Hidden gauge formalism for the radiative decays of axial-vector mesons

The radiative decay of the axial-vector resonances into a pseudoscalar meson and a photon is studied using the vector meson Lagrangian obtained from the hidden gauge symmetry (HGS) formalism. The formalism is well suited to study this problem since it deals with pseudoscalar and vector mesons in a unified way, respecting chiral invariance. We show explicitly the gauge invariance of the set of diagrams that appear in the approach and evaluate the radiative decay width of the a1(1260) and b1(1235) axial vector meson resonances into pi gamma. We also include the contribution of loops involving anomalous couplings and compare the results to those obtained previously within another formalism.Comment: 24 pages, 6 tables, 11 figure

Two-point correlation function with pion in QCD sum rules

Within the framework of the conventional QCD sum rules, we study the pion two-point correlation function, $i\int d^4x e^{iq\cdot x} < 0| T J_N(x) {\bar J}_N(0)|\pi(p)>$, beyond the soft-pion limit. We construct sum rules from the three distinct Dirac structures, i \gamma_5 \notp, i \gamma_5, \gamma_5 \sigma_{\mu \nu} {q^\mu p^\nu} and study the reliability of each sum rule. The sum rule from the third structure is found to be insensitive to the continuum threshold, $S_\pi$, and contains relatively small contribution from the undetermined single pole which we denote as $b$. The sum rule from the $i \gamma_5$ structure is very different even though it contains similar contributions from $S_\pi$ and $b$ as the ones coming from the $\gamma_5 \sigma_{\mu \nu} {q^\mu p^\nu}$ structure. On the other hand, the sum rule from the i \gamma_5 \notp structure has strong dependence on both $S_\pi$ and $b$, which is clearly in constrast with the sum rule for $\gamma_5 \sigma_{\mu \nu} {q^\mu p^\nu}$. We identify the source of the sensitivity for each of the sum rules by making specific models for higher resonance contributions and discuss the implication.Comment: slightly revised. version accepted for publication in Physical Review

Effective Nucleon-Nucleon Interaction and Fermi Liquid Theory

We present two novel relations between the quasiparticle interaction in nuclear matter and the unique low momentum nucleon-nucleon interaction in vacuum. These relations provide two independent constraints on the Fermi liquid parameters of nuclear matter. Moreover, the new constraints define two combinations of Fermi liquid parameters, which are invariant under the renormalization group flow in the particle-hole channels. Using empirical values for the spin-independent Fermi liquid parameters, we are able to compute the major spin-dependent ones by imposing the new constraints as well as the Pauli principle sum rules.Comment: 4 pages, 5 figures, in Proc. 11th International Conference on Recent Progress in Many-Body Theories, Manchester, UK, July 9-13, 200

Deconstructing 1S0 nucleon-nucleon scattering

A distorted-wave method is used to analyse nucleon-nucleon scattering in the 1S0 channel. Effects of one-pion exchange are removed from the empirical phase shift to all orders by using a modified effective-range expansion. Two-pion exchange is then subtracted in the distorted-wave Born approximation, with matrix elements taken between scattering waves for the one-pion exchange potential. The residual short-range interaction shows a very rapid energy dependence for kinetic energies above about 100 MeV, suggesting that the breakdown scale of the corresponding effective theory is only 270MeV. This may signal the need to include the Delta resonance as an explicit degree of freedom in order to describe scattering at these energies. An alternative strategy of keeping the cutoff finite to reduce large, but finite, contributions from the long-range forces is also discussed.Comment: 10 pages, 2 figures (introduction revised, references added; version to appear in EPJA

Baryon structure in a quark-confining non-local NJL model

We study the nucleon and diquarks in a non-local Nambu-Jona-Lasinio model. For certain parameters the model exhibits quark confinement, in the form of a propagator without real poles. After truncation of the two-body channels to the scalar and axial-vector diquarks, a relativistic Faddeev equation for nucleon bound states is solved in the covariant diquark-quark picture. The dependence of the nucleon mass on diquark masses is studied in detail. We find parameters that lead to a simultaneous reasonable description of pions and nucleons. Both the diquarks contribute attractively to the nucleon mass. Axial-vector diquark correlations are seen to be important, especially in the confining phase of the model. We study the possible implications of quark confinement for the description of the diquarks and the nucleon. In particular, we find that it leads to a more compact nucleon.Comment: 21 pages (RevTeX), 18 figures (eps

