We consider two-loop QCD corrections to the element $$ {\Gamma}_{12}^q $$ Γ 12 q of the decay matrix in Bq−$$ {\overline{B}}_q $$ B ¯ q mixing, q = d, s, in the leading power of the Heavy Quark Expansion. The calculated contributions involve one current-current and one penguin operator and constitute the next step towards a theory prediction for the width difference ∆Γs matching the precise experimental data. We present compact analytic results for all matching coefficients in an expansion in mc/mb up to second order. Our new corrections are comparable in size to the current experimental error and slightly increase ∆Γs.

An important ingredient for the calculation of Higgs boson properties in the infinite top quark mass limit is the knowledge of the effective coupling between the Higgs bosons and gluons, i.e. the Wilson coefficients C H and C HH for one and two Higgs bosons, respectively. In this work we calculate for the first time C HH to four loops in a direct, diagrammatic way, discussing in detail all issues arising due to the renormalization of operator products. Furthermore, we also calculate the Wilson coefficient C H for the coupling of a single Higgs boson to gluons as well as all four loop decoupling relations in QCD with general SU(N c ) colour factors. The latter are related to C H and C HH via low-energy theorems. 4524863

We complete the calculation of the element $$ {\Gamma}_{12}^q $$ Γ 12 q of the decay matrix in $$ {B}_q-{\overline{B}}_q $$ B q − 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 $$ {\alpha}_s^2 $$ α 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 $$ {\Gamma}_{12}^s $$ Γ 12 s is expressed in terms of the $$ \overline{\mathrm{MS}} $$ MS ¯ b-quark mass, while we find ∆Γs/∆Ms = (4.70 ± 0.96) · 10−3 instead for the use of the pole mass.

We consider the Lagrange density of non-relativistic Quantum Chromodynamics expanded up to order 1/m 2 , where m is the heavy quark mass, and compute several matching coefficients up to two-loop order. Our results are building blocks for nextto-next-to-next-to-leading logarithmic and next-to-next-to-next-to-next-to-leading order corrections to the threshold production of top quark pairs and the decay of heavy quarkonia. We describe the techniques used for the calculation and provide analytic results for a general covariant gauge.

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