Penguin contribution to the width difference and CP asymmetry in Bq - (B)over-barq mixing at order αs2Nf

We present new contributions to the decay matrix element Gamma(q)(12) of the B-q - (B) over bar (q) mixing complex, where q = d or s. Our new results constitute the order a(s)(2)N(f) corrections to the penguin contributions to the Wilson coefficients entering Gamma(q)(12) with full dependence on the charm quark mass. This is the first step toward the prediction of the CP asymmetry a(fs)(q) quantifying CP violation in mixing at next-to-next-to-leading logarithmic order (NNLO) in quantum chromodynamics (QCD) and further improves the prediction of the width difference Delta Gamma(q) between the two neutral-meson eigenstates. We find a sizable effect from the nonzero charm mass and our partial NNLO result decreases the NLO penguin corrections to a(fs)(q) by 37% and those to Delta Gamma(q) by 16%. We further update the Standard-Model NLO predictions for a(fs)(q) and the ratio of the width and mass differences of the B-q eigenstates: If we express the results in terms of the pole mass of the bottom quark, we fmd a(fs)(s) = (2.07 +/- 0.10) x 10(-5), a(fs)(d) = (-4.71 +/- 0.24) x 10(-4), Delta Gamma(s)/Delta M-s = (4.33 +/- 1.26) x 10(-3), and Delta Gamma(d)/Delta M-d = (4.48 +/- 1.19) x 10(-3). In the (MS) over bar scheme these numbers read a(fs)(s) = (2.04-+/- 0.11) x 10(-5), a(fs)(d) (-4.64 +/- 0.25) x 10(-4), Delta Gamma(s)/Delta M-s = (4.97 +/- 1.02) x 10(-3), and Delta Gamma(d)/Delta M-d = (5.07 +/- 0.96) x 10(-3).