Higher-order perturbative QCD in the Higgs decay to bottom quarks - London, Cristiane Yumi Mise (2021)
In the absence of direct observation of physics beyond the Standard Model at the LHC, precise tests both in theory and experiment require higher precision. The perturbative QCD corrections to the decay width of the Higgs boson into bottom quarks is known up to fourth order in the strong coupling, αs. This series is divergent and assumed to be asymptotic and its properties are better analyzed if we consider its Borel transform. In this work, we employ the method of Padé approximants to the Borel transform to reconstruct the series of the imaginary part of the scalar quark- antiquark correlator, directly related to the decay width, and study its renormalons and higher-order corrections. We begin by testing this method in the large-β0 limit of QCD, where the perturbative series is known to all orders, using it as a testing ground to determine the best strategy to build the series at higher orders using only the first four coefficients. In this limit, we observe that varying the renormalization scheme of the strong coupling αs and also employing the D-log Padé approximants can improve the convergence to the original function. We apply this procedure in full QCD in order to predict some of the main features of the series at (yet unknown) higher orders. We estimate the coefficient of order α5s (six loops) in a model-independent way as −8200 ± 308 and we could conclude that, although very small, this correction is important to stabilize the series. Thus, at present, the limiting factors in the precision of the decay rate of Higgs into bb are the uncertainties of the strong coupling αs and the bottom-quark mass mb.