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 \( {B}_s-{\overline{B}}_s \) system. The considered diagrams contain a closed fermion loop in a gluon propagator and constitute the order α 2 s 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 \( \overline{\mathrm{MS}} \) 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.
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Asatrian, H.M., Hovhannisyan, A., Nierste, U. et al. Towards next-to-next-to-leading-log accuracy for the width difference in the \( {B}_s-{\overline{B}}_s \) system: fermionic contributions to order (m c /m b )0 and (m c /m b )1 . J. High Energ. Phys. 2017, 191 (2017). https://doi.org/10.1007/JHEP10(2017)191
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DOI: https://doi.org/10.1007/JHEP10(2017)191