Background: In $pi^+n$ and $pi^-p$ electroproduction, conventional models cannot satisfactory explain the data above the resonance region, in particular the transverse cross section. Although no high-energy L-T-separated cross-section data is availab
le to date, a similar scenario can be inferred for $K^+Lambda$ electroproduction. Purpose: Develop a phenomenological model for the $p(gamma^*,K^+)Lambda$ reaction at forward angles and high-energies. Propose a universal framework for interpreting charged-kaon and charged-pion electroproduction above the resonance region. Method: Guided by the recent model for charged-pion electroproduction, developed by the authors, a framework for $K^+Lambda$ electroproduction at high energies and forward angles is constructed. To this end, a Reggeized background model for $K^+Lambda$ photoproduction is first developed. This model is used as a starting base to set up an electroproduction framework. Results: The few available data of the unseparated $p(gamma^*,K^+)Lambda$ cross section are well explained by the model. Predictions for the L-T-separation experiment planned with the 12 GeV upgrade at Jefferson Lab are given. The newly-proposed framework predicts an increased magnitude for the transverse structure function, similar to the situation in charged-pion electroproduction. Conclusions: Within a hadronic framework featuring Reggeized background amplitudes, $s$-channel resonance-parton effects can explain the observed magnitude of the unseparated $p(gamma^*,K^+)Lambda$ cross section at high energies and forward angles. Thereby, no hardening of the kaon electromagnetic form factor is required.
Pseudoscalar-meson photoproduction is characterized by four complex reaction amplitudes. A complete set is a minimum theoretical set of observables that allow to determine these amplitudes unambiguously. It is studied whether complete sets remain com
plete when experimental uncertainty is involved. To this end, data from the GRAAL Collaboration and simulated data from a realistic model, both for the $gamma p to K^+ Lambda$ reaction, are analyzed in the transversity representation of the reaction amplitudes. It is found that only the moduli of the transversity amplitudes can be determined without ambiguity but not the relative phases.
[Background] Above the nucleon resonance region, the $N(e,epi^pm)N$ data cannot be explained by conventional hadronic models. For example, the observed magnitude of the transverse cross section is significantly underestimated in a framework with Regg
eized background amplitudes. [Purpose] Develop a phenomenological framework for the $N(e,epi^pm)N$ reaction at high invariant mass $W$ and deep photon virtuality $Q^2$. [Method] Building on the work of Kaskulov and Mosel, a gauged pion-exchange current is introduced with a running cutoff energy for the proton electromagnetic transition form factor. A new transition form factor is proposed. It respects the correct on-shell limit, has a simple physical interpretation and reduces the number of free parameters by one. [Results] A study of the $W$ dependence of the $N(e,epi^pm)N$ lends support for the newly proposed transition form factor. In addition, an improved description of the separated and unseparated cross sections at $-t lesssim 0.5 ;text{GeV}^2$ is obtained. The predictions overshoot the measured unseparated cross sections for $-t > 0.5 ;text{GeV}^2$. Introducing a strong hadronic form factor in the Reggeized background amplitudes brings the calculations considerably closer to the high $-t$ data. [Conclusions] Hadronic models corrected for resonance/parton duality describe the separated pion electroproduction cross sections above the resonance region reasonably well at low $-t$. In order to validate the applicability of these models at high $-t$, separated cross sections are needed. These are expected to provide a more profound insight into the relevant reaction mechanisms.
[Background] A complete set is a minimum set of observables which allows one to determine the underlying reaction amplitudes unambiguously. Pseudoscalar-meson photoproduction from the nucleon is characterized by four such amplitudes and complete sets
involve single- and double-polarization observables. [Purpose] Identify complete sets of observables, and study how measurements with finite error bars impact their potential to determine the reaction amplitudes unambiguously. [Method] The authors provide arguments to employ the transversity representation in order to determine the amplitudes in pseudoscalar-meson photoproduction. It is studied whether the amplitudes in the transversity basis for the $gamma p to K^+Lambda$ reaction can be estimated without ambiguity. To this end, data from the GRAAL collaboration and mock data from a realistic model are analyzed. [Results] It is illustrated that the moduli of normalized transversity amplitudes can be determined from precise single-polarization data. Starting from mock data with achievable experimental resolution, it is quite likely to obtain imaginary solutions for the relative phases of the amplitudes. Also the real solutions face a discrete phase ambiguity which makes it impossible to obtain a statistically significant solution for the relative phases at realistic experimental conditions. [Conclusions] Single polarization observables are effective in determining the moduli of the amplitudes in a transversity basis. Determining the relative phases of the amplitudes from double-polarization observables is far less evident. The availability of a complete set of observables does not allow one to unambiguously determine the reaction amplitudes with statistical significance.
