Bayesian analysis with information field approach and the inference of the temperature-dependent jet transport parameter*

Bayesian inference has been widely applied to extract physical parameters with correlated uncertainty quantification. Many quantities of interest in high-energy nuclear physics are functions, such as the temperature- and energy-dependent transport coefficients and parton distribution functions. For functional inference, the choice of the prior distribution is subtle but also critical to obtaining reliable results. Existing studies performing functional inference heavily rely on explicit parametrization, which can impose unwanted long-range correlations in the input parameter space of the function, limiting the ability to incorporate datasets that are supposed to provide independent constraints in different input regions. 

We propose to use the information field method to solve the above problem, where the unconstrained function is treated as a random field with a typical correlation length that removes long-range correlations. As proof of the principle of this method, we performed a global Bayesian analysis on the temperature-dependent jet transport parameter using the NLO parton model calculations with Higher-Twist modified fragmentation. This study has included single hadron, dihadron, and gamma-hadron nuclear modification factors at both RHIC and LHC energies. We illustrate how the value of jet transport parameters from low to high temperatures is progressively constrained by incrementally including datasets from peripheral to central collisions from lower to higher beam energies. Furthermore, the information field approach allows straightforward sensitivity analysis to guide future measurements to target temperature regions with insufficient constraints.