On the numerical closeness of the effective phenomenological electroweak mixing angle $\theta$ and the $\MS$ 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 $170\GeV$, so no deep physical reason can be attributed to it. However, another puzzle of the Standard Model, the degeneracy of $s_\Eff^2$ and $s^2$, is not independent of the previous one since a good physical reason exists for $s_\Eff^2$ and $\hat s^2$ degeneracy. We present explicit formulas which relate these three angles.