On Higgs decays to hadrons and the R-ratio at N4LO

Abstract

We present the first determination of Higgs-boson decay to hadrons at the nextto-next-to-next-to-next-to-leading order of perturbative QCD in the limit of a heavy top quark and massless light flavours. This result has been obtained by computing the absorptive parts of the relevant five-loop self-energy for a general gauge group and combining the outcome with the corresponding coefficient function already known to this order in QCD. Our new result reduces the uncertainty due to the truncation of the perturbation series to a fraction of the uncertainty due to the present error of the strong coupling constant. We have also performed the corresponding but technically simpler computations for direct Higgs decay to bottom quarks and for the electromagnetic R-ratio in e + e − → hadrons, thus verifying important fifth-order results obtained only by one group so far.

Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property?

“…[48] after getting analytical four-loop SU(N c ) expressions for the D NS (a s )-function (confirmed recently by the independent calculation of ref. [49]) and for the C NS Bjp (a s )-function, and taking into account the explicit expression for the three-loop SU(N c ) RG β-function, computed in ref. [50] and confirmed in ref.…”

“…[70]. It is widely used in different QCDoriented studies [49,[93][94][95][96][97][98][99][100]. In this section we will use this mMOM-scheme in the SU(N c ) theory to find out the constraints imposed by its gauge-dependence on the conditions of existence of the fundamental property of the β-function factorization in the GCR.…”

Infrared fixed point physics in SO(Nc) and Sp(Ryttov1, Shrock2 2017Phys. Rev. D357460View full textAdd to dashboardCite

“…This is a singlet for N c = 2, so in the present discussion we restrict to (even) N c ≥ 4. We have 28) and…”

“…In general, the calculation of the scheme-independent coefficient d j requires, as inputs, the b [27,28]. A detailed analysis of the region of convergence of the series expansions (1.2) and (2.33) in powers of ∆ f was given in [11][12][13], and we refer the reader to these references for a discussion of this analysis.…”

Anomalous dimensions at five loops

“…Perturbative corrections have then been pushed to two-loop [3,4], three-loop [5,6] and four-loop [7,8] level. Five-loop results have appeared over the last ten years or so, first for the case of Quantum Electrodynamics (QED) [9,10,11], then for physical QCD with gauge group SU(3) [12,13], and finally for a generalization of QCD to arbitrary simple gauge (Lie) groups [14,15,18,19].…”