QCD Sum Rules Research Articles

B c meson and its scalar cousin with QCD sum rules* *Supported by the National Natural Science Foundation, China (12175068)

In this study, we use the optical theorem to calculate the next-to-leading order corrections to the QCD spectral densities directly in the QCD sum rules for the pseudoscalar and scalar B c mesons. We use experimental data for guidance to perform an updated analysis. We obtain the masses and, in particular, decay constants, which are the fundamental input parameters in high energy physics. Ultimately, we obtain the pure leptonic decay widths, which can be compared with experimental data in the future.

QCD sum rules for positive and negative parity heavy baryons at next-to-leading order in αs -expansion

QCD sum rules for positive and negative parity heavy baryons in the heavy quark limit are formulated. We apply the method to Λ and Σ channels. We include the next-to-leading order corrections in αs-expansion to dimension 0 and 3 terms in the operator product expansion. The corrections lead to the considerable reduction of the predicted masses and significantly improves the stability with respect to the Borel parameter, especially for negative parity states. It is also found that, in the heavy quark limit, chiral odd condensates do not contribute to the negative parity states. Published by the American Physical Society 2024

Hyperon semileptonic decays in QCD sum rules

We investigate the hyperon semileptonic decays within the framework of QCD sum rules. The flavor SU(3) symmetry breaking effects are analyzed via the relevant form factors and corresponding branching fractions. Employing the z-series parameterization to capture the q2 dependence of form factors, we calculate the hyperon semileptonic decay rates and confront them with the recent experimental measurements. Moreover, we calculate as well the non-standard tensor form factors, which involve certain new physics beyond the standard model.

Properties of the ground and excited states of triply heavy spin-1/2 baryons

We study the triply heavy spin-1/2 baryons with quark contents ccb and bbc, and calculate their mass and residue using QCD sum rules. In the calculations, we consider the ground (1 S), first orbitally excited (1P) and first radially excited (2 S) states. Aiming to achieve higher accuracies in the results, we perform the computations by taking into account the non-perturbative operators up to eight mass dimensions. We compare our results with the predictions of other theoretical studies existing in the literature. The obtained results may help experimental groups in their search for these yet unseen, but previously predicted by the quark model, interesting particles.

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

Strong decays of the vector tetraquark states with the masses about 4.5 GeV via the QCD sum rules

We suppose that there exist three vector hidden-charm tetraquark states with the JPC=1−− at the energy about 4.5GeV, and investigate the two-body strong decays systematically. We obtain thirty QCD sum rules for the hadronic coupling constants based on rigorous quark-hadron duality, then obtain the partial decay widths, therefore the total widths approximately, which are compatible with the experimental data of the Y(4500) from the BESIII collaboration. The Y(4500) may be one vector tetraquark state having three main Fock components, or consists of three different vector tetraquark states. We can search for the typical decays Y→D¯10D0−D¯0D102, D¯1−D+−D¯−D1+2, D¯00D⁎0−D¯⁎0D002, D¯0−D⁎+−D¯⁎−D0+2, ηcω, J/ψω to diagnose the nature of the Y(4500).

0– – hidden-heavy tetraquark states via QCD sum rules* *Supported in part by the National Natural Science Foundation of China(12247113), the Project funded by China Postdoctoral Science Foundation (2022M723117), and the Specific Fund of Fundamental Scientific Research Operating Expenses for Undergraduate Universities in Liaoning Province, China (2024)

In this study, we evaluated the mass spectra of the prospective hidden-charm and hidden-bottom tetraquark states in molecular configuration via QCD sum rules. In our calculation, the nonperturbative condensate contributions are considered up to dimension eight in operator product expansion. It is found that there could exist 4 possible hidden-charm tetraquark states with masses , , , and GeV. Their corresponding hidden-bottom partners are found lying at , , , and GeV, respectively. The possible tetraquark decay modes were analyzed, which are expected to be measured in BESIII, BELLEII, and LHCb experiments.

