On the massless contributions to the vacuum polarization of heavy quarks

Recently Groote and Pivovarov have given notice of a possible fault in the use of sum rules involving two-point correlation functions to extract information on heavy quark parameters, due to the presence of massless contributions that invalidate the construction of moments of the spectral densities. Here we show how to circumvent this problem through a new definition of the moments, providing an infrared safe and consistent procedure.Comment: 1+9 pages, 3 figures. Discussion on QCD sum rules applications added. Conclusions unchanged. Version to be published in Journal of Physics

Odd Parity Light Baryon Resonances

We use a consistent SU(6) extension of the meson-baryon chiral Lagrangian within a coupled channel unitary approach in order to calculate the T-matrix for meson-baryon scattering in s-wave. The building blocks of the scheme are the pion and nucleon octets, the rho nonet and the Delta decuplet. We identify poles in this unitary T-matrix and interpret them as resonances. We study here the non exotic sectors with strangeness S=0,-1,-2,-3 and spin J=1/2, 3/2 and 5/2. Many of the poles generated can be associated with known N, Delta, Sigma, Lambda and Xi resonances with negative parity. We show that most of the low-lying three and four star odd parity baryon resonances with spin 1/2 and 3/2 can be related to multiplets of the spin-flavor symmetry group SU(6). This study allows us to predict the spin-parity of the Xi(1620), Xi(1690), Xi(1950), Xi(2250), Omega(2250) and Omega(2380) resonances, which have not been determined experimentally yet.Comment: New appendix and references adde

Multichannel parametrization of \pi N scattering amplitudes and extraction of resonance parameters

We present results of a new multichannel partial-wave analysis for \pi N scattering in the c.m. energy range 1080 to 2100 MeV. This work explicitly includes \eta N and K \Lambda channels and the single pion photoproduction channel. Resonance parameters were extracted by fitting partial-wave amplitudes from all considered channels using a multichannel parametrization that is consistent with S-matrix unitarity. The resonance parameters so obtained are compared to predictions of quark models

Non-perturbative Landau gauge and infrared critical exponents in QCD

We discuss Faddeev-Popov quantization at the non-perturbative level and show that Gribov's prescription of cutting off the functional integral at the Gribov horizon does not change the Schwinger-Dyson equations, but rather resolves an ambiguity in the solution of these equations. We note that Gribov's prescription is not exact, and we therefore turn to the method of stochastic quantization in its time-independent formulation, and recall the proof that it is correct at the non-perturbative level. The non-perturbative Landau gauge is derived as a limiting case, and it is found that it yields the Faddeev-Popov method in Landau gauge with a cut-off at the Gribov horizon, plus a novel term that corrects for over-counting of Gribov copies inside the Gribov horizon. Non-perturbative but truncated coupled Schwinger-Dyson equations for the gluon and ghost propagators $D(k)$ and $G(k)$ in Landau gauge are solved asymptotically in the infrared region. The infrared critical exponents or anomalous dimensions, defined by $D(k) \sim 1/(k^2)^{1 + a_D}$ and $G(k) \sim 1/(k^2)^{1 + a_G}$ are obtained in space-time dimensions $d = 2, 3, 4$. Two possible solutions are obtained with the values, in $d = 4$ dimensions, $a_G = 1, a_D = -2$, or $a_G = [93 - (1201)^{1/2}]/98 \approx 0.595353, a_D = - 2a_G$.Comment: 26 pages. Modified 2.25.02 to update references and to clarify Introduction and Conclusio

Effective boost and "point-form" approach

Triangle Feynman diagrams can be considered as describing form factors of states bound by a zero-range interaction. These form factors are calculated for scalar particles and compared to point-form and non-relativistic results. By examining the expressions of the complete calculation in different frames, we obtain an effective boost transformation which can be compared to the relativistic kinematical one underlying the present point-form calculations, as well as to the Galilean boost. The analytic expressions obtained in this simple model allow a qualitative check of certain results obtained in similar studies. In particular, a mismatch is pointed out between recent practical applications of the point-form approach and the one originally proposed by Dirac.Comment: revised version as accepted for publicatio

