Validity of first-order truncation for the energy-flow correlator

Determine whether the mean-squared energy-flow harmonic relation in Eq. (linearLinearEEC) can be consistently truncated at first order in the event-by-event energy-density fluctuation, corresponding to retaining only the p=1 response term.

Background

The response of the final-state energy-flow harmonic is represented as a functional expansion in powers of the initial event-by-event energy-density fluctuation. The p=1 term gives the linear response contribution, while higher-p terms encode nonlinear response and mode coupling. The leading expression for the mean-squared harmonic is therefore subject to corrections beginning at higher powers of the fluctuation.

Although the paper develops the formal expansion and motivates a leading eccentricity-like approximation, it does not establish whether the p=1 contribution is sufficient in general. The authors explicitly state that this truncation cannot be decided a priori, making its validity an unresolved question.