# Poster presented by Ken-Ichi Ishikawa

**Poster Session**
**Topic:** Heavy Quarks

### $O(a\alpha_s)$ matching coefficients for the $\Delta B$=2 operators in the lattice static theory

**Abstract:** We present the perturbative matching coefficients which relate the effective $\Delta B =2$ 4-Fermi operator in the continuum to that of the lattice static theory. We employ SW action for the lattice light quarks and Wilson gluonic action and the coefficients are calculated to $O(a\alpha_s)$. We find that the dimension six operators mix with two new dimension seven operators at $O(a\alpha_s)$ with the $O(1)$ coefficients, which suggests that there are large $a$ dependence in B_B((8/3)(f_{B}M_{B})^2)=\langle\overline{B}|\Op_L|B\rangle$ without improving the operator to $O(a \alpha_s)$. We also discuss the possible cancellation of $O(a\alpha_s)$ correction in the ratio $B_B=\langle\overline{B}|\Op_L|B\rangle/((8/3)(f_{B}M_{B})^2)$ using the vacuum saturation approximation qualitatively.

Massimo Campostrini,
`campo@mailbox.difi.unipi.it`