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Multi-leg calculations with the GRACE/1-LOOP system. --Toward Radiative Corrections to e+e- -> mu nu-bar u d-bar --

F. Boudjema, J. Fujimoto, T. Ishikawa, T. Kaneko, K. Kato, Y. Kurihara, Y. Shimizu

TL;DR

This work delivers the first full O(α) electroweak corrections to the 2→4 process e+e− → μ− ν̄ u d̄ using GRACE/1-LOOP, situating it within the progression from 2→3 corrections to more complex multi-leg processes. It introduces an efficient reduction scheme that expresses N(≥5)-point tensor integrals as sums of 4-point functions and validates it against a large set of SM diagrams, including non-linear gauge checks. A key finding is that finite-width effects introduce gauge-invariance breaking in infrared 5-point functions, highlighting the need for careful width treatment in the IR sector and suggesting alternative reduction identities can mitigate some instabilities. Overall, the study demonstrates that full radiative corrections to 2→4 processes are computable with current tools, but numerically delicate, requiring ongoing methodological refinements especially in IR-width handling.

Abstract

We performed the calculation of the full O(alpha) corrections to e+e- -> mu- nu-bar u d-bar with the help of the GRACE/1-LOOP system. We discuss how a finite decay width introduces a serious gauge invariance breaking, particularly for infrared 5-point functions. This is related to the way the reduction of those functions is performed and to the treatment of the width in the reduction.

Multi-leg calculations with the GRACE/1-LOOP system. --Toward Radiative Corrections to e+e- -> mu nu-bar u d-bar --

TL;DR

This work delivers the first full O(α) electroweak corrections to the 2→4 process e+e− → μ− ν̄ u d̄ using GRACE/1-LOOP, situating it within the progression from 2→3 corrections to more complex multi-leg processes. It introduces an efficient reduction scheme that expresses N(≥5)-point tensor integrals as sums of 4-point functions and validates it against a large set of SM diagrams, including non-linear gauge checks. A key finding is that finite-width effects introduce gauge-invariance breaking in infrared 5-point functions, highlighting the need for careful width treatment in the IR sector and suggesting alternative reduction identities can mitigate some instabilities. Overall, the study demonstrates that full radiative corrections to 2→4 processes are computable with current tools, but numerically delicate, requiring ongoing methodological refinements especially in IR-width handling.

Abstract

We performed the calculation of the full O(alpha) corrections to e+e- -> mu- nu-bar u d-bar with the help of the GRACE/1-LOOP system. We discuss how a finite decay width introduces a serious gauge invariance breaking, particularly for infrared 5-point functions. This is related to the way the reduction of those functions is performed and to the treatment of the width in the reduction.

Paper Structure

This paper contains 10 sections, 11 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Motivation
  3. Structure of the calculations
  4. The reduction algorithm of $N(\geq 5)$ point functions
  5. 1-loop diagrams for $e^+e^- \rightarrow \mu^- \overline{\nu}u\overline{d}$
  6. Check of codes
  7. Status of calculation
  8. Test run of integration
  9. Summary
  10. Acknowledgment

Figures (2)

  • Figure 1: Example of unstable 4-point functions obtained in the reduction of a 6-point function
  • Figure 2: An IR 5-point function and a tree diagram.