Doubly charmed pentaquark states in QCD sum rules

We have studied the mass spectra of doubly charmed pentaquark states in the Λc(*)D(*) and Σc(*)D(*) channels with JP=1/2±, 3/2±, and 5/2± within the framework of quantum chromodynamics sum rules. We use the parity projected sum rules to separate the contributions of negative and positive parities from the two-point correlations induced by the pentaquark interpolating currents. Our results show that the bound states of Pcc pentaquarks may exist in the ΛcD(12−), ΣcD(12−), ΣcD*(32−), Λc*D(32−), Λc*D*(52−) channels with negative-parity and ΣcD(12+), ΣcD*(32+), Σc*D(32+) channels with positive-parity, since their masses are predicted to be lower than the corresponding meson-baryon thresholds. However, they are still allowed to decay into the Ξcc(*)π final states via strong interaction. The triply charged Pcc+++(ccuud¯) and neutral Pcc0(ccddu¯) in the isospin quartet would definitely be pentaquark states due to their exotic charges. We suggest searching for these characteristic doubly charmed pentaquark signals in the Pcc+++→Ξcc(*)++π+/ρ+, Σc(*)++D(*)+ and Pcc0→Ξcc(*)+π−/ρ−, Σc(*)0D(*)0 decays in the near future. 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].

Interpretation of X(3960) as the hidden charm-strange tetraquark states via QCD sum rules

Recently, a hadronic state, named X(3960), about 3.96 GeV with JPC=0++ was observed in LHCb experiment. From its the decay modes, it's reasonable to categorize this structure to novel hadronic state. In this paper, we examine the tetraquark interpretation for the structure of X(3960) in the configurations of [3c]cs⊗[3¯c]c¯s¯, and the QCD sum rules calculations of the mass spectrum are performing. Numerical results indicted that the observed X(3900) could be embedded into the [3c]cs⊗[3¯c]c¯s¯ configuration. Various X(3960) decay modes are evaluated, which are critical for pinning down its configuration and left for experimental verification. In the same way, we evaluate as well the c¯qc¯q, b¯sb¯s, and b¯qb¯q tetraquark state with 0++ quantum number in the configuration of [3c]cs⊗[3¯c]c¯s¯ and find that there might exist six such ground states.

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

Investigation of Λ(1405)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda (1405)$$\\end{document} as a molecular pentaquark state

Λ(1405)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda (1405)$$\\end{document} is one of the interesting particles with its unclear structure and distinct properties. It has a light mass compared to its non-strange counterpart, despite the strange quark it carries. This situation puts the investigation of this resonance among the hot topics in hadron physics and collects attention to clarify its properties. In this study, we focus on the calculation of the mass and residue of the Λ(1405)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda (1405)$$\\end{document} resonance within the framework of QCD sum rules. We assign a structure in the form of a molecular pentaquark composed from admixture of K-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K^-$$\\end{document} meson-proton and K¯0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\bar{K}^0$$\\end{document} meson-neutron. Using an interpolating current in this form, the masses and the current coupling constant are attained as m=1406±128MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m=1406\\pm 128~\ ext {MeV}$$\\end{document} and λ=(3.35±0.35)×10-5GeV6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda =(3.35\\pm 0.35)\ imes 10^{-5}~\ ext {GeV}^6$$\\end{document} for and m=1402±141MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m=1402\\pm 141~\ ext {MeV}$$\\end{document} and λ=(4.08±1.08)×10-5GeV6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda =(4.08\\pm 1.08)\ imes 10^{-5}~\ ext {GeV}^6$$\\end{document} for I Lorentz structures entering the calculations, respectively. The obtained mass values agree well with the experimental data supporting the plausibility of the considered structure.

Analysis of the vector hidden-charm-hidden-strange tetraquark states with implicit P-waves via the QCD sum rules

We take the scalar, pseudoscalar, axialvector, vector and tensor diquarks as the basic building blocks to construct the four-quark currents with implicit P-waves, and investigate the hidden-charm-hidden-strange tetraquark states with the JPC=1−− and 1−+ via the QCD sum rules in a comprehensive and consistent way, and revisit the assignments of the X/Y states, especially the Y(4500), X(4630), Y(4660), Y(4710) and Y(4790), in the tetraquark picture.

ρ-meson longitudinal leading-twist distribution amplitude revisited and the D→ρ semileptonic decay* *Supported in part by the National Natural Science Foundation of China (12265009, 12265010, 12147102), the Project of Guizhou Provincial Department of Science and Technology (ZK[2021]024, ZK[2023]142), the Project of Guizhou Provincial Department of Education (KY[2021]030) and the Chongqing Graduate Research and Innovation Foundation (ydstd1912)

Motivated by our previous study [Phys. Rev. D 104(1), 016021 (2021)] on the pionic leading-twist distribution amplitude (DA), we revisit the ρ-meson leading-twist longitudinal DA in this study. A model proposed by Chang based on the Dyson-Schwinger equations is adopted to describe the behavior of . However, the ξ-moments of are calculated with the QCD sum rules in the framework of the background field theory. The sum rule formulas for these moments are improved. More accurate values for the first five nonzero ξ-moments at the typical scale are given, e.g., at , , , , , and . By fitting these values with the least squares method, the DSE model for is determined. By taking the left-handed current light-cone sum rule approach, we obtain the transition form factor in the large recoil region, i.e., , , and , and the ratio , . After extrapolating with a rapidly converging series based on -expansion, we present the -independent decay width for the semileptonic decays . Finally, the branching fractions are , , , and .

