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Register a new userFinite Temperature QCD Sum Rules: a Review
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The method of QCD sum rules at finite temperature is reviewed, with emphasis on recent results. These include predictions for the survival of charmonium and bottonium states, at and beyond the critical temperature for de-confinement, as later confirmed by lattice QCD simulations. Also included are determinations in the light-quark vector and axial-vector channels, allowing to analyse the Weinberg sum rules, and predict the dimuon spectrum in heavy ion collisions in the region of the rho-meson. Also in this sector, the determination of the temperature behaviour of the up-down quark mass, together with the pion decay constant, will be described. Finally, an extension of the QCD sum rule method to incorporate finite baryon chemical potential is reviewed.
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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.
For special kinematic configurations involving a single momentum scale, certain standard relations, originating from the Slavnov-Taylor identities of the theory, may be interpreted as ordinary differential equations for the ``kinetic term of the gluon propagator. The exact solutions of these equations exhibit poles at the origin, which are incompatible with the physical answer, known to diverge only logarithmically; their elimination hinges on the validity of two integral conditions that we denominate ``asymmetric and ``symmetric sum rules, depending on the kinematics employed in their derivation. The corresponding integrands contain components of the three-gluon vertex and the ghost-gluon kernel, whose dynamics are constrained when the sum rules are imposed. For the numerical treatment we single out the asymmetric sum rule, given that its support stems predominantly from low and intermediate energy regimes of the defining integral, which are physically more interesting. Adopting a combined approach based on Schwinger-Dyson equations and lattice simulations, we demonstrate how the sum rule clearly favors the suppression of an effective form factor entering in the definition of its kernel. The results of the present work offer an additional vantage point into the rich and complex structure of the three-point sector of QCD.
The up and down quark masses are determined from an optimized QCD Finite Energy Sum Rule (FESR) involving the correlator of axial-vector divergences, to five loop order in Perturbative QCD (PQCD), and including leading non-perturbative QCD and higher order quark mass corrections. This FESR is designed to reduce considerably the systematic uncertainties arising from the (unmeasured) hadronic resonance sector, which in this framework contributes less than 3-4% to the quark mass. This is achieved by introducing an integration kernel in the form of a second degree polynomial, restricted to vanish at the peak of the two lowest lying resonances. The driving hadronic contribution is then the pion pole, with parameters well known from experiment. The determination is done in the framework of Contour Improved Perturbation Theory (CIPT), which exhibits a very good convergence, leading to a remarkably stable result in the unusually wide window $s_0 = 1.0 - 4.0 {GeV}^2$, where $s_0$ is the radius of the integration contour in the complex energy (squared) plane. The results are: $m_u(Q= 2 {GeV}) = 2.9 pm 0.2 $ MeV, $m_d(Q= 2 {GeV}) = 5.3 pm 0.4$ MeV, and $(m_u + m_d)/2 = 4.1 pm 0.2$ Mev (at a scale Q=2 GeV).
In the past years there has been a revival of hadron spectroscopy. Many interesting new hadron states were discovered experimentally, some of which do not fit easily into the quark model. This situation motivated a vigorous theoretical activity. This is a rapidly evolving field with enormous amount of new experimental information. In the present report we include and discuss data which were released very recently. The present review is the first one written from the perspective of QCD sum rules (QCDSR), where we present the main steps of concrete calculations and compare the results with other approaches and with experimental data.
The saturation of QCD chiral sum rules of the Weinberg-type is analyzed using ALEPH and OPAL experimental data on the difference between vector and axial-vector correlators (V-A). The sum rules exhibit poor saturation up to current energies below the tau-lepton mass. A remarkable improvement is achieved by introducing integral kernels that vanish at the upper limit of integration. The method is used to determine the value of the finite remainder of the (V-A) correlator, and its first derivative, at zero momentum: $bar{Pi}(0) = - 4 bar{L}_{10} = 0.0257 pm 0.0003 ,$ and $bar{Pi}^{prime}(0) = 0.065 pm 0.007 {GeV}^{-2}$. The dimension $d=6$ and $d=8$ vacuum condensates in the Operator Product Expansion are also determined: $<{cal {O}}_{6}> = -(0.004 pm 0.001) {GeV}^6,$ and $<{cal {O}}_{8}> = -(0.001 pm 0.006) {GeV}^8.$
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