$B^0-\bar{B}^0$ Mixing at Next-to-Leading Order

TL;DR

This paper calculates next-to-leading order perturbative corrections to the $B^0-ar{B}^0$ mixing matrix element, improving theoretical precision and enabling better comparison with lattice results.

Contribution

It provides the first analytical computation of non-factorizable $ ext{O}(oldsymbol{ extalpha_s})$ corrections at three-loop level for the bag parameter in $B^0$ mixing.

Findings

Numerical value for the renormalization group invariant bag parameter.

Comparison with recent lattice determinations.

Enhanced theoretical understanding of $B^0-ar{B}^0$ mixing at NLO.

Abstract

We compute the perturbative corrections to the HQET sum rules for the matrix element of the \Delta B=2 operator that determines the mass shift of $B^0$, $\bar{B}^0$ states. Technically, we obtain analytically the non-factorizable contributions at order $\alpha_s$ to the bag parameter that first appear at the three-loop level. Together with the known non-perturbative corrections due to vacuum condensates and $1/m_b$ corrections, the full next-to-leading order result is now available. We present a numerical value for the renormalization group invariant bag parameter that is phenomenologically relevant and discuss comparison with recent lattice determinations.