  The determination of nuclear symmetry energy, and in particular, its density
dependence, is a long-standing problem for nuclear physics community. Previous
studies have found that the product of electric dipole polarizability
$\alpha_D$ and symmetry energy at saturation density $J$ has a strong linear
correlation with $L$, the slope parameter of symmetry energy. However, current
uncertainty of $J$ hinders the precise constraint on $L$. We investigate the
correlations between electric dipole polarizability $\alpha_D$ (or times
symmetry energy at saturation density $J$) in Sn isotopes and the slope
parameter of symmetry energy $L$ using the quasiparticle random-phase
approximation based on Skyrme Hartree-Fock-Bogoliubov. A strong and
model-independent linear correlation between $\alpha_D$ and $L$ is found in
neutron-rich Sn isotopes where pygmy dipole resonance (PDR) gives a
considerable contribution to $\alpha_D$, attributed to the pairing correlations
playing important roles through PDR. This newly discovered linear correlation
would help one to constrain $L$ and neutron-skin thickness $\Delta
R_\textnormal{np}$ stiffly if $\alpha_D$ is measured with high resolution in
neutron-rich nuclei. Besides, a linear correlation between $\alpha_D J$ in a
nucleus around $\beta$-stability line and $\alpha_D$ in a neutron-rich nucleus
can be used to assess $\alpha_D$ in neutron-rich nuclei.
