Bayesian constraint of the initial condition for the Balitsky-Kovchegov equation at NLO

TL;DR

The paper tackles the uncertainty in the non-perturbative initial condition for the Balitsky-Kovchegov equation at next-to-leading order (NLO) by performing Bayesian inference against HERA DIS data. A combination of Markov Chain Monte Carlo (MCMC) and Gaussian Process Emulator is used to infer the posterior for the initial-condition parameters [$Q_{s,0}^2, gamma, C^2, sigma_0/2, m_c$] under two running-coupling schemes: Bal+SD and the parent dipole. The analysis yields posterior distributions with chi2/dof values around 1.2–1.4, demonstrating a successful simultaneous description of the total HERA cross section and heavy-quark data, and shows a preference for a steep dipole with $gamma>1$. These results enable principled uncertainty propagation to future NLO CGC calculations and lay the groundwork for a full NLO treatment including resummation of large transverse logarithms.

Abstract

We use Bayesian inference to constrain the parameters describing the initial amplitude input to the Balitsky-Kovchegov evolution equation at next-to-leading order accuracy against precise HERA total inclusive cross section and heavy quark data. The datasets are found to provide stringent constraints and, with consistent NLO treatment, a successful description of the data is obtained. The posterior distributions define the theoretical uncertainites that surround the non-perturbative initial condition and, thus, provide a way to propagate said uncertainties to CGC calculations at NLO.

Figures (2)

• Figure 1: Posterior distribution for the fit using the Bal+SD running coupling scheme.
• Figure 2: Posterior distribution for the fit using the parent dipole running coupling scheme.