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Characterising hadronisation across the phase space

Andrea Banfi, Basem Kamal El-Menoufi

TL;DR

The paper develops a general dispersive framework to characterize hadronisation-induced shifts of event-shape distributions across the full phase space, explicitly showing that an extra soft wide-angle gluon introduces a correction missing in the two-emitter approximation and deriving a unified $(2 ext{ jet} ightarrow 3 ext{ jet})$ shift formula. By analyzing the $qar{q}$ and $qg$ dipoles, it extracts the 2-jet and 3-jet limits for the thrust observable, identifies the separate roles of soft-collinear and soft-wide-angle emissions, and provides a master expression that interpolates between regimes via a controlled color-decomposition. A concrete thrust implementation is presented, including a bootstrap for the NP shift’s dependence on the ultra-soft scale $oldsymbol{ ext{kappa}}_{ m us}$, and a matching procedure to combine with NLL resummation and fixed-order results. The work offers a framework to include higher-order and multi-emission power corrections in a systematic way, improving the precision of strong coupling extractions and enabling a more universal understanding of power corrections in QCD across the entire phase space.

Abstract

Leading hadronisation corrections to two-jet global event shapes amount to a shift in the corresponding perturbative distributions. It has been recently established that this shift depends significantly on the value of the considered event shape. These analyses consider perturbative configurations with only three partons emitting an ultra-soft non-perturbative gluon. These are dominant in the three-jet region. However, multiple soft and/or collinear emissions need to be considered to accurately describe event shape distributions near their Sudakov peak. In this region, non-perturbative shifts are usually computed by considering only two hard emitters. In this paper, we find that this approximation misses an important correction to the shift due to the emission of an additional soft wide-angle gluon. We then compute its contribution, and embed it in a general treatment for the shift that is valid in both the two-jet and three-jet regions.

Characterising hadronisation across the phase space

TL;DR

The paper develops a general dispersive framework to characterize hadronisation-induced shifts of event-shape distributions across the full phase space, explicitly showing that an extra soft wide-angle gluon introduces a correction missing in the two-emitter approximation and deriving a unified shift formula. By analyzing the and dipoles, it extracts the 2-jet and 3-jet limits for the thrust observable, identifies the separate roles of soft-collinear and soft-wide-angle emissions, and provides a master expression that interpolates between regimes via a controlled color-decomposition. A concrete thrust implementation is presented, including a bootstrap for the NP shift’s dependence on the ultra-soft scale , and a matching procedure to combine with NLL resummation and fixed-order results. The work offers a framework to include higher-order and multi-emission power corrections in a systematic way, improving the precision of strong coupling extractions and enabling a more universal understanding of power corrections in QCD across the entire phase space.

Abstract

Leading hadronisation corrections to two-jet global event shapes amount to a shift in the corresponding perturbative distributions. It has been recently established that this shift depends significantly on the value of the considered event shape. These analyses consider perturbative configurations with only three partons emitting an ultra-soft non-perturbative gluon. These are dominant in the three-jet region. However, multiple soft and/or collinear emissions need to be considered to accurately describe event shape distributions near their Sudakov peak. In this region, non-perturbative shifts are usually computed by considering only two hard emitters. In this paper, we find that this approximation misses an important correction to the shift due to the emission of an additional soft wide-angle gluon. We then compute its contribution, and embed it in a general treatment for the shift that is valid in both the two-jet and three-jet regions.

Paper Structure

This paper contains 17 sections, 79 equations, 7 figures.

Table of Contents

  1. Non-perturbative shift in the $3$-jet limit
  2. Case I: $\mathbf{sgn(B) = -\,sgn(A) = - sgn(C)}$.
  3. Case II: $\mathbf{sgn(B) = \,sgn(A) = sgn(C)}$.
  4. Recovery of known results
  5. The $q\Bar{q}$ dipole.
  6. The $qg$ dipole.
  7. Extracting the $2$-jet limit
  8. $q\Bar{q}$ dipole.
  9. $qg$ dipole.
  10. Hard-collinear region.
  11. Final result.
  12. Arbitrary number of soft-collinear emissions
  13. The thrust and similar observables
  14. Matching
  15. Conclusions
  16. ...and 2 more sections

Figures (7)

  • Figure 1: The numerical evaluation of $\zeta_{q\bar{q}}(\tau)/\zeta_T(0)$ both in linear (a) and logarithmic (b) bins.
  • Figure 2: The numerical evaluation of $\zeta_{qg}(\tau)/\zeta_T(0)$ both in linear (a) and logarithmic (b) bins.
  • Figure 3: The numerical evaluation of $c_{q\bar{q}}(\tau)$ both in linear (a) and logarithmic (b) bins.
  • Figure 4: (a) The rapidity function $g_T(\tau)$ that determines $\bar{\zeta}_{qg}(\tau)$, (b) The rapidity function $f_T(\tau)$, which is integrable everywhere in $\eta$.
  • Figure 5: The numerical evaluation of $c_{qg}(\tau)$ both in linear (a) and logarithmic (b) bins.
  • ...and 2 more figures