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

Lenz, Alexander and Piscopo, Maria Laura and Rusov, Aleksey V. (2020) 'Contribution of the Darwin operator to non-leptonic decays of heavy quarks.', Journal of high energy physics., 2020 (12). p. 199.


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.

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Publisher 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.
Date accepted:08 November 2020
Date deposited:13 April 2021
Date of first online publication:30 December 2020
Date first made open access:13 April 2021

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