Field diffeomorphisms and the algebraic structure of perturbative expansions

We consider field diffeomorphisms in the context of real scalar field theories. Starting from free field theories we apply non-linear field diffeomorphisms to the fields and study the perturbative expansion for the transformed theories. We find that tree level amplitudes for the transformed fields must satisfy BCFW type recursion relations for the S-matrix to remain trivial. For the massless field theory these relations continue to hold in loop computations. In the massive field theory the situation is more subtle. A necessary condition for the Feynman rules to respect the maximal ideal and co-ideal defined by the core Hopf algebra of the transformed theory is that upon renormalization all massive tadpole integrals (defined as all integrals independent of the kinematics of external momenta) are mapped to zero.Comment: 8 pages, 2 figure

Gauge equivalence in QCD: the Weyl and Coulomb gauges

The Weyl-gauge ($A_0^a=0)$ QCD Hamiltonian is unitarily transformed to a representation in which it is expressed entirely in terms of gauge-invariant quark and gluon fields. In a subspace of gauge-invariant states we have constructed that implement the non-Abelian Gauss's law, this unitarily transformed Weyl-gauge Hamiltonian can be further transformed and, under appropriate circumstances, can be identified with the QCD Hamiltonian in the Coulomb gauge. We demonstrate an isomorphism that materially facilitates the application of this Hamiltonian to a variety of physical processes, including the evaluation of $S$-matrix elements. This isomorphism relates the gauge-invariant representation of the Hamiltonian and the required set of gauge-invariant states to a Hamiltonian of the same functional form but dependent on ordinary unconstrained Weyl-gauge fields operating within a space of ``standard'' perturbative states. The fact that the gauge-invariant chromoelectric field is not hermitian has important implications for the functional form of the Hamiltonian finally obtained. When this nonhermiticity is taken into account, the ``extra'' vertices in Christ and Lee's Coulomb-gauge Hamiltonian are natural outgrowths of the formalism. When this nonhermiticity is neglected, the Hamiltonian used in the earlier work of Gribov and others results.Comment: 25 page

The Rarita--Schwinger field: renormalization and phenomenology

We discuss renormalization of propagator of interacting Rarita--Schwinger field. Spin-3/2 contribution after renormalization takes usual resonance form. For non-leading spin-1/2 terms we found procedure, which guarantees absence of poles in energy plane. The obtained renormalized propagator has one free parameter and is a straight generalization of the famous free propagator of Moldauer and Case. Application of this propagator for production of $\Delta^{++}(1232)$ in \pi^{+}\particle{p}\to \pi^{+}\particle{p} leads to good description of total cross-section and to reasonable agreement with results of partial wave analysis.Comment: 19 pages, 3 figures, revtex4; misprints, min editorial change

Electromagnetic Meson Form Factors in the Salpeter Model

We present a covariant scheme to calculate mesonic transitions in the framework of the Salpeter equation for $q\bar{q}$-states. The full Bethe Salpeter amplitudes are reconstructed from equal time amplitudes which were obtained in a previous paper\cite{Mue} by solving the Salpeter equation for a confining plus an instanton induced interaction. This method is applied to calculate electromagnetic form factors and decay widths of low lying pseudoscalar and vector mesons including predictions for CEBAF experiments. We also describe the momentum transfer dependence for the processes $\pi^0,\eta,\eta'\rightarrow\gamma\gamma^*$.Comment: 22 pages including 10 figure

The energies and residues of the nucleon resonances N(1535) and N(1650)

We extract pole positions for the N(1535) and N(1650) resonances using two different models. The positions are determined from fits to different subsets of the existing $\pi N\to\pi N$, $\pi N\to\eta N$ and $\gamma p\to\eta p$ data and found to be 1515(10)--i85(15)MeV and 1660(10)--i65(10)MeV, when the data is described in terms of two poles. Sensitivity to the choice of fitted data is explored. The corresponding $\pi \pi$ and $\eta \eta$ residues of these poles are also extracted.Comment: 9 page