Casimir-Polder interactions with massive photons: Implications for BSM physics

We present the derivation of the Casimir-Polder interactions mediated by a massive photon between two neutral systems described in terms of their atomic polarizability tensors. We find a compact expression for the leading term at large distances between the two systems. Our result reduces, in the massless photon limit, to the standard Casimir-Polder. We discuss implications of our findings with respect to recent scenarios of physics beyond the standard model such as universal extra dimensions, Randall-Sundrum and scale-invariant models. For each model we compute the correction to the Casimir-Polder interaction in terms of the free parameters.

Figure 1

Contribution of the KK-tower in the universal extra dimension model to the Casimir-Polder interaction potential relative to the standard QED (massless photon). The solid (blue) line is the numerical result from Eq. (50) obtained truncating the series at $N_{\max }=60$. The full (blue) disks are the results from Eq. (53). The dotted (blue) line is the approximated form as given in Eq. (55). The other curves represent the Randall-Sundrum contribution for different values of the dimensionless parameter $\kappa R$ (with $\xi \to a\xi$ and $a$ given in Eq. (62a)), respectively equal to 0.2 dashed (orange), 0.4 dot-dashed (orange) and 1.2 long-dashed (orange). The full (orange) disks superimposed with the dashed curve represent the result through Eq. (53) with $\xi \to a\xi$.

Figure 2

Unparticle Casimir-Polder interaction potential $U_{d_{\mathcal{U}}}$ relative to the standard QED (massless photon) Casimir-Polder interaction $U$ as a function of the distance, in units of ${\mathrm{\Lambda }}_{\mathcal{U}}^{-1}$, at a fixed value of the coupling $\lambda /e=0.9$. The solid (blue) line is the result for $d_{\mathcal{U}}=2$, the long-dashed (orange) line is for $d_{\mathcal{U}}=1.5$ result and the short-dashed (green) line is for $d_{\mathcal{U}}=1.05$.