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We point out that chiral condensates at nonzero temperature and magneticfields are in strict connection to the space-time integral of correspondingtwo-point neutral meson correlation functions in the pseudoscalar channel viathe Ward-Takahashi identity. Screening masses of neutral pseudoscalar mesons,which are defined as the exponential decay of the corresponding spatialcorrelation functions in the long distance, thus are intrinsically connected to(inverse) magnetic catalysis of chiral condensates. To study this we performedlattice simulations of $(2+1)$-flavor QCD on $32^3\times N_t$ lattices withpion mass $M_\pi\simeq 220$ MeV in a fixed scale approach having temperature$T\in[17, 281]$ MeV and magnetic field strength $eB\in[0, 2.5]$ GeV$^2$. Wefind that screening lengths, i.e. inverses of screening masses of $\pi^0$,$K^0$ and $\eta^0_{s\bar{s}}$, turn out to have the similar complex $eB$ and$T$ dependences of the corresponding chiral condensates. Although thetransition temperature is found to always decrease as $eB$ grows, we show thatthe suppression due to magnetic fields becomes less significant for hadronscreening length and chiral condensates with heavier quarks involved, andceases to occur for $\eta^0_{s\bar{s}}$ and strange quark chiral condensate.The complex $eB$ and $T$ dependences of both screening masses and chiralcondensates, reflecting the crossover nature of the QCD transition, areattributed to the competition between sea and valence quark effects. Thesefindings could be useful to guide low-energy models and effective theories ofQCD.

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