Analysis of the heavy quarkonium states $h_c$ and $h_b$ with QCD sum rules

Abstract

In this article, we take the tensor currents $\bar{Q}(x){\sigma }_{\mu \nu }Q(x)$ to interpolate the $P$-wave spin-singlet heavy quarkonium states $h_Q$, and study the masses and decay constants with the Borel sum rules and moments sum rules. The masses and decay constants from the Borel sum rules and moments sum rules are consistent with each other, the masses are also consistent with the experimental data. We can take the decay constants as basic input parameters and study other phenomenological quantities with the three-point correlation functions via the QCD sum rules. The heavy quarkonium states $h_Q$ couple potentially to the tensor currents $\bar{Q}(x){\sigma }_{\mu \nu }Q(x)$, and have the quark structure ${\epsilon }^{ijk}{\xi }^{†}{\sigma }^k\zeta$ besides the quark structure $i{k}_2^i{\xi }^{†}\sigma \cdot ({\vec{k}}_1-{\vec{k}}_2)\zeta$. In calculations, we take into account the leading-order, next-to-leading-order perturbative contributions, and the gluon condensate, four-quark condensate contributions in the operator product expansion. The analytical expressions of the perturbative QCD spectral densities have applications in studying the two-body decays of a boson to two fermions with the vertexes ${\sigma }_{\mu \nu }{\gamma }_5$ and ${\sigma }_{\mu \nu }$.

16 pages, 21 figures, correct two writing errors

References in corpus (4)

• Gluon Condensates and m_{c,b} from QCD-Moments and their ratios to Order alpha_s^3 and <G^4>
• QCD sum rule determination of the charm-quark mass
• Renormalization Group Improved Bottom Mass from Upsilon Sum Rules at NNLL Order
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Cited by in corpus (14)

• Reanalysis of the $Y(3940)$, $Y(4140)$, $Z_c(4020)$, $Z_c(4025)$ and $Z_b(10650)$ as molecular states with QCD sum rules
• Lattice QCD and QCD Sum Rule determination of the decay constants of eta_c, J/psi and hc states
• The $Z_b(10610)$ and $Z_b(10650)$ as axial-vector tetraquark states in the QCD sum rules
• Bottomonium spectrum in the relativistic flux tube model
• Spectroscopic parameters and decays of the resonance $Z_b(10610)$
• Strong coupling constants and radiative decays of the heavy tensor mesons
• Decay properties of the $Z_c(3900)$ through the Fierz rearrangement
• Analysis of the strong coupling form factors of ${\Sigma }_{b}NB$ and ${\Sigma }_{c}ND$ in QCD sum rules
• Mass spectra and decay constants of heavy-light axial quarkonia in the framework of Bethe-Salpeter equation
• Bottomonia in an unquenched quark model
• Spectroscopy of excited quarkonium states in the light-front quark model
• Analysis of the strong vertices of ${\Sigma }_{c}N{D}^{\ast }$ and ${\Sigma }_{b}N{B}^{\ast }$ in QCD sum rules
• Analysis of the strong vertexes of ${\Sigma }_c^{\ast }ND$ and ${\Sigma }_b^{\ast }NB$ in QCD sum rules
• Systematic analysis of the form factors of $B_c$ to $P$-wave charmonia and corresponding weak decays