QCD improved electroweak parameterρ

2014/02/28 by Sheng-Quan Wang, Xing-Gang Wu, Jian-Ming Shen +3
Mathematics · Physics and Astronomy · #Computer science #Cosmology and Gravitation Theories #Electroweak interaction #Mathematics #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #hep-ph

paper · pdf · doi:10.1103/physrevd.89.116001

published as Phys. Rev. D 89, 116001 (2014) · 8 pages, 2 figures. Discussions improved. To be published in Phys.Rev.D

arxiv created 2014/05/21 · openalex publication_date 2014/06/02 · arxiv updated 2014/06/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In the present paper, we make a detailed analysis for the QCD corrections to the electroweak \ensuremathρ parameter by applying the principle of maximum conformality (PMC). As a comparison, we show that under the conventional scale setting, we have \mathrm\ensuremathΔ\ensuremathρ|_N³LO=(8.257_\ensuremath-0.012^+0.045)\ifmmode×\else\texttimes\fi10^\ensuremath-3 by varying the scale \ensuremathμ_r\ensuremath∈[M_t/2,2M_t]. By defining a ratio, \mathrm\ensuremathΔR=\mathrm\ensuremathΔ\ensuremathρ/3X_t\ensuremath-1, which shows the relative importance of the QCD corrections, it is found that its scale error is \ensuremath∼\ifmmode±\else\textpm\fi9% at the two-loop level, which changes to \ensuremath∼\ifmmode±\else\textpm\fi4% at the three-loop level, and \ensuremath∼\ifmmode±\else\textpm\fi2.5% at the four-loop level, respectively. These facts well explain why the conventional scale uncertainty constitutes an important error for estimating the \ensuremathρ parameter. On the other hand, by applying the principle of maximum conformality scale setting, the four-loop estimation \mathrm\ensuremathΔ\ensuremathρ|_N³LO shall be almost fixed to 8.228\ifmmode×\else\texttimes\fi10^\ensuremath-3, which indicates that the conventional scale error has been eliminated. We observe that the pQCD convergence for the \ensuremathρ parameter has also been greatly improved due to the elimination of the divergent renormalon terms. As applications of the present QCD improved \ensuremathρ parameter, we show the shifts of the W-boson mass and the effective leptonic weak-mixing angle due to \mathrm\ensuremathΔ\ensuremathρ can be reduced to \ensuremathδM_W|_N³LO=0.7 MeV and \ensuremathδsin²\ensuremathθ_eff|_N³LO=\ensuremath-0.4\ifmmode×\else\texttimes\fi10^\ensuremath-5.

Citations

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