Chiral condensates and screening masses of neutral pseudoscalar mesons in thermomagnetic QCD medium

We point out that chiral condensates at nonzero temperature and magnetic fields are in strict connection to the space-time integral of corresponding two-point neutral meson correlation functions pseudoscalar channel via Ward-Takahashi identity. Screening masses mesons, which defined as exponential decay spatial long distance, thus intrinsically connected (inverse) catalysis condensates. To study this we performed lattice simulations ($2+1$)-flavor QCD on ${32}^{3}\ifmmode\times\else\texttimes\fi{}{N}_{t}$ lattices with pion mass ${M}_{\ensuremath{\pi}}\ensuremath{\simeq}220\text{ }\text{ }\mathrm{MeV}$ a fixed scale approach having $T\ensuremath{\in}[17,281]\text{ field strength $eB\ensuremath{\in}[0,2.5]\text{ }{\mathrm{GeV}}^{2}$. find screening lengths, i.e., inverses ${\ensuremath{\pi}}^{0}$, ${K}^{0}$ ${\ensuremath{\eta}}_{s\overline{s}}^{0}$, turn have similar complex $eB$ $T$ dependences Although transition is found always decrease grows, show suppression due becomes less significant for hadron length heavier quarks involved, ceases occur ${\ensuremath{\eta}}_{s\overline{s}}^{0}$ strange quark condensate. The both condensates, reflecting crossover nature transition, attributed competition between sea valence effects. These findings could be useful guide low-energy models effective theories QCD.