The production model of Ishida et al. and unitarity
The relation between scattering and production amplitudes imposed by unitarity and analyticity, recently criticised by Ishida et al., is explained.
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arXiv subjects
M. R. Pennington
Publications and source records attributed to M. R. Pennington.
Dressing the Scalar Glueball
The hadronic dressing of the ten lightest scalar mesons, the $q{\bar q}$ nonet and a glueball, is discussed.
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The non-perturbative three-point vertex in massless quenched QED and perturbation theory constraints
Dong, Munczek and Roberts have shown how the full 3-point vertex that appears in the Schwinger-Dyson equation for the fermion propagator can be expressed in terms of a constrained function $W_1$ in massless quenched QED. However, this analysis involved two key assumptions: that the fermion anomalous dimension vanishes in the Landau gauge and that the transverse vertex has a simplified dependence on momenta. Here we remove these assumptions and find the general form for a new constrained function $U_1$ that ensures the multiplicative renormalizability of the fermion propagator non-perturbatively. We then study the restriction imposed on $U_1$ by recent perturbative calculations of the vertex and compute its leading logarithmic expansion. Since $U_1$ should reduce to this expansion in the weak coupling regime, this should serve as a guide to its non-perturbative construction. We comment on the perturbative realization of the constraints on $U_1$.
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Unquenching the scalar glueball
Computations in the quenched approximation on the lattice predict the lightest glueball to be a scalar in the 1.5-1.8 GeV region. Here we calculate the dynamical effect the coupling to two pseudoscalars has on the mass, width and decay pattern of such a scalar glueball. These hadronic interactions allow mixing with the $q \overline q$ scalar nonet, which is largely fixed by the well-established K_0^*(1430). This non-perturbative mixing means that, if the pure gluestate has a width to two pseudoscalar channels of ~100 MeV as predicted on the lattice, the resulting hadron has a width to these channels of only ~30 MeV with a large eta-eta component. Experimental results need to be reanalyzed in the light of these predictions to decide if either the f_0(1500) or an f_0(1710) coincides with this dressed glueball.
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Testing Chiral Symmetry Breaking at DAPHNE
The spontaneous breakdown of the chiral symmetry of the QCD Lagrangian ensures that $ππ$ interactions are weak at low energies. How weak depends on the nature of explicit symmetry breaking. Measurements of $K_{e4}$ decays at DA$Φ$NE will provide a unique insight into this mechanism and test whether the $q{\overline q}$--condensate is large or small.
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Calculating hadronic properties in strong QCD
This talk, given at the Second Workshop on ELFE Physics, St Malo, France, September 1996, presents a brief review of the progress that has been made in calculating the properties of hadrons in strong QCD.
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Standard vs. Generalized Chiral Perturbation Theory : the Chell-Olsson test
A way of testing the $ππ$ predictions of Chiral Perturbation Theory against experimental data is to use dispersion relations to continue experimental information into the subthreshold region where the theory should unambiguously apply. Chell and Olsson have proposed a test of the subthreshold behaviour of chiral expansions which highlights potential differences between the Standard and the Generalized forms of the theory. We illustrate how, with current experimental uncertainties, data cannot distinguish between these particular {\em discriminatory} coefficients despite their sensitivity. Nevertheless, the Chell--Olsson test does provide a consistency check of the chiral expansion, requiring that the ${\cal O}(p^6)$ corrections to the {\em discriminatory} coefficients in the Standard theory must be $\sim 100%$. Indeed, some of these have been deduced from the new ${\cal O}(p^6)$ computations and found to give such large corrections. One can then check that the ${\cal O}(p^8)$ corrections must be much smaller. We conclude that this test, like others, cannot distinguish between the different forms of Chiral Symmetry Breaking embodied in the alternative versions of Chiral Perturbation Theory without much more precise experimental information near threshold.
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Chiral poles and zeros and the role of the left hand cut
It has been recently claimed that the Inverse Amplitude Method provides a reliable unitarisation of Chiral Perturbation Theory allowing resonance poles to be accurately uncovered. We illustrate the sensitivity of these claims to the treatment of the Adler zero and to assumptions about the left hand cut (and hence about the underlying exchange forces). Previously favoured methods are shown to mistreat the Adler zeros and violate crossing symmetry casting doubt on the precision of their phenomenology. A more reliable solution is proposed.
