QCD Sum Rules Research Articles

Strong $$ B _{QQ'}^* B_{QQ'} V $$ vertices and the radiative decays of $$ B _{QQ}^* \rightarrow B_{QQ} \gamma $$ in the light-cone sum rules

The strong coupling constants of spin-3/2 to spin-1/2 doubly heavy baryon transitions with light vector mesons are estimated within the light-cone QCD sum rules method. Moreover, using the vector-meson dominance ans\"atz, the widths of radiative decays $B_{QQ}^* \to B_{QQ} \gamma$ are calculated. The results for the said decay widths are compared to the predictions of other approaches.

The magnetic moment of P_{c}(4312) as a bar{D}Sigma _{c} molecular state

In this paper, we tentatively assign the P_{c}(4312) to be a bar{D}Sigma _{c} molecular state with quantum number J^{P}=frac{1}{2}^{-}, and calculate its magnetic moment using the QCD sum rule method in external weak electromagnetic field. Starting with the two-point correlation function in external electromagnetic field and expanding it in power of the electromagnetic interaction Hamiltonian, we extract the magnetic moment from the linear response to the external electromagnetic field. The numerical value of the magnetic moment of P_{c}(4312) is mu _{P_{c}}=1.75^{+0.15}_{-0.11}.

Hadronic coupling constants of the lowest hidden-charm pentaquark state, using QCD sum rules with rigorous quark-hadron duality * *Supported by National Natural Science Foundation of China (11775079)

In this article, we illustrate how to calculate the hadronic coupling constants of the pentaquark states with QCD sum rules based on rigorous quark-hadron quality. We then study the hadronic coupling constants of the lowest diquark-diquark-antiquark type hidden-charm pentaquark state with spin-parity in detail, and calculate the partial decay widths. The total width is compatible with the experimental value from the LHCb collaboration, and favors assigning the to be the pentaquark state with . The hadronic coupling constants have the relation , and favor the hadronic dressing mechanism. The may have a diquark-diquark-antiquark type pentaquark core with the typical size of the -type baryon states. The strong couplings to the meson-baryon pairs lead to some pentaquark molecule components, and the may spend a rather large time as the molecular state.

Fully heavy pentaquark states

Developing the calculation techniques to fivefold heavy hadrons, we perform the study of novel fully-heavy $QQQQ\bar{Q}$ pentaquark states by the QCD sum rule approach that is firmly based on the QCD basic theory. Numerically, masses of fully-heavy pentaquark states are calculated to be $7.41^{+0.27}_{-0.31}~\mbox{GeV}$ for $cccc\bar{c}$ and $21.60^{+0.73}_{-0.22}~\mbox{GeV}$ for $bbbb\bar{b}$, respectively. In experiment, these predicted all-heavy pentaquark states could be searched for in the $\Omega_{QQQ}\eta_{Q}$ invariant mass spectrum.

Monte-Carlo based QCD sum rules analysis of X 0(2900) and X 1(2900)

Motivated by the very recent discovery of fully open-flavor exotic states X 0(2900) and X 1(2900) by the LHCb collaboration [], we study possible interpretations of these exotic states by QCD sum rules method. We have calculated mass and decay constant by traditional QCD sum rules analysis and Monte-Carlo based analysis. X 0(2900) and X 1(2900) are studied in molecular and diquark–antidiquark tetraquark pictures, respectively. Obtained mass results agree well with the masses observed in the experiment. We also made a Monte-Carlo based analysis within QCD sum rules for the mass and decay constant distributions to investigate the possible assignments for the structures of X 0(2900) and X 1(2900).

Analysis of the Pcs(4459) as the hidden-charm pentaquark state with QCD sum rules

In this paper, we study the scalar-diquark–scalar-diquark–antiquark-type [Formula: see text] pentaquark state with the QCD sum rules, the predicted mass [Formula: see text] is in excellent agreement with the experimental data [Formula: see text] from the LHCb collaboration, and supports assigning the [Formula: see text] to be the hidden-charm pentaquark state with the spin-parity [Formula: see text]. We take into account the flavor [Formula: see text] mass-breaking effect, and estimate the mass spectrum of the diquark–diquark–antiquark-type [Formula: see text] pentaquark states with the strangeness [Formula: see text].

