帶 𝐿𝜇−𝐿𝜏 規範對稱與純量輕子夸克的模型下之同調微中子–核子彈性散射與緲子磁偶極矩、W 規範玻色子質量及 𝑅(𝐷^(∗)) 反常的兼容

Abstract

受近年來同調微中子－核子彈性散射實驗進展的啟發。因該過程是由百萬電子伏特能量級以下的動量傳遞所觸發，其對極輕的純量及向量玻色子作為傳遞粒子極為敏感。這使我們專注於一個標準模型的擴展，其中引入了 SU(3)_C×SU(2)_L×U(1)_Y× U(1)_{𝐿𝜇−𝐿𝜏} 規範對稱群。其相應的 U(1)_{𝐿𝜇−𝐿𝜏} 規範玻色子不僅用於解釋緲子的磁偶極矩異常，還可作為參與同調微中子－核子彈性散射的潛在候選者，以至於能透過此過程來探尋其蹤跡。此外，我們還進一步考慮帶有 U(1)_{𝐿𝜇−𝐿𝜏} 規範的雙希格斯二重態模型，不僅透過非零真空期望值引入 U(1)_{𝐿𝜇−𝐿𝜏} 規範玻色子的質量，還可影響三個傾斜參數 S, T, U。因此，U(1)_{𝐿𝜇−𝐿𝜏} 規範玻色子的耦合常數與質量是相關的，同時透過 T 參數的大幅增加可以解決 CDF II 量測到的 W 規範玻色子質量異常。此外，U(1)_{em} 與 U(1)_{𝐿𝜇−𝐿𝜏} 規範對稱之間的混合導致了樹級 Z'-Z 混合，此效應的影響大過於已在許多文獻中所探討的動力學混合。與傳統的第一型雙希格斯二重態模型相比，除了被 W 和 Z 規範玻色子吞噬的帶電分量和中性贗純量，另一個質量為零的中性贗純量作為戈德斯通玻色子為 U(1)_{𝐿𝜇−𝐿𝜏} 規範玻色子所吞噬並成為其縱向分量。因此，雙希格斯二重態模型中剩餘的物理自由度為兩個中性純量和一個帶電分量。然而，這些帶電希格斯玻色子對 𝑏 → 𝑐𝜏𝜈_𝜏 衰變的額外影響並不足以與實驗量測到的 R(D^(*)) 異常相容。為了解決 R(D^(*)) 異常，我們引入了一個在 SU(3)_C×SU(2)_L×U(1)_Y 規範對稱群下表示的純量輕子夸克 S=(3,1,2/3)。除此之外，因為此純量輕子夸克帶有 U(1)_{𝐿𝜇−𝐿𝜏} 荷，它與輕子的耦合強度原則上可隨輕子風味的不同而改變，其中與 𝜏 輕子的耦合主導此衰變。最後，我們預測了 𝜏→𝜇𝑍 →𝜇𝑒+𝑒- 以及 𝜏→𝜇𝑍∗ →3𝜇 衰變能被實驗檢驗，因其衰變率落在 Belle II 的靈敏度之中。

Motivated by the recent progress of the coherent elastic neutrino-nucleus scattering experiment featured in the sub-MeV momentum transfer sensitive to the very light scalar and the vector boson as the mediator, we concentrate on a Standard Model extension under SU(3)_C×SU(2)_L×U(1)_Y×U(1)_{𝐿𝜇−𝐿𝜏} gauge groups, where the corresponding U(1)_{𝐿𝜇−𝐿𝜏} gauge boson is introduced not only to explain the muon g-2 anomaly but also to be the potential candidate for coherent elastic neutrino-nucleus scattering to search for its hint. Furthermore, a scenario with a U(1)_{𝐿𝜇−𝐿𝜏} gauged two-Higgs-doublet model is considered further to not only induce the mass of U(1)_{𝐿𝜇−𝐿𝜏} gauge boson by a non-zero vacuum expectation value, but also contribute to the oblique parameters S, T and U. In this sense, the coupling and the mass of a U(1)_{𝐿𝜇−𝐿𝜏} gauge boson are correlated and W boson anomaly from CDF II can be resolved simultaneously by a sizable increase of T parameter. In addition, the mixing between U(1)_{em} and U(1)_{𝐿𝜇−𝐿𝜏} leads to the tree-level Z'-Z mixing dominating over the kinetic mixing already discussed in numerous literatures. In contrast to the conventional type-I two-Higgs-doublet model, a neutral pseudoscalar component as a massless Goldstone boson is swallowed up by U(1)_{𝐿𝜇−𝐿𝜏} gauge boson and becomes its longitudinal component in addition to the charged and the other neutral pseudoscalar component eaten by W and Z gauge bosons, respectively. Therefore, the remaining physical degrees of freedom in the two Higgs doublets are the two neutral scalar components and a charged component. However, the extra effect by the charged Higgs in the process 𝑏 → 𝑐𝜏𝜈_𝜏 isn't significant enough to be compatible with the measured excesses of R(D^(*)). In order to resolve the R(D^(*)) anomaly, a scalar leptoquark S=(3,1,2/3) carrying U(1)_{𝐿𝜇−𝐿𝜏} charges under SU(3)_C×SU(2)_L×U(1)_Y gauge groups is applied to achieve the flavor-dependent couplings in the lepton sector where the coupling to 𝜏 lepton is dominant. Finally, the promising predictions are made for the decay processes 𝜏→𝜇𝑍 →𝜇𝑒+𝑒- and 𝜏→𝜇𝑍∗ →3𝜇 able to be tested since their decay rates are at the sensitivity level of Belle II.