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Constraint on the QED Vertex from the Mass Anomalous Dimension $γ_m = 1$
We discuss the structure of the non-perturbative fermion-boson vertex in quenched QED. We show that it is possible to construct a vertex which not only ensures that the fermion propagator is multiplicatively renormalizable, obeys the appropriate Ward-Takahashi identity, reproduces perturbation theory for weak couplings and guarantees that the critical coupling at which the mass is dynamically generated is gauge independent but also makes sure that the value for the anomalous dimension for the mass function is strictly 1, as Holdom and Mahanta have proposed.
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Hadron '95 --- Summary: Part I
Part I of this summary is concerned with selected results on natural parity states presented at this conference, in particular the glueball candidates the $f_0(1510)$ and $ξ(2230)$. Unnatural parity and exotic states are discussed by Suh-Urk Chung
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Should the Pomeron and imaginary parts be modelled by two gluons and real quarks?
We illustrate that solution of the Schwinger-Dyson equation for the gluon propagator in QCD does not support an infrared softened behaviour, but only an infrared enhancement. This has consequences for the modelling of the Pomeron in terms of dressed gluon exchange. It highlights that an understanding of the Pomeron within QCD must take account of the bound state nature of hadrons.
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Infrared Behaviour of the Gluon Propagator: Confining or Confined?
The possible infrared behaviour of the gluon propagator is studied analytically, using the Schwinger-Dyson equations, in both the axial and the Landau gauge. The possibility of a gluon propagator less singular than $1/k^{2}$ when $k^{2} \rightarrow 0$ is investigated and found to be inconsistent, despite claims to the contrary, whereas an infrared enhanced one is consistent. The implications for confinement are discussed.
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ONE LOOP QED VERTEX IN ANY COVARIANT GAUGE: ITS COMPLETE ANALYTIC FORM
The one loop vertex in QED is calculated in arbitrary covariant gauges as an analytic function of its momenta. The vertex is decomposed into a longitudinal part, that is fully responsible for ensuring the Ward and Ward-Takahashi identities are satisfied, and a transverse part. The transverse part is decomposed into 8 independent components each being separately free of kinematic singularities in $\bf any$ covariant gauge in a basis that modifies that proposed by Ball and Chiu. Analytic expressions for all 11 components of the ${O(α)}$ vertex are given explicitly in terms of elementary functions and one Spence function. These results greatly simplify in particular kinematic regimes.
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Numerical cancellation of photon quadratic divergence in the study of the Schwinger-Dyson equations in Strong Coupling QED
The behaviour of the photon renormalization function in strong coupling QED has been recently studied by Kondo, Mino and Nakatani. We find that the sharp decrease in its behaviour at intermediate photon momenta is an artefact of the method used to remove the quadratic divergence in the vacuum polarization. We discuss how this can be avoided in numerical studies of the Schwinger-Dyson equations.
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The Chiral Lagrangian parameters, $\overline{\ell}_1$, $\overline{\ell}_2$, are determined by the $ρ$--resonance
The all--important consequence of Chiral Dynamics for $ππ$ scattering is the Adler zero, which forces $ππ$ amplitudes to grow asymptotically. The continuation of this subthreshold zero into the physical regions requires a $P$--wave resonance, to be identified with the $ρ$. It is a feature of $ππ$ scattering that convergent dispersive integrals for the $I=1$ channel are essentially saturated by the $ρ$--resonance and are much larger than those with $I=2$ quantum numbers. These facts predict the parameters $\overline{\ell}_1$, $\overline{\ell}_2$ of the Gasser--Leutwyler Chiral Lagrangian, as well as reproducing the well--known KSFR relation and self-consistently generating the $ρ-$resonance.
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Gauge independent Chiral Symmetry Breaking in Quenched QED
In quenched QED we construct a non-perturbative fermion-boson vertex that ensures the fermion propagator satisfies the Ward-Takahashi identity, is multiplicatively renormalizable, agrees with perturbation theory for weak couplings and has a critical coupling for dynamical mass generation that is strictly gauge independent. This is in marked contrast to the rainbow approximation in which the critical coupling changes by 50% just between the Landau and Feynman gauges. The use of such a vertex should lead to a more believable study of mass generation.
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Theoretical Predictions for Pion Polarizabilities
The polarizabilities of the pion have been predicted in several different theoretical frameworks. The status of these is reviewed.
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