NLO QCD renormalization group evolution for nonleptonic ΔF=2 transitions in the SMEFT

Jason Aebischer (Physik-Institut, Universität Zürich, CH-8057 Zürich, Switzerland) ; Andrzej J. Buras (TUM Institute for Advanced Study, Lichtenbergstrasse 2a, D-85747 Garching, Germany) ; Jacky Kumar (TUM Institute for Advanced Study, Lichtenbergstrasse 2a, D-85747 Garching, Germany)

We present for the first time Next-to-Leading (NLO) QCD renormalization group (RG) evolution matrices for nonleptonic ΔF=2 transitions in the Standard Model effective field theory (SMEFT). To this end we transform first the known two-loop QCD anomalous dimension matrices (ADMs) of the BSM (Beyond the SM) operators in the so-called Buras Misiak Urban basis into the ones in the common weak effective theory (WET) basis (the so-called Jenkins Manohar Stoffer basis) for which tree-level and one-loop matching to the SMEFT are already known. This subsequently allows us to find the two-loop QCD ADMs for the SMEFT nonleptonic ΔF=2 operators in the Warsaw basis. Having all these ingredients we investigate the impact of these NLO QCD effects on the QCD RG evolution of SMEFT Wilson coefficients for nonleptonic ΔF=2 transitions from the new physics scale Λ down to the electroweak scale μew. The main benefit of these new contributions is that they allow one to remove renormalization scheme dependences present in the one-loop matchings both between the WET and SMEFT and also between SMEFT and a chosen UV completion. But the Next-to-Leading (NLO) QCD effects, calculated here in the Naive dimensional regularisation minimal subtraction scheme, turn out to be small, in the ballpark of a few percent but larger than one-loop Yukawa top effects when only the ΔF=2 operators are considered. The more complicated class of nonleptonic ΔF=1 decays will be presented soon in another publication.

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      "title": "NLO QCD renormalization group evolution for nonleptonic <math><mi>\u0394</mi><mi>F</mi><mo>=</mo><mn>2</mn></math> transitions in the SMEFT"
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      "source": "APS", 
      "value": "We present for the first time Next-to-Leading (NLO) QCD renormalization group (RG) evolution matrices for nonleptonic <math><mi>\u0394</mi><mi>F</mi><mo>=</mo><mn>2</mn></math> transitions in the Standard Model effective field theory (SMEFT). To this end we transform first the known two-loop QCD anomalous dimension matrices (ADMs) of the BSM (Beyond the SM) operators in the so-called Buras Misiak Urban basis into the ones in the common weak effective theory (WET) basis (the so-called Jenkins Manohar Stoffer basis) for which tree-level and one-loop matching to the SMEFT are already known. This subsequently allows us to find the two-loop QCD ADMs for the SMEFT nonleptonic <math><mi>\u0394</mi><mi>F</mi><mo>=</mo><mn>2</mn></math> operators in the Warsaw basis. Having all these ingredients we investigate the impact of these NLO QCD effects on the QCD RG evolution of SMEFT Wilson coefficients for nonleptonic <math><mi>\u0394</mi><mi>F</mi><mo>=</mo><mn>2</mn></math> transitions from the new physics scale <math><mi>\u039b</mi></math> down to the electroweak scale <math><msub><mi>\u03bc</mi><mi>ew</mi></msub></math>. The main benefit of these new contributions is that they allow one to remove renormalization scheme dependences present in the one-loop matchings both between the WET and SMEFT and also between SMEFT and a chosen UV completion. But the Next-to-Leading (NLO) QCD effects, calculated here in the Naive dimensional regularisation minimal subtraction scheme, turn out to be small, in the ballpark of a few percent but larger than one-loop Yukawa top effects when only the <math><mi>\u0394</mi><mi>F</mi><mo>=</mo><mn>2</mn></math> operators are considered. The more complicated class of nonleptonic <math><mi>\u0394</mi><mi>F</mi><mo>=</mo><mn>1</mn></math> decays will be presented soon in another publication."
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Published on:
01 August 2022
Publisher:
APS
Published in:
Physical Review D , Volume 106 (2022)
Issue 3
DOI:
https://doi.org/10.1103/PhysRevD.106.035003
arXiv:
2203.11224
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

Fulltext files: