arXiv subjects
Publications and source records attributed to M. R. Pennington.
We compare the low-energy partial wave analyses $πN$ scattering with a high-energy data via finite energy sum rules. We construct a new set of amplitudes by matching the imaginary part from the low-energy analysis with the high-energy, Regge parametrization and reconstruct the real parts using dispersion relations.
A recent analysis of data on the two photon production of the $η_c$ and its decay to $K(Kπ)$ has determined the $Kπ$ $S$-wave amplitude in a "model-independent" way assuming primarily that the additional kaon is a spectator in this decay. The purpose of this paper is to fit these results, together with classic $Kπ$ production data from LASS, within a formalism that implements unitarity for the di-meson interaction. This fixes the $I=1/2$ $Kπ\to Kπ$ $S$-wave amplitude up to 2.4 GeV. This resolves the Barrelet ambiguity in the original LASS analysis, and constrains the amount of inelasticity in $Kπ$ scattering, highlighting that this becomes significant beyond 1.8 GeV. This result needs to be checked by experimental information on the many inelastic channels, in particular $Kη^\prime$ and $Kπππ$. Our analysis provides a single representation for the $Kπ$ $S$-wave from threshold, controlled by Chiral Perturbation Theory, through the broad $κ$, $K_0^*(1430)$ and $K_0^*(1950)$ resonances. There is no arbitrary sum of Breit-Wigner forms and random backgrounds for real $Kπ$ masses. Rather the form provides a representation that can be translated to other processes with $Kπ$ interactions with their own coupling functions, while automatically maintaining consistency with the chiral dynamics near threshold, with the LASS data and the new results on $η_c$ decay.
We report measurements of the photon beam asymmetry $Σ$ for the reactions $\vecγp\to pπ^0$ and $\vecγp\to pη$ from the GlueX experiment using a 9 GeV linearly-polarized, tagged photon beam incident on a liquid hydrogen target in Jefferson Lab's Hall D. The asymmetries, measured as a function of the proton momentum transfer, possess greater precision than previous $π^0$ measurements and are the first $η$ measurements in this energy regime. The results are compared with theoretical predictions based on $t$-channel, quasi-particle exchange and constrain the axial-vector component of the neutral meson production mechanism in these models.
With the introduction of a spectral representation, the Schwinger-Dyson equation (SDE) for the fermion propagator is formulated in Minkowski space in QED. After imposing the on-shell renormalization conditions, analytic solutions for the fermion propagator spectral functions are obtained in four dimensions with a renormalizable version of the Gauge Technique anzatz for the fermion-photon vertex in the quenched approximation in the Landau gauge. Despite the limitations of this model, having an explicit solution provides a guiding example of the fermion propagator with the correct analytic structure. The Padé approximation for the spectral functions is also investigated.
Light-by-light scattering sumrules based on general field theory principles relate cross-sections with different helicities. In this paper the simplest sumrule is tested for the $I=0$ and $2$ channels for "real" photon-photon collisions. Important contributions come from the long-lived pseudoscalar mesons and from di-meson intermediate states. The latest Amplitude Analysis of $γγ\toππ, \overline{K}K$ allows this contribution to be evaluated. However, we find that other multi-meson contributions up to 2.5 GeV are required to satisfy the sumrules. While data on three and four pion cross-sections exist, there is no information about their isospin and helicity decomposition. Nevertheless, we show the measured cross-sections are sufficiently large to ensure the sumrules for the helicity differences are likely fulfilled.
We derive the gauge covariance requirement imposed on the QED fermion-photon three-point function within the framework of a spectral representation for fermion propagators. When satisfied, such requirement ensures solutions to the fermion propagator Schwinger-Dyson equation (SDE) in any covariant gauge with arbitrary numbers of spacetime dimensions to be consistent with the Landau-Khalatnikov-Fradkin transformation (LKFT). The general result has been verified by the special cases of three and four dimensions. Additionally, we present the condition that ensures the vacuum polarization is independent of the gauge parameter. As an illustration, we show how the Gauge Technique dimensionally regularized in 4D does not satisfy the covariance requirement.
Any practical application of the Schwinger-Dyson equations to the study of $n$-point Green's functions of a field theory requires truncations, the best known being finite order perturbation theory. Strong coupling studies require a different approach. In the case of QED, gauge covariance is a powerful constraint. By using a spectral representation for the massive fermion propagator in QED, we are able to show that the constraints imposed by the Landau-Khalatnikov-Fradkin transformations are linear operations on the spectral densities. Here we formally define these group operations and show with a couple of examples how in practice they provide a straightforward way to test the gauge covariance of any viable truncation of the Schwinger-Dyson equation for the fermion 2-point function.
We explore the dependence of fermion propagators on the covariant gauge fixing parameter in quantum electrodynamics (QED) with the number of spacetime dimensions kept explicit. Gauge covariance is controlled by the the Landau-Khalatnikov-Fradkin transformation (LKFT). Utilizing its group nature, the LKFT for a fermion propagator in Minkowski space is solved exactly. The special scenario of 3D is used to test claims made for general cases. When renormalized correctly, a simplification of the LKFT in 4D has been achieved with the help of fractional calculus.
