Abstract
We use rational approximants to study missing higher orders in the massless scalar-current quark correlator. We predict the yet unknown six-loop coefficient of its imaginary part, related to Γ(H → b overline{b} ), to be c5 = −6900 ± 1400. With this result, the perturbative series becomes almost insensitive to renormalization scale variations and the intrinsic QCD truncation uncertainty is tiny. This confirms the expectation that higher-order loop computations for this quantity will not be required in the foreseeable future, as the uncertainty in Γ(H → b overline{b} ) will remain largely dominated by the Standard Model parameters.
Highlights
This confirms the expectation that higher-order loop computations for this quantity will not be required in the foreseeable future, as the uncertainty in Γ(H → bb) will remain largely dominated by the Standard Model parameters
We are concerned with estimating higher orders in the Higgs-bottom Yukawa induced contributions in the massless limit, starting at N5LO, or six loops, which may never be calculated exactly, with the aim of reassessing the intrinsic truncation error associated with perturbative QCD
We will employ different types of rational approximants, or Padé approximants [13, 14], in order to exploit the exact knowledge of the first four terms in the perturbative series to reconstruct the series to even higher orders
Summary
Order results obtained for massless bottom quarks (in the quark propagators), receiving small mb/mH corrections (top mass effects, on the other hand, can be sizeable) In this framework, the corrections in the limit mb/mH → 0 are completely known up to αs thanks to the impressive five-loop computation of the terms originating from the Higgs-bottom Yukawa coupling [9, 10] and the work of ref. We obtain estimates for even higher orders, starting at N6LO, albeit with an increasingly large error With these results we can calculate the total perturbative QCD contribution to the decay width of the Higgs boson into bb with an associated uncertainty for missing higher orders. Our results confirm the expectation that the dominant QCD contributions arising from the scalar qqcorrelator are under very good control, with a small error from the truncation of the series, and they reinforce that the major limiting factors for this decay are, and will be in the foreseeable future, the precision of the b-quark mass and of the strong coupling
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