2022 journal article

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


By: A. Arifi*, H. Choi*, C. Ji n & Y. Oh*

Source: Web Of Science
Added: August 29, 2022

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, $\mathrm{\ensuremath{\Delta}}{M}_{P}>\mathrm{\ensuremath{\Delta}}{M}_{V}$, where $\mathrm{\ensuremath{\Delta}}{M}_{P(V)}={M}_{P(V)}^{2S}\ensuremath{-}{M}_{P(V)}^{1S}$ and the hierarchy of the decay constants, ${f}_{1S}>{f}_{2S}$, 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 $\ensuremath{\theta}$ between $1S$ and $2S$ states as ${\ensuremath{\theta}}_{c}={\mathrm{cot}}^{\ensuremath{-}1}(2\sqrt{6})/2\ensuremath{\simeq}6\ifmmode^\circ\else\textdegree\fi{}$ and obtain the optimum value of the mixing angle around 12\ifmmode^\circ\else\textdegree\fi{} 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 ${D}_{s}$ meson is predicted to have a mass of 2600 MeV, which is very close to the mass of the newly discovered ${D}_{s0}(2590{)}^{+}$ meson by the LHCb Collaboration. This supports the interpretation of the observed state as a radial excitation of the ${D}_{s}^{+}$ meson.