Heavy quark spectroscopy and matrix elements: A lattice study using the static approximation

We present results of a lattice analysis of the $B$ parameter $B_B$, the decay constant $f_B$, and several mass splittings using the static approximation. Results were obtained for 60 quenched gauge configurations computed at $\beta =6.2\mathrm{}$ on a lattice size of ${24}^3$×48. Light quark propagators were calculated using the $O\left(a\right)\mathrm{}$-improved Sheikholeslami-Wohlert action. We find $B_B^{\mathrm{static}}\left(m_b\right)={0.69}_{-4\mathrm{}}^{+3\mathrm{}}{\left(\mathrm{stat}\right)}_{-1\mathrm{}}^{+2\mathrm{}}\left(\mathrm{syst}\right)$, corresponding to $B_B^{\mathrm{static}}={1.02}_{-6\mathrm{} -2\mathrm{}}^{+5\mathrm{} +3\mathrm{}}$, $f_B^{\mathrm{static}}={266}_{-20\mathrm{} -27\mathrm{}}^{+18\mathrm{} +28\mathrm{}}$ MeV, and $\frac{f_{B_s}^2{B}_{B_s}}{f_B^2{B}_B}={1.34}_{-8\mathrm{} -3\mathrm{}}^{+9\mathrm{} +5\mathrm{}}$, where a variational fitting technique was used to extract $f_B^{\mathrm{static}}$. For the mass splittings we obtain $M_{B_s}-M_{B_d}={87}_{-12\mathrm{} -12\mathrm{}}^{+15\mathrm{} +6\mathrm{}}$ MeV, $M_{{\Lambda }_b}-M_{B_d}={420}_{-90\mathrm{} -30\mathrm{}}^{+100\mathrm{} +30\mathrm{}}$ MeV, and $M_{B^{*}}^2-M_B^2={0.281}_{-16\mathrm{} -37\mathrm{}}^{+15\mathrm{} +40\mathrm{}}$ Ge${\mathrm{V}}^2$. We compare different smearing techniques intended to improve the signal/noise ratio. From a detailed assessment of systematic effects, we conclude that the main systematic uncertainties are associated with the renormalization...