The last few years have been witness to a proliferation of new results concerning heavy exotic hadrons. Experimentally, many new signals have been discovered that could be pointing towards the existence of tetraquarks, pentaquarks, and other exotic configurations of quarks and gluons. Theoretically, advances in lattice field theory techniques place us at the cusp of understanding complex coupled-channel phenomena, modelling grows more sophisticated, and effective field theories are being applied to an ever greater range of situations. It is thus an opportune time to evaluate the status of the field. In the following, a series of high priority experimental and theoretical issues concerning heavy exotic hadrons is presented.
It has long been expected that the spectrum of hadrons in QCD would be far richer and extensive than experiment has so far revealed. While there have been experimental hints of this richness for some time, it is really only in the last few years that dramatic progress has been seen in the exploration both experimentally and in calculations on the lattice. Precision studies enabled by new technology both with detectors and high performance computations are converging on an understanding of the spectrum in strong coupling QCD. These methodologies are laying the foundation for a decade of potential discovery that electro and photoproduction experiments at Jefferson Lab, which when combined with key results on $B$ and charmonium decays from both $e^+e^-$ and $pp$ colliders, should turn mere impressions of the light meson spectrum into a high definition picture.
We apply the generalized Veneziano model ($B_5$ model) in the double-Regge exchange limit to the $γp \to K^+ K^- p$ reaction. Four different cases defined by the possible combinations of the signature factors of leading Regge exchanges (($K^*,a_2/f_2$), ($K^*,ρ/ω$), ($K_2^*,a_2/f_2$), and ($K_2^*,ρ/ω$)) have been simulated through the Monte Carlo method. Suitable event candidates for the double-Regge exchange high-energy limit were selected employing \textit{Van Hove} plots as a better alternative to kinematical cuts in the $K^+ K^- p$ Dalitz plot. In this way we predict and analyze the double-Regge contribution to the $K^+ K^- p$ Dalitz plot, which constitutes one of the major backgrounds in the search for strangeonia, hybrids and exotics using $γp\rightarrow K^+K^-p$ reaction. We expect that data currently under analysis, and that to come in the future, will allow verification of the double-Regge behavior and a better assessment of this component of the amplitude.
Amplitude Analysis of two photon production of $ππ$ and ${\overline K}K$, using S-matrix constraints and fitting all available data, including the latest precision results from Belle, yields a single partial wave solution up to 1.4 GeV. The two photon couplings of the $σ/f_0(500)$, $f_0(980)$ and $f_2(1270)$ are determined from the residues of the resonance poles.
We adapt the Veneziano model to the analysis of vector charmonium decays. Starting from a set of covariant Veneziano terms we show how to construct partial waves amplitudes that receive contributions from selected Regge trajectories. The amplitudes, nevertheless retain the proper asymptotic limit. This arises from duality between directly produced resonances and cross-channel Reggeon and in practical applications helps remove uncertainties in the parametrization of backgrounds.
A brief overview is given of what we know of the baryon and meson spectra, with a focus on what are the key internal degrees of freedom and how these relate to strong coupling QCD. The challenges, experimental, theoretical and phenomenological, for the future are outlined, with particular reference to a program at Jefferson Lab to extract hadronic states in which glue unambiguously contributes to their quantum numbers.
The contribution that Jefferson Lab has made, with its 6 GeV electron beam, and will make, with its 12 GeV upgrade, to our understanding of the way the fundamental interactions work, particularly strong coupling QCD, is outlined. The physics at the GeV scale is essential even in TeV collisions.
Tremendous progress has been made in mapping out the spectrum of hadrons over the past decade with plans to make further advances in the decade ahead. Baryons and mesons, both expected and unexpected, have been found, the results of precision experiments often with polarized beams, polarized targets and sometimes polarization of the final states. All these hadrons generate poles in the complex energy plane that are consequences of strong coupling QCD. They reveal how this works.
The non-perturbative gluon and ghost propagators in Landau gauge QCD are obtained using the Schwinger-Dyson equation approach. The propagator equations are solved in Euclidean space using Landau gauge with a range of vertex inputs. Initially we solve for the ghost alone, using a model gluon input, which leads us to favour a finite ghost dressing in the non-perturbative region. In order to then solve the gluon and ghost equations simultaneously, we find that non-trivial vertices are required, particularly for the gluon propagator in the small momentum limit. We focus on the properties of a number vertices and how these differences influence the final solutions. The self-consistent solutions we obtain are all qualitatively similar and contain a masslike term in the gluon propagator dressing in agreement with related studies, supporting the long-held proposal of Cornwall.
The Gluon and Ghost propagators in Landau gauge QCD are investigated using the Schwinger-Dyson equation approach. Working in Euclidean spacetime, we solve for these propagators using a selection of vertex inputs, initially for the ghost equation alone and then for both propagators simultaneously. The results are shown to be highly sensitive to the choices of vertices. We favor the infrared finite ghost solution from studying the ghost equation alone where we argue for a specific unique solution. In order to solve this simultaneously with the gluon using a dressed-one-loop truncation, we find that a non-trivial full ghost-gluon vertex is required in the vanishing gluon momentum limit. The self-consistent solutions we obtain correspond to having a mass-like term in the gluon propagator dressing, in agreement with similar studies supporting the long held proposal of Cornwall.