tetraquark currents [Formula: see text] and [Formula: see text]. To verify whether the tetraquark assignment is correct or not, we replace the up and down quarks by the strange quarks, and apply the QCD sum rule method to study the other four chiral tetraquark currents [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. We calculate their correlation functions, and find that non-perturbative QCD effects do not contribute much to them. Our results suggest that there may exist four almost degenerate tetraquark states with masses about [Formula: see text] MeV. Each of these states is composed of four bare quarks, either [Formula: see text] or [Formula: see text].

Investigations of Λ states with spin-parity 32±

The present study provides spectroscopic investigations of spin-32 Λ baryons with both positive and negative parities. The analysis mainly focuses on three states, namely 1P, 2P, and 2S, and corresponding masses are calculated using the QCD sum rule method. To implement the method, we apply two types of interpolating currents with octet and singlet quantum numbers and compare the corresponding results with the reported masses of experimentally observed states. From the comparisons, it is extracted that the results of interpolating current with octet quantum numbers are in good agreement with the experimentally measured masses. The masses obtained with this interpolating current are m=1513.64±8.76 MeV for 1P state with JP=32−, m′=1687.91±0.31 MeV for 2P state with JP=32− and m˜=1882.37±11.95 MeV for 2S state with JP=32+ and they are consistent with the experimental masses of Λ(1520), Λ(1690), and Λ(1890), respectively, which confirm their spin-parity quantum numbers. Besides, we calculate the corresponding current coupling constants, which are utilized as inputs in the calculations of different form factors defining the widths of the states under study. Published by the American Physical Society 2024

Heavy axial-vector structures [formula omitted

The fully heavy axial-vector diquark-antidiquark structures bbc‾c‾ are explored by means of the QCD sum rule method. They are modeled as four-quark mesons T1 and T2 composed of bTCσμνγ5b, c‾γνCc‾T and bTCγμγ5b, c‾Cc‾T diquarks, respectively. The spectroscopic parameters of the tetraquarks T1 and T2 are determined in the context of the QCD two-point sum rule method. Results obtained for masses of these states m1=(12715±86)MeV and m2=(13383±92)MeV are used to fix their strong decay channels. The full width Γ(T1) of the diquark-antidiquark state T1 is estimated by considering the processes T1→Bc−Bc⁎− and T1→Bc⁎−Bc⁎−. The decays to mesons Bc−Bc⁎−, Bc−(2S)Bc⁎− and Bc⁎−Bc⁎− are employed to evaluate Γ(T2). Results obtained for the widths Γ(T1)=(44.3±8.8)MeV and Γ(T2)=(82.5±13.7)MeV of these tetraquarks in conjunction with their masses are useful for future experimental studies of fully heavy resonances.

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

Nucleon Resonance Masses from QCD Sum Rules

We calculate the masses of the nucleon resonances [N+(1440), N-(1535), N- (1650), N+(1710), N+(1880), N-(1895), N+(2100)] using an adaptation of the method of finite energy QCD sum rules (FESR) introduced recently in the determination of the masses of the vector meson resonances. This variation of finite energy sum rules involves as usual integration over a closed contour consisting of a circle of a large radius R and a cut in the complex energy (squared) plane. A specific integration kernel is used, however, which minimizes the integral over the cut. We obtain remarkably stable results over a wide range R, where R is the radius of the integration contour. The sum rule predictions agree well with the experimental values. We make use of the nucleonic correlator discussed in our previous FESR calculation of the nucleon mass.

Constraining inverse moment of B-meson distribution amplitude using Lattice QCD data

We constrain the inverse moment of the B-meson light-cone distribution amplitude (LCDA), λB in heavy quark effective theory, using form factor estimates from Lattice QCD collaboration. The estimation of the parameter λB has, until now, relied solely on QCD sum rule methods and deals with significant uncertainty. In this work, we express the form factors for the B→K channel, calculated within the light-cone sum rule (LCSR) approach, in terms of the B-meson LCDAs. By incorporating recent Lattice results from the HPQCD collaboration for the B→K form factors at zero momentum transfer (q2 = 0), we impose constraints on this parameter. Consequently, we achieve a twofold reduction in uncertainty compared to the QCD sum rule estimate, yielding λB=338±68 MeV, when the B-meson LCDAs are expressed in the Exponential model. Additionally, we compare the form factor predictions, using the constrained λB value, with the earlier analyses for other channels as well, such as B→π and B→D.

