Jishnu Dey

Problem of the statistical model in deep inelastic scattering phenomenology

Abstract Recent deep inelastic data leads to an up-down quark asymmetry of the nucleon sea. Explanations of the flavour asymmetry and the di-lepton production in proton-nucleus collisions call for a temperature T ≈ 100 MeV in a statistical model. This T may be conjectured as being due to the Fulling-Davies-Unruh effect. But it is not possible to fit the structure function itself.

SCALING LAW FOR BARYON COUPLING TO ITS CURRENT AND ITS POSSIBLE APPLICATIONS

The baryon coupling to its current (λB), in conventional QCD sum rule calculations (QCDSR), is shown to scale as the cubic power of the baryon mass, MB. Some theoretical justification for it comes from a simple light-cone model and also general scaling arguments for QCD. But more importantly, taken as a phenomenological ansatz for the present, this may find very good use in current explorations of possible applications of QCDSR to baryon physics both at temperature T=0, T≠0 and/or density ρ=0, ρ≠0.

QCD phase transitions from relativistic hadron models

The models of translationally invariant infinite nuclear matter in the relativistic mean field models are very interesting and simple, since the nucleon can connect only to a constant vector and scalar meson field. Can one connect these to the complicated phase transitions of QCD? For an affirmative answer to this question, one must consider models where the coupling contstants to the scalar and vector fields depend on density in a nonlinear way, since as such the models are not explicitly chirally invariant. Once this is ensured, indeed one can derive a quark condensate indirectly from the energy density of nuclear matter which goes to zero at large density and temperature. The change to zero condensate indicates a smooth phase transition.

The Topological and Non-Topological Soliton Models

We have already talked about large N c expansion of ‘t Hooft and Witten’s application to baryons. Witten had, in particular, observed that the mass of baryons go as 1/g2(≈ N c ) and this looks remarkably like topological Hamiltonian or action terms discussed in our Chapters 5 and 6. Could baryons be described as solitons in meson fields? The answer was affirmative. One only had to go back 30 years to Skyrme’s papers of 1960-s. Balachandran et al. (1982, 1983) had already revived these papers. So Adkins, Nappi and Witten (1983) reformulated Skyrme’s solutions for N and Δ. This was also done by Jackson and Rho (1983). Since then there has been lot of work on Skyrme model and it is reviewed in Zahed and Brown (1986) and in Bhaduri’s book (1988). After 1988 there have been two interesting new developments. One of these is the connection between the Skyrmion and the instanton, already discussed in Chapter 6. We will describe the Skyrme Lagrangian and then refer to the other work: quantum stabilization of the Skyrme soliton.

QCD Sum Rules

The coupling constant g in the gluon tensor G µv a = ∂ µ A v a −∂ v A µ a + gf abc A µ b A v c is a bare one. Actually, all physical processes are described by the running or effective coupling α s (Q2) ≡ g2(Q2)/4π, characterizing interactions at momenta Q2, where Q2 = −q2 (at distances r ≈ Q−1). The asymptotic freedom (Politzer, 1973; Gross and Wilzcek, 1973) takes place for α s (Q2) ≈ 2π/(9 ln Q/Λ) (for 3 flavours). Because of logarithmic fall off of the coupling the structure of the theory at short distance is simple; the dynamical analysis can be carried out in terms of quarks and gluons interacting perturbatively. Here more or less the same logarithims occur as in electrodynamics. The genuine hadronic theory starts at a length of 0.5 fm and larger.

More on Chiral Anomaly

Start with the Dirac-Maxwell Lagrangian density. Let us consider n n

Chiral Perturbation Theory (CHPT)

begin{gathered} mathcal{L}{text{ = }}left( {1/4{{text{e}}^2}} right){F_{mu upsilon }}{F^{mu upsilon }} + overline psi i{gamma _mu }{D^mu }psi - moverline psi psi hfill {D^mu } = {partial _mu } + {A_mu } hfill end{gathered}

Introduction to Instantons

n n(4.1.1)