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Register a new userSix-Photon Amplitudes in Scalar QED
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The analytical result for the six-photon helicity amplitudes in scalar QED is presented. To compute the loop, a recently developed method based on multiple cuts is used. The amplitudes for QED and $QED^{caln=1}$ are also derived using the supersymmetric decomposition linking the three theories.
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Non perturbative studies of Schwinger-Dyson equations (SDEs) require their infnite, coupled tower to be truncated in order to reduce them to a practically solvable set. In this connection, a physically acceptable ansatz for the three point vertex is the most favorite choice. Scalar quantum electrodynamics (sQED) provides a simple and neat platform to address this problem. The most general form of the three point scalar-photon vertex can be expressed in terms of only two independent form factors, a longitudinal and a transverse one. Ball and Chiu have demonstrated that the longitudinal vertex is fixed by requiring the Ward-Fradkin-Green-Takahashi identity (WFGTI), while the transverse vertex remains undetermined. In massless quenched sQED, we construct the transverse part of the non perturbative scalar-photon vertex. This construction (i) ensures multiplicative renormalizability (MR) of the scalar propagator in keeping with the Landau-Khalatnikov-Fradkin transformations (LKFTs), (ii) has the same transformation properties as the bare vertex under charge conjugation, parity and time reversal, (iii) has no kinematic singularities and (iv) reproduces one loop asymptotic result in the weak coupling regime of the theory.
In spatially structured strong laser fields, quantum electrodynamical vacuum behaves like a nonlinear Kerr medium with modulated third-order susceptibility where new coherent nonlinear effects arise due to modulation. We consider the enhancement of vacuum polarization and magnetization via coherent spatial vacuum effects in the photon-photon interaction process during scattering of a probe laser beam on parallel focused laser beams. Both processes of elastic and inelastic four wave-mixing in structured QED vacuum accompanied with Bragg interference are investigated. The phase-matching conditions and coherent effects in the presence of Bragg grating are analyzed for photon-photon scattering.
Thanks to the absence of tree order, the six-photon processes is a good laboratory to study multi-leg one-loop diagrams. Particularly, there are enough on-shell external legs to observe a special Landau singularity: the double parton scattering.
We introduce photon and gluon propagators in which the scalar polarization component is subtracted systematically by making use of the BRST invariance of the off-shell vector boson created from physical on-shell states. The propagator has the light-cone gauge form, where the spacial component of the gauge vector points along the negative of the off-shell vector boson momentum. We call the gauge as parton-shower gauge, since in collinear configurations the absolute value squared of each Feynman amplitude reproduces all the singular behaviors of the corresponding parton shower in this gauge. We introduce new HELAS codes that can be used to calculate the tree-level helicity amplitudes of arbitrary QED and QCD processes by using MadGraph. The absence of subtle gauge cancellation among Feynman amplitudes allows numerical codes to evaluate singular behaviors accurately, and helps us gaining physical insights on interference patterns.
Scattering and production amplitudes involving scalar resonances are known, according to Watsons theorem, to share the same phase $delta(s)$. We show that, at low energies, the production amplitude is fully determined by the combination of $delta(s)$ with another phase $omega(s)$, which describes intermediate two-meson propagation and is theoretically unambiguous. Our main result is a simple and almost model independent expression, which generalizes the usual $K$-matrix unitarization procedure and is suited to be used in analyses of production data involving scalar resonances.
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