Total Solar Eclipse: August 21, 2017

We present an interpretation of the functions appearing in the Wei–Norman factorization of the evolution operator for a Hamiltonian belonging to the SU(1,1) algebra in terms of the classical solutions of the Generalized Caldirola–Kanai (GCK) oscillator (with time-dependent mass and frequency). Choosing P2, X2, and the dilation operator as a basis for the Lie algebra, we obtain that, out of the six possible orderings for the Wei–Norman factorization of the evolution operator for the GCK Hamiltonian, three of them can be expressed in terms of its classical solutions and the other three involve the classical solutions associated with a mirror Hamiltonian obtained by inverting the mass. In addition, we generalize the Wei–Norman procedure to compute the factorization of other operators, such as a generalized Fresnel transform and the Arnold transform (and its generalizations), obtaining also in these cases a semiclassical interpretation for the functions in the exponents of the Wei–Norman factorization. The singularities of the functions appearing in the Wei–Norman factorization are related to the caustic points of Morse theory, and the expression of the evolution operator at the caustics is obtained using a limiting procedure, where the Fourier transform of the initial state appears along with the Guoy phase.

Recent anomalies in ⁸Be and ⁴He nuclear decays can be explained by postulating a fifth force mediated by a new boson X. The distributions of both transitions are consistent with the same X mass, 17 MeV, providing kinematic evidence for a single new particle explanation. In this work, we examine whether the new results also provide dynamical evidence for a new particle explanation, that is, whether the observed decay rates of both anomalies can be described by a single hypothesis for the X boson’s interactions. We consider the observed ⁸Be and ⁴He excited nuclei, as well as a ¹²C excited nucleus; together these span the possible JP quantum numbers up to spin 1 for excited nuclei. For each transition, we determine whether scalar, pseudoscalar, vector, or axial vector X particles can mediate the decay, and we construct the leading operators in a nuclear physics effective field theory that describes them. Assuming parity conservation, the scalar case is excluded and the pseudoscalar case is highly disfavored. Remarkably, however, the protophobic vector gauge boson, first proposed to explain only the ⁸Be anomaly, also explains the ⁴He anomaly within experimental uncertainties. We predict signal rates for other closely related nuclear measurements, which, if confirmed by the ATOMKI group and others, would provide overwhelming evidence that a fifth force has been discovered.

We present the discoveries of KELT-25 b (TIC 65412605, TOI-626.01) and KELT-26 b (TIC 160708862, TOI-1337.01), two transiting companions orbiting relatively bright, early A stars. The transit signals were initially detected by the KELT survey and subsequently confirmed by Transiting Exoplanet Survey Satellite (TESS) photometry. KELT-25 b is on a 4.40 day orbit around the V = 9.66 star CD-24 5016 (Teff = 8280 K, M⋆ = 2.18 M⊙), while KELT-26 b is on a 3.34 day orbit around the V = 9.95 star HD 134004 (Teff = 8640, K, M⋆ = 1.93 M⊙), which is likely an Am star. We have confirmed the substellar nature of both companions through detailed characterization of each system using ground-based and TESS photometry, radial velocity measurements, Doppler tomography, and high-resolution imaging. For KELT-25, we determine a companion radius of RP = 1.64 RJ and a 3σ upper limit on the companion’s mass of ∼64 MJ. For KELT-26 b, we infer a planetary mass and radius of MP = 1.41 MJ  and RP = 1.94 RJ. From Doppler tomographic observations, we find KELT-26 b to reside in a highly misaligned orbit. This conclusion is weakly corroborated by a subtle asymmetry in the transit light curve from the TESS data. KELT-25 b appears to be in a well-aligned, prograde orbit, and the system is likely a member of the cluster Theia 449.