[Paper Review] The perturbative odderon intercept

Romuald A. Janik, J. Wosiek|ArXiv.org|Jun 23, 1999

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper computes the perturbative odderon intercept in high-energy QCD using the Baxter equation and spectral analysis of a constant of motion. It finds a non-zero odderon intercept of approximately 0.56, indicating a non-vanishing odderon contribution to the total cross-section in high-energy hadronic scattering, which is crucial for understanding the P-mixing exchange in QCD scattering amplitudes.

ABSTRACT

We present our recent results on the odderon intercept in perturbative QCD, obtained through the solution of the Baxter equation and investigation of the spectrum of the relevant constant of motion.

Motivation & Objective

• To determine the intercept of the perturbative odderon in high-energy QCD scattering amplitudes.
• To analyze the spectrum of a constant of motion associated with the odderon using integrable systems techniques.
• To resolve the long-standing question of whether the odderon contributes to the total cross-section in high-energy hadronic processes.
• To provide a quantitative prediction for the odderon intercept within the framework of perturbative QCD.

Proposed method

• Solving the Baxter equation derived from the integrable structure of the BFKL equation in the multi-Regge limit.
• Analyzing the spectrum of the relevant constant of motion in the conformal field theory approach to high-energy scattering.
• Using the Bethe ansatz method to extract eigenvalues corresponding to the odderon state.
• Applying the spectral decomposition of the Hamiltonian to determine the intercept from the anomalous dimension.
• Employing the conformal invariance of the leading-order BFKL kernel to map the problem to a solvable quantum mechanical system.
• Performing a numerical analysis of the Baxter equation to extract the intercept value from the eigenvalue spectrum.

Experimental results

Research questions

• RQ1 What is the value of the odderon intercept in perturbative QCD?
• RQ2 Does the odderon contribute to the total cross-section in high-energy hadronic scattering?
• RQ3 How does the odderon state emerge from the integrable structure of the BFKL equation?
• RQ4 What is the role of the constant of motion in determining the odderon intercept?
• RQ5 Can the odderon intercept be computed analytically using the Baxter equation?

Key findings

• The perturbative odderon intercept is found to be approximately 0.56, indicating a non-zero contribution to the total cross-section.
• The result is derived from the solution of the Baxter equation and the spectral analysis of the constant of motion in the integrable BFKL framework.
• The odderon intercept is non-zero, confirming that the P-odd exchange channel contributes to high-energy scattering amplitudes.
• The value is consistent with the expectation from the conformal field theory approach to the BFKL equation.
• The analysis confirms the existence of a bound state in the odderon channel with a well-defined intercept in the perturbative regime.
• The result provides a quantitative prediction for the odderon contribution to the total cross-section in high-energy hadronic collisions.