Mira Dey

Radiative decays of S-wave charmed baryons

Abstract We calculated radiative decay widths of possible radiative transitions between S -wave charmed baryons in naive static quark model and in non-relativistic quark potential model. The results obtained in these two approaches are in a fair agreement. We predict the following life time for Ω c + and ξ c ′ baryons: τ(Ω c + ) ≈ 10 −18 s , τ ( Ξ c ′) ≈ 10 −19 s .

Instantons and charmed baryon mass splittings

Abstract Masses of baryons with one charmed valence quark are calculated using the approach of Shuryak and Rosner. In their model the masses of vector and scalar diquarks inside baryons are different. It is shown that the parameters of this model for charmed baryons should differ from non-charmed baryons. In the family of such single charmed baryons we predict at least one baryon Ω c ∗ which shoud decay with the emission of photons, while the rest with J P = 3 2 + (∑ c ∗ and ξ c ∗ ) might decay via strong interaction with the emission of pions. A generalisation of the Gell-Mann-Okubo relation and the masses of the single charmed baryons are predicted.

Baryon and meson density of states

Abstract In a finite size bag like picture consisting of quarks (2 flavour) and gluons with SU (3) colour singlet restriction on the partition function and the chemical potential μ ≠ 0 with the constraint that the baryon number b = 0 and b = 1 for mesons and baryons, respectively we find a very good agreement with baryon density of states upto 2 GeV and with mesonic ones uptto 1.3 GeV. Similar to a hadron-scale string theory our calculation also suggests that beyond 1.3 GeV there should exist exotic mesons.

Observed supersymmetry of hadrons and the tachyonless string models

Abstract The experimental mesonic density of states ϱ meson ( m ) ≅ ϱ baryon ( m ) from 0.9 to 1.3 GeV. In this region the ϱ meson fits the ϱ ( m ) deduced for it from discrete bag model states. Beyond 1.3 GeV one can expect exotic mesons. If ϱ meson is replaced by the baryon density (as suggested by string model studies [D. Kutasov and N. Seiberg, Nucl. Phys. B 358 (1991) 600; P.G.O. Freund and J.L. Rosner, Phys. Rev. Lett. 68 (1992) 765]), agreement with theory is obtained up to 1.7 GeV. Beyond 1.7 GeV exotic baryons may be expected.

Meson properties from a bag model compared to lattice theory and heavy ion experiments

A bag at temperature (T) with pressureB(T)=B(0)[1−(T/Tc)4] is shown to be consistent with recent lattice data on the π and the ρ mesons. The limiting temperature,Tl, of the pion bag from the Bekenstein entropy bound is lower than that of other mesons. This agrees with the thermal distribution of π,K and the ρ in heavy ion collisions, which (unlike proton-nucleus or pp data) show a marked difference inT of pion and other mesons in the mid-rapidity region.

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

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 - m\overline \psi \psi \hfill \\{D^\mu } = {\partial _\mu } + {A_\mu } \hfill \\\end{gathered}