Properties of the P c(4312) pentaquark and its bottom partner

We present an analysis of the newly observed pentaquark to shed light on its quantum numbers. To do that, the QCD sum rules approach is used. The measured mass of this particle is close to the threshold and has a small width, which supports the possibility of its being a molecular state. We consider an interpolating current in a molecular form and analyze both the positive and negative parity states with spin- . We also consider the bottom counterpart of the state with similar molecular form. Our mass result for the charm pentaquark state supports that the quantum numbers of the observed state are consistent with .

Analysis of the tetraquark and hexaquark molecular states with the QCD sum rules

In this article, we construct the color-singlet-color-singlet type currents and the color-singlet-color-singlet-color-singlet type currents to study the scalar , tetraquark molecular states and the vector , hexaquark molecular states with the QCD sum rules in details. In calculations, we choose the pertinent energy scales of the QCD spectral densities with the energy scale formula and for the tetraquark and hexaquark molecular states respectively in a consistent way. We obtain stable QCD sum rules for the scalar , tetraquark molecular states and the vector hexaquark molecular state, but cannot obtain stable QCD sum rules for the vector hexaquark molecular state. The connected (nonfactorizable) Feynman diagrams at the tree level (or the lowest order) and their induced diagrams via substituting the quark lines make positive contributions for the scalar tetraquark molecular state, but make negative or destructive contributions for the vector hexaquark molecular state. It is of no use or meaningless to distinguish the factorizable and nonfactorizable properties of the Feynman diagrams in the color space in the operator product expansion so as to interpret them in terms of the hadronic observables, we can only obtain information about the short-distance and long-distance contributions.

Scalar fully-heavy tetraquark states QQ^prime {bar{Q}} bar{Q^prime } in QCD sum rules

Very recently, the LHCb Collaboration observed distinct structures with the cc{bar{c}}{bar{c}} in the J/Psi -pair mass spectrum. In this work, we construct four scalar (J^{PC} = 0^{++}) [8_c]_{Qbar{Q^prime }}otimes [8_c]_{Q^prime {bar{Q}}} type currents to investigate the fully-heavy tetraquark state Q Q^prime {bar{Q}} bar{Q^prime } in the framework of QCD sum rules, where Q=c, b and Q^prime = c, b. Our results suggest that the broad structure around 6.2-6.8 GeV can be interpreted as the 0^{++} octet–octet tetraquark states with masses 6.44pm 0.11 GeV and 6.52pm 0.10 GeV, and the narrow structure around 6.9 GeV can be interpreted as the 0^{++} octet–octet tetraquark states with masses 6.87pm 0.11 GeV and 6.96pm 0.11 GeV, respectively. Extending to the b-quark sector,the masses of their fully-bottom partners are found to be around 18.38-18.59 GeV. Additionally, we also analyze the spectra of the [8_c]_{c{bar{c}}}otimes [8_c]_{b {bar{b}}} and [8_c]_{c{bar{b}}}otimes [8_c]_{b {bar{c}}} tetraquark states, which lie in the range of 12.51–12.74 GeV and 12.49–12.81 GeV, respectively.

Magnetic dipole moments of the hidden-charm pentaquark states: P_c(4440), P_c(4457) and P_{cs}(4459)

In this work, we employ the light-cone QCD sum rule to calculate the magnetic dipole moments of the P_c(4440), P_c(4457) and P_{cs}(4459) pentaquark states by considering them as the diquark–diquark–antiquark and molecular pictures with quantum numbers J^P = frac{3}{2}^-, J^P = frac{1}{2}^- and J^P = frac{1}{2}^-, respectively. In the analyses, we use the diquark–diquark–antiquark and molecular form of interpolating currents, and photon distribution amplitudes to obtain the magnetic dipole moment of pentaquark states. Theoretical examinations on magnetic dipole moments of the hidden-charm pentaquark states, are essential as their results can help us better figure out their substructure and the dynamics of the QCD as the theory of the strong interaction. As a by product, we extract the electric quadrupole and magnetic octupole moments of the P_c(4440) pentaquark. These values show a non-spherical charge distribution.

