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We establish a relation between the equation of state (EOS) of nuclear matterand the fourth-order symmetry energy $a_{\rm{sym,4}}(A)$ of finite nuclei in asemi-empirical nuclear mass formula by self-consistently considering the bulk,surface and Coulomb contributions to the nuclear mass. Such a relation allowsus to extract information on nuclear matter fourth-order symmetry energy$E_{\rm{sym,4}}(\rho_0)$ at normal nuclear density $\rho_0$ from analyzingnuclear mass data. Based on the recent precise extraction of$a_{\rm{sym,4}}(A)$ via the double difference of the "experimental" symmetryenergy extracted from nuclear masses, for the first time, we estimate a valueof $E_{\rm{sym,4}}(\rho_0) = 20.0\pm4.6$ MeV. Such a value of$E_{\rm{sym,4}}(\rho_0)$ is significantly larger than the predictions frommean-field models and thus suggests the importance of considering the effectsof beyond the mean-field approximation in nuclear matter calculations.

Empirical information on nuclear matter fourth-order symmetry energy from an extended nuclear mass formula