- 學位論文
標準模型之實數純量擴展:電弱相變之規範與方策依賴探討
Standard Model with a Real Singlet Scalar: An Investigation of Scheme Dependence and Gauge Dependence in Electroweak Phase Transition
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摘要
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。
並列摘要
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.
參考文獻
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延伸閱讀
- Li, Y. H. (2021). 對抗性擾動下的組合量化群試：基本極限和演算法 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU202100377
- Kuo, S. H. (2007). 量子態非模糊區辨之可行條件探討 [master's thesis, National Tsing Hua University]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0016-1411200715113011
- Huang, C. T. (2022). 利用全局擬合方法探討Georgi-Machacek模型的理論與實驗限制、電弱相變以及重力波 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU202201164
- Lui, C. J. (2009). Analyzing the influence of surface treatment and different top electrodes on the leakage current of organic thin-film transistors [master's thesis, National Chiao Tung University]. Airiti Library. https://doi.org/10.6842/NCTU.2009.01125
- Ananthaswamy, V., Padmavathi, P., & Rajendran, L. (2014). Simple Analytical Expressions of the Steady State Concentration and Flux in Immobilized Glucose Isomerase of Packed- Bed Reactors. Review of Bioinformatics and Biometrics, 3(), 29-37. https://www.airitilibrary.com/Article/Detail?DocID=P20150529012-201412-201507270025-201507270025-29-37