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The finite temperature phase diagram of QCD with two massless quark flavorsis not yet understood because of the subtle effects of anomalous $U_A(1)$symmetry. In this work we address this issue by studying the fate of theanomalous $U_A(1)$ symmetry in $2+1$ flavor QCD just above the chiral crossovertransition temperature $T_c$, lowering the light quark mass towards the chirallimit along line of constant physical strange quark mass. We use the gaugeconfigurations generated using the Highly Improved Staggered Quark (HISQ)discretization on lattice volumes $32^3\times8$ and $56^3\times 8$ to study therenormalized eigenvalue spectrum of QCD with valence overlap Dirac operator. Wehave implemented new numerical techniques that have allowed us to measure about$100$-$200$ eigenvalues of the gauge ensembles with light quark masses $\gtrsim0.6$ MeV. From a detailed analysis of the dependence of the renormalizedeigenvalue spectrum and $U_A(1)$ breaking observables on the light quark mass,our study suggests $U_A(1)$ is broken at $T\gtrsim T_c$ even when the chirallimit is approached.

Eigenvalue spectra of QCD and the fate of $U_A(1)$ breaking towards the chiral limit