Dynamical Mass of the Exoplanet Host Star HR 8799

HR 8799 is a young A5/F0 star hosting four directly imaged giant planets at wide separations (∼16–78 au), which are undergoing orbital motion and have been continuously monitored with adaptive optics imaging since their discovery over a decade ago. We present a dynamical mass of HR 8799 using 130 epochs of relative astrometry of its planets, which include both published measurements and new medium-band 3.1 μm observations that we acquired with NIRC2 at Keck Observatory. For the purpose of measuring the host-star mass, each orbiting planet is treated as a massless particle and is fit with a Keplerian orbit using Markov chain Monte Carlo. We then use a Bayesian framework to combine each independent total mass measurement into a cumulative dynamical mass using all four planets. The dynamical mass of HR 8799 is 1.47 − 0.17 + 0.12 M ⊙ assuming a uniform stellar mass prior, or 1.46 − 0.15 + 0.11 M ⊙ with a weakly informative prior based on spectroscopy. There is a strong covariance between the planets’ eccentricities and the total system mass; when the constraint is limited to low-eccentricity solutions of e < 0.1, which are motivated by dynamical stability, our mass measurement improves to 1.43 − 0.07 + 0.06 M ⊙. Our dynamical mass and other fundamental measured parameters of HR 8799 together with Modules for Experiments in Stellar Astrophysics Isochrones and Stellar Tracks grids yields a bulk metallicity most consistent with [Fe/H] ∼ −0.25–0.00 dex and an age of 10–23 Myr for the system. This implies hot-start masses of 2.7–4.9 M Jup for HR 8799 b and 4.1–7.0 M Jup for HR 8799 c, d, and e, assuming they formed at the same time as the host star.

Quaternionic Dirac free particle

In this paper, we solve the quaternionic Dirac equation [Formula: see text] in the real Hilbert space, and we ascertain that their free particle solutions set comprises eight elements in the case of a massive particle, and a four elements solutions set in the case of a massless particle, a richer situation when compared to the four elements solutions set of the usual complex Dirac equation [Formula: see text]. These free particle solutions were unknown in the previous solutions of anti-Hermitian quaternionic quantum mechanics, and constitute an essential element in order to build a quaternionic quantum field theory [Formula: see text].

AdS3/AdS2 degression of massless particles

We study a 3d/2d dimensional degression which is a Kaluza-Klein type mechanism in AdS3 space foliated into AdS2 hypersurfaces. It is shown that an AdS3 massless particle of spin s = 1, 2, …, ∞ degresses into a couple of AdS2 particles of equal energies E = s. Note that the Kaluza-Klein spectra in higher dimensions are always infinite. To formulate the AdS3/AdS2 degression we consider branching rules for AdS3 isometry algebra o(2,2) representations decomposed with respect to AdS2 isometry algebra o(1,2). We find that a given o(2,2) higher-spin representation lying on the unitary bound (i.e. massless) decomposes into two equal o(1,2) modules. In the field-theoretical terms, this phenomenon is demonstrated for spin-2 and spin-3 free massless fields. The truncation to a finite spectrum can be seen by using particular mode expansions, (partial) diagonalizations, and identities specific to two dimensions.

Soft matters, or the recursions with massive spinors

We discuss recursion relations for scattering amplitudes with massive particles of any spin. They are derived via a two-parameter shift of momenta, combining a BCFW-type spinor shift with the soft limit of a massless particle involved in the process. The technical innovation is that spinors corresponding to massive momenta are also shifted. Our recursions lead to a reformulation of the soft theorems. The well-known Weinberg’s soft factors are recovered and, in addition, the subleading factors appear reshaped such that they are directly applicable to massive amplitudes in the modern on-shell language. Moreover, we obtain new results in the context of non-minimal interactions of massive matter with photons and gravitons. These soft theorems are employed for practical calculations of Compton and higher-point scattering. As a by-product, we introduce a convenient representation of the Compton scattering amplitude for any mass and spin.

Symmetries and strings of adjoint QCD2

We revisit the symmetries of massless two-dimensional adjoint QCD with gauge group SU(N). The dynamics is not sufficiently constrained by the ordinary symmetries and anomalies. Here we show that the theory in fact admits ∼ 22N non-invertible symmetries which severely constrain the possible infrared phases and massive excitations. We prove that for all N these new symmetries enforce deconfinement of the fundamental quark. When the adjoint quark has a small mass, m ≪ gYM, the theory confines and the non-invertible symmetries are softly broken. We use them to compute analytically the k-string tension for N ≤ 5. Our results suggest that the k-string tension, Tk, is Tk ∼ |m| sin(πk/N) for all N. We also consider the dynamics of adjoint QCD deformed by symmetric quartic fermion interactions. These operators are not generated by the RG flow due to the non-invertible symmetries, thus violating the ordinary notion of naturalness. We conjecture partial confinement for the deformed theory by these four-fermion interactions, and prove it for SU(N ≤ 5) gauge theory. Comparing the topological phases at zero and large mass, we find that a massless particle ought to appear on the string for some intermediate nonzero mass, consistent with an emergent supersymmetry at nonzero mass. We also study the possible infrared phases of adjoint QCD allowed by the non-invertible symmetries, which we are able to do exhaustively for small values of N. The paper contains detailed reviews of ideas from fusion category theory that are essential for the results we prove.

Hybrid nature of the abnormal solutions of the Bethe–Salpeter equation in the Wick–Cutkosky model

In the Wick–Cutkosky model, where two scalar massive constituents interact by means of the exchange of a scalar massless particle, the Bethe–Salpeter equation has solutions of two types, called “normal” and “abnormal”. In the non-relativistic limit, the normal solutions correspond to the usual Coulomb spectrum, whereas the abnormal ones do not have non-relativistic counterparts – they are absent in the Schrödinger equation framework. We have studied, in the formalism of the light-front dynamics, the Fock-space content of the abnormal solutions. It turns out that, in contrast to the normal ones, the abnormal states are dominated by the massless exchange particles (by 90 % or more), what provides a natural explanation of their decoupling from the two-body Schrödinger equation. Assuming that one of the massive constituents is charged, we have calculated the electromagnetic elastic form factors of the normal and abnormal states, as well as the transition form factors. The results on form factors confirm the many-body nature of the abnormal states, as found from the Fock-space analysis. The abnormal solutions have thus properties similar to those of hybrid states, made here essentially of two massive constituents and several or many massless exchange particles. They could also be interpreted as the Abelian scalar analogs of the QCD hybrid states. The question of the validity of the ladder approximation of the model is also examined.

Quantized Field of Single Photons

We present theoretical developments expressing the physical characteristics of a single photon in conformity with the experimental evidence. The quantization of the electromagnetic field vector potential amplitude is enhanced to a free of cavity photon state. Coupling the Schrödinger equation with the relativistic massless particle Hamiltonian to a symmetrical vector potential relation, we establish the vector potential - energy equation for the photon expressing the simultaneous wave-particle nature of a single photon, an intrinsic physical property. It is shown that the vector potential can be naturally considered as a real wave function for the photon entailing a coherent localization probability. We deduce directly the electric and magnetic field amplitudes of the cavity-free single photon, which are revealed to be proportional to the square of the angular frequency. The zero-energy electromagnetic field ground state (EFGS), a quantum vacuum real component, issues naturally from Maxwell’s equations and the vector potential quantization procedure. The relation of the quantized amplitude of the photon vector potential to the electron-positron charge results directly showing the physical relationship between photons and electrons-positrons that might be at the origin of their mutual transformations. It becomes obvious that photons, as well as electrons-positrons, are issued from the same quantum vacuum field.