Towards next-to-next-to-leading-log accuracy for the width difference in the Bs−B¯s system: fermionic contributions to order (mc/mb)⁰ and (mc/mb)¹

We calculate a class of three-loop Feynman diagrams which contribute to the next-to-next-to-leading logarithmic approximation for the width difference ΔΓs in the B s −B ¯ s system. The considered diagrams contain a closed fermion loop in a gluon propagator and constitute the order αs2Nf, where Nf is the number of light quarks. Our results entail a considerable correction in that order, if ΔΓs is expressed in terms of the pole mass of the bottom quark. If the MS ¯ scheme is used instead, the correction is much smaller. As a result, we find a decrease of the scheme dependence. Our result also indicates that the usually quoted value of the NLO renormalization scale dependence underestimates the perturbative error.