Researchers have presented hydrodynamic predictions for a new observable, $v_{02}(p_T)$, which quantifies the correlation between particle spectra and elliptic flow. This observable arises from the need to more precisely characterize the quark-gluon plasma (QGP) formed in heavy-ion collisions. The study focuses on lead-lead (Pb+Pb) collisions at a center-of-mass energy of $\sqrt{s_{NN}}=5.02$~TeV, a typical experimental setup at CERN's Large Hadron Collider (LHC).

To obtain these predictions, the hydrodynamic calculations were adjusted using a data-driven correction for the standard elliptic flow, $v_2(p_T)$. The corrected results show fair agreement with existing $v_0(p_T)$ data up to high transverse momenta ($p_T$). Predictions are extended to unidentified charged hadrons up to $p_T=10$~GeV$/c$, and to pions, kaons, and protons up to $p_T=5-6$~GeV$/c$, across several collision centrality windows.

Among the key findings, a decrease in $v_{02}(p_T)$ for charged hadrons in mid-central collisions is predicted for $p_T>4$~GeV$/c$. A meson-baryon splitting is also observed in this $p_T$ range. A distinctive feature of this new observable is the non-monotonic variation of $v_{02}(p_T)$ for protons at low $p_T$ above 30% centrality. This characteristic is unique to $v_{02}(p_T)$ and has not been observed in traditional flow observables like $v_2(p_T)$ and $v_0(p_T)$, making it a promising tool for unraveling the properties of the QGP.