Strong vertices of doubly heavy spin- 3/2 –spin- 1/2 baryons with light mesons in light-cone QCD sum rules

In this paper, we analyze the doubly heavy spin-3/2--spin-1/2 baryons and light meson vertices within the method of light-cone QCD sum rules. These vertices are parametrized in terms of one (three) coupling constant(s) for the pseudoscalar (vector) mesons. The said coupling constants are calculated for all possible transitions. The results presented here can serve to be useful information in experimental as well as theoretical studies of the properties of doubly heavy baryons.

Open-charm tetraquark candidate: Note on X0(2900)

Motivated by the LHCb's very recent observation of exotic $X_{0}(2900)$ in the $B^{+}\rightarrow D^{+}D^{-}K^{+}$ process, for which could be a good open charm $ud\bar{c}\bar{s}$ tetraquark candidate, we endeavor to investigate its possibility by means of QCD sum rules. In technique, four configurations of interpolating currents with $J^{P}=0^{+}$ are studied for the $ud\bar{c}\bar{s}$ tetraquark state. In the end, mass values are calculated to be $2.76^{+0.16}_{-0.23}~\mbox{GeV}$ for the axial vector diquark-axial vector antidiquark configuration and $2.75^{+0.15}_{-0.24}~\mbox{GeV}$ for the scalar diquark-scalar antidiquark configuration, both of which are consistent with the experimental data $2.866\pm0.007\pm0.002~\mbox{GeV}$ of $X_{0}(2900)$ in view of the uncertainty. These results support that $X_{0}(2900)$ could be a $0^{+}$ tetraquark state with open charm flavor.

Light tetraquark states with the exotic quantum number JPC=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 $\rho\phi/\omega\phi$ channel but not into the $\rho f_2(1525)/\omega f_2(1525)/\phi f_2(1270)$ 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.

Gravitational formfactors of the ρ , π , and K mesons in the light-cone QCD sum rules

Taking into account only the quark part of the energy-momentum tensor, the gravitational form-factors of the $ \pi $ and $ K $ mesons are calculated within the light-cone sum rules method using the distribution amplitudes of these pseudoscalar mesons. The $ Q^2 $-dependence of the relevant form-factors are obtained. Moreover, the mean square mass radii of $ \pi $ and $ K $ mesons are calculated and we find that $ \sqrt{\langle r_{\pi}^2 \rangle} = 0.31 {\rm\ fm} $ and $ \sqrt{\langle r_{K}^2 \rangle} = 0.24 {\rm\ fm} $, respectively. We compare our results for gravitational form-factors with the existing literature results. We obtain that our results on $ \sqrt{\langle r_\pi^2 \rangle} $ are in good agreement with the predictions of NJL model, AdS/QCD model, and other models as well as with the existing experimental data.

Semileptonic and nonleptonic decays of the axial-vector tetraquark $$T_{bb;\overline{u} \overline{d}}^{-}$$

The semileptonic and nonleptonic decays of the double-beauty axial-vector tetraquark $T_{bb;\overline{u} \overline{d}}^{-}$ to a state $\widetilde{T}_{bc; \overline{u}\overline{d}}^{0}$ (hereafter $T_{bb}^{-}$ and $\widetilde{T} _{bc}^{0}$, respectively) are investigated in the context of the QCD sum rule method. The final-state tetraquark $\widetilde{T}_{bc}^{0}$ is treated as an axial-vector particle built of a heavy axial-vector diquark $ b^{T}\gamma _{\mu }Cc$ and light scalar antidiquark $\overline{u}C\gamma_{5} \overline{d}^{T}$. Its spectroscopic parameters are calculated using the two-points sum rules by taking into account contributions of quark, gluon and mixed condensates up to dimension $10$. We study the dominant semileptonic $T_{bb}^{-} \to \widetilde{T}_{bc}^{0}l\overline{\nu }_{l}$ and nonleptonic decays $T_{bb}^{-} \to \widetilde{T}_{bc}^{0}M$, where $M$ is one of the pseudoscalar mesons $\pi^{-}, K^{-}, D^{-}$ and $D_s^{-}$. The partial widths of these processes are computed in terms of weak form factors $G_{i}(q^2),\ i=1,2,3,4$, extracted by employing the QCD three-point sum rule approach. Predictions obtained for partial widths of considered decays are used to improve accuracy of theoretical predictions for full width and lifetime of the tetraquark $T_{bb}^{-}$, which are important for experimental exploration of this exotic meson.

