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

Abstract

我們以Georgi-Machacek模型為基礎，利用公開的模擬器HEPfit進行全局擬合。該模擬器整合了貝氏推論與馬可夫鏈蒙地卡羅方法，讓我們在計算Georgi-Machacek模型的同時可以考慮理論極限以及最新的實驗數據。除此之外，我們還改善了Georgi-Machacek模型的數值計算，使模擬器可以找到更大更完整的參數空間。擬合結果會給予目前Georgi-Machacek模型的可行參數空間。我們可以在假設高溫的情況下，近一步在這個參數空間中找出其中可以引發第一類型的強電弱相變。我們利用模組cosmoTransitions進行此部分的數值計算。根據結果，我們發現以下幾件特點:所有電弱相變都是一步完成的，且它們的強度分布主要落在1到3.5之間。此強度已經足以讓我們找到的電弱相變成為重子生成的關鍵因素之一。另外，透過在HEPfit設定不同理論極限和實驗數據組合，我們觀察到有關希格斯粒子的實驗數據給予電弱相變之熱力學臨界點很強的範圍限制。建立在第一類型的強電弱相變的基礎上，我們更進一步的估算他們能夠產生的重力波頻譜。根據我們的結果，該頻譜強度可以在重力波頻率約為10-2赫茲時達到10-12，並且在未來有機會被BBO與DECIGO等實驗探測到。 除了重力波，我們也可以拿引發第一類型的強電弱相變的參數空間來回過頭探討Georgi-Machacek模型，並視該參數空間為Georgi-Machacek模型的預測。同時，我們透過呈現一些Georgi-Machacek模型的重要參數的圖表，對Georgi-Machacek模型進行一系列定性分析。我們也預測了雙希格斯粒子產生時的截面將可以達到20倍相較於標準模型目前的預測值。根據過去的實驗項目，我們也從中找出未來最有可能發現Georgi-Machacek模型粒子的項目。

In this thesis, we consider the Georgi-Machacek (GM) model and perform a global fit of the allowed parameter space with Bayesian Markov-Chain Monte-Carlo in the open-source package \texttt{HEPfit}. We use the numerical setup provided in \texttt{HEPfit} and refined the numerical analysis of the GM model. In the scan, we take into account the constraints that consist of currently available experimental data and some standard theoretical constraints. In addition to the global fit, we scan the surviving parameter space for inducing strong first-order electroweak phase transitions (EWPTs) in the high-temperature scheme with the help of another package called \texttt{cosmoTransitions}. We conclude that only the one-step phase transition is phenomenologically viable, and the strength $v_C/T_C$ can range from 1 to 3.5, which is high enough to meet the criteria of electroweak baryogenesis (EWBG). By comparing the result of the different setups of the constraints in the global fit, we also find that the Higgs measurement is the most constraining factor to the critical VEVs of EWPTs. Furthermore, We estimate the spectra amplitude $h^2\Omega_\mathrm{GW}$ of the gravitational waves (GWs) generated by strong first-order EWPTs can reach up to $10^{-12}$ where the peak frequency is at $10^{-2}$~Hz. Based on the result, most of the EWPTs can be detected by several proposed experiments, such as BBO and DIEGO. With the allowed parameter spaces for the GM model and its EWPTs, we make several predictions on processes that may serve as promising probes to the GM model in the future at the LHC. The cross section of di-Higgs productions of the GM model can reach 50 times larger than the SM value and 20 times larger for strong first-order EWPTs. Several exotic scalar production channels, such as $VV \to H^{\pm\pm}_5 \to W^\pm W\pm$ and $gg \to H_3 \to h Z \to bbZ$, are currently imposing strong constraints on the parameter space and are expected to probe the EWPT behavior of the GM model.