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The mass spectra and wave functions of both $1S$ and $2S$ state heavypseudoscalar ($P$) and vector ($V$) mesons are analyzed within the light-frontquark model. Important empirical constraints employed in our analysis of themass spectra and wave functions are the experimental mass-gap relation, $\DeltaM_P > \Delta M_V$, where $\Delta M_{P(V)}=M^{2S}_{P(V)}-M^{1S}_{P(V)}$ and thehierarchy of the decay constants, $f_{1S}>f_{2S}$, between $1S$ and $2S$ mesonstates. We maintain the orthogonality of the trial wave functions of the $1S$and $2S$ states in our variational calculation of the Hamiltonian with theCoulomb plus confining potentials and treat the hyperfine interactionperturbatively for the heavy-heavy and heavy-light $P$ and $V$ mesons due tothe nature of the heavy quark symmetry. Realizing that the empiricalconstraints cannot be satisfied without mixing of the $1S$ and $2S$ states, wefind the lower bound of the mixing angle $\theta$ between $1S$ and $2S$ statesas $\theta_c = {\rm cot}^{-1}(2\sqrt{6})/2\simeq 6^{\circ}$ and obtain theoptimum value of the mixing angle around $12^\circ$ to cover both the charm andbottom flavors of the heavy quark. The mixing effects are found to be moresignificant to the $2S$ state mesons than to the $1S$ state mesons. Theproperties of $1S$ and $2S$ state mesons including the mass spectra, decayconstants, twist-2 distribution amplitudes, and electromagnetic form factorsare computed. Our results are found to be in a good agreement with theavailable data and lattice simulations. In particular, the $2S$ statepseudoscalar $D_s$ meson is predicted to have a mass of $2600$ MeV, which isvery close to the mass of the newly discovered $D_{s0}(2590)^+$ meson by theLHCb Collaboration. This supports the interpretation of the observed state as aradial excitation of the $D^+_s$ meson.

Mixing effects on 1S and 2S state heavy mesons in the light-front quark model