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<p>In the determination of the Cabibbo-Kobayashi-Maskawa matrix element |<i>V</i><sub><i>cb</i></sub>| from inclusive semileptonic <i>B</i>-meson decays, moments of the leptonic invariant mass spectrum constitute valuable observables. To evaluate them with sufficient precision, perturbative <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25462_Article_IEq1.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">O</mi> <mfenced close=")" open="("> <msubsup> <mi>α</mi> <mi>s</mi> <mn>2</mn> </msubsup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{O}\left({\alpha}_s^2\right) \)</EquationSource> </InlineEquation> corrections to the analogous spectrum in the partonic <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25462_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="76" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi>b</mi> <mo>→</mo> <msub> <mi>X</mi> <mi>c</mi> </msub> <mi>l</mi> <msub> <mover accent="true"> <mi>ν</mi> <mo stretchy="true">¯</mo> </mover> <mi>l</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">\( b\to {X}_cl{\overline{\nu}}_l \)</EquationSource> </InlineEquation> decay are necessary. In the present paper, we compute such perturbative corrections in a complete manner, including contributions from the triple-charm channel, namely from the <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25462_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="italic">cc</mi> <mover accent="true"> <mi>c</mi> <mo stretchy="true">¯</mo> </mover> <mi>l</mi> <msub> <mover accent="true"> <mi>ν</mi> <mo stretchy="true">¯</mo> </mover> <mi>l</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">\( cc\overline{c}l{\overline{\nu}}_l \)</EquationSource> </InlineEquation> final states. We present our results in terms of numerical fits in both the single- and triple-charm cases. We confirm the recently found results for the single-charm correction, and analyze the triple-charm channel impact on centralized moments of the spectrum.</p>

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Complete \( \mathcal{O}\left({\alpha}_s^2\right) \) corrections to the leptonic invariant mass spectrum in \( b\to {X}_cl{\overline{\nu}}_l \) decay

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  • 发表日期：

    2025年2月5日

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  • Mateusz Czaja,
  • Mikołaj Misiak,
  • Abdur Rehman

摘要

In the determination of the Cabibbo-Kobayashi-Maskawa matrix element |Vcb| from inclusive semileptonic B-meson decays, moments of the leptonic invariant mass spectrum constitute valuable observables. To evaluate them with sufficient precision, perturbative O α s 2 \( \mathcal{O}\left({\alpha}_s^2\right) \) corrections to the analogous spectrum in the partonic b → X c l ν ¯ l \( b\to {X}_cl{\overline{\nu}}_l \) decay are necessary. In the present paper, we compute such perturbative corrections in a complete manner, including contributions from the triple-charm channel, namely from the cc c ¯ l ν ¯ l \( cc\overline{c}l{\overline{\nu}}_l \) final states. We present our results in terms of numerical fits in both the single- and triple-charm cases. We confirm the recently found results for the single-charm correction, and analyze the triple-charm channel impact on centralized moments of the spectrum.