We derive high-precision results for the e+e− heavy jet mass (HJM) dσ/dρ and dihemisphere mass (DHM) d2σ/(ds1ds2) distributions, for s1 ~ s2, in the dijet region. New results include: i) the N3LL resummation for HJM of large logarithms lnn(ρ) at small ρ including the exact two-loop non-global hemisphere soft function, the 4-loop cusp anomalous dimension and the 3-loop hard and jet functions, ii) N3LL results for DHM with resummation of logarithms ln(s1,2/Q2) when there is no large separation between s1 and s2, iii) profile functions for HJM to give results simultaneously valid in the peak and tail regions, iv) a complete two-dimensional basis of non-perturbative functions which can be used for double differential observables, that are needed for both HJM and DHM in the peak region, and v) an implementation of renormalon subtractions for large-angle soft radiation to <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27172_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>3</mn> </msubsup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{O}\left({\alpha}_s^3\right) $</EquationSource> </InlineEquation> together with a resummation of the additional large ln(Qρ/ΛQCD) logarithms. Here Q is the e+e− center-of-mass energy. Our resummation results are combined with known fixed-order <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27172_Article_IEq1.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">O</mi> <mfenced close=")" open="("> <msubsup> <mi>α</mi> <mi>s</mi> <mn>3</mn> </msubsup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{O}\left({\alpha}_s^3\right) $</EquationSource> </InlineEquation> results and we discuss the convergence and remaining perturbative uncertainty in the cross section. We also prove that, at order 1/Q, the first moment of the HJM distribution involves an additional non-perturbative parameter compared to the power correction that shifts the tail of the spectrum (where 1 ≫ ρ ≫ ΛQCD/Q). This differs from thrust where a single non-perturbative parameter at order 1/Q describes both the first moment and the tail, and it disfavors models of power corrections employing a single non-perturbative parameter, such as the low-scale effective coupling model. In this paper we focus only on the dijet region, not the far-tail distribution for ρ ≳ 0.2 beyond which the trijet factorization and resummation become important.

Precision e⁺e⁻ hemisphere masses in the dijet region with power corrections

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2025年9月10日

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André H. Hoang,
Vicent Mateu,
Matthew D. Schwartz,
Iain W. Stewart

摘要

We derive high-precision results for the e⁺e⁻ heavy jet mass (HJM) dσ/dρ and dihemisphere mass (DHM) d²σ/(ds₁ds₂) distributions, for s₁ ~ s₂, in the dijet region. New results include: i) the N³LL resummation for HJM of large logarithms lnⁿ(ρ) at small ρ including the exact two-loop non-global hemisphere soft function, the 4-loop cusp anomalous dimension and the 3-loop hard and jet functions, ii) N³LL results for DHM with resummation of logarithms ln(s_1,2/Q²) when there is no large separation between s₁ and s₂, iii) profile functions for HJM to give results simultaneously valid in the peak and tail regions, iv) a complete two-dimensional basis of non-perturbative functions which can be used for double differential observables, that are needed for both HJM and DHM in the peak region, and v) an implementation of renormalon subtractions for large-angle soft radiation to $O (α_{s}^{3})$ $ \mathcal{O}\left({\alpha}_s^3\right) $ together with a resummation of the additional large ln(Qρ/Λ_QCD) logarithms. Here Q is the e⁺e⁻ center-of-mass energy. Our resummation results are combined with known fixed-order $O (α_{s}^{3})$ $ \mathcal{O}\left({\alpha}_s^3\right) $ results and we discuss the convergence and remaining perturbative uncertainty in the cross section. We also prove that, at order 1/Q, the first moment of the HJM distribution involves an additional non-perturbative parameter compared to the power correction that shifts the tail of the spectrum (where 1 ≫ ρ ≫ Λ_QCD/Q). This differs from thrust where a single non-perturbative parameter at order 1/Q describes both the first moment and the tail, and it disfavors models of power corrections employing a single non-perturbative parameter, such as the low-scale effective coupling model. In this paper we focus only on the dijet region, not the far-tail distribution for ρ ≳ 0.2 beyond which the trijet factorization and resummation become important.

Precision e+e− hemisphere masses in the dijet region with power corrections

摘要

Precision e⁺e⁻ hemisphere masses in the dijet region with power corrections