Abstract: An invertible field transformation is such that the old field variables correspond one-to-one to the new variables. As such, one may think that two systems that are related by an invertible transformation are physically equivalent. However, if the transformation depends on field derivatives, the equivalence between the two systems is nontrivial due to the appearance of higher derivative terms in the equations of motion. To address this problem, we prove the following theorem on the relation between an invertible transformation and Euler-Lagrange equations: If the field transformation is invertible, then any solution of the original set of Euler-Lagrange equations is mapped to a solution of the new set of Euler-Lagrange equations, and vice versa. We also present applications of the theorem to scalar-tensor theories.

Abstract: One of the fundamental parameters entering the neutrino oscillation framework is the leptonic CP phase delta(13), and its measurement is an important goal of the planned long baseline experiments. It should be noted that ordinary matter effects complicate the determination of this parameter, and there are studies in the literature that deal with separation of intrinsic vs extrinsic CP violation. It is important to investigate the consequences of new physics effects that can not only hamper the measurement of delta(13) but also impact the consequences of discrete symmetries such as CP, T, and unitarity in different oscillation channels. In the present work, we explore these discrete symmetries and implications on unitarity in the presence of two new physics scenarios (nonstandard interaction in propagation and the presence of sterile neutrinos) that serve as good examples of going beyond the standard scenario in different directions. We uncover the impact of new physics scenarios on disentangling intrinsic and extrinsic CP violation.

Abstract: Prompt.-ray spectroscopy of the neutron-rich Kr-96, produced in transfer-and fusion-induced fission reactions, has been performed using the combination of the Advanced Gamma Tracking Array and the VAMOS + +spectrometer. A second excited state, assigned to J pi = 4(+), is observed for the first time, and a previously reported level energy of the first 2+ excited state is confirmed. The measured energy ratio R-4/2 = E(4(+))/E(2(+)) = 2.12(1) indicates that this nucleus does not show a well-developed collectivity contrary to that seen in heavier N = 60 isotones. This new measurement highlights an abrupt transition of the degree of collectivity as a function of the proton number at Z = 36, of similar amplitude to that observed at N = 60 at higher Z values. A possible reason for this abrupt transition could be related to the insufficient proton excitations in the g(9/2), d(5/2), and s(1/2) orbitals to generate strong quadrupole correlations or to the coexistence of competing different shapes. An unexpected continuous decrease of R-4/2 as a function of the neutron number up to N = 60 is also evidenced. This measurement establishes the Kr isotopic chain as the low-Z boundary of the island of deformation for N = 60 isotones. A comparison with available theoretical predictions using different beyond mean-field approaches shows that these models fail to reproduce the abrupt transitions at N = 60 and Z = 36.