Weinberg operator contribution to the nucleon electric dipole moment in the quark model

We evaluate the contribution of the CP violating gluon chromo-electric dipole moment (the so-called Weinberg operator, denoted as $w$) to the electric dipole moment (EDM) of nucleons in the nonrelativistic quark model. The CP-odd interquark potential is modeled by the perturbative one-loop level gluon exchange generated by the Weinberg operator with massive quarks and gluons. The nucleon EDM is obtained by solving the nonrelativistic Schr\"{o}dinger equation of the three-quark system using the Gaussian expansion method. It is found that the resulting nucleon EDM, which may reasonably be considered as the irreducible contribution, is smaller than the one obtained after $\gamma_5$-rotating the anomalous magnetic moment using the CP-odd mass calculated with QCD sum rules. We estimate the total contribution to be $d_n = w \times 20 \, e \, {\rm MeV}$ and $d_p = - w \times 18 \, e \, {\rm MeV}$ with 60% of theoretical uncertainty.

Nucleon electric dipole moment from polarized deep inelastic scattering

In a previous paper [1], we have pointed out the connection between the CP-odd three-gluon (Weinberg) operator and certain twist-four corrections in polarized deep inelastic scattering. Based on this observation, we give a numerical estimate of the electric dipole moment of the proton and neutron induced by the Weinberg operator. Our result tends to be smaller than the previous estimates based on QCD sum rules by a factor of about 3 or more, though they are not entirely inconsistent considering theoretical uncertainties.

Analysis of the excited Ω c states as the ± pentaquark states with QCD sum rules

We construct both the scalar-diquark-scalar-diquark-antiquark type and axialvector-diquark-axialvector-diquark-antiquark type interpolating currents to study the charmed pentaquark states with . We employ the QCD sum rules to investigate the masses and pole residues of the charmed pentaquark states by taking into account the vacuum condensates up to dimension 13 in the operator product expansion. Our calculation results indicate that the scalar-diquark-scalar-diquark-antiquark type and axialvector-diquark-axialvector-diquark-antiquark type charmed pentaquark states with can be possible candidates of the excited Ω c states observed in the LHCb collaboration.

Correlators of vector, tensor, and scalar composite vertices of order O( {alpha}_{mathrm{s}}^2 \u03b20)

We present analytical results for massless correlators of two vector, tensor, and scalar composite vertices with the Bjorken fractions x and y of order {alpha}_s^2 β0 of QCD. The structure of these correlators ΠV,T,S(x, y; p2) and properties of its main elements are discussed in detail. Special attention is paid to verifying the results and comparing them with known particular cases. We apply the correlators to evaluate radiative corrections to the distribution amplitudes of light mesons within the QCD sum rules.

Exotic ΩΩ dibaryon states in a molecular picture * *Supported by the National Natural Science Foundation of China (11722540, 12075019), the Fundamental Research Funds for the Central Universities, and the National Key Research and Development Program of China (2020YFA0406400)

We investigate the exotic dibaryon states with and in a molecular picture. We construct a tensor molecular interpolating current and calculate the two-point correlation function within the method of QCD sum rules. Our calculations indicate that the masses of the scalar and tensor dibaryon states are and , respectively, which are below the threshold. Within error, these results do not negate the existence of loosely bound molecular dibaryon states. These exotic strangeness and doubly-charged dibaryons, if they exist, may be identified in heavy-ion collision processes in the future.