arXiv subjects
Publications and source records attributed to Thomas D. Cohen.
We analyze the chiral limit in dense isospin-asymmetric nuclear matter. It is shown that the pseudo-Goldstone modes in this system are qualitatively different from the case of isospin-symmetric matter.
Standard QCD sum-rule analyses of the nucleon mass give results that are inconsistent with chiral perturbation theory due to an overly simple continuum ansatz on the phenomenological side of the sum rule. We show that a careful treatment of the continuum, including $π$-$N$ states and other states with virtual pions, resolves the inconsistency associated with chiral logs.
A model combining vector meson dominance, $ω- ϕ$ mixing and a kaon cloud contribution is used to estimate the strangeness vector form factors of the nucleon in the momentum range of the planned measurements at MIT-Bates and CEBAF. We compare our results with some other theoretical estimates and discuss the nucleon strangeness radius in models based on dynamically dressed, extended constituent quarks. For a quantitative estimate in the latter framework we use the Nambu-Jona-Lasinio model.
Relations connecting various zero momentum correlators of interpolating fields for pseudoscalar and scalar channel, containing one heavy and one light quark field, are derived from the Euclidean space formulation of the QCD functional integral. These relations may serve as constraints on the phenomenological models or approaches motivated from QCD, and suggest a method to extract the chiral quark condensates. It is also found that the correlator for pseudoscalar channel differs from that for scalar channel even in the large heavy quark mass limit.
QCD sum rules are useful tools for studying the spectral properties of hadrons; however, assumptions underlying standard sum-rule analyses can lead to inconsistencies with known results of chiral perturbation theory. This possibility is demonstrated with QCD sum-rule extractions of the nucleon mass and $σ$ term. In both cases, inconsistent chiral behavior leads to an uncertainty in the sum-rule predictions of $\sim 100\,\text{MeV}$.
Classical considerations suggest that the probability distribution $P(R)$, where $R$ is the ratio of neutral pions to total pions emitted from a disoriented chiral condensate (which has been hypothesized to form in heavy ion reactions) is $R^{-1/2}/2$. Quantum mechanical isospin correlations between the condensate and the remainder of the system can alter this. Moments of the P(R) distribution can be expressed in terms of expectation values of $(I^2/N^2)^m$ where $I$ is the isospin carried by the condensate, $N$ is the number of pions emitted and m is an arbitrary integer. We find that the probability distribution is very similar to the classical distribution for $0.1 < R < 0.9$ unless the isospin carried by the condensate is very large.
Two-pion induced self-energy contributions to the $ρ$-meson mass are examined in relation to the quenched approximation of QCD, where the physics associated with two-pion intermediate states has been excluded from vector-isovector correlation functions. Corrections to quenched QCD calculations of the $ρ$-meson mass are estimated to be small at the order of a few percent of the $ρ$-meson mass. The two-pion contributions display nonanalytic behavior as a function of the pion mass as the two-pion cut is encountered. The implications of this nonanalytic behavior in extrapolations of full QCD calculations are also discussed. We note that for full QCD, the error made in making a linear extrapolation of the $ρ$ mass, neglecting nonanalytic behavior, increases as one approaches the two-pion cut.
We consider a simple model for the strangeness radius of the nucleon. The model is based on vector meson dominance (VMD) and $ω- ϕ$ mixing in addition to a kaon cloud contribution. We find that the VMD contribution is similar in magnitude and of the same sign as the kaon contribution to the Sachs strangeness radius and is significantly larger than the kaon contribution to the Dirac radius. Two figures (not included) can be obtained through the authors (marina@quark.umd.edu).
Diagrammatic methods and Large $N_c$ QCD are used to argue that the nucleon as calculated in quenched QCD contains physics which can be ascribed to the pion cloud of the nucleon. In particular, it is argued that the physics corresponding to one-pion loops in chiral perturbation theory are included in the quenched approximation.
Logarithmic divergences in pion and proton charge radii associated with chiral loops are investigated to assess systematic uncertainties in current lattice determinations of charge radii. The chiral corrections offer a possible solution to the long standing problem of why present lattice calculations yield proton and pion radii which are similar in size.
Hedgehog model predictions for the leading nonanalytic behavior (in $m^{2}_{π}$) of certain observables are shown to agree with the predictions of chiral perturbation theory up to an overall factor which depends on the operator. This factor can be understood in terms of contributions of the $Δ$ isobar in chiral loops. These physically motivated contributions are analyzed in an expansion in which both $m_π$ and $M_Δ-M_N$ are taken as small parameters, and are shown to yield large corrections to both hedgehog models and chiral perturbation theory.