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We studied the temporal correlation function of mesons in the pseudo-scalarchannel in (2+1)-flavor QCD in the presence of external magnetic fields at zerotemperature. The simulations were performed on $32^3 \times 96$ lattices usingthe Highly Improved Staggered Quarks (HISQ) action with $m_{\pi} \approx $ 230MeV. The strength of magnetic fields $|eB|$ ranges from 0 to around 3.3 GeV$^2$($\sim 60 m_\pi^2$). We found that the masses of neutral pseudo-scalarparticles, e.g. neutral pion and kaon, monotonouslly decrease as the magneticfield grows and then saturate at a nonzero value. It is observed that heavierneutral pseudo-scalars are less affected by magnetic fields. Moreover, we founda non-monotonous behavior of charged pion and kaon mass in magnetic field forthe first time. In the case of small magnetic field (0 $\leq~|eB| \lesssim$ 0.3GeV$^2~\sim 6m_\pi^2$ ) the mass of charged pseudo-scalar grows with magneticfield and can be well described by the Lowest Landau Level approximation, whilefor $|eB|$ larger than 0.3 GeV$^2$ the mass starts to decrease. The possibleconnection between $|eB|$ dependences of neutral pion mass and the decreasingbehavior of pseudo-critical temperature in magnetic field is discussed. Due tothe nonzero value of neutral pion mass our simulation indicates that thesuperconducting phase of QCD does not exist in the current window of magneticfield.

Meson masses in external magnetic fields with HISQ fermions