Operator product expansion and duality at finite temperature

The operator product expansion of current correlators at short distances, and the notion of QCD-hadron duality are the cornerstone of QCD sum rules. The extension of this programme to $T \neq 0$ is discussed, together with applications to hot hadronic propagators. Indications are that the hadronic spectrum suffers a substantial rearrangement with increasing temperature, and hint on the existence of a quark deconfining phase transition. Phenomenological order parameters to characterize this phase transition are discussed.Comment: UCT-TP-209/94. Invited talk at QCD-94, Montpellier, July 1994. LATEX file. 5 pages. NO figure

QCD determination of the axial-vector coupling of the nucleon at finite temperature

A thermal QCD Finite Energy Sum Rule (FESR) is used to obtain the temperature dependence of the axial-vector coupling of the nucleon, $g_{A}(T)$. We find that $g_{A}(T)$ is essentially independent of $T$, in the very wide range $0 \leq T \leq 0.9 T_{c}$, where $T_{c}$ is the critical temperature. While $g_{A}$ at T=0 is $q^{2}$-independent, it develops a $q^{2}$ dependence at finite temperature. We then obtain the mean square radius associated with $g_{A}$ and find that it diverges at $T=T_{c}$, thus signalling quark deconfinement. As a byproduct, we study the temperature dependence of the Goldberger-Treiman relation.Comment: 8 pages and 3 figure

Determination of the strange-quark mass from QCD pseudoscalar sum rules

A new determination of the strange-quark mass is discussed, based on the two-point function involving the axial-vector current divergences. This Green function is known in perturbative QCD up to order O(alpha_s^3), and up to dimension-six in the non-perturbative domain. The hadronic spectral function is parametrized in terms of the kaon pole, followed by its two radial excitations, and normalized at threshold according to conventional chiral-symmetry. The result of a Laplace transform QCD sum rule analysis of this two-point function is: m_s(1 GeV^2) = 155 pm 25 MeV.Comment: Invited talk given by CAD at QCD98, Montpellier, July 1998. To appear in Nucl.Phys.B Proc.Suppl. Latex File. Four (double column) page

Vector Meson Dominance and gρππg_{\rho\pi\pi} at Finite Temperature from QCD Sum Rules

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 $T \neq 0$ 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 $T=T_c$.Comment: 7 pages, Latex, 3 figures to be delivered from the authors by request, to appear in Phys. Lett.

Electromagnetic pion form factor at finite temperature

The electromagnetic form factor of the pion in the space-like region, and at finite temperature, $F_{\pi}(Q^{2},T)$, is obtained from a QCD Finite Energy Sum Rule. The form factor decreases with increasing T, and vanishes at some critical temperature, where the pion radius diverges. This divergence may be interpreted as a signal for quark deconfinement.Comment: LATEX File. UCT-TP-215/94. One figure available on request. To be published in Phys. Lett.

Pion form factor in large NcN_c QCD

The electromagnetic form factor of the pion is obtained using a particular realization of QCD in the large $N_c$ limit, which sums up the infinite number of zero-width resonances to yield an Euler's Beta function of the Veneziano type. This form factor agrees with space-like data much better than single rho-meson dominance. A simple unitarization ansatz is illustrated, and the resulting vector spectral function in the time-like region is shown to be in reasonable agreement with the ALEPH data from threshold up to about 1.3 ${GeV}^2$.Comment: Plain Latex, 9 pages, 2 figure

QCD sum rules and thermal properties of Charmonium in the vector channel

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.Comment: 4 pages, two figures, contribution to QCD 10, Montpellier 28th June-2nd July 201

Ratio of strange to non-strange quark condensates in QCD

Laplace transform QCD sum rules for two-point functions related to the strangeness-changing scalar and pseudoscalar Green's functions $\psi(Q^2)$ and $\psi_5(Q^2)$, are used to determine the subtraction constants $\psi(0)$ and $\psi_5(0)$, which fix the ratio $R_{su}\equiv \frac{}{}$. Our results are $\psi(0)= - (1.06 \pm 0.21) \times 10^{-3} {GeV}^4$, $\psi_5(0)= (3.35 \pm 0.25) \times 10^{-3} {GeV}^4$, and $R_{su}\equiv \frac{}{} = 0.5 \pm 0.1$. This implies corrections to kaon-PCAC at the level of 50%, which although large, are not inconsistent with the size of the corrections to Goldberger-Treiman relations in $SU(3)\otimes SU(3)$.Comment: Latex file, 14 pages including 3 figure

Axial anomaly, vector meson dominance and π0→γγ\pi^0 \to \gamma \gamma at finite temperature

A thermal Finite Energy QCD Sum Rule is used to determine the temperature behaviour of the $\omega \rho \pi$ strong coupling. This coupling decreases with increasing $T$ and vanishes at the critical temperature, a likely signal for quark deconfinement. This is then used in the Vector Meson Dominance (VMD) expression for the $\pi^0 \to \gamma \gamma$ amplitude, which is also found to vanish at the critical temperature, as expected. This result supports the validity of VMD at $T \neq 0$. However, if VMD would not hold at finite temperature, then there is no prediction for the $\pi^0 \to \gamma \gamma$ amplitude.Comment: 8 pages, no figure

Spectral Functions for Heavy-Light Currents and Form Factor Relations in Hqet

We derive relations among form factors describing the current-induced transitions: (vacuum) $\rightarrow B,B^{*}, B \pi, B^{*} \pi, B \rho$ and $B^{*} \rho$ using heavy quark symmetry. The results are compared to corresponding form factor relations following from identities between scalar and axial vector, and pseudoscalar and vector spectral functions in the heavy quark limit.Comment: LaTeX, 7 pages, UCT-TP 188/92, MZ-TH/92-5