Reanalysis of rare radiative Ξb−→Ξ−γ decay in QCD

The upper limit of the branching ratio of the rare Ξb−→Ξ−γ decay is obtained as BR(Ξb−→Ξ−γ)<1.3×10−4 by the LHCb. In the present work we study this decay within the light cone QCD sum rules employing the Ξb distribution amplitudes. At the first stage, the form factors entering the Ξb−→Ξ−γ decay are obtained. Next, using the results for the form factors the corresponding branching ratio for this decay is estimated to be BR(Ξb−→Ξ−γ)=(4.8±1.3)×10−5. This value lies below the upper limit established by the LHCb collaboration. Our finding for the branching ratio is also compared with the results of the other theoretical approaches existing in the literature. Published by the American Physical Society 2024

Decay process within the QCDSR approach* *Supported in part by the National Natural Science Foundation of China (12265010, 12265009) and the Project of Guizhou Provincial Department of Science and Technology (ZK[2021]024, ZK[2023]142)

In this paper, we investigate the charmed meson rare decay process using an approach based on QCD sum rules. First, the pion twist-2, 3 distribution amplitude (DA) moments and are calculated up to the tenth and fourth orders, respectively, in the QCD sum rules according to the background field theory. After constructing the light-cone harmonic oscillator model for the pion twist-2, 3 DAs, we obtain their behaviors by matching the calculated ξ-moments. Then, the transition form factors (TFFs) are calculated using an approach based on QCD light-cone sum rules. The vector form factor at the large recoil region is . Using the rapidly converging simplified series expansion of , we present the TFFs and corresponding angular coefficients in the whole squared momentum transfer physical region. Based on non-standard neutrino interactions, the decay can be related to the decay indirectly. Thus, we first describe the semileptonic decay process , differential decay widths, and branching fraction with . The differential/total predictions for forward-backward asymmetry, -differential flat terms, and lepton polarization asymmetry are also reported. The prediction for the branching fraction is .

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.

QCD sum rule study of J P = 1± exotic states with two heavy quarks in the molecular picture

In this study, the spectroscopic parameters of exotic molecular states composed of mesons containing two heavy quarks (scalar - axial and pseudoscalar - axial meson combinations) are investigated within the QCD sum rules. Our findings reveal that molecular states containing charm quarks do not form bound states, whereas states with b-quarks can form exotic molecular states. This observation has significant implications for understanding the structure of these exotic states.

Properties of doubly heavy spin- 12 baryons: The ground and excited states

We determine the masses and residues of the ground and excited spin-12 baryons consist of two heavy b or c quark utilizing the QCD sum rule formalism. In the calculations, we consider the nonperturbative operators up to ten mass dimensions in order to increase the accuracy compared to the previous calculations. We report the obtained results for both the symmetric and antisymmetric currents defining the doubly heavy baryons of the ground state (1S), first orbitally excited state (1P), and first radially excited state (2S). We compare our results with the predictions of other nonperturbative approaches as well as existing experimental data which is available only for the ground state of Ξcc channel. These predictions can help the experimental groups in their searches for all members of the doubly heavy baryons in their ground and exited states. Published by the American Physical Society 2024

Investigation of Light Baryons in Hot QCD

We investigate the behavior of light baryons in hot QCD. To this aim, we evaluate the light baryons mass and residue in hot medium using the thermal correlation function with two-point by means of the thermal QCD sum rule. In sum rule calculations, we consider the additional thermal condensates appearing in Wilson expansion at T≠0. We determine the thermal continuum threshold using obtained sum rules expressions to analyze numerically. We observe that the masses and residues of light baryons stay approximately the same until the temperature reaches a certain value and then they fall with the temperature increase. We see that vacuum values of parameters in our calculations are in good consistency with other studies in the literature. Also, we define the fit functions that show how the spectroscopic parameters for light baryons behave at T≠0.