<p>In this article we study, via analytical methods, 1/<i>Q</i> non-perturbative power corrections to event shape mean values, addressing in particular the question of their interplay with soft perturbative emissions. Specifically we point out that energy-ordered soft perturbative emissions that precede a non-perturbative emission, give rise to terms of the form <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27140_Article_IEq1.gif" Format="GIF" Height="33" Rendition="HTML" Resolution="72" Type="Linedraw" Width="89" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mfrac> <mn>1</mn> <mi>Q</mi> </mfrac> <msup> <mfenced close=")" open="("> <mrow> <msub> <mi>α</mi> <mi>s</mi> </msub> <mo>ln</mo> <mfrac> <mi>Q</mi> <mi mathvariant="normal">Λ</mi> </mfrac> </mrow> </mfenced> <mi>n</mi> </msup> </math></EquationSource> <EquationSource Format="TEX">\( \frac{1}{Q}{\left({\alpha}_s\ln \frac{Q}{\Lambda}\right)}^n \)</EquationSource> </InlineEquation>. While such terms are formally higher order in the strong coupling, their form suggests that they can numerically compete with the leading 1/<i>Q</i> term while also modifying the <i>Q</i> dependence of the result. The resummation of such power-suppressed but logarithmically enhanced terms lends an anomalous dimension to the leading 1/<i>Q</i> power correction. In order to argue for the presence of such an anomalous dimension, we formulate a method to compute the first order in <i>α</i><sub><i>s</i></sub> correction for the mean values of the thrust 1 – <i>T</i> and <i>C</i>-parameter observables. We comment on our findings in light of the standard picture of universality of 1/<i>Q</i> power corrections for event shape variables and implications for phenomenology.</p>

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Exploring soft anomalous dimensions for 1/Q power corrections

  • Mrinal Dasgupta,
  • Farid Hounat

摘要

In this article we study, via analytical methods, 1/Q non-perturbative power corrections to event shape mean values, addressing in particular the question of their interplay with soft perturbative emissions. Specifically we point out that energy-ordered soft perturbative emissions that precede a non-perturbative emission, give rise to terms of the form 1 Q α s ln Q Λ n \( \frac{1}{Q}{\left({\alpha}_s\ln \frac{Q}{\Lambda}\right)}^n \) . While such terms are formally higher order in the strong coupling, their form suggests that they can numerically compete with the leading 1/Q term while also modifying the Q dependence of the result. The resummation of such power-suppressed but logarithmically enhanced terms lends an anomalous dimension to the leading 1/Q power correction. In order to argue for the presence of such an anomalous dimension, we formulate a method to compute the first order in αs correction for the mean values of the thrust 1 – T and C-parameter observables. We comment on our findings in light of the standard picture of universality of 1/Q power corrections for event shape variables and implications for phenomenology.