Hadronic Correlators and Condensate Fluctuations in QCD Vacuum

Phenomenological results of equal time, point to point spatial correlation functions of hadronic currents are used to deduce the structure of the QCD vacuum. It is found that a model with only quark condensate is not adequate to explain the observations. Inclusion of condensate fluctuations (explicit four point structure in the vacuum) leads to excellent overall agreement with the phenomenological curves and parameters in various channels. PACS number(s): 12.38.Gc Typeset using REVTEX Electronic address: [email protected] On leave from : The Mehta Research Institute for Mathematics and Mathematical Physics, 10 Kasturba Gandhi Marg, Allahabad 211 022, India Electronic address: [email protected] 1 The most interesting question in Quantum Chromodynamics (QCD) is concerned with the nature of the vacuum state [1]. It is well known that the vacuum is non-trivial and is composed of gluon and quark field condensates [2,3]. Much of the understanding of nonperturbative phenomena in QCD is expected to result from a proper knowledge of the ground state of QCD. In this note, we adopt a phenomenological approach to determine the salient features of the QCD vacuum. We consider here spacelike separated correlation functions of hadron currents in QCD vacuum [3]. More precisely, we use phenomenological results of equal time, point to point spatial ground state correlation functions of hadronic currents [4] to guide us towards a “true” structure of QCD vacuum. As a first step, we employ the explicit construct for QCD vacuum with quark and gluon condensates proposed by us [5]. In this the trial ansatz for the QCD vacuum was [5] |vac >= exp (BF † −BF ) exp (BG − BG)|0 > (1) where |0 > is the perturbative vacuum and BF † and BG are the Bogoliubov operators corresponding to creation of quark antiquark pairs and gluon pairs respectively. Such a construct gives rise to the equal time propagator [6] as (with x = |~x|), Sαβ(~x) = 〈 vac| 2 [ ψ α(~x), ψ̄ i β(0) ]