QCD improved electroweak parameter ρ

Feb 5, 2014
8 pages
Published in:
  • Phys.Rev.D 89 (2014) 11, 116001
  • Published: Jun 2, 2014
e-Print:

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Abstract: (APS)

In the present paper, we make a detailed analysis for the QCD corrections to the electroweak ρ parameter by applying the principle of maximum conformality (PMC). As a comparison, we show that under the conventional scale setting, we have Δρ|N3LO=(8.257-0.012+0.045)×10-3 by varying the scale μr[Mt/2,2Mt]. By defining a ratio, ΔR=Δρ/3Xt-1, which shows the relative importance of the QCD corrections, it is found that its scale error is ±9% at the two-loop level, which changes to ±4% at the three-loop level, and ±2.5% at the four-loop level, respectively. These facts well explain why the conventional scale uncertainty constitutes an important error for estimating the ρ parameter. On the other hand, by applying the principle of maximum conformality scale setting, the four-loop estimation Δρ|N3LO shall be almost fixed to 8.228×10-3, which indicates that the conventional scale error has been eliminated. We observe that the pQCD convergence for the ρ parameter has also been greatly improved due to the elimination of the divergent renormalon terms. As applications of the present QCD improved ρ parameter, we show the shifts of the W-boson mass and the effective leptonic weak-mixing angle due to Δρ can be reduced to δMW|N3LO=0.7MeV and δsin2θeff|N3LO=-0.4×10-5.

Note:
  • 8 pages, 2 figures. Discussions improved. To be published in Phys.Rev.D
  • 12.38.Bx
  • 12.15.-y
  • 11.15.Bt
  • electroweak interaction: rho parameter
  • Weinberg angle
  • quantum chromodynamics: perturbation theory
  • quantum chromodynamics: correction
  • correction: higher-order
  • higher-order: 3
  • scaling: conformal