Fully charmed resonance X(6900) and its beauty counterpart

The fully heavy scalar tetraquarks T4Q=QQQ‾Q‾, (Q=c,b) are explored in the context of QCD sum rule method. We model T4Q as diquark-antidiquark systems composed of pseudoscalar constituents, and calculate their masses m(′) and couplings f(′) within the two-point sum rule approach. Our results m=(6928±50)MeV and m′=(18858±50)MeV for masses of the tetraquarks T4c and T4b prove that they can decay to hidden-flavor heavy mesons. The full width Γ4c of the T4c is evaluated by taking into account the decay channels T4c→J/ψJ/ψ, J/ψψ′, ηcηc, ηcηc(2S), ηcχc1(1P), and χc0χc0. The partial widths of these processes depend on strong couplings gi at vertices T4cJ/ψJ/ψ, T4cJ/ψψ′ etc., which are computed using the QCD three-point sum rule method. The decay T4b→ηbηb is used to find the width Γ4b of the T4b. The predictions for m and Γ4c=(128±22)MeV are compared with parameters of the fully charmed resonances reported by the LHCb, ATLAS, and CMS Collaborations. Based on this analysis, we interpret the tetraquark T4c as a candidate to the resonance X(6900). The mass m′ and width Γ4b=(94±28)MeV of the exotic meson T4b can be used in future experimental investigations of these states.

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.

QCD sum rule study on the fully strange tetraquark states of JPC = 2++

We apply the QCD sum rule method to systematically study the fully strange tetraquark states with the quantum number JPC = 2++. We construct both the diquark–antidiquark and mesonic–mesonic currents and calculate both their diagonal and off-diagonal correlation functions. Based on the obtained results, we further construct three mixing currents that are nearly non-correlated. We use one mixing current to extract the mass of the lowest-lying state to be 2.03−0.15+0.16 GeV, which can be used to explain f2(2010) as a fully strange tetraquark state of JPC = 2++. This state was observed by BESIII in the ϕϕ channel, and we propose to confirm it in the η(′)η(′) channel.

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.

Axial-vector and pseudoscalar tetraquarks [ud][{overline{c}}{overline{s}}

Spectroscopic parameters and widths of the fully open-flavor axial-vector and pseudoscalar tetraquarks X_{textrm{AV}} and X_{textrm{PS}} with content [ud][{overline{c}}{overline{s}}] are calculated by means of the QCD sum rule methods. Masses and current couplings of X_{textrm{AV}} and X_{textrm{PS}} are found using two-point sum rule computations performed by taking into account various vacuum condensates up to dimension 10. The full width of the axial-vector state X_{textrm{AV}} is evaluated by including into analysis S-wave decay modes X_{textrm{AV}}rightarrow D^{*}(2010)^{-}K^{+}, {overline{D}}^{*}(2007)^{0}K^{0}, D^{-}K^{*}(892)^{+}, and {overline{D}}^{0}K^{*}(892)^{0}. In the case of X_{textrm{PS}}, we consider S-wave decay X_{textrm{PS}}rightarrow {overline{D}} _{0}^{*}(2300)^{0}K^{0}, and P-wave processes X_{textrm{PS}}rightarrow D^{-}K^{*}(892)^{+} and X_{textrm{PS}}rightarrow {overline{D}} ^{0}K^{*}(892)^{0}. To determine partial widths of these decay modes, we employ the QCD light-cone sum rule method and soft-meson approximation, which are necessary to estimate strong couplings at tetraquark–meson–meson vertices X_{textrm{AV}}D^{-}D^{*}(2010)^{-}K^{+} , etc. Our predictions for the mass m_{textrm{AV}}=(2800 pm 75)~text {MeV} and width Gamma _{textrm{AV}}=(58 pm 10)~text {MeV} of the tetraquark X_{ textrm{AV}}, as well as results m_{textrm{PS}}=(3000 pm 60)~text {MeV} and Gamma _{textrm{PS}}=(65 pm 12)~text {MeV} for the same parameters of X_{textrm{PS}} may be useful in future experimental studies of multiquark hadrons.

