QCD Sum Rule Method Research Articles

Applications of diagrammatic renormalization methods in QCD sum-rules

In QCD sum-rule methods, the fundamental field-theoretical quantities are correlation functions of composite operators that serve as hadronic interpolating fields. One of the challenges of loop corrections to QCD correlation functions in conventional approaches is the renormalization-induced mixing of composite operators. This involves a multi-step process of first renormalizing the operators, and then calculating the correlation functions in this mixed basis. This process becomes increasingly complicated as the number of operators mixed under renormalization increases, a situation that is exacerbated as the operator mass dimension increases in important physical systems such as tetraquarks, pentaquarks, and hybrids. Diagrammatic renormalization provides an alternative to the conventional operator renormalization approach. Diagrammatic renormalization methods are outlined and applied to a variety of QCD sum-rule examples of increasing complexity. The results are benchmarked, and the diagrammatic method is contrasted with the conventional operator mixing approach. Advantages and conceptual interpretations of the diagrammatic renormalization approach are outlined and technical subtleties are explored.

Heavy-light hybrid mesons with different spin-parities

The spectroscopic parameters of the heavy-light hybrid mesons with different spin-parities and different quark contents are investigated in the framework of the QCD sum rule method. The mass and current coupling of these states are calculated by taking into account the quark, gluon and mixed vacuum condensates up to dimension 10. The obtained results are compared with the existing QCD Laplace sum rule predictions. The results of mass and current coupling for all the considered channels are obtained to be stable and reliable. Our results can be useful for future experimental searches as well as theoretical studies of different parameters related to the hybrid mesons and their decays and interactions with other particles.

Masses of doubly heavy tetraquarks QQq̄n̄ with JP = 1+

In this paper, we apply the method of QCD sum rules to study the doubly heavy tetraquark states [Formula: see text] with spin-parity [Formula: see text] and strangeness [Formula: see text] using careful estimates of the Borel and threshold parameters involved. Masses of the doubly bottom and charmed tetraquarks with isospin [Formula: see text] are computed precisely via taking into account multifarious condensates up to dimension 10. Compared with the two-heavy meson thresholds, we find that all nonstrange doubly-bottom tetraquarks and a doubly-charmed tetraquarks associated with [Formula: see text] with [Formula: see text] are stable against strong decay into two bottom mesons while a doubly-charmed tetraquark associated with current [Formula: see text] is unstable against strong decay. By the way, weak decay widths of the doubly bottom tetraquarks are also given.

Covalent hadronic molecules induced by shared light quarks

After examining Feynman diagrams corresponding to the , , , and hadronic molecular states, we propose a possible binding mechanism induced by shared light quarks. This mechanism is similar to the covalent bond in chemical molecules induced by shared electrons. We use the method of QCD sum rules to calculate its corresponding light-quark-exchange diagrams, and the obtained results indicate a model-independent hypothesis: the light-quark-exchange interaction is attractive when the shared light quarks are totally antisymmetric so they obey the Pauli principle. We build a toy model with four parameters to formulize this picture and estimate binding energies of some possibly-existing covalent hadronic molecules. A unique feature of this picture is that the binding energies of the (I)J P = (0)1+ hadronic molecules are much larger than those of the (I)J P = (0)1+ ones, while the (I)J P = (1/2)1/2+ hadronic molecules have similar binding energies.

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.

Two- and three-gluon glueballs within QCD sum rules

We study two- and three-gluon glueballs using the method of QCD sum rules. We systematically construct their interpolating currents and calculate their masses. We propose to search for the JPC=3±− three-gluon glueballs in their three-meson decay channels in future BESIII, GlueX, LHC, and PANDA experiments.

Covalent hadronic molecules via QCD sum rules

After carefully examining Feynman diagrams corresponding to the $\bar D \Sigma_c$ hadronic molecular state, we propose a possible binding mechanism induced by shared light quarks. We systematically study its corresponding light-quark-exchange interaction using the method of QCD sum rules, and the obtained results suggest that there can be the $\bar D \Sigma_c$ covalent molecule of $I=1/2$. Our QCD sum rule analyses further indicate a model-independent hypothesis: the light-quark-exchange interaction is attractive when the shared light quarks are totally antisymmetric so that obey the Pauli principle.

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.

