Precision Higgs Physics in the Standard Model Effective Field Theory

We consider the application of the dimension-6 standard model effective field theory (SMEFT) as a method to parameterize the effects of heavy new physics in processes involving the Higgs boson. We calculate the full set of next-to-leading order (NLO) corrections to the phenomenologically relevant Higgs decay into fermion pairs, summarized as , for . This work forms the basis of precision studies of these decay modes in effective field theory, and is an important constituent to the precision study of the Higgs in the SMEFT. We address several technical issues relating to the dimension-6 SMEFT at NLO. These issues include subtleties in the Higgs- boson mixing, development of a physically consistent electric charge renormalization constant built from two-point functions, our own implementation of gauge fixing, and the treatment of tadpoles in the SMEFT. Additionally, we consider the role of decoupling relations as a method of removing anomalously large tadpole corrections to the decay rate when using a hybrid renormalization scheme, where some parameters are renormalized in the scheme, while others are renormalized in the on-shell scheme. The results are calculated fully analytically. We provide illustrative subsets of analytical results, and full numerical results for the decay rates calculated here. Furthermore, we study the convergence of the results, and estimate the size of uncalculated higher-order corrections by considering scale variations. We also explore the benefits of ratios of decay rates. In these ratios, full or partial cancellation of universal counterterms reduce the Wilson coefficient dependence as compared with decay rates alone. In some scenarios we find an enhanced sensitivity to operators generating the effective and couplings. In particular, we find that these ratios present an interesting test of minimal flavor violation.