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Four-fermion production near the W pair production threshold

Martin Beneke, Pietro Falgari, Christian Schwinn, Adrian Signer, Giulia Zanderighi

TL;DR

This work develops and applies unstable-particle effective field theory to four-fermion production near the W-pair threshold, aiming for a precision determination of the W mass. By organizing corrections into resonant production/decay operators and non-resonant four-fermion operators, and by treating hard, soft, collinear, and Coulomb effects at NLO, the authors achieve a robust prediction for the cross section near threshold. A careful treatment of initial-state radiation reveals ISR as the dominant theoretical uncertainty, while the EFT calculation yields an MW sensitivity of approximately 10–15 MeV, reducible to around 5 MeV with the full NLO four-fermion result. The results agree well with full NLO four-fermion calculations and demonstrate the viability of a systematic, analytic EFT approach for unstable-particle processes at colliders.

Abstract

We perform a dedicated study of the four-fermion production process e- e+ -> mu- nubar_mu u dbar X near the W pair-production threshold in view of the importance of this process for a precise measurement of the W boson mass. Accurate theoretical predictions for this process require a systematic treatment of finite-width effects. We use unstable-particle effective field theory (EFT) to perform an expansion in the coupling constants, GammaW/MW, and the non-relativistic velocity v of the W boson up to next-to-leading order in GammaW/MW ~ alpha_ew ~ v^2. We find that the dominant theoretical uncertainty in MW is currently due to an incomplete treatment of initial-state radiation. The remaining uncertainty of the NLO EFT calculation translates into delta MW ~ 10-15 MeV, and to about 5 MeV with additional input from the NLO four-fermion calculation in the full theory.

Four-fermion production near the W pair production threshold

TL;DR

This work develops and applies unstable-particle effective field theory to four-fermion production near the W-pair threshold, aiming for a precision determination of the W mass. By organizing corrections into resonant production/decay operators and non-resonant four-fermion operators, and by treating hard, soft, collinear, and Coulomb effects at NLO, the authors achieve a robust prediction for the cross section near threshold. A careful treatment of initial-state radiation reveals ISR as the dominant theoretical uncertainty, while the EFT calculation yields an MW sensitivity of approximately 10–15 MeV, reducible to around 5 MeV with the full NLO four-fermion result. The results agree well with full NLO four-fermion calculations and demonstrate the viability of a systematic, analytic EFT approach for unstable-particle processes at colliders.

Abstract

We perform a dedicated study of the four-fermion production process e- e+ -> mu- nubar_mu u dbar X near the W pair-production threshold in view of the importance of this process for a precise measurement of the W boson mass. Accurate theoretical predictions for this process require a systematic treatment of finite-width effects. We use unstable-particle effective field theory (EFT) to perform an expansion in the coupling constants, GammaW/MW, and the non-relativistic velocity v of the W boson up to next-to-leading order in GammaW/MW ~ alpha_ew ~ v^2. We find that the dominant theoretical uncertainty in MW is currently due to an incomplete treatment of initial-state radiation. The remaining uncertainty of the NLO EFT calculation translates into delta MW ~ 10-15 MeV, and to about 5 MeV with additional input from the NLO four-fermion calculation in the full theory.

Paper Structure

This paper contains 43 sections, 116 equations, 12 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Method of calculation
  3. Unstable-particle effective theory for pair production near threshold
  4. Production vertex, production-decay vertices and the lead-ing-order cross section
  5. Classification of corrections up to NLO
  6. Short-distance coefficients in the effective Lagrangian
  7. Matching coefficients of the production operators
  8. Matching coefficients of four-electron operators
  9. Calculations in the effective theory
  10. One-loop diagrams with insertions of subleading operators.
  11. Coulomb corrections.
  12. NLO corrections from soft and collinear photons.
  13. Expansion of the Born cross section
  14. Expansion in the potential region
  15. Decay-width correction for the flavour-specific cross section
  16. ...and 28 more sections

Figures (12)

  • Figure 1: Diagrams contributing to the tree-level matching of ${\cal O}_p^{(0)}$.
  • Figure 2: Leading-order effective-theory diagram for the forward-scattering amplitude.
  • Figure 3: Cut one-loop diagrams contributing to non-resonant production-decay operator matching.
  • Figure 4: Example of a two-loop diagram with one hard and one potential loop. Cut (2) is part of the Born cross section, but subleading as discussed in the text.
  • Figure 5: Two-loop cut diagrams. Symmetric diagrams are not shown.
  • ...and 7 more figures