為了實現兩步電弱相變,此碩論探討了將標準模型擴增一個實數單態粒子。我們利用許多不同方策(scheme)去探討且量化模型中的方策以及規範依賴。在考慮第一階圈圖計算時,on-shell (OS)-like方策中的Nambu-Goldstone 波色子需要被重求和以避免紅外發散,而我們量化其重求和後對電弱相變的影響。在OS-like以及MS-bar方策中,兩者所計算的電弱相變之臨界溫度相當一致。在規範依賴的探討中,採用High-temperature以及Patel-Ramsey-Musolf方策來做比較。在某些方策中,分析出的結果對重整化能量尺度有依賴性,此顯示了高階修正是必須的。但無論是對規範有依賴或無依賴的方策,最終資料分析顯示,兩者都在理論誤差以內。
In this thesis, the standard model is extended with a real singlet scalar $S$ to achieve a two-step electroweak phase transition (EWPT). The model is investigated with several schemes to quantify the scheme dependence and the gauge dependence issue. In on-shell(OS)-like scheme, at the one-loop order, Nambu-Goldstone boson contributions are needed to be resummed to circumvent the IR divergence; their effects in the EWPT are studied and quantified. The critical temperatures and critical vacuum expectation values of the EWPT in the OS-like and the MS-bar schemes are highly consistent to each other; we also compare the results with two gauge-independent schemes (the high temperature and the Patel-Ramsey-Musolf schemes). Even though higher order corrections are needed for scale-dependent schemes, the general trend of the results are consistent and the analyses show the differences of gauge-dependent and -independent schemes are within theoretical uncertainties.