Local gauge-invariant vector operators in the adjoint $SU(2)$ Higgs model

Abstract

In this work, we scrutinize local gauge-invariant vector operators of dimension four in the adjoint $SU(2)$ Higgs model, which are candidates for interpolating fields of the fundamental excitations of the model due to the so-called FMS mechanism. We use the equations of motion and the properties of the BRST operator to derive a Ward identity that allows us to determine whether a given operator can propagate. To corroborate this analysis, we explicitly compute the two-point function of the non-propagating operator at the one-loop level.

Figures (4)

• Figure 1: Diagrammatic representation of the relevant propagators.
• Figure 2: One-loop Feynman diagrams contributing to $\left\langle O_{\mu}\left(x\right)O_{\nu}\left(y\right)\right\rangle$. The full two-point function $\left\langle A_{\mu}^{a}\left(x\right)A_{\nu}^{b}\left(y\right)\right\rangle$ and the full one-point function $\left\langle h\left(x\right)\right\rangle$ are represented by shaded circles.
• Figure 3: One-loop Feynman diagrams contributing to $\left\langle A_{\mu}^{a}\left(x\right)A_{\nu}^{b}\left(y\right)\right\rangle$. The full one-point function $\left\langle h\left(x\right)\right\rangle$ is represented by a shaded circle.
• Figure 4: Tadpole diagrams that contribute to the one-point 1PI function $\left\langle H^{3}\left(0\right)\right\rangle _{1PI}$.