A Bayesian analysis of the worlds $p(gamma,K^+)Lambda$ data is presented. We adopt a Regge-plus-resonance framework featuring consistent interactions for nucleon resonances up to spin $J = 5/2$. The power of the momentum dependence of the consistent
interaction structure rises with the spin of the resonance. This leads to unphysical structures in the energy dependence of the computed cross sections when the short-distance physics is cut off with standard hadronic form factors. A plausible, spin-dependent modification of the hadronic form factor is proposed which suppresses the unphysical artifacts. Next, we evaluate all possible combinations of 11 candidate resonances. The best model is selected from the 2048 model variants by calculating the Bayesian evidence values against the worlds $p(gamma,K^+)Lambda$ data. From the proposed selection of 11 resonances, we find that the following nucleon resonances have the highest probability of contributing to the reaction: $S_{11}(1535)$, $S_{11}(1650)$, $F_{15}(1680)$, $P_{13}(1720)$, $D_{13}(1900)$, $P_{13}(1900)$, $P_{11}(1900)$, and $F_{15}(2000)$.
We address the issue of unbiased model selection and propose a methodology based on Bayesian inference to extract physical information from kaon photoproduction $p(gamma,K^+)Lambda$ data. We use the single-channel Regge-plus-resonance (RPR) framework
for $p(gamma,K^+)Lambda$ to illustrate the proposed strategy. The Bayesian evidence Z is a quantitative measure for the models fitness given the worlds data. We present a numerical method for performing the multidimensional integrals in the expression for the Bayesian evidence. We use the $p(gamma,K^+)Lambda$ data with an invariant energy W > 2.6 GeV in order to constrain the background contributions in the RPR framework with Bayesian inference. Next, the resonance information is extracted from the analysis of differential cross sections, single and double polarization observables. This background and resonance content constitutes the basis of a model which is coined RPR-2011. It is shown that RPR-2011 yields a comprehensive account of the kaon photoproduction data and provides reasonable predictions for $p(e,e K^+)Lambda$ observables.
A Bayesian analysis of the worlds p(gamma,K^+)Lambda data is presented. From the proposed selection of 11 resonances, we find that the following nucleon resonances have the highest probability of contributing to the reaction: S11(1535), S11(1650), F1
5(1680), P13(1720), D13(1900), P13(1900), P11(1900), and F15(2000). We adopt a Regge-plus-resonance framework featuring consistent couplings for nucleon resonances up to spin J=5/2. We evaluate all possible combinations of 11 candidate resonances. The best model is selected from the 2048 model variants by calculating the Bayesian evidence values against the worlds p(gamma,K^+)Lambda data.
Consistent interactions for off-shell fermion fields of arbitrary spin are constructed from the gauge-invariance requirement of the interaction Lagrangians. These interactions play a crucial role in the quantum hadrodynamical description of high-spin
baryon resonances in hadronic processes. We find that the power of the momentum dependence of a consistent interaction rises with the spin of the fermion field. This leads to unphysical structures in the energy dependence of the computed tree-level cross sections when the short-distance physics is cut off with standard hadronic form factors. A novel, spin-dependent hadronic form factor is proposed that suppresses the unphysical artifacts.
We address the issue of consistent interactions for off-shell fermion fields of arbitrary spin. These interactions play a crucial role in the quantum hadrodynamical description of high-spin baryon resonances in hadronic processes. The Rarita-Schwinge
r description of high-spin fermion fields involves unphysical degrees of freedom, associated with their lower-spin content. These enter the interaction if not eliminated outright. The invariance condition of the interaction under the unconstrained Rarita-Schwinger gauge removes the lower-spin content of the fermion propagator and leads to a consistent description of the interaction. We develop the most general, consistent interaction structure for high-spin fermions. We find that the power of the momentum dependence of a consistent interaction rises with the spin of the fermion field. This leads to unphysical structures in the energy dependence of the computed cross sections when the short-distance physics is cut off with standard hadronic form factors. A novel, spin-dependent hadronic form factor is proposed that suppresses the unphysical artifacts.