Investigation of hidden-charm double strange pentaquark candidate P_{css} via its mass and strong decays

This work presents an analysis of a hidden charmed pentaquark candidate state with double strange quark in its quark content. The investigation is performed in two parts, which provide the mass prediction of the considered state and its partial decay widths for the P_{css}rightarrow Xi ^0 J/psi and P_{css}rightarrow Xi _c^+ D_s^- channels. For the analyses, two-point and three-point QCD sum rule methods are applied to get the mass and the widths, respectively. The mass for this candidate state is obtained as m_{P_{css}}=4600 pm 155 MeV with corresponding current coupling constant lambda _{P_{css}}=(0.81 pm 0.21)times 10^{-3} GeV^6. These results are used in the analysis of the partial widths of this state for the decays P_{css}rightarrow Xi ^0 J/psi and P_{css}rightarrow Xi _c^+ D_s^-. From these decays, the total width is obtained as Gamma = 12.29pm 2.94 MeV. These results may shed light on the future experimental searches in which such types of states are probed and may provide information to discriminate between such possible observations.

Investigation of Δ0Δ0 dibaryon in QCD

We study a hypothetical ${\mathrm{\ensuremath{\Delta}}}^{0}{\mathrm{\ensuremath{\Delta}}}^{0}$ dibaryon state by means of the QCD sum rule method. We construct a scalar interpolating current to extract the mass and decay constant of this state taking into account contributions of various quark, gluon, and mixed vacuum condensates. The predictions for the mass and decay constants are ${m}_{D}=232{6}_{\ensuremath{-}126}^{+114}\text{ }\text{ }\mathrm{MeV}$ and ${f}_{D}=2.9{4}_{\ensuremath{-}0.34}^{+0.30}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\text{ }\text{ }{\mathrm{GeV}}^{7}$, respectively. We also made an estimation about binding energy and size of the ${\mathrm{\ensuremath{\Delta}}}^{0}{\mathrm{\ensuremath{\Delta}}}^{0}$ dibaryon. The obtained mass value is below the ${\mathrm{\ensuremath{\Delta}}}^{0}{\mathrm{\ensuremath{\Delta}}}^{0}$ threshold and may be a good dibaryon candidate for being observed experimentally.

Excited states of spin-(3/2) doubly-heavy baryons within the QCD sum rules method

Within the framework of the QCD sum rules method, the masses and pole residues of the excited states 2S and 1P of the doubly-heavy spin-(3/2) baryons Xi _{cc}^*, Xi _{bb}^*, Xi _{bc}^*, Omega _{cc}^*, Omega _{bb}^*, and Omega _{bc}^* are investigated. The excited state masses and pole residues are predicted with reasonable accuracy. We expect that soon, the current predictions can be tested against future experimental data.

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.

P-wave Ω b states: masses and pole residues * *Supported by the National Natural Science Foundation of China (11675263)

In this study, we consider all P-wave states represented by interpolating currents with a derivative and calculate the corresponding masses and pole residues using the QCD sum rule method. Because of the large uncertainties in our calculation compared with the small difference in the masses of the excited states observed by the LHCb collaboration, it is necessary to study other properties of the P-wave states represented by the interpolating currents investigated in the present work to gain a better understanding of the four excited states observed by the LHCb collaboration.

Weak decays of the double-beauty tetraquark

The spectroscopic parameters and decay channels of the axial-vector tetraquark 213 built of heavy diquark bb and light antidiquark us are explored using QCD sum rule method. Because this state is stable against strong and electromagnetic decays, we consider its semileptonic and nonleptonic decay modes. Partial widths of weak processes TAVb:s¯ → Z0b:s¯ lv¯l and Tb:s¯AV → Z0b:s¯ M are calculated using weak form factors Gi(q2) computed by QCD three-point sum rules: Z0b:s¯ is the scalar tetraquark with quark content bcus¯ and M is a vector meson. The full width and mean lifetime of the tetraquark TAVb:s¯ obtained in this work shed light on features of double-beauty tetraquarks and are useful for their experimental investigations.

Modifications on the Properties of \(D^*_{s0}\)(2317) as Four-quark State in Thermal Medium

Since the low mass of $D^*_{s0}(2317)$ has still been a problem to the conventional quark model, one can consider other options regarding as multi-quark system. Therefore we investigate the scalar open-charm state $D^*_{s0}(2317)$ by Thermal QCD Sum Rules (TQCDSR) method using the two-point correlation function together with contributions of the non-perturbative condensates up to dimension six. Deriving and numerically analyzing thermal mass and pole residue sum rules, we accomplish the effects on the properties of $D^*_{s0}(2317)$ resonance in hot medium. Our numerical evaluations indicate that the variations in mass and pole residue values are stable through the growing temperature up to $T\cong100~\mathrm{MeV}$, but they begin to fall after this point. At critical temperature, the values of mass and pole residue change up to $91\%, 70\% $ of their values in vacuum in the molecular scenario and $ 91\%, 69\% $ in the diquark-antidiquark scenario. Our results does not give any definite information as to whether $D^*_{s0}(2317)$ resonance has molecular or diquark-antidiquark structure since they are very close to each other to differentiate them. Besides, we predict the hadronic parameters of the bottom partner of the $D^*_{s0}(2317)$ resonance in both molecular and diquark-antidiquark pictures. This bound state is worth investigating in future experiments. Also the detailed search of hot medium effects on the hadronic parameters of open-charm meson $D^*_{s0}(2317)$ and the bottom partner could have some implications to define the QCD phase diagram obtained from heavy-ion collision experiments. Moreover these results can be useful in distinguishing conventional quark model mesons from exotica.

