Comment on ``Improved Calculation of Electroweak Radiative Corrections and the Value of $V_{ud}$ by Marciano and Sirlin''

Abstract

In a recent letter Marciano and Sirlin (Phys. Rev. Lett. 96, 032002, (2006)) presented an improved calculation of the electroweak radiative correction to derive a precision value of the quark mixing angle $V_{ud}$ by improving the continuation from long to short distance contributions. At the precision level considered by them, however, there is a more important contribution from weak magnetism that was not included by their calculation. The addition of the weak magnetism contribution to the superallowed beta-decay radiative corrections lowers $V_{ud}$ by 0.00023, which is compared with the increase 0.00007 of Marciano and Sirlin and their error estimate $\pm 0.0002$.