Gauge Dependence of the Quantum Field Theory Effective Potential

Using the absolute stability requirement of the Standard Model vacuum, we compute the Higgs mass bound for the 1-loop Standard Model effective potential with gauge dependence in the $R_\xi$ gauges together with 3-loop beta functions, 3-loop anomalous dimension and 2-loop threshold corrections. We find that the bound changes by +0.1GeV when we change the gauge parameter $\xi$ from 0 to 50. We also report that the Higgs bound plateaus as we increase $\xi$ beyond 100