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Register a new userBayesian Model Selection for Electromagnetic Kaon Production on the Nucleon
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We present the results of a Bayesian analysis of a Regge model for K+ Lambda photoproduction. The model is based on the exchange of K+(494) and K*+(892) trajectories in the t-channel. For different prior widths, we find decisive Bayesian evidence (Delta ln Z ~ 24) for a K+ Lambda photoproduction Regge model with a positive vector coupling and a negative tensor coupling constant for the K+(892) trajectory, and a rotating phase factor for both trajectories. Using the chi^2 minimization method, one could not draw this conclusion from the same dataset.
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We present the results of a Bayesian analysis of a Regge model to describe the background contribution for K+ Lambda and K+ Sigma0 photoproduction. The model is based on the exchange of K+(494) and K*+(892) trajectories in the t-channel. We utilise the Bayesian evidence Z to determine the best model variant for each channel. The Bayesian evidence integrals were calculated using the Nested Sampling algorithm. For different prior widths, we find decisive Bayesian evidence (Delta ln Z ~ 24) for a K+ Lambda photoproduction Regge model with a positive vector coupling and a negative tensor coupling constant for the K*+(892) trajectory, and a rotating phase factor for both trajectories. Using the chi^2 minimisation method, one could not draw this conclusion from the same dataset. For the K+ Sigma0 photoproduction Regge model, on the other hand, the difference between the evidence integrals is insufficient to pinpoint one model variant.
The Regge-plus-resonance (RPR) framework for kaon photoproduction on the proton and the neutron is an economical single-channel model with very few parameters. Not only does the RPR model allow one to extract resonance information from the data, it has predictive power. As an example we show that the RPR model makes fair predictions for the $p(e,eK^{+})Lambda$ and the $n(gamma,K^{+})Sigma ^{-}$ observables starting from amplitudes optimized for the reaction $p(gamma, K ^{+})Lambda$ and $p(gamma,K^{+})Sigma ^{0}$ respectively.
The electromagnetic kaon production amplitudes associated to Lambda/Sigma hyperons can be described by phenomenological models, most notably by isobar approaches. Experimental data on kaon production have been collected at ELSA, SPring8, GRAAL, LNS Tohoku, and Jefferson Lab in the past, the measurements at Jefferson Lab providing the largest kinematic coverage and statistical significance. However, ambiguities inherent in the models, some data inconsistency in the cross-sections taken at different laboratories, and the problem of missing acceptance in forward direction of the experimental set-ups hinders a reliable extraction of resonance parameters. Predictions for the hypernuclear photo-production cross-section rely on a consistent and comprehensive description of the elementary process at forward kaon angles, where the current strong variation of the models is very unsatisfactory. A number of new experiments are now addressing these issues, among them the charged kaon electro-production programme with the Kaos spectrometer at the Mainz Microtron MAMI. In this work predictions of the two prominent isobar models, Kaon-Maid and Saclay-Lyon A, are compared for the kinematics at MAMI.
The weak kaon production off the nucleon induced by neutrinos is studied at the low and intermediate energies of interest for some ongoing and future neutrino oscillation experiments. This process is also potentially important for the analysis of proton decay experiments. We develop a microscopical model based on the SU(3) chiral Lagrangians. The basic parameters of the model are fpi, the pion decay constant, Cabibbos angle, the proton and neutron magnetic moments and the axial vector coupling constants for the baryons octet, D and F, that are obtained from the analysis of the semileptonic decays of neutron and hyperons. The studied mechanisms are the main source of kaon production for neutrino energies up to 1.2 to 1.5 GeV for the various channels and the cross sections are large enough to be amenable to be measured by experiments such as Minerva and T2K.
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.
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