A lattice NRQCD calculation of the $B^0-\bar{B}^0$ mixing parameter B_B

Abstract

We present a lattice calculation of the B meson B-parameter B_B using the NRQCD action. The heavy quark mass dependence is explicitly studied over a mass range between m_b and 4m_b with the $O(1/m_Q)$ and $O(1/m_Q^2)$ actions. We find that the ratios of lattice matrix elements $<O_N^{lat}>/<A_0^{lat}>^2$ and $<O_S^{lat}>/<A_0^{lat}>^2$, which contribute to B_B through mixing, have significant $1/m_Q$ dependence while that of the leading operator $<O_L^{lat}>/<A_0^{lat}>^2$ has little $1/m_Q$ effect. The combined result for B_B(m_b) has small but non-zero mass dependence, and the B_B(m_b) becomes smaller by 10% with the 1/m_Q correction compared to the static result. Our result in the quenched approximation at \beta=5.9 is B_{B_d}(5 GeV) = 0.75(3)(12), where the first error is statistical and the second is a systematic uncertainty.