On the Equivalence of Three-Particle Scattering Formalisms

In recent years, different on-shell $\mathbf{3}\to\mathbf{3}$ scattering formalisms have been proposed to be applied to both lattice QCD and infinite volume scattering processes. We prove that the formulation in the infinite volume presented by Hansen and Sharpe in Phys.~Rev.~D92, 114509 (2015) and subsequently Brice\~no, Hansen, and Sharpe in Phys.~Rev.~D95, 074510 (2017) can be recovered from the $B$-matrix representation, derived on the basis of $S$-matrix unitarity, presented by Mai {\em et al.} in Eur.~Phys.~J.~A53, 177 (2017) and Jackura {\em et al.} in Eur.~Phys.~J.~C79, 56 (2019). Therefore, both formalisms in the infinite volume are equivalent and the physical content is identical. Additionally, the Faddeev equations are recovered in the non-relativistic limit of both representations.Comment: 13 pages, 5 figure

The frequency map for billiards inside ellipsoids

The billiard motion inside an ellipsoid Q \subset \Rset^{n+1} is completely integrable. Its phase space is a symplectic manifold of dimension $2n$, which is mostly foliated with Liouville tori of dimension $n$. The motion on each Liouville torus becomes just a parallel translation with some frequency $\omega$ that varies with the torus. Besides, any billiard trajectory inside $Q$ is tangent to $n$ caustics $Q_{\lambda_1},...,Q_{\lambda_n}$, so the caustic parameters $\lambda=(\lambda_1,...,\lambda_n)$ are integrals of the billiard map. The frequency map $\lambda \mapsto \omega$ is a key tool to understand the structure of periodic billiard trajectories. In principle, it is well-defined only for nonsingular values of the caustic parameters. We present four conjectures, fully supported by numerical experiments. The last one gives rise to some lower bounds on the periods. These bounds only depend on the type of the caustics. We describe the geometric meaning, domain, and range of $\omega$. The map $\omega$ can be continuously extended to singular values of the caustic parameters, although it becomes "exponentially sharp" at some of them. Finally, we study triaxial ellipsoids of \Rset^3. We compute numerically the bifurcation curves in the parameter space on which the Liouville tori with a fixed frequency disappear. We determine which ellipsoids have more periodic trajectories. We check that the previous lower bounds on the periods are optimal, by displaying periodic trajectories with periods four, five, and six whose caustics have the right types. We also give some new insights for ellipses of \Rset^2.Comment: 50 pages, 13 figure

Hints on the quadrupole deformation of the Δ\Delta(1232)

The E2/M1 ratio (EMR) of the $\Delta$(1232) is extracted from the world data in pion photoproduction by means of an Effective Lagrangian Approach (ELA).This quantity has been derived within a crossing symmetric, gauge invariant, and chiral symmetric Lagrangian model which also contains a consistent modern treatment of the $\Delta$(1232) resonance. The \textit{bare} s-channel $\Delta$(1232) contribution is well isolated and Final State Interactions (FSI) are effectively taken into account fulfilling Watson's theorem. The obtained EMR value, EMR$=(-1.30\pm0.52)$%, is in good agreement with the latest lattice QCD calculations [Phys. Rev. Lett. 94, 021601 (2005)] and disagrees with results of current quark model calculations.Comment: Enlarged conclusions and explanations on the E2/M1 ratio. Figure 3 improved. References updated. 5 pages. 3 figures. 2 tables. Accepted for publication in Physical Review

On the η\eta and η′\eta' Photoproduction Beam Asymmetry at High Energies

We show that, in the Regge limit, beam asymmetries in $\eta$ and $\eta'$ photoproduction are sensitive to hidden strangeness components. Under reasonable assumptions about the couplings we estimate the contribution of the $\phi$ Regge pole, which is expected to be the dominant hidden strangeness contribution. The ratio of the asymmetries in $\eta'$ and $\eta$ production is estimated to be close to unity in the forward region $0 < -t/\text{GeV}^2 \leq 1$ at the photon energy $E_\text{lab} = 9$~GeV, relevant for the upcoming measurements at Jefferson Lab.Comment: 9 pages, 4 figure

Chemical (in)homogeneity and atomic diffusion in the open cluster M67

Context. The benchmark open cluster M67 is known to have solar metallicity and similar age as the Sun. It thus provides us a great opportunity to study the properties of solar twins, as well as the evolution of Sun-like stars. Aims. Previous spectroscopic studies reported to detect possible subtle changes in stellar surface abundances throughout the stellar evolutionary phase, namely the effect of atomic diffusion, in M67. In this study we attempt to confirm and quantify more precisely the effect of atomic diffusion, as well as to explore the level of chemical (in)homogeneity in M67. Methods. We presented a strictly line-by-line differential chemical abundance analysis of two groups of stars in M67: three turn-off stars and three sub-giants. Stellar atmospheric parameters and elemental abundances were obtained with very high precision using the Keck/HIRES spectra. Results. The sub-giants in our sample show negligible abundance variations ($\le$ 0.02 dex), which implies that M67 was born chemically homogeneous. We note there is a significant abundance difference ($\sim$ 0.1 - 0.2 dex) between sub-giants and turn-off stars, which can be interpreted as the signature of atomic diffusion. Qualitatively stellar models with diffusion agree with the observed abundance results. Some turn-off stars do not follow the general pattern, which suggests that in some cases diffusion can be inhibited, or they might suffered some sort of mixing event related to planets. Conclusions. Our results pose additional challenges for chemical tagging when using turn-off stars. In particular, the effects of atomic diffusion, which could be as large as 0.1 - 0.2 dex, must be taken into account in order for chemical tagging to be successfully applied.Comment: 19 pages, 21 figures; submitted to A&A on February, 2019, accepted for publication in A&A on June, 201

Searching for galactic sources in the Swift GRB catalog

Since the early 1990s Gamma Ray Bursts have been accepted to be of extra-galactic origin due to the isotropic distribution observed by BATSE and the redshifts observed via absorption line spectroscopy. Nevertheless, upon further examination at least one case turned out to be of galactic origin. This particular event presented a Fast Rise, Exponential Decay (FRED) structure which leads us to believe that other FRED sources might also be Galactic. This study was set out to estimate the most probable degree of contamination by galactic sources that certain samples of FREDs have. In order to quantify the degree of anisotropy the average dipolar and quadripolar moments of each sample of GRBs with respect to the galactic plane were calculated. This was then compared to the probability distribution of simulated samples comprised of a combination of isotropically generated sources and galactic sources. We observe that the dipolar and quadripolar moments of the selected subsamples of FREDs are found more than two standard deviations outside those of random isotropically generated samples.The most probable degree of contamination by galactic sources for the FRED GRBs of the Swift catalog detected until February 2011 that do not have a known redshift is about 21 out of 77 sources which is roughly equal to 27%. Furthermore we observe, that by removing from this sample those bursts that may have any type of indirect redshift indicator and multiple peaks gives the most probable contamination increases up to 34% (17 out of 49 sources). It is probable that a high degree of contamination by galactic sources occurs among the single peak FREDs observed by Swift.Comment: Published to A&A, 4 pages, 5 figures, this arXiv version includes appended table with all the bursts considered in this stud