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Contribution of the Darwin operator to non-leptonic decays of heavy quarks

Lenz, Alexander; Piscopo, Maria Laura; Rusov, Aleksey V.

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Alexander Lenz

Maria Laura Piscopo

Aleksey V. Rusov


We compute the Darwin operator contribution (1/m3b correction) to the width of the inclusive non-leptonic decay of a B meson (B+, Bd or Bs), stemming from the quark flavour-changing transition b → q1q¯¯2q3, where q1, q2 = u, c and q3 = d, s. The key ideas of the computation are the local expansion of the quark propagator in the external gluon field including terms with a covariant derivative of the gluon field strength tensor and the standard technique of the Heavy Quark Expansion (HQE). We confirm the previously known expressions of the 1/m3b contributions to the semi-leptonic decay b → q1ℓν¯¯¯ℓ, with ℓ = e, μ, τ and of the 1/m2b contributions to the non-leptonic modes. We find that this new term can give a sizeable correction of about −4 % to the non-leptonic decay width of a B meson. For Bd and Bs mesons this turns out to be the dominant correction to the free b-quark decay, while for the B+ meson the Darwin term gives the second most important correction — roughly 1/2 to 1/3 of the phase space enhanced Pauli interference contribution. Due to the tiny experimental uncertainties in lifetime measurements the incorporation of the Darwin term contribution is crucial for precision tests of the Standard Model.


Lenz, A., Piscopo, M. L., & Rusov, A. V. (2020). Contribution of the Darwin operator to non-leptonic decays of heavy quarks. Journal of High Energy Physics, 2020(12), Article 199.

Journal Article Type Article
Acceptance Date Nov 8, 2020
Online Publication Date Dec 30, 2020
Publication Date 2020-12
Deposit Date Apr 13, 2021
Publicly Available Date Apr 13, 2021
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2020
Issue 12
Article Number 199
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Copyright Statement
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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