D-wave excited tetraquark states with and * *Supported by the National Natural Science Foundation of China (12175318), the National Key R & D Program of China (2020YFA0406400), the Natural Science Foundation of Guangdong Province of China (2022A1515011922), and the Fundamental Research Funds for the Central Universities

We study the mass spectra of D-wave excited tetraquark states with and in both symmetric and antisymmetric color configurations using the QCD sum rule method. We construct the D-wave diquark-antidiquark type of tetraquark interpolating currents in various excitation structures with . Our results support the interpretation of the recently observed resonance as a D-wave tetraquark state with in the or excitation mode, although some other possible excitation structures cannot be excluded exhaustively within theoretical errors. Moreover, our results provide the mass relations and for the positive and negative -parity D-wave tetraquarks, respectively. We suggest searching for these possible D-wave tetraquarks in both the hidden-charm channels and , as well as open-charm channels such as and .

Isovector meson masses from QCD sum rules

We present a calculation of the masses of the isovector mesons (vector, scalar and pseudoscalar including the established recurrences) using a new method of finite energy QCD sum rules. The method is based on the idea of choosing a suitable integration kernel which minimizes the occurring integral over the cut in the complex energy (squared) plane. We obtain remarkably stable results in a wide range [Formula: see text], where [Formula: see text] is the radius of the integration contour. The sum rule predictions agree with the experimental values within the expected accuracy showing that QCD describes single resonances.

QCD sum rule analysis of heavy quarkonium states in magnetized matter: Effects of magnetic and inverse magnetic catalysis

In-medium masses of the $1S$ and $1P$ states of heavy quarkonia are investigated in the magnetized asymmetric nuclear medium, accounting for the Dirac sea effects, using a combined approach of chiral effective model and QCD sum rule method. Masses are calculated from the in-medium scalar and twist-2 gluon condensates, calculated within the chiral model. The gluon condensate is simulated through the scalar dilaton field, $\ensuremath{\chi}$ introduced in the model through a scale-invariance breaking logarithmic potential. Contribution of the Dirac sea is incorporated through the nucleonic tadpole diagrams. Treating the scalar fields as classical, the dilaton field, $\ensuremath{\chi}$, the isoscalar nonstrange $\ensuremath{\sigma}(\ensuremath{\sim}(⟨\overline{u}u⟩+⟨\overline{d}d⟩))$, strange $\ensuremath{\zeta}(\ensuremath{\sim}⟨\overline{s}s⟩)$ and isovector $\ensuremath{\delta}(\ensuremath{\sim}(⟨\overline{u}u⟩\ensuremath{-}⟨\overline{d}d⟩))$ fields, are obtained by solving their coupled equations of motion as derived from the chiral model Lagrangian. The effects of magnetic field are incorporated through the Dirac sea as well as the Landau energy levels of the protons, and the anomalous magnetic moments of the nucleons. The scalar fields modify appreciably with magnetic field due to the Dirac sea contribution. In-medium masses of the charmonium and bottomonium ground states are observed to have significant modifications with magnetic field due to the effects of (inverse) magnetic catalysis. In presence of an external magnetic field, there is mixing between the longitudinal component of the vector and the pseudoscalar mesons (PV mixing) in both quarkonia sectors, leading to a rise (drop) of the masses of $J/{\ensuremath{\psi}}^{||}({\ensuremath{\eta}}_{c})$ and ${\mathrm{\ensuremath{\Upsilon}}}^{||}(1S)({\ensuremath{\eta}}_{b})$ states. These might show in the experimental observables, e.g., the dilepton spectra in the noncentral, ultrarelativistic heavy ion collision experiments at RHIC and LHC, where the produced magnetic field is huge.