Search

We interpret the $X_1(2900)$ as an $S$-wave $\bar{D}_1K$ molecular state in the Bethe-Salpeter equation approach with the ladder and instantaneous approximations for the kernel. By solving the Bethe-Salpeter equation numerically with the kernel containing one-particle-exchange diagrams and introducing three different form factors (monopole, dipole, and exponential form factors) in the verties, we find the bound state exists. We also study the decay width of the decay $X_1(2900)$ to $D^-K^+$., Comment: 13 pages, 4 figures. arXiv admin note: text overlap with arXiv:2004.14085, arXiv:1906.09002

We calculate the complete form of the dimension-8 condensate contributions in the two-point correlator of the ( 1 − + , 0 + + ) light hybrid current considering the operator mixing under renormalization. We find the inclusion these higher power corrections as well as the update of 〈 g 3 G 3 〉 increase the QCD sum rule mass prediction for the 1 − + light hybrid. The obtained conservative mass range 1.72–2.60 GeV does not favor the π 1 ( 1400 ) and the π 1 ( 1600 ) to be pure hybrid states and suggests the π 1 ( 2015 ) observed by E852 is more likely to have much of a hybrid constituent. We also study the b 1 π and ρπ decay patterns of the 1 − + light hybrid with light-cone QCD sum rules. We obtain a relatively large partial decay width of the b 1 π mode, which is consistent with the predictions from the flux tube models and lattice QCD. More interestingly, using the tensor interpolating current we find the partial decay width of the ρπ mode is very small due to the lack of the leading twist contribution in the light-cone expansion of the correlation function.

Within the quasi-two-body decay model, we study the localized CP violation and branching fraction of the four-body decay when the and pair invariant masses are and , with the pairs being dominated by the , , , and , and , , and resonances, respectively. When dealing with the dynamical functions of these resonances, , , and are modeled with the Bugg model, Gounaris-Sakurai function, Flatté formalism and LASS lineshape, respectively, while the others are described by the relativistic Breit-Wigner function. Adopting the end point divergence parameters and , our predicted results are and , based on the hypothetical structures for the scalar mesons in the QCD factorization approach. Meanwhile, we calculate the CP violating asymmetries and branching fractions of the two-body decays and all the individual four-body decays , respectively. Our theoretical results for the two-body decays , , , , and are consistent with the available experimental data, with the remaining predictions await testing in future high precision experiments.

In this paper, we reanalyze the $I=0$ scalar channel with the improved Monte-Carlo-based QCD sum rules, which combines the rigorous H\"older-inequality-determined sum rule window and a parametrization with two-Breit-Wigner-type resonances for the phenomenological spectral density that satisfies the low-energy theorem for the scalar form factor. Considering the uncertainties of the QCD parameters and the experimental masses and widths of the scalar resonances $\ensuremath{\sigma}$ and ${f}_{0}(980)$, we obtain a prediction for light quark mass ${m}_{q}(2\text{ }\text{ }\mathrm{GeV})=\frac{1}{2}({m}_{u}(2\text{ }\text{ }\mathrm{GeV})+{m}_{d}(2\text{ }\text{ }\mathrm{GeV}))={4.7}_{\ensuremath{-}0.7}^{+0.8}\text{ }\text{ }\mathrm{MeV}$, which is consistent with the Particle Data Group value and QCD sum rule determinations in the pseudoscalar channel. This agreement provides a consistent framework connecting QCD sum rules and low-energy hadronic physics. We also obtain the decay constants of $\ensuremath{\sigma}$ and ${f}_{0}(980)$ at 2 GeV, which are approximately 0.64--0.83 and 0.40--0.48 GeV, respectively.

We study the exotic ${J}^{PC}={0}^{\ensuremath{-}\ensuremath{-}}$ four-quark states in Laplace sum rules and finite energy sum rules. We use the vector tetraquarklike currents as interpolating currents in the correlator, from which the ${1}^{+\ensuremath{-}}$ states are also studied. In the mass extraction, we use the standard stability criterion with respect to the Borel parameters and the QCD continuum thresholds and consider the effect of the violation of factorization in estimating the high dimensional condensates as a source of uncertainties. The obtained mass prediction $1.76\ifmmode\pm\else\textpm\fi{}0.15\text{ }\text{ }\mathrm{GeV}$ is much lower than the previous sum rule predictions obtained using the pseudoscalar currents. Our result favors the four-quark interpretation of the possible $\ensuremath{\rho}\ensuremath{\pi}$ dominance in the ${D}^{0}$ decay. We also discuss the possible decay patterns of these exotic four-quark states.

We improve the Monte-Carlo based QCD sum rules by introducing the rigorous H\"older-inequality-determined sum rule window and a Breit-Wigner type parametrization for the phenomenological spectral function. In this improved sum rule analysis methodology, the sum rule analysis window can be determined without any assumptions on OPE convergence or the QCD continuum.Therefore an unbiased prediction can be obtained for the phenomenological parameters (the hadronic mass and width etc.). We test the new approach in the $\rho$ meson channel with re-examination and inclusion of $\alpha_s$ corrections to dimension-4 condensates in the OPE. We obtain results highly consistent with experimental values. We also discuss the possible extension of this method to some other channels., Comment: 12 pages, 8 figures, accepted for publication in Chinese Physics C

