The role of non-universal Couplings in Explaining the Anomaly
Ashutosh Kumar Alok (Indian Institute of Technology Jodhpur, Jodhpur, India); Amol Dighe (Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai, India); Shireen Gangal (Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai, India); Jacky Kumar (Physique des Particules, Universite de Montreal, C.P. 6128, succ. centre-ville, Montreal, Canada)
The tension among measurements of from different channels, the so-called Cabibbo Angle Anomaly, can be interpreted as a signal of lepton flavor universality (LFU) violation in the W boson couplings. We investigate this issue in the framework of effective field theory, keeping the gauge structure of the Standard Model (SM) unchanged. We introduce gauge-invariant dimension-6 effective operators that couple the Higgs doublet to leptons, thereby giving non-universal tree-level contributions to the couplings of electroweak gauge bosons. Due to the gauge symmetry, a tension arises between the measurements that are affected by new W couplings, and the electroweak precision measurements, which are also affected by the new Z couplings. We show that this tension can be alleviated by allowing additional sources of gauge-invariant couplings of Z boson to left- or right-handed leptons, and find the optimal regions indicated by the current data in the Wilson-coefficient space. We illustrate our model-independent results with the examples of minimal extensions of the SM involving the vector-like lepton (VLL) models. We point out that dimension-6 operators coupling the Higgs doublet to leptons can affect the rate of decay significantly in general, however this effect is restricted to less than a per cent level for the minimal VLL models.