Towards next-to-next-to-leading-log accuracy for the width difference in the B s − B ¯ s $$ {B}_s-{\overline{B}}_s $$ system: fermionic contributions to order (m c /m b )0 and (m c /m b )1

Abstract

Abstract We calculate a class of three-loop Feynman diagrams which contribute to the next-to-next-to-leading logarithmic approximation for the width difference ΔΓ s in the B s − B ¯ s $$ {B}_s-{\overline{B}}_s $$ system. The considered diagrams contain a closed fermion loop in a gluon propagator and constitute the order α s 2 N f , where N f is the number of light quarks. Our results entail a considerable correction in that order, if ΔΓ s is expressed in terms of the pole mass of the bottom quark. If the M S ¯ $$ \overline{\mathrm{MS}} $$ 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.

Keywords

• NLO Computations