On the numerical closeness of the effective phenomenological electroweak mixing angle $\theta$ and the $\text{MS}$ parameter $\hat{\theta }$

Abstract

It happens that $s^2$ and ${\hat{s}}^2$ are equal with 0.1% accuracy, though they are split by radiative corrections and a natural estimate for their difference is 1%. This degeneracy occurs only for $m_t$ value close to $170\text{GeV}$, so no deep physical reason can be attributed to it. However, another puzzle of the Standard Model, the degeneracy of $s_{\text{Eff}}^2$ and $s^2$, is not independent of the previous one since a good physical reason exists for $s_{\text{Eff}}^2$ and ${\hat{s}}^2$ degeneracy. We present explicit formulas which relate these three angles.

Comments: 10 pages, latex, 3 figures included; published on MPLA. A few numerical estimates are improved; journal-ref is added