Exotic fully heavy QQ¯QQ¯ tetraquark states in 8[QQ¯]⊗8[QQ¯] color configuration

We have systematically calculated the mass spectra for S-wave and P-wave fully-charm $c\bar{c}c\bar{c}$ and fully-bottom $b\bar{b}b\bar{b}$ tetraquark states in the $\mathbf{8}_{[Q\bar{Q}]}\otimes \mathbf{8}_{[Q\bar{Q}]}$ color configuration, by using the moment QCD sum rule method. The masses for the fully-charm $c\bar cc\bar c$ tetraquark states are predicted about $6.3-6.5$ GeV for S-wave channels and $7.0-7.2$ GeV for P-wave channels. These results suggest the possibility that there are some $\mathbf{8}_{[c\bar{c}]}\otimes \mathbf{8}_{[c\bar{c}]}$ components in LHCb's di-$J/\psi$ structures. For the fully-bottom $b\bar{b}b\bar{b}$ system, their masses are calculated around 18.2 GeV for S-wave tetraquark states while 18.4-18.8 GeV for P-wave ones, which are below the $\eta_b\eta_b$ and $\Upsilon(1S)\Upsilon(1S)$ two-meson decay thresholds.

Two- and three-gluon glueballs of C=+

We study two- and three-gluon glueballs of $C=+$ using the method of QCD sum rules. We systematically construct their interpolating currents, and find that all the spin-1 currents of $C=+$ vanish. This suggests that the ``ground-state'' spin-1 glueballs of $C=+$ do not exist within the relativistic framework. We calculate masses of the two-gluon glueballs with ${J}^{PC}={0}^{\ifmmode\pm\else\textpm\fi{}+}/{2}^{\ifmmode\pm\else\textpm\fi{}+}$ and the three-gluon glueballs with ${J}^{PC}={0}^{\ifmmode\pm\else\textpm\fi{}+}/{2}^{\ifmmode\pm\else\textpm\fi{}+}$. We propose searching for the ${J}^{PC}={0}^{\ensuremath{-}+}/{2}^{\ensuremath{-}\ifmmode\pm\else\textpm\fi{}}/{3}^{\ifmmode\pm\else\textpm\fi{}\ensuremath{-}}$ three-gluon glueballs in their three-meson decay channels in the future BESIII, GlueX, LHC, and PANDA experiments.

Strong and electromagnetic decays of the radially excited D_s and B_s mesons in light cone QCD sum rules

Recently, LHCb Collaboration announced the discovery of radial excitations of D_s and B_s mesons. In present work, we calculate the most promising strong and electromagnetic decay widths of radially excited D_s(2S) and B_s(2S) mesons within the light cone QCD sum rules method.

Doubly charged vector tetraquark [formula omitted

We explore properties of the doubly charged vector tetraquark ZV++=[cu][s‾d‾] built of four quarks of different flavors using the QCD sum rule methods. The mass and current coupling of ZV++ are computed in the framework of the QCD two-point sum rule approach by taking into account quark, gluon and mixed vacuum condensates up to dimension 10. The full width of this tetraquark is saturated by S-wave ZV++→π+Ds1(2460)+, ρ+Ds0⁎(2317)+, and P-wave ZV++→π+Ds+,K+D+ decays. Strong couplings required to find partial widths of aforementioned decays are calculated in the context of the QCD light-cone sum rule method and a soft-meson approximation. Our predictions for the mass m=(3515±125) MeV and full width Γfull=156−30+56 MeV of ZV++ are useful to search for this exotic meson in various processes. Recently, the LHCb collaboration discovered neutral states X0(1)(2900) as resonance-like peaks in D−K+ invariant mass distribution in the decay B+→D+D−K+. We argue that mass distribution of D+K+ mesons in the same B decay can be used to observe the doubly charged scalar ZS++ and vector ZV++ tetraquarks.

The Radiative Δ(1600) → γN Decay in the Light-Cone QCD Sum Rules

Within the framework of the light-cone QCD sum rules method (LCSR’s), the radiative Δ(1600)→γN decay is studied. In particular, the magnetic dipole moment GM1(0) and the electric quadrupole moment GE1(0) are estimated. We also calculate the ratio REM=−GE1(0)GM1(0) and the decay rate. The predicted multipole moments and the decay rate strongly agree with the existing experimental results as well as with the other available phenomenological approaches.