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Register a new user$rho$-Meson Form Factors in the Point Form
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We present a calculation of the electromagnetic form factors of the $rho^+$ meson. Our formalism is based on the point-form of relativistic quantum mechanics. Electron-$rho$-meson scattering is formulated as a coupled-channel problem for a Bakamjian-Thomas mass operator, such that the dynamics of the exchanged photon is taken explicitly into account. The $rho$-meson current is extracted from on-shell matrix elements of the optical potential of the scattering process. As a consequence of the violation of cluster separability in the Bakamjian-Thomas framework, our current includes additional, unphysical contributions, which can be separated from the physical ones uniquely. Our results for the form factors are in good agreement with other approaches.
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The electromagnetic structure of the pseudoscalar meson nonet is completely described by the sophisticated Unitary&Analytic model, respecting all known theoretical properties of the corresponding form factors.
We shortly review point-form quantum field theory, i.e. the canonical quantization of a relativistic field theory on a Lorentz-invariant surface of the form $x_mu x^mu = tau^2$. As an example of how point-form quantum field theory may enter the framework of relativistic quantum mechanics we discuss the calculation of the electromagnetic form factor of a confined quark-antiquark pair (e.g. the pion).
Hadron wave functions and form factors can be extracted using four-point correlators. Stochastic techniques are used to estimate the all to all propagators, which are required for the exact calculation of four-point functions. We apply the so called one-end trick to evaluate meson four-point functions. We demonstrate the effectiveness of the technique in the case of the pion and the $rho$-meson where we extract their charge distribution, as well as the form factors.
To obtain further information on the geometric shape of the nucleon, the proton charge form factor is decomposed into two terms, which are connected respectively with a spherically symmetric and an intrinsic quadrupole part of the protons charge density. Quark model relations are employed to derive expressions for both terms. In particular, the protons intrinsic quadrupole form factor is obtained from a relation between the N -> Delta and neutron charge form factors. The proposed decomposition shows that the neutron charge form factor is an observable manifestation of an intrinsic quadrupole form factor of the nucleon. Furthermore, it affords an interpretation of recent electron-nucleon scattering data in terms of a nonspherical distribution of quark-antiquark pairs in the nucleon.
We attempt to solve the Schwinger model, i.e. massless QED in 1+1 dimensions, by quantizing it on a space-time hyperboloid x_mu x^mu =tau^2. The Fock-space representation of the 2-momentum operator is derived and its algebraic structure is analyzed. We briefly outline a solution strategy.
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