Abstract
We complete the calculation of the element \( {\Gamma}_{12}^q \) of the decay matrix in \( {B}_q-{\overline{B}}_q \) mixing, q = d, s, to order αs in the leading power of the Heavy Quark Expansion. To this end we compute one- and two-loop contributions involving two four-quark penguin operators. Furthermore, we present two-loop QCD corrections involving a chromomagnetic operator and either a current-current or four-quark penguin operator. Such contributions are of order \( {\alpha}_s^2 \), i.e. next-to-next-to-leading-order. We also present one-loop and two-loop results involving two chromomagnetic operators which are formally of next-to-next-to-leading and next-to-next-to-next-to-leading-order, respectively. With our new corrections we obtain the Standard-Model prediction ∆Γs/∆Ms = (5.20 ± 0.69) · 10−3 if \( {\Gamma}_{12}^s \) is expressed in terms of the \( \overline{\mathrm{MS}} \) b-quark mass, while we find ∆Γs/∆Ms = (4.70 ± 0.96) · 10−3 instead for the use of the pole mass.
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Gerlach, M., Nierste, U., Shtabovenko, V. et al. The width difference in \( B-\overline{B} \) beyond mixing at order αs and. J. High Energ. Phys. 2022, 6 (2022). https://doi.org/10.1007/JHEP04(2022)006
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DOI: https://doi.org/10.1007/JHEP04(2022)006