Gauge Dependence of Lower Bounds on the Higgs Mass Derived from Electroweak Vacuum Stability Constraints

Abstract

We examine the gauge dependence of lower bounds on the Higgs mass obtained from the requirement that the electroweak vacuum be the global minimum of the effective potential. We study a simple model, the spontaneously-broken Abelian Higgs model coupled to a chiral quark doublet in a two-parameter gauge and demonstrate that the lower bounds on the Higgs mass obtained in this model are dependent on the choice of gauge parameters. We discuss the significance of this result for calculations in the Standard Model.

Figures (5)

• Figure 1: Divergent Higgs One-Point Function for $\mu^2 >0$ in $R_{\xi,u}$ Gauge
• Figure 2: $\lambda_{\rm{eff}}\left( s\right)$ (dashed line), $\lambda(s)$ (solid line), and $V_{\rm{eff}}\left( s \right)$ (bold line) vs. $\log{s}$. $g^2_i=0.15, y_{ti}^2=0.5, \lambda_i=0.2,\xi g^2=10$. $V_{\rm{eff}}$ has been scaled down to fit the plot.
• Figure 3: $\lambda_{\rm{eff}}\left( s,\xi g^2,\hat{g}_i \right)$ vs. $\log{s}$ for $\xi g^2= 0$ (upper curve) and $\xi g^2=50$ (lower curve). $g^2_i=0.15, y_{ti}^2=0.5, \lambda_i=0.2$
• Figure 4: Log of vacuum instability scale vs. $\xi g^2$ for $g^2_i=0.15, y_{ti}^2=0.5, \lambda_i=0.2$.
• Figure 5: $\lambda_i$ vs. $\xi g^2$ for $g^2_i=0.15, y_{ti}^2=0.5$, assuming a vacuum instability at $\log{s_{VI}}=3.7$ and $\lambda_{\rm{eff}}(s_{VI})=0$.