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We present lattice QCD results for masses and magnetic polarizabilities oflight and strange pseudoscalar mesons, chiral condensates, decay constants ofneutral pion, and neutral kaon in the presence of background magnetic fieldswith $eB$ ranging up to around 3.35 GeV$^2$ ($\sim70~M_\pi^2$) in the vacuum.The computations were carried out in (2+1)-flavor QCD mostly on $32^3 \times96$ lattices using the highly improved staggered quark action with $M_{\pi}\approx $ 220 MeV at zero temperature. We find that the masses of neutralpseudoscalar mesons monotonously decrease as the magnetic field strength growsand then saturate at a nonzero value, while there exists a nonmonotonousbehavior of charged pion and kaon masses in the magnetic field. We observe a$qB$ scaling of the up and down quark flavor components of neutral pion mass,neutral pion decay constant as well as the quark chiral condensates at 0.05$\lesssim eB\lesssim$ 3.35 GeV$^2$. We show that the correction to theGell-Mann-Oakes-Renner relation involving the neutral pion is less than 6% andthe correction for the relation involving neutral kaon is less than 30% at$eB\lesssim$ 3.35 GeV$^2$. We also derive the Ward-Takahashi identities for QCDin the magnetic field in the continuum formulation including the relationbetween integrated neutral pseudoscalar meson correlators and chiralcondensates.

Chiral properties of (2+1)-flavor QCD in strong magnetic fields at zero temperature