Optimal renormalization and the extraction of the strange quark mass from moments of the τ -decay spectral function

Abstract

We introduce an optimal renormalization group analysis pertinent to the analysis of polarization functions associated with the s-quark mass relevant in τ -decay. The technique is based on the renormalization group invariance constraints which lead to closed form summation of all the leading and next-to-leading logarithms at each order in perturbation theory. The new perturbation series exhibits reduced sensitivity to the renormalization scale and improved behavior in the complex plane along the integration contour. Using improved experimental and theory inputs, we have extracted the value of the strange quark mass ms(2GeV) = 106.70 ± 9.36 MeV and ms(2GeV) = 74.47 ± 7.77 MeV from presently available ALEPH and OPAL data respectively. These determinations are in agreement with the determinations in other phenomenological methods and from the lattice.

Optimal Renormalization and the Extraction of Strange Quark Mass from Semi-leptonic $$\tau $$-Decay

“…Here the intermediate quantities are defined as D mg k [a s L] = ∞ n=k d mg n,n−k (a s L) n−k , d mg are the series coefficients that can be extracted from the expression of D mg given in the appendix of Ref. [8], L = ln(µ 2 /Q 2 ), and a s = α s (µ)/π. We substitute the un-summed expression of D mg in the homogeneous RG equation that it satisfies and collect the coefficients of a n s L n−1−k which leads to a recursion relation in terms of the series coefficients d mg .…”

“…These differential equations are solved with suitable boundary conditions and the re- term within the bracket is the contribution of the condensate [12]. The vales of S EW , f kl and ss are collected in [8]. The flavor breaking term δR kl τ for different moments (k, l) have been measured by ALEPH [1] and OPAL [2] collaborations.…”

“…For our determination, we have used the moments (0, 0), (1, 0), (2, 0) of ALEPH and (2, 0), (3, 0) and (4, 0) of OPAL. The determinations for individual moments for both ALEPH and OPAL are tabulated in [8] and are compared with the determinations in FOPT, CIPT and MEC schemes. We find that RGSPT is consistent with other schemes.…”

“…We follow the optimal renormalization group analysis [6,7] in Ref. [8] that uses the RG constraints of a given perturbation series to obtain a closed form sum all the RG-accessible logarithms which substantially reduce the RG scale (µ) dependence. The RG-accessible logarithms are defined as all the leading and the next-to-leading logarithms that can be accessed through RG equation.…”

Renormalization-group improved Higgs to two gluons decay rate

“…The RGSPT expansions have been employed in various decays and observables in literature, and is shown to exhibit remarkable improvement in the sensitivity to the renormalization scale. For instance, these are used to study the e + e − hadronic cross-section [24], extraction of the strong coupling constant from the hadronic width of the τ -decays [31,32], extraction of the strange quark mass from moments of the τ -decay spectral function [33] and to investigate the QCD static energy at the four-loop in reference [34]. Moreover, RGSPT expansions can further be improved by the method of conformal mapping [31,32,35,36,37,38,39,40].…”