Lorentz violation in simple QED processes

We determine the effect of a $CPT$-even and Lorentz violating nonminimal coupling on the differential cross sections for some of the most important tree-level processes in QED, namely, Compton and Bhabha scatterings, as well as electron-positron annihilation. Experimental limits constraining the allowed deviation of the differential cross sections relative to pure QED allow us to place upper bounds on the Lorentz violating parameters. A constraint based on the decay rate of parapositronium is also obtained.

Figure 1

Feynman diagrams contributing to the processes considered and associated Mandelstam variables. The blob represents the effective vertex, Eq. (2).

Figure 2

Instantaneous angular profile (low-energy regime) of Eq. (8) for ${\varphi }_{\xi }=0$ (top) and ${\varphi }_{\xi }=\pi /2$ (bottom), with $N_{\sigma }={[\frac{\alpha |\mathit{\xi }{|}^2}{8\pi }{(\frac{\omega }{m})}^2]}^{-1}d{\sigma }_{\mathrm{LV}}^{e\gamma ,\perp }/d\mathrm{\Omega }$.

Figure 3

The top panel displays the differential cross sections for the usual QED (solid line) and the timelike LV contribution (dashed line) assuming ${\xi }_0={10}^{-3}{\mathrm{GeV}}^{-1}$, and the inset shows the nonmonotonic angular dependence of the LV sector. The bottom panel shows the deviation [LHS of Eq. (13)] as a function of the scattering angle.

Figure 4

Instantaneous LV differential cross sections for pure spacelike background ($\mathit{\xi }\perp \widehat{\mathbf{z}}$, i.e., ${\theta }_{\xi }=\pi /2$). The vertical axes are given by $N_{\sigma }={[\alpha |\mathit{\xi }{|}^2]}^{-1}d{\sigma }_{\mathrm{LV}}^{ee,\perp }/d\mathrm{\Omega }$ with ${\varphi }_{\xi }=0$ (bottom) and ${\varphi }_{\xi }=\pi /2$ (top).