Bayesian inference of the path-length dependence of jet energy loss

A simple model for medium modification of the jet function can be used to extract energy loss distribution through a parameterized form. We carry out comprehensive Bayesian analysis world data on single inclusive spectra in heavy-ion collisions at both BNL Relativistic Heavy Ion Collider and CERN Large Hadron energies. average $\ensuremath{\langle}\mathrm{\ensuremath{\Delta}}E\ensuremath{\rangle}$ as transverse momentum ${p}_{T}$ each collision system centrality independently. Assuming is proportional initial parton density $\ensuremath{\rho}\ensuremath{\sim}d{N}_{\mathrm{ch}}/d\ensuremath{\eta}/\ensuremath{\pi}{R}_{\mathrm{eff}}^{2}$ estimated from pseudorapidity charged hadron multiplicity $d{N}_{\mathrm{ch}}/d\ensuremath{\eta}$ effective size ${R}_{\mathrm{eff}}\ensuremath{\sim}{N}_{\mathrm{part}}^{1/3}$ given by number participant nucleons ${N}_{\mathrm{part}}$, scaled $\ensuremath{\langle}\mathrm{\ensuremath{\Delta}}E\ensuremath{\rangle}/\ensuremath{\rho}\ensuremath{\sim}{R}_{\mathrm{eff}}^{0.59}{p}_{T}^{0.13}ln{p}_{T}$ cone-size $R=0.4$ found have dependence that slightly stronger than logarithmic form while or length slower linear one. The fluctuation is, however, independent size.