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arXiv · 2511.17759

Decay matrix of B-\bar{B} mixing: Mixing of dimension-seven operators into dimension-six operators under renormalization

Artyom Hovhannisyan·Ulrich Nierste
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Abstract

The precise measurement of the width difference \Delta\Gamma_s among the mass eigenstates of the B_s-\bar{B}_s system requires the calculation of the corresponding decay matrix to order \alpha_s/m_b. QCD corrections to power-suppressed terms in the Heavy Quark Expansion involve the renormalization of dimension-7 four-quark operators for which no general methodology is available yet. In the \overline{MS} scheme one-loop corrections to matrix elements of dimension-7 operators violate the power counting, but we find the responsible terms to be infrared-finite and show that they can be absorbed into finite counterterms proportional to dimension-6 operators. We calculate all these counterterms and subsequently verify the consistency of our results with hadronic matrix elements calculated in the limit of a large number N_c of colours. The condition of correct power counting implies constraints on the possible definitions of evanescent operators.

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Artyom Hovhannisyan, Ulrich Nierste. 2025-11-21. Decay matrix of B-\bar{B} mixing: Mixing of dimension-seven operators into dimension-six operators under renormalization. https://doi.org/10.1007/jhep03(2026)236

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