The quadratic form of the isobaric multiplet mass equation (IMME), which was originally suggested by Wigner and has been generally regarded as valid, is seriously questioned by recent high-precision nuclear mass measurements. The usual resolution to this problem is to add empirically the cubic and quartic T z -terms to characterize the deviations from the IMME, but finding the origin of these terms remains an unsolved difficulty. Based on a strategy beyond the Wigner's first-order perturbation, we derive explicitly the cubic and quartic T z -terms. These terms are shown to be generated by the effective charge-symmetry breaking and chargeindependent breaking interactions in nuclear medium combined with the Coulomb polarization effect. Calculations for the sdand lower f p-shells explore a systematical emergence of the cubic T z -term, suggesting a general deviation from the original IMME. Intriguingly, the magnitude of the deviation exhibits an oscillationlike behavior with mass number, modulated by the shell effect. PACS numbers: 24.80.+y, 13.75.Cs, 21.65.Ef, 21.10.Dr I. INTRODUCTIONShortly after the discovery of neutron, Heisenberg introduced isospin to describe different charge states of nucleon [1]. In this concept, proton (p) and neutron (n) are treated as an isospin T = 1/2 doublet distinguished by different projections T z (p) = −1/2 and T z (n) = +1/2. As one of the most important predictions in nuclear physics, the isobaric multiplet mass equation (IMME) proposed later by Wigner [2,3] suggests that the mass excesses ME(A, T, T z ) of the nuclei belonging to an isospin multiplet of mass number A and total isospin T follow a simple quadratic equationwhere T z = (N − Z)/2 is the isospin projection, and the parameters a, b and c are constants for a given multiplet. The elegant IMME, though derived by using the 1st-order perturbation approximation, has been widely employed to predict the unknown masses of unstable neutron-deficient nuclei. Since its establishment, the IMME is believed to be generally valid [4]. With recent advances in radioactive beam facilities, a wealth of exotic masses with increasing precision became available [5]. Unexpectedly large discrepancies between the measured masses and the ones given by the quadratic form of the IMME were observed [6][7][8]. This calls for an addition of a cubic term dT 3 z or even a quartic term eT 4 z to Eq. (1) [9][10][11]. The origin of these higher-order terms, which clearly lies beyond the original IMME of Eq. (1), requires explanation. * dongjm07@impcas.ac.cn

With 1.06 × 10 8 ψ(3686) events collected with the BESIII detector, the branching fraction of ψ(3686) → ωK + K − is measured to be (1.54± 0.04± 0.11)× 10 −4 . This is the most precise result to date, due to the largest ψ(3686) sample, improved signal reconstruction efficiency, good simulation of the detector performance, and a more accurate knowledge of the continuum contribution. Using the branching fraction of J/ψ → ωK + K − , the ratio B(ψ(3868) → K + K − )/B(J/ψ → K + K − ) is determined to be (18.4 ± 3.7) %. This constitutes a significantly improved test of the 12 % rule, with the uncertainty now dominated by the J/ψ branching fraction.