Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Final state interactions in single- and multi-particle inclusive cross sections for hadronic collisions

Alexander Mitov, George Sterman

TL;DR

Understanding whether soft final-state interactions (FSI) spoil factorization in hadronic collisions, the paper uses all-orders light-cone ordered perturbation theory to analyze cancellations in single- and multi-particle inclusive cross sections. For 1PI observables, FSI cancel at leading power to all orders, with residual nonperturbative corrections suppressed by a hard scale such as $m_t$ or by $ rac{ ext{nonperturbative scale}}{p'_T}$ in multi-particle cases; 2PI cancellations require additional high-$p_T$ radiation, otherwise factorization can fail and nonperturbative corrections appear. The work highlights that inclusive observables remain robust to FSI, while exclusive or jet-vetoed channels can exhibit measurable nonperturbative FSI effects, informing precision top-quark phenomenology and jet-veto resummations. These insights refine the understanding of factorization in QCD for complex final states and guide interpretations of collider data where recoil radiation is restricted.

Abstract

We study the role of low momentum transfer (soft) interactions between high-transverse momentum heavy particles and beam remnants (spectators) in hadronic collisions. Such final-state interactions are power suppressed for single-particle inclusive cross sections whenever that particle is accompanied by a recoiling high-p_T partner whose momentum is not fixed. An example is the single-top inclusive cross section in top pair production. Final-state soft interactions in multi-particle inclusive cross sections, including transverse momentum distributions, however, produce leading power corrections in the absence of hard recoiling radiation. Nonperturbative corrections due to scattering from spectators are generically suppressed by powers of Λ/p'_T, where Λis a hadronic scale, and p'_T is the largest transverse momentum of radiation recoiling against the particles whose momenta are observed.

Final state interactions in single- and multi-particle inclusive cross sections for hadronic collisions

TL;DR

Understanding whether soft final-state interactions (FSI) spoil factorization in hadronic collisions, the paper uses all-orders light-cone ordered perturbation theory to analyze cancellations in single- and multi-particle inclusive cross sections. For 1PI observables, FSI cancel at leading power to all orders, with residual nonperturbative corrections suppressed by a hard scale such as or by in multi-particle cases; 2PI cancellations require additional high- radiation, otherwise factorization can fail and nonperturbative corrections appear. The work highlights that inclusive observables remain robust to FSI, while exclusive or jet-vetoed channels can exhibit measurable nonperturbative FSI effects, informing precision top-quark phenomenology and jet-veto resummations. These insights refine the understanding of factorization in QCD for complex final states and guide interpretations of collider data where recoil radiation is restricted.

Abstract

We study the role of low momentum transfer (soft) interactions between high-transverse momentum heavy particles and beam remnants (spectators) in hadronic collisions. Such final-state interactions are power suppressed for single-particle inclusive cross sections whenever that particle is accompanied by a recoiling high-p_T partner whose momentum is not fixed. An example is the single-top inclusive cross section in top pair production. Final-state soft interactions in multi-particle inclusive cross sections, including transverse momentum distributions, however, produce leading power corrections in the absence of hard recoiling radiation. Nonperturbative corrections due to scattering from spectators are generically suppressed by powers of Λ/p'_T, where Λis a hadronic scale, and p'_T is the largest transverse momentum of radiation recoiling against the particles whose momenta are observed.

Paper Structure

This paper contains 14 sections, 61 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Top pair final states in light cone ordered perturbation theory
  3. The notation of LCOPT
  4. Choice of Frame
  5. Cut diagram notation, initial and final states
  6. Leading regions, initial state jets and final state interactions
  7. Cancellation of final state interactions in single-particle inclusive cross sections
  8. Lowest order
  9. Final state interactions at arbitrary order
  10. Power corrections
  11. Multiparticle cross sections and corrections to factorization
  12. Summary and discussion
  13. General considerations
  14. Phenomenological implications

Figures (4)

  • Figure 1: Born cut diagram. The oval blobs are related to the parton distributions and the circle with a cross represents the hard scattering.
  • Figure 2: Generic higher-order diagram. The oval blobs are related to the parton distributions and the round blob with a cross represents the hard scattering. The momenta refer to the discussion of the initial state labelled 0 in connection with Eq. (\ref{['initialDA']}).
  • Figure 3: The LCOPT diagrams with first-order final state interactions discussed in the text.
  • Figure 4: The two cuts of the left diagram on Fig. \ref{['fig:NLO']}. The relevant three-momenta are shown and $Q \equiv P_A+P_B-l-l'$.