<p>We present a calculation of the thrust distribution in Higgs decays to quarks and gluons, <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi>H</mi> <mo>→</mo> <mi>b</mi> <mover accent="true"> <mi>b</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( H\to b\overline{b} \)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi>H</mi> <mo>→</mo> <mi>c</mi> <mover accent="true"> <mi>c</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( H\to c\overline{c} \)</EquationSource> </InlineEquation>, and <i>H</i> → <i>gg</i>, including the resummation of large logarithmic corrections that arise in the two-particle limit at next-to-next-to-leading logarithmic (NNLL) accuracy, and match it to fixed-order results for three-particle decays at next-to-next-to-leading order (NNLO) in the strong coupling. The resummation is performed analytically within the A<span>res</span> framework and combined with the fixed-order results using the logR matching technique. The fixed-order calculation is carried out numerically with the NNLO<span>jet</span> parton-level event generator, using the antenna subtraction method. We perform detailed cross-validation in the two-particle region, demonstrating that the expansion of the NNLL resummed result correctly reproduces the logarithmic structure of the fixed-order calculation to <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">O</mi> <mfenced close=")" open="("> <msubsup> <mi>α</mi> <mi mathvariant="normal">s</mi> <mn>3</mn> </msubsup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{O}\left({\alpha}_{\textrm{s}}^3\right) \)</EquationSource> </InlineEquation>, up to a predictable N<sup>3</sup>LL term at <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">O</mi> <mfenced close=")" open="("> <mrow> <msubsup> <mi>α</mi> <mi mathvariant="normal">s</mi> <mn>3</mn> </msubsup> <mi>L</mi> </mrow> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{O}\left({\alpha}_{\textrm{s}}^3L\right) \)</EquationSource> </InlineEquation>. In addition to providing the first NNLO+NNLL accurate predictions for the thrust distribution in Higgs decays to quarks and gluons, we analytically extract the <InlineEquation ID="IEq5"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">O</mi> <mfenced close=")" open="("> <msubsup> <mi>α</mi> <mi mathvariant="normal">s</mi> <mn>2</mn> </msubsup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{O}\left({\alpha}_{\textrm{s}}^2\right) \)</EquationSource> </InlineEquation> hard-virtual correction <i>c</i><sub>2</sub> and the <InlineEquation ID="IEq6"> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>α</mi> <mi mathvariant="normal">s</mi> <mn>3</mn> </msubsup> <mi>L</mi> </math></EquationSource> <EquationSource Format="TEX">\( {\alpha}_{\textrm{s}}^3L \)</EquationSource> </InlineEquation> term <i>G</i><sub>31</sub> in both the <InlineEquation ID="IEq7"> <EquationSource Format="MATHML"><math display="inline"> <mi>H</mi> <mo>→</mo> <mi>q</mi> <mover accent="true"> <mi>q</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( H\to q\overline{q} \)</EquationSource> </InlineEquation> (<i>q</i> = <i>b</i>, <i>c</i>) and <i>H → gg</i> decay channels.</p>

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The thrust distribution at NNLO+NNLL in Higgs decays to quarks and gluons

  • Elliot Fox,
  • Aude Gehrmann-De Ridder,
  • Thomas Gehrmann,
  • Nigel Glover,
  • Matteo Marcoli,
  • Christian T. Preuss

摘要

We present a calculation of the thrust distribution in Higgs decays to quarks and gluons, H b b ¯ \( H\to b\overline{b} \) , H c c ¯ \( H\to c\overline{c} \) , and Hgg, including the resummation of large logarithmic corrections that arise in the two-particle limit at next-to-next-to-leading logarithmic (NNLL) accuracy, and match it to fixed-order results for three-particle decays at next-to-next-to-leading order (NNLO) in the strong coupling. The resummation is performed analytically within the Ares framework and combined with the fixed-order results using the logR matching technique. The fixed-order calculation is carried out numerically with the NNLOjet parton-level event generator, using the antenna subtraction method. We perform detailed cross-validation in the two-particle region, demonstrating that the expansion of the NNLL resummed result correctly reproduces the logarithmic structure of the fixed-order calculation to O α s 3 \( \mathcal{O}\left({\alpha}_{\textrm{s}}^3\right) \) , up to a predictable N3LL term at O α s 3 L \( \mathcal{O}\left({\alpha}_{\textrm{s}}^3L\right) \) . In addition to providing the first NNLO+NNLL accurate predictions for the thrust distribution in Higgs decays to quarks and gluons, we analytically extract the O α s 2 \( \mathcal{O}\left({\alpha}_{\textrm{s}}^2\right) \) hard-virtual correction c2 and the α s 3 L \( {\alpha}_{\textrm{s}}^3L \) term G31 in both the H q q ¯ \( H\to q\overline{q} \) (q = b, c) and H → gg decay channels.