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Helicity amplitude for the process $q\Bar{q} \rightarrow q\Bar{q} g$

Vibhu Pandya, Radhika Vinze, Anuradha Misra

TL;DR

The paper addresses the tree-level S-matrix calculation for the real-gluon emission process qqbar → qqbar g in the high-energy, massless-quark limit, focusing on photon- and gluon-mediated diagrams with Z exchange neglected. Using the spinor-helicity formalism, the authors derive helicity amplitudes for photon- and gluon-mediated contributions, employing a judicious reference-momentum choice to simplify the algebra and reveal cancellations. The resulting squared amplitude |M|^2 comprises seven non-zero terms, with diagonal and interference pieces organized by the couplings e and g, and expressed in terms of invariants s_ij and traces. This approach provides a compact, scalable framework for precision QCD/QED predictions at colliders and can be extended to include Z-mediated and electroweak effects.

Abstract

Precision calculations in hadronic processes at high energy colliders are crucial for improving the understanding of the standard phenomena as well as for the discovery of new physics. Spinor-helicity formalism serves as one of the most efficient ways to simplify the calculations of $S$ matrix elements. In this article, we compute the $S$ matrix elements for the process $q\Bar{q}\rightarrow q\Bar{q}g$ mediated by photon and gluon. Ignoring the contribution of $Z$ boson exchange, we show that the calculation of $S$ matrix elements for this process simplifies to a great extent by using spinor-helicity formalism.

Helicity amplitude for the process $q\Bar{q} \rightarrow q\Bar{q} g$

TL;DR

The paper addresses the tree-level S-matrix calculation for the real-gluon emission process qqbar → qqbar g in the high-energy, massless-quark limit, focusing on photon- and gluon-mediated diagrams with Z exchange neglected. Using the spinor-helicity formalism, the authors derive helicity amplitudes for photon- and gluon-mediated contributions, employing a judicious reference-momentum choice to simplify the algebra and reveal cancellations. The resulting squared amplitude |M|^2 comprises seven non-zero terms, with diagonal and interference pieces organized by the couplings e and g, and expressed in terms of invariants s_ij and traces. This approach provides a compact, scalable framework for precision QCD/QED predictions at colliders and can be extended to include Z-mediated and electroweak effects.

Abstract

Precision calculations in hadronic processes at high energy colliders are crucial for improving the understanding of the standard phenomena as well as for the discovery of new physics. Spinor-helicity formalism serves as one of the most efficient ways to simplify the calculations of matrix elements. In this article, we compute the matrix elements for the process mediated by photon and gluon. Ignoring the contribution of boson exchange, we show that the calculation of matrix elements for this process simplifies to a great extent by using spinor-helicity formalism.

Paper Structure

This paper contains 9 sections, 27 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Amplitude for $q\overline{q} \rightarrow q\overline{q} g$ in helicity basis
  3. Helicity amplitude for photon and gluon exchange diagrams
  4. Photon-Mediated Diagrams
  5. Gluon-Mediated Diagrams
  6. $\mathcal{M}^{2}$ for $q\overline{q}\rightarrow q\overline{q}g$
  7. Conclusion
  8. Feynman Rules
  9. Spinor-Helicity Formalism

Figures (4)

  • Figure 1: quark-anti-quark scattering representation with helicity-spinors
  • Figure 2: Photon mediated diagrams for $q\overline{q}\rightarrow q\overline{q}g$ process
  • Figure 3: Gluon mediated diagrams for $q\overline{q}\rightarrow q\overline{q}g$ process
  • Figure 4: Non-zero diagrams after the choice $q=l$ in $q\overline{q}\rightarrow q\overline{q}g$ process