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We investigate temperature ($T$) dependence of quark number densities ($n_q$)at imaginary and real chemical potential ($\mu$) by using $N_f = 2$ lattice QCDand the hadron resonance gas (HRG) model. Quark number densities are calculatedat imaginary $\mu$ with lattice QCD on an $8^2 \times 16 \times 4$ lattice withthe clover-improved $N_f =2$ Wilson fermion action and therenormalization-group-improved Iwasaki gauge action. The results are consistentwith the previous results of the staggered-type quark action. The $n_q$obtained are extrapolated to real $\mu$ by assuming the Fourier series for theconfinement region and the polynomial series for the deconfinement region. Theextrapolated results are consistent with the previous results of the Taylorexpansion method for the reweighting factor. The upper bound$(\mu/T)_{\mathrm{max}}$ of the region where the extrapolation is considered tobe reliable is estimated for each temperature $T$ . We test whether $T$dependence of nucleon and $\Delta$-resonance masses can be determined from LQCDdata on $n_q$ at imaginary $\mu$ by using the HRG model. In the testcalculation, nucleon and $\Delta$-resonance masses reduce by about 10% in thevicinity of the pseudocritical temperature.

Quark number densities at imaginary chemical potential in $N_f=2$ lattice QCD with Wilson fermions and its model analyses