The Lamb shift contribution of very light millicharged particles

Abstract

The leading order vacuum polarization contribution of very light millicharged fermions and scalar (spin-0) particles with charge εe and mass μto the Lamb shift of the hydrogen atom is shown to imply universal, i.e. μ-independent, upper bounds on ε: ε\lsim 10^{-4} for μ\lsim 1 keV in the case of fermions, and for scalars this bound is increased by a factor of 2. This is in contrast to expectations based on the commonly used approximation to the Uehling potential relevant only for conventionally large fermion (and scalar) masses.

Figures (3)

• Figure 1: Allowed upper bounds of $\varepsilon$ according to the exact leading order contribution (6) and (11) of fermions and scalars, respectively, to the Lamb shift of the hydrogen atom corresponding to a $1\sigma$ discrepancy of 0.01 MHz between theory and experiment. The dashed 'fermion' curve corresponds to the bound suggested in ref3ref8 being based on the approximate expression (2) as discussed in the text. The dashed 'scalar' curve is obtained from the approximate expression (14). (In order to avoid any confusion it should be stressed that the area above the respective curves is excluded.)
• Figure 2: As in Fig. 1 for fermions but using a linear scale for $\varepsilon$.
• Figure 3: As in Fig. 1 for scalars but using a linear scale for $\varepsilon$.