We study the $\ensuremath{\rho}\ensuremath{\pi}$ and ${b}_{1}\ensuremath{\pi}$ decay modes of the ${1}^{\ensuremath{-}+}$ light hybrid state within the framework of light-cone QCD sum rules. We use both the tensor current $\overline{\ensuremath{\psi}}{\ensuremath{\sigma}}_{\ensuremath{\mu}\ensuremath{\nu}}\ensuremath{\psi}$ and the derivative current $\overline{\ensuremath{\psi}}{\stackrel{\ensuremath{\leftrightarrow}}{D}}_{\ensuremath{\mu}}{\ensuremath{\gamma}}_{5}\ensuremath{\psi}$ as interpolating currents to calculate the partial decay width of the ${b}_{1}\ensuremath{\pi}$ decay mode. Comparing the sum rules obtained by using different currents, we obtain $\mathrm{\ensuremath{\Gamma}}({\ensuremath{\pi}}_{1}\ensuremath{\rightarrow}{b}_{1}\ensuremath{\pi})=8--23$, 32--86 and 52--151 MeV for ${m}_{{1}^{\ensuremath{-}+}}=1.6$, 1.8 and 2.0 GeV respectively, which favor the results from the flux tube models and lattice simulations. We also use the tensor current to study the $\ensuremath{\rho}\ensuremath{\pi}$ decay mode, and although an extended stability criterion is needed, our results suggest a small partial decay width.

We calculate the coefficients of the dimension-8 quark and gluon condensates in the current-current correlator of $1^{-+}$ light hybrid current $g\bar{q}(x)\gamma_{\nu}iG_{\mu\nu}(x)q{(x)}$. With inclusion of these higher-power corrections and updating the input parameters, we re-analyze the mass of the $1^{-+}$ light hybrid meson from Monte-Carlo based QCD sum rules. Considering the possible violation of factorization of higher dimensional condensates and variation of $\langle g^3G^3\rangle$, we obtain a conservative mass range 1.72--2.60\,GeV, which favors $\pi_{1}(2015)$ as a better hybrid candidate compared with $\pi_{1}(1600)$ and $\pi_{1}(1400)$., Comment: 12pages, 2 figures, the version appearing in JHEP

In this paper, we study instanton contributions to the correlator of the hybrid current $g\bar q \sigma_{\mu\nu}G^a_{\nu\mu}T^a q$. These contributions are then included in a QCD sum-rule analysis of the isoscalar $0^{++}$ hybrid mass. We find a mass at 1.83 GeV for the $(\bar uug+\bar ddg)/\sqrt{2}$ hybrid. However, for the $\bar ssg$ hybrid, we find the sum rules are unstable. We also study non-zero width effects, which affect the mass prediction. The mixing effects between these two states are studied and we find QCD sum rules support the existence of a flavor singlet hybrid with mass at around 1.9 GeV. Finally, we study the mixing effects between hybrid and glueball currents. The mixing between the $(\bar uug+\bar ddg)/\sqrt{2}$($\bar ssg$) and the glueball causes two states, one in the region 1.4-1.8 GeV(1.4-2.2 GeV), and the other in the range 1.8-2.2 GeV(2.2-2.6 GeV)., Comment: 12 pages, revised version

By use of single instanton approximation the twist-3 light-cone distribution amplitudes of pion as well as the p-wave mesons, i.e., $f_{0}(1370)$, $K_{0}^{\ast}(1430)$ and $a_{0}(1450)$ are investigated within the framework of QCD moment sum rules with inclusion of instanton effects based on the valence quark model. Results show that there is much change on light-cone distribution amplitudes by the isospin- and chirality-dependent instanton contribution compared with the instanton-free ones. We find the intanton involved twist-3 LCDAs are non-positive-definite within some range of momentum fraction and there are rapid changes at two ends of momentum fraction. To guarantee the convergence of moments by the method in this work a low instanton density should be adopted, for instance $n_{c}=1/2\rm{fm^{-4}}$ is welcomed. Possible ingredients which might have impact on the results are briefly discussed. These light-cone distribution amplitudes may be helpful to analyze exclusive heavy flavored processes., 25 pages, 6 figures, the version appearing in PRD

Motivated by the similar mass splitting in light-light and heavy-light meson system in $J^{P}=0^{-}$ and $J^{P}=0^{+}$ channel, taking into account the operator mixing to obtain an infrared stable OPE as well as a complete both non-perturbative and perturbative $\mathcal {O}(m_{q})$ corrections to the correlation function, the SU(3)-symmetry breaking effects in mass splitting in $0^{-}$ and $0^{+}$ channel of $D$ meson are analyzed by QCD sum rule approach based on a $c\bar{q}$ underlying structure. Within the sum rule we get, taking same threshold and Borel window for same channel, we find a correct mass splitting tendency in both channel which agrees with observed spectrum. We find $m_{D_{s}}-m_{D_{d}}\sim35\rm{MeV}$ in $0^{-}$ channel and $m_{D_{d}}-m_{D_{s}}\sim12\rm{MeV}$ in $0^{+}$ channel at scale $\mu=1\rm{GeV}$. These splitting can be accommodated with the different role of combination of mass effects and the parity-dependent "force" induced from non-perturbative QCD vacuum. When we scale up to $\mu=1.3\rm{GeV}$, the splitting remains unchanged which demonstrates a correct scale invariance. Combined with HQET, generalization to other channel of charmed meson and $b$-system are discussed briefly also., Comment: 24pages, six figures and three tables, the version appears in PRD.

In this paper, we re-analyze the $1^{-+}$ and $0^{++}$ light hybrids from QCD sum rules with a Monte-Carlo based uncertainty analysis. With $30\%$ uncertainties in the accepted central values for QCD condensates and other input parameters, we obtain a prediction on $1^{-+}$ hybrid mass of $1.71 \pm 0.22$\,GeV, which covers the mass of $\pi_1(1600)$. However, the $0^{++}$ hybrid mass prediction is more than 4\,GeV, which is far away from any known $a_0$ meson. We also study the correlations between the input and output parameters of QCD sum rules.