Weak Interaction Contribution to the Muonium Hyperfine Structure in the Standard Model

Abstract

The contribution of the weak interaction to the hyperfine splitting of the ground state of muonium is investigated. The amplitudes of the one- and two-quantum exchange determined by the Z and W bosons are calculated. One-loop corrections in the photon and Z boson propagators and their contribution to the hyperfine structure of the spectrum are obtained.

Figures (5)

• Figure 1: One-boson interaction amplitude and one-photon interaction with vertex and self-energy corrections. The dashed line denotes the $Z$ boson, the wavy line denotes the photon and the curlicue line denotes the W-boson.
• Figure 2: Self-energy correction to the photon propagator function with loops of $W$ bosons -- (a,b), gauge bosons -- (b,c), and ghosts -- (d). The wavy line denotes the photon. The dashed line denotes the pseudo-Goldstone boson $\omega$, and the dotted line denotes the ghost field.
• Figure 3: One-loop corrections in the $Z\gamma$ interaction amplitude: fermion loop -- (a), $W^\pm$-boson loop -- (b), loops of pseudo-Goldstone bosons $\omega^\pm$ and ghosts -- (c), (d), loop of $W^\pm$ bosons and pseudo-Goldstone bosons $\omega^\pm$ -- (e). The wavy line denotes the photon, and the dashed line denotes the $Z$ boson.
• Figure 4: Amplitude of photon and $Z$-boson interaction. The wavy line represents the photon and the dotted line represents the $Z$ boson.
• Figure 5: $W$-boson interaction amplitudes. The dashed line in the intermediate state denotes a neutrino.