Electroweak effects in the $B^0-{\bar B}^0$ mixing

Details Electroweak effects in the $B^0-{\bar B}^0$ mixing Electroweak effects in the $B^0-{\bar B}^0$ mixing

1998-10-19

arxiv.org/abs/hep-ph/9810400v1

Nucl.Phys. B544 (1999) 532-556

Physics

High Energy Physics

High Energy Physics - Phenomenology

LaTeX, 29 pages, 6 postscript figures included

Scientific paper

10.1016/S0550-3213(98)00860-8

We compute analytically the complete electroweak two-loop corrections to the $B^0-{\bar B}^0$ mixing. These corrections fix the normalization of the electroweak coupling employed in the extraction of $|V_{td}|$ and reduce the theoretical uncertainty due to higher order electroweak effects from several percent to a few parts in a thousand. If the LO result is expressed in terms of $G_\mu$ or of the $\bar{MS}$ coupling $\hat{g}(M_Z)$, the two-loop corrections are $O(1%)$, the exact value depending on the mass of the Higgs boson. We discuss in detail the renormalization procedure and the scheme and scale dependence, and provide practical formulas for the numerical implementation of our results. We also consider the heavy top mass expansion and show that in the case at hand it converges very slowly.

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