Markoff-Rosenberger triples in geometric progression

Solutions of the Markoff-Rosenberger equation ax^2+by^2+cz^2 = dxyz such that their coordinates belong to the ring of integers of a number field and form a geometric progression are studied.Comment: To appear in Acta Mathematica Hungaric

An algorithm for determining torsion growth of elliptic curves

We present a fast algorithm that takes as input an elliptic curve defined over $\mathbb Q$ and an integer $d$ and returns all the number fields $K$ of degree $d'$ dividing $d$ such that $E(K)_{tors}$ contains $E(F)_{tors}$ as a proper subgroup, for all $F \varsubsetneq K$. We ran this algorithm on all elliptic curves of conductor less than 400.000 (a total of 2.483.649 curves) and all $d \leq 23$ and collected various interesting data. In particular, we find a degree 6 sporadic point on $X_1(4,12)$, which is so far the lowest known degree a sporadic point on $X_1(m,n)$, for $m\geq 2$.Comment: 15 pages, Added Supplementary materia

Strangeness on the nucleon

Observables from parity violation in elastic electron-nucleon scattering and neutral current quasi-elastic neutrino-nucleus scattering are employed as tools to improve the current knowledge on the strangeness content in the nucleon.Comment: Proceedings of International Scientific Meeting on Nuclear Physics, 9-13th September 2012. La R\'abida, Huelva, Spai

Markoff-Rosenberger triples in arithmetic progression

We study the solutions of the Rosenberg--Markoff equation ax^2+by^2+cz^2 = dxyz (a generalization of the well--known Markoff equation). We specifically focus on looking for solutions in arithmetic progression that lie in the ring of integers of a number field. With the help of previous work by Alvanos and Poulakis, we give a complete decision algorithm, which allows us to prove finiteness results concerning these particular solutions. Finally, some extensive computations are presented regarding two particular cases: the generalized Markoff equation x^2+y^2+z^2 = dxyz over quadratic fields and the classic Markoff equation x^2+y^2+z^2 = 3xyz over an arbitrary number field.Comment: To appear in Journal of Symbolic Computatio

Pion production within the hybrid relativistic plane wave impulse approximation model at MiniBooNE and MINERvA kinematics

The hybrid model for electroweak single-pion production (SPP) off the nucleon, presented in [Gonz\'alez-Jim\'enez et al., Phys. Rev. D 95, 113007 (2017)], is extended here to the case of incoherent pion-production on the nucleus. Combining a low-energy model with a Regge approach, this model provides valid predictions in the entire energy region of interest for current and future accelerator-based neutrino-oscillation experiments. The Relativistic Mean-Field model is used for the description of the bound nucleons while the outgoing hadrons are considered as plane waves. This approach, known as Relativistic Plane-Wave Impulse Approximation (RPWIA), is a first step towards the development of more sophisticated models, it is also a test of our current understanding of the elementary reaction. We focus on the charged-current $\nu$($\bar\nu$)-nucleus interaction at MiniBooNE and MINERvA kinematics. The effect on the cross sections of the final-state interactions, which affect the outgoing hadrons on their way out of the nucleus, is judged by comparing our results with those from the NuWro Monte Carlo event generator. We find that the hybrid-RPWIA predictions largely underestimate the MiniBooNE data. In the case of MINERvA, our results fall below the $\nu$-induced 1$\pi^0$ production data, while a better agreement is found for $\nu$-induced 1$\pi^+$ and $\bar\nu$-induced 1$\pi^0$ production.Comment: 13 pages, 10 figure

Rotochemical heating with a density-dependent superfluid energy gap in neutron stars

When a rotating neutron star loses angular momentum, the reduction of the centrifugal force makes it contract. This perturbs each fluid element, raising the local pressure and originating deviations from beta equilibrium, inducing reactions that release heat (rotochemical heating). This effect has previously been studied by Fern\'andez and Reisenegger for neutron stars of non-superfluid matter and by Petrovich and Reisenegger for superfluid matter, finding that the system in both cases reaches a quasi-steady state, corresponding to a partial equilibration between compression, due to the loss of angular momentum, and reactions that try to restore the equilibrium. However, Petrovich and Reisenegger assumes a constant value of the superfluid energy gap, whereas theoretical models predict density-dependent gap amplitudes, and therefore gaps that depend on the location in the star. In this work, we try to discriminate between several proposed gap models, comparing predicted surface temperatures to the value measured for the nearest millisecond pulsar, J0437-4715.Comment: 2 pages, 1 figure. VIII Symposium in Nuclear Physics and Applications: Nuclear and Particle Astrophysics. Appearing in the American Institute of Physics (AIP) conference proceedings

Parity violation in quasielastic electron-nucleus scattering within the relativistic impulse approximation

We study parity violation in quasielastic (QE) electron-nucleus scattering using the relativistic impulse approximation. Different fully relativistic approaches have been considered to estimate the effects associated with the final-state interactions. We have computed the parity-violating quasielastic (PVQE) asymmetry and have analyzed its sensitivity to the different ingredients that enter in the description of the reaction mechanism: final-state interactions, nucleon off-shellness effects, current gauge ambiguities. Particular attention has been paid to the description of the weak neutral current form factors. The PVQE asymmetry is proven to be an excellent observable when the goal is to get precise information on the axial-vector sector of the weak neutral current. Specifically, from measurements of the asymmetry at backward scattering angles good knowledge of the radiative corrections entering in the isovector axial-vector sector can be gained. Finally, scaling properties shown by the interference $\gamma-Z$ nuclear responses are also analyzed.Comment: 15 pages, 11 figure