Pertinent Dirac structure for QCD sum rules of meson-baryon coupling constants

Using general baryon interpolating fields $J_B$ for $B= N, \Xi, \Sigma,$ without derivative, we study QCD sum rules for meson-baryon couplings and their dependence on Dirac structures for the two-point correlation function with a meson i\int d^4x e^{iqx} \bra 0|{\rm T}[J_B(x)\bar{J}_B(0)] |{\cal M}(p)\ket. Three distinct Dirac structures are compared: $i\gamma_5$, i\gamma_5\fslash{p}, and $\gamma_5\sigma_{\mu\nu}q^\mu p^\nu$ structures. From the dependence of the OPE on general baryon interpolating fields, we propose criteria for choosing an appropriate Dirac structure for the coupling sum rules. The $\gamma_5\sigma_{\mu\nu}q^\mu p^\nu$ sum rules satisfy the criteria while the $i\gamma_5$ sum rules beyond the chiral limit do not. For the i\gamma_5\fslash{p} sum rules, the large continuum contributions prohibit reliable prediction for the couplings. Thus, the $\gamma_5\sigma_{\mu\nu}q^\mu p^\nu$ structure seems pertinent for realistic predictions. In the SU(3) limit, we identify the OPE terms responsible for the $F/D$ ratio. We then study the dependence of the ratio on the baryon interpolating fields. We conclude the ratio $F/D \sim 0.6-0.8$ for appropriate choice of the interpolating fields.Comment: To be published in Phys.Rev.C ; 21 pages,8 figures, revtex ; references are adde

Power counting and renormalization group invariance in the subtracted kernel method for the two-nucleon system

We apply the subtracted kernel method (SKM), a renormalization approach based on recursive multiple subtractions performed in the kernel of the scattering equation, to the chiral nucleon-nucleon (NN) interactions up to next-to-next-to-leading-order (NNLO). We evaluate the phase-shifts in the 1S0 channel at each order in Weinberg's power counting scheme and in a modified power counting scheme which yields a systematic power-law improvement. We also explicitly demonstrate that the SKM procedure is renormalization group invariant under the change of the subtraction scale through a non-relativistic Callan-Symanzik flow equation for the evolution of the renormalized NN interactions.Comment: Accepted for publication in Journal of Physics G: Nuclear and Particle Physic

Scattering of unstable particles in a finite volume: The case of pi rho scattering and the a(1)(1260) resonance

We present a way to evaluate the scattering of unstable particles quantized in a finite volume with the aim of extracting physical observables for infinite volume from lattice data. We illustrate the method with the πρ scattering which generates dynamically the axial-vector a1(1260) resonance. Energy levels in a finite box are evaluated both considering the ρ as a stable and unstable resonance and we find significant differences between both cases. We discuss how to solve the problem to get the physical scattering amplitudes in the infinite volume, and hence phase shifts, from possible lattice results on energy levels quantized inside a finite box

What does a change in the quark condensate say about restoration of chiral symmetry in matter?

The contribution of nucleons to the quark condensate in nuclear matter includes a piece of first order in $m_\pi$, arising from the contribution of low-momentum virtual pions to the $\pi N$ sigma commutator. Chiral symmetry requires that no term of this order appears in the $NN$ interaction. The mass of a nucleon in matter thus cannot depend in any simple way on the quark condensate alone. More generally, pieces of the quark condensate that arise from low-momentum pions should not be associated with partial restoration of chiral symmetry.Comment: 9 pages (RevTeX). Definition of effective mass changed; numerical value of leading nonanalytic term corrected, along with various misprint

Response of nucleons to external probes in hedgehog models: II. General formalism

Linear response theory for SU(2) hedgehog soliton models is developed.Comment: 25 pages, DOE/ER/40322-163, U. of MD PP \#92-225, (ReVTeX