ν-point energy correletors with FASTEEC Small-x physics from LHC jets

In recent years, energy correlators have emerged as a powerful tool for studying jet substructure, with promising applications such as probing the hadronization transition, analyzing the quark-gluon plasma, and improving the precision of top quark mass measurements. The projected N-point correlator measures correlations between N final-state particles by tracking the largest separation between them, showing a scaling behavior related to DGLAP splitting functions. These correlators can be analytically continued in N, commonly referred to as ν-correlators, allowing access to non-integer moments of the splitting functions. Of particular interest is the ν→0 limit, where the small momentum fraction behavior of the splitting functions requires resummation. Originally, the computational complexity of evaluating ν-correlators for M particles scaled as 2^2M, making it impractical for real-world analyses. However, by using recursion, we reduce this to M2^M, and through the FASTEEC method of dynamically resolving subjets, M is replaced by the number of subjets. This breakthrough enables, for the first time, the computation of ν-correlators for LHC data. In practice, limiting the number of subjets to 16 is sufficient to achieve percent-level precision, which we validate using known integer-ν results and convergence tests for non-integer ν. We have implemented this in an update to FASTEEC and conducted an initial study of power-law scaling in the perturbative regime as a function of ν, using CMS Open Data on jets. The results agree with DGLAP evolution, except at small ν, where the anomalous dimension saturates to a value that matches the BFKL anomalous dimension.