The photon energy spectrum in B → X s γ at N3LL′

Bahman Dehnadi (Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, Hamburg, 22607, Germany) ; Ivan Novikov (Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, Hamburg, 22607, Germany) ; Frank Tackmann (Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, Hamburg, 22607, Germany)

We present predictions for the photon energy spectrum in inclusive B → X s γ decays mediated by the electromagnetic penguin operator O 7 to N3LL′. We use soft-collinear effective theory (SCET) to resum the singular contributions in the peak region at large photon energy. In the tail region the resummed predictions are matched to fixed order at N3LO, where we include the known fixed-order contributions for O 7 up to O $$ \mathcal{O} $$ ( α s 2 $$ {\alpha}_s^2 $$ ). We develop a method to suitably parametrize the still unknown O $$ \mathcal{O} $$ ( α s 3 $$ {\alpha}_s^3 $$ ) nonsingular corrections in terms of theory nuisance parameters, whose variations provide an estimate of the associated theory uncertainty. In this context, we also study different ways to treat higher-order cross terms in the matching. Another important aspect of our analysis is the short-distance scheme used for the b-quark mass m b . We find that in the present context, the 1S mass scheme, which was previously used up to 2-loop order, fails to work at 3-loop order, because the mass scheme enters at a soft scale much smaller than m b here, for which the 1S scheme was not devised. Using instead the MSR mass scheme with R ~ 1 GeV, we obtain stable results with good perturbative convergence up to N3LL′.

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      "title": "The photon energy spectrum in B \u2192 X  s  \u03b3 at N3LL\u2032"
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  "abstracts": [
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      "source": "Springer", 
      "value": "We present predictions for the photon energy spectrum in inclusive B \u2192 X  s  \u03b3 decays mediated by the electromagnetic penguin operator O 7 to N3LL\u2032. We use soft-collinear effective theory (SCET) to resum the singular contributions in the peak region at large photon energy. In the tail region the resummed predictions are matched to fixed order at N3LO, where we include the known fixed-order contributions for O 7 up to   <math> <mi>O</mi> </math>  $$ \\mathcal{O} $$ (  <math> <msubsup> <mi>\u03b1</mi> <mi>s</mi> <mn>2</mn> </msubsup> </math>  $$ {\\alpha}_s^2 $$ ). We develop a method to suitably parametrize the still unknown   <math> <mi>O</mi> </math>  $$ \\mathcal{O} $$ (  <math> <msubsup> <mi>\u03b1</mi> <mi>s</mi> <mn>3</mn> </msubsup> </math>  $$ {\\alpha}_s^3 $$ ) nonsingular corrections in terms of theory nuisance parameters, whose variations provide an estimate of the associated theory uncertainty. In this context, we also study different ways to treat higher-order cross terms in the matching. Another important aspect of our analysis is the short-distance scheme used for the b-quark mass m  b . We find that in the present context, the 1S mass scheme, which was previously used up to 2-loop order, fails to work at 3-loop order, because the mass scheme enters at a soft scale much smaller than m  b  here, for which the 1S scheme was not devised. Using instead the MSR mass scheme with R ~ 1 GeV, we obtain stable results with good perturbative convergence up to N3LL\u2032."
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Published on:
27 July 2023
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2023 (2023)
Issue 7
Pages 1-44
DOI:
https://doi.org/10.1007/JHEP07(2023)214
arXiv:
2211.07663
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: