Scalar Correlator at O(alpha_s^4), Higgs Decay into b-quarks and Bounds on the Light Quark Masses

TL;DR

This work delivers the first complete ${ m O}( ilde{a}_s^4)$ calculation of the absorptive part of the massless scalar-current correlator in QCD, enabling precise predictions for the Higgs decay width to quarks and refined bounds on light-quark masses from QCD sum rules. By computing the five-loop contributions via a $1/D$ expansion and reconstruction, the authors extract the Minkowskian spectral function $ ilde{R}$ and reveal significant cancellations between genuine five-loop terms and $ ext{π}^2$-driven continuations, affecting the reliability of various estimation methods. The results yield a robust, progressively convergent description of the scalar correlator at high energy and, critically, stabilize and lower the quadratic and linear bounds on $(m_s+m_u)$ at $ extmu=2$ GeV, aligning with lattice findings and reducing potential conflicts. Overall, the paper advances perturbative QCD at five loops, informs Higgs phenomenology, and strengthens the use of QCD sum rules for light-quark mass determinations.

Abstract

We compute, for the first time, the absorptive part of the massless correlator of two quark scalar currents in five loops. As physical applications we consider the O(alpha_s^4) corrections to the decay rate of the Standard Model Higgs boson into quarks, as well as the constraints on the strange quark mass following from QCD sum rules.