Assessing lattice QCD charm space diffusion coefficient and thermalization time by mean of D meson observables at LHC

A central goal in the study of heavy-flavour production is to determine the interaction strength between Heavy Quarks (HQs) and the Quark-Gluon Plasma (QGP), quantified by the spatial diffusion coefficient D s ( T ). Recent lattice QCD (lQCD) results with dynamical fermions suggest a remarkably low value of 2 πTD s ≈ 1 at T = T c for charm quarks - significantly lower than both quenched QCD estimates and most phenomenological models - which typically yield 2 π T D s ≈ 3.5 − 5 . This discrepancy raises the question of whether such a small D s ( T ), corresponding to a thermalization time τ t h ≈ 1 − 1.5 fm/c, is compatible with experimental measurements of key observables like the nuclear modification factor R AA , the elliptic and triangular flow coefficients v 2 and v 3 for D mesons. Using an event-by-event Langevin transport framework, we analyze several scenarios and highlight the pivotal role played by the momentum dependence of the drag coefficient A ( p ) = τ t h − 1 ( p ) . Our findings show that a small 2 π T D s ( p → 0 ) ≈ 1 − 2 values can align with experimental data only if a significant momentum dependence in τ t h ( p ) = 1 / A ( p ) is included, as predicted by T-matrix approaches, or by the extended Quasi-Particle Model (QPMp). In contrast, assuming a momentum-independent τ t h = M c D s lQCD / T , it fails to reproduce the observed phenomenology. Furthermore, a short thermalization time of τ th ≈ 1.5 fm/c implies a loss of sensitivity of the final-state observables to the initial charm-quark momentum distribution up p T ≈ M c , suggesting a possible universal behavior driven by a dynamical attractor.