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

The mass spectra and wave functions of both 1S and 2S state heavy pseudoscalar (P) and vector (V) mesons are analyzed within the light-front quark model. Important empirical constraints employed in our analysis of the mass spectra and wave functions are the experimental mass-gap relation, ΔMP>ΔMV, where ΔMP(V)=MP(V)2S-MP(V)1S and the hierarchy of the decay constants, f1S>f2S, between 1S and 2S meson states. We maintain the orthogonality of the trial wave functions of the 1S and 2S states in our variational calculation of the Hamiltonian with the Coulomb plus confining potentials and treat the hyperfine interaction perturbatively for the heavy-heavy and heavy-light P and V mesons due to the nature of the heavy quark symmetry. Realizing that the empirical constraints cannot be satisfied without mixing of the 1S and 2S states, we find the lower bound of the mixing angle θ between 1S and 2S states as θc=cot-1(26)/2≃6° and obtain the optimum value of the mixing angle around 12° to cover both the charm and bottom flavors of the heavy quark. The mixing effects are found to be more significant to the 2S state mesons than to the 1S state mesons. The properties of 1S and 2S state mesons including the mass spectra, decay constants, twist-2 distribution amplitudes, and electromagnetic form factors are computed. Our results are found to be in a good agreement with the available data and lattice simulations. In particular, the 2S state pseudoscalar Ds meson is predicted to have a mass of 2600 MeV, which is very close to the mass of the newly discovered Ds0(2590)+ meson by the LHCb Collaboration. This supports the interpretation of the observed state as a radial excitation of the Ds+ meson.