[Paper Review] The Five Gluon Amplitude and One-Loop Integrals

Zvi Bern, Lance J. Dixon+1 more|ArXiv.org|Dec 9, 1992

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper presents a field-theory computation of the one-loop five-gluon amplitude using a string-inspired technique, developing a general method for evaluating dimensionally regulated one-loop integrals—particularly for pentagon diagrams. It provides explicit results for key integrals and computes two specific five-gluon helicity amplitudes, advancing precision calculations in quantum chromodynamics at next-to-leading order.

ABSTRACT

We review the conventional field theory description of the string motivated technique. This technique is applied to the one-loop five-gluon amplitude. To evaluate the amplitude a general method for computing dimensionally regulated one-loop integrals is outlined including results for one-loop integrals required for the pentagon diagram and beyond. Finally, two five-gluon helicity amplitudes are given.

Motivation & Objective

• To compute the one-loop five-gluon scattering amplitude in quantum chromodynamics using a field-theory formulation of string-inspired techniques.
• To develop a general method for evaluating dimensionally regulated one-loop integrals, especially those arising in pentagon diagrams.
• To provide explicit results for one-loop integrals necessary for the five-gluon amplitude beyond the box-level diagrams.
• To present two explicit five-gluon helicity amplitudes at one-loop order for phenomenological applications.
• To support precision calculations in high-energy collider physics by extending one-loop amplitude techniques to five-parton processes.

Proposed method

• Adopts a string-inspired field theory approach to compute one-loop amplitudes, leveraging known techniques from string theory to simplify gauge theory calculations.
• Applies dimensional regularization to handle ultraviolet and infrared divergences in loop integrals, maintaining gauge invariance.
• Derives general expressions for one-loop tensor and scalar integrals in D dimensions, focusing on pentagon and box-type diagrams.
• Uses helicity state methods to compute the amplitude in terms of spinor-helicity variables, simplifying the structure of the final result.
• Performs explicit algebraic reduction of tensor integrals to scalar integrals using standard techniques in one-loop field theory.
• Validates the method by computing two specific helicity configurations of the five-gluon amplitude at one-loop order.

Experimental results

Research questions

• RQ1 How can string-inspired techniques be systematically applied to compute one-loop amplitudes in pure Yang-Mills theory?
• RQ2 What is the general form of dimensionally regulated one-loop integrals for pentagon diagrams in five-parton amplitudes?
• RQ3 Which scalar and tensor integrals are required to compute the full one-loop five-gluon amplitude?
• RQ4 What are the explicit helicity amplitudes for five-gluon scattering at one-loop order?
• RQ5 How can gauge invariance and infrared finiteness be preserved in the computation of multi-gluon one-loop amplitudes?

Key findings

• The paper derives a general method for computing one-loop integrals in dimensional regularization, applicable to pentagon and higher-point diagrams.
• It provides explicit results for the scalar and tensor integrals needed in the one-loop five-gluon amplitude, including those from pentagon diagrams.
• Two specific five-gluon helicity amplitudes are computed explicitly at one-loop order, offering benchmark results for phenomenological studies.
• The method successfully maintains gauge invariance and handles infrared divergences through dimensional regularization.
• The results lay the groundwork for higher-multiplicity one-loop calculations in quantum chromodynamics.
• The approach demonstrates the utility of string-inspired techniques in simplifying complex one-loop field theory amplitudes.