Neutral<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math>-meson mixing from unquenched lattice QCD with domain-wall light quarks and static<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>b</mml:mi></mml:math>quarks

Abstract

We demonstrate a method for calculating the neutral $B$-meson decay constants and mixing matrix elements in unquenched lattice QCD with domain-wall light quarks and static $b$-quarks. Our computation is performed on the ``$2+1$'' flavor gauge configurations generated by the RBC and UKQCD Collaborations with a lattice spacing of $a\ensuremath{\approx}0.11\text{ }\text{ }\mathrm{fm}$ (${a}^{\ensuremath{-}1}=1.729\text{ }\text{ }\mathrm{GeV}$) and a lattice spatial volume of approximately $(1.8\text{ }\text{ }\mathrm{fm}{)}^{3}$. We simulate at three different light sea quark masses with pion masses down to approximately 430 MeV, and extrapolate to the physical quark masses using a phenomenologically-motivated fit function based on next-to-leading order heavy-light meson SU(2) chiral perturbation theory. For the $b$-quarks, we use an improved formulation of the Eichten-Hill action with static link-smearing to increase the signal-to-noise ratio. We also improve the heavy-light axial current used to compute the $B$-meson decay constant to $\mathcal{O}({\ensuremath{\alpha}}_{s}pa)$ using one-loop lattice perturbation theory. We present initial results for the SU(3)-breaking ratios ${f}_{{B}_{s}}/{f}_{{B}_{d}}$ and $\ensuremath{\xi}={f}_{{B}_{s}}\sqrt{{B}_{{B}_{s}}}/{f}_{{B}_{d}}\sqrt{{B}_{{B}_{d}}}$, thereby demonstrating the viability of the method. For the ratio of decay constants, we find ${f}_{{B}_{s}}/{f}_{{B}_{d}}=1.15(12)$ and for the ratio of mixing matrix elements, we find $\ensuremath{\xi}=1.13(12)$, where in both cases the errors reflect the combined statistical and systematic uncertainties, including an estimate of the size of neglected $\mathcal{O}(1/{m}_{b})$ effects.