Bell, Guido

We study the role of renormalon cancellation schemes and perturbative scale choices in extractions of the strong coupling constant <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>α</a:mi><a:mi>s</a:mi></a:msub><a:mo stretchy="false">(</a:mo><a:msub><a:mi>m</a:mi><a:mi>Z</a:mi></a:msub><a:mo stretchy="false">)</a:mo></a:math> and the leading nonperturbative shift parameter <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi mathvariant="normal">Ω</e:mi><e:mn>1</e:mn></e:msub></e:math> from resummed predictions of the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msup><h:mi>e</h:mi><h:mo>+</h:mo></h:msup><h:msup><h:mi>e</h:mi><h:mo>−</h:mo></h:msup></h:math> event shape thrust. We calculate the thrust distribution to <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mrow><j:mi mathvariant="normal">N</j:mi><j:mrow><j:mmultiscripts><j:mrow><j:mi mathvariant="normal">L</j:mi></j:mrow><j:mprescripts/><j:none/><j:mrow><j:mn>3</j:mn></j:mrow></j:mmultiscripts></j:mrow><j:msup><j:mrow><j:mi mathvariant="normal">L</j:mi></j:mrow><j:mrow><j:mo>′</j:mo></j:mrow></j:msup></j:mrow></j:math> resummed accuracy in soft-collinear effective theory (SCET) matched to the fixed-order <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi mathvariant="script">O</o:mi><o:mo stretchy="false">(</o:mo><o:msubsup><o:mi>α</o:mi><o:mi>s</o:mi><o:mn>2</o:mn></o:msubsup><o:mo stretchy="false">)</o:mo></o:math> prediction, and perform a new high-statistics computation of the <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi mathvariant="script">O</t:mi><t:mo stretchy="false">(</t:mo><t:msubsup><t:mi>α</t:mi><t:mi>s</t:mi><t:mn>3</t:mn></t:msubsup><t:mo stretchy="false">)</t:mo></t:math> matching in , although we do not include the latter in our final <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi>α</y:mi><y:mi>s</y:mi></y:msub></y:math> fits due to some observed systematics that require further investigation. We are primarily interested in testing the phenomenological impact sourced from varying amongst three renormalon cancellation schemes and two sets of perturbative scale profile choices. We then perform a global fit to available data spanning center-of-mass energies between 35–207 GeV in each scenario. Relevant subsets of our results are consistent with prior SCET-based extractions of <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msub><ab:mi>α</ab:mi><ab:mi>s</ab:mi></ab:msub><ab:mo stretchy="false">(</ab:mo><ab:msub><ab:mi>m</ab:mi><ab:mi>Z</ab:mi></ab:msub><ab:mo stretchy="false">)</ab:mo></ab:math>, but we are also led to a number of novel observations. Notably, we find that the combined effect of altering the renormalon cancellation scheme and profile parameters can lead to few-percent-level impacts on the extracted values in the <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msub><eb:mi>α</eb:mi><eb:mi>s</eb:mi></eb:msub><eb:mo>−</eb:mo><eb:msub><eb:mi mathvariant="normal">Ω</eb:mi><eb:mn>1</eb:mn></eb:msub></eb:math> plane, indicating a potentially important systematic theory uncertainty that should be accounted for. We also observe that fits performed over windows dominated by dijet events are typically of a higher quality than those that extend into the far tails of the distributions, possibly motivating future fits focused more heavily in this region. Finally, we discuss how different estimates of the three-loop soft matching coefficient <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:msubsup><hb:mi>c</hb:mi><hb:mover accent="true"><hb:mi>S</hb:mi><hb:mo stretchy="false">˜</hb:mo></hb:mover><hb:mn>3</hb:mn></hb:msubsup></hb:math> can also lead to measurable changes in the fitted <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:mo stretchy="false">{</lb:mo><lb:msub><lb:mi>α</lb:mi><lb:mi>s</lb:mi></lb:msub><lb:mo>,</lb:mo><lb:msub><lb:mi mathvariant="normal">Ω</lb:mi><lb:mn>1</lb:mn></lb:msub><lb:mo stretchy="false">}</lb:mo></lb:math> values. Published by the American Physical Society 2024

We compute the gluon beam function for jet-veto resummation to next-to-next-to-leading order (NNLO) in the strong-coupling expansion. Our calculation is based on an automated framework that was previously used for the computation of the respective quark beam function, and which we significantly extended for the present calculation. In particular, the perturbative matching kernels are directly calculated in momentum space, without the need to perform an additional Mellin transform. We present results for both gluon and quark-initiated processes, which we cross-checked with an independent semi-analytical method that exploits the similarity of the beam functions to the more familiar case of transverse-momentum resummation. Our computation is relevant for jet-veto resummations at NNLL′ accuracy.

We consider the quark beam function that describes collinear initial-state radiation that is constrained by a veto on reconstructed jets. As the veto is imposed on the transverse momenta of the jets, the beam function is subject to rapidity divergences, and we use the collinear-anomaly framework to extract the perturbative matching kernels to next-to-next-to-leading order (NNLO) in the strong-coupling expansion. Our calculation is based on a novel framework that automates the computation of beam functions in Mellin space and it provides the ingredients to extend jet-veto resummations for quark-initiated processes to NNLL′ accuracy.

Bell, Guido

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