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Register a new userCharmonium in the vector channel at finite temperature from QCD sum rules
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Thermal Hilbert moment QCD sum rules are used to obtain the temperature dependence of the hadronic parameters of charmonium in the vector channel, i.e. the $J$ / $psi$ resonance mass, coupling (leptonic decay constant), total width, and continuum threshold. The continuum threshold $s_0$, which signals the end of the resonance region and the onset of perturbative QCD (PQCD), behaves as in all other hadronic channels, i.e. it decreases with increasing temperature until it reaches the PQCD threshold $s_0 = 4 m_Q^2$, with $m_Q$ the charm quark mass, at $Tsimeq 1.22 T_c$. The rest of the hadronic parameters behave very differently from those of light-light and heavy-light quark systems. The $J$ / $psi$ mass is essentially constant in a wide range of temperatures, while the total width grows with temperature up to $T simeq 1.04 T_c$ beyond which it decreases sharply with increasing T. The resonance coupling is also initially constant and then begins to increase monotonically around $T simeq T_c$. This behaviour of the total width and of the leptonic decay constant provides a strong indication that the $J$ / $psi$ resonance might survive beyond the critical temperature for deconfinement.
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The thermal evolution of the hadronic parameters of charmonium in the vector channel, i.e. the J/psi resonance mass, coupling (leptonic decay constant), total width, and continuum threshold is analyzed in the framework of thermal Hilbert moment QCD sum rules. The continuum threshold $s_0$, as in other hadronic channels, decreases with increasing temperature until the PQCD threshold s_0 = 4, m_Q^2 is reached at T simeq 1.22T_c (m_Q is the charm quark mass) and the J/psi mass is essentially constant in a wide range of temperatures. The other hadronic parameters behave in a very different way from those of light-light and heavy-light quark systems. The total width grows with temperature up to T simeq 1.04T_c beyond which it decreases sharply with increasing T. The resonance coupling is also initially constant beginning to increase monotonically around T simeq T_c. This behavior strongly suggests that the J/psi resonance might survive beyond the critical temperature for deconfinement, in agreement with lattice QCD results.
We review our results in Refs.[1,2] for the masses and couplings of heavy-light DD(BB)-like molecules and (Qq)(Qq)-like four-quark states from relativistic QCD Laplace sum rules (LSR) where next-to-next-to-leading order (N2LO) PT corrections in the chiral limit, next-to-leading order (NLO) SU3 PT corrections and non-perturbative contributions up to dimension d=6-8 are included. The factorization properties of molecule and four-quark currents have been used for the estimate of the higher order PT corrections. New integrated compact expressions of the spectral functions at leading order (LO) of perturbative QCD and up to dimensions d< (6 - 8) non-perturbative condensates are presented. The results are summarized in Tables 5 to 10, from which we conclude, within the errors, that the observed XZ states are good candidates for being 1^{++} and 0^{++} molecules or/and four-quark states, contrary to the observed Y states which are too light compared to the predicted 1^{-pm} and 0^{-pm} states. We find that the SU3 breakings are relatively small for the masses (< 10(resp. 3)%) for the charm (resp. bottom) channels while they are large (< 20%) for the couplings which decrease faster (1/m_{b}^{3/2}) than 1/m_{b}^{1/2} of HQET. QCD spectral sum rules (QSSR) approach cannot clearly separate (within the errors) molecules from four-quark states having the same quantum numbers. Results for the BK (DK)-like molecules and (Qq)(us)-like four-quark states from [3] are also reviewed which do not favour the molecule or/and four-quark interpretation of the X(5568). We suggest to scan the charm (2327 ~ 2444) MeV and bottom (5173 ~ 5226) MeV regions for detecting the (unmixed)(cu)ds and (bu)ds states. We expect that future experimental data and lattice results will check our predictions.
We present a global analysis of the observed Z_c, Z_cs and future Z_css-like spectra using the inverse Laplace transform (LSR) version of QCD spectral sum rules (QSSR) within stability criteria. Integrated compact QCD expressions of the LO spectral functions up to dimension-six condensates are given. Next-to-Leading Order (NLO) factorized perturbative contributions are included. We re-emphasize the importance to include PT radiative corrections (though numerically small) for heavy quark sum rules in order to justify the (ad hoc) definition and value of the heavy quark mass used frequently at LO in the literature. We also demonstrate that, contrary to a naive qualitative 1/N_c counting, the two-meson scattering contributions to the four-quark spectral functions are numerically negligible confirming the reliability of the LSR predictions. Our results are summarized in Tables III to VI. The Z_c(3900) and Z_cs(3983) spectra are well reproduced by the T_c(3900) and T_cs(3973) tetramoles (superposition of quasi-degenerated molecules and tetraquark states having the same quantum numbers and with almost equal couplings to the currents). The Z_c(4025) or Z_c(4040) state can be fitted with the D*_0D_1 molecule having a mass 4023(130) MeV while the Z_cs bump around 4.1 GeV can be likely due to the (D^*_s0D_1+ D^*_0D_s1) molecules. The Z_c(4430) can be a radial excitation of the Z_c(3900) weakly coupled to the current, while all strongly coupled ones are in the region (5634-6527) MeV. The double strange tetramole state T_css which one may identify with the future Z_css is predicted to be at 4064(46) MeV. It is remarkable to notice the regular mass-spliitings of the tetramoles due to SU(3) breakings M_{T_cs}-M_{T_c}= M_{T_css}-M_{T_cs= (73- 91) MeV.
A Finite Energy QCD sum rule at non-zero temperature is used to determine the $q^2$- and the T-dependence of the $rho pi pi$ vertex function in the space-like region. A comparison with an independent QCD determination of the electromagnetic pion form factor $F_{pi}$ at $T eq 0$ indicates that Vector Meson Dominance holds to a very good approximation at finite temperature. At the same time, analytical evidence for deconfinement is obtained from the result that $g_{rho pi pi}(q^{2},T)$ vanishes at the critical temperature $T_c$, independently of $q^{2}$. Also, by extrapolating the $rho pi pi$ form factor to $q^2 = 0$, it is found that the pion radius increases with increasing $T$, and it diverges at $T=T_c$.
These talks review and summarize our results in [1,2] on $XYZ$-like spectra obtained from QCD Laplace Sum Rules in the chiral limit at next-to-next-leading order (N2LO) of perturbation theory (PT) and including leading order (LO) contributions of dimensions $dleq 6-8$ non-perturbative condensates. We conclude that the observed $XZ$ states are good candidates for $1^{+}$ and $0^+$ molecules or / and four-quark states while the predictions for $1^-$ and $0^-$ states are about 1.5 GeV above the $Y_{c,b}$ experimental candidates and hadronic thresholds. We (numerically) find that these exotic molecules couple weakly to the corresponding interpolating currents than ordinary $D,B$ heavy-light mesons while we observe that these couplings decrease faster [$1/m_b^{3/2}$ (resp. $1/m_b$) for the $1^+,0^+$ (resp. $1^-,0^-)$ states] than $1/m_b^{1/2}$. Our results do not also confirm the existence of the $X(5568)$ state in agreement with LHCb findings.
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