Phenomenological Analysis of pppp and pˉp\bar{p}p Elastic Scattering Data in the Impact Parameter Space

We use an almost model-independent analytical parameterization for $pp$ and $\bar{p}p$ elastic scattering data to analyze the eikonal, profile, and inelastic overlap functions in the impact parameter space. Error propagation in the fit parameters allows estimations of uncertainty regions, improving the geometrical description of the hadron-hadron interaction. Several predictions are shown and, in particular, the prediction for $pp$ inelastic overlap function at $\sqrt{s}=14$ TeV shows the saturation of the Froissart-Martin bound at LHC energies.Comment: 15 pages, 16 figure

The age-metallicity dependence for white dwarfs

We present a theoretical study on the metallicity dependence of the initial$-$to$-$final mass relation and its influence on white dwarf age determinations. We compute a grid of evolutionary sequences from the main sequence to $\sim 3\, 000$ K on the white dwarf cooling curve, passing through all intermediate stages. During the thermally-pulsing asymptotic giant branch no third dredge-up episodes are considered and thus the photospheric C/O ratio is below unity for sequences with metallicities larger than $Z=0.0001$. We consider initial metallicities from $Z=0.0001$ to $Z=0.04$, accounting for stellar populations in the galactic disk and halo, with initial masses below $\sim 3M_{\odot}$. We found a clear dependence of the shape of the initial$-$to$-$final mass relation with the progenitor metallicity, where metal rich progenitors result in less massive white dwarf remnants, due to an enhancement of the mass loss rates associated to high metallicity values. By comparing our theoretical computations with semi empirical data from globular and old open clusters, we found that the observed intrinsic mass spread can be accounted for by a set of initial$-$to$-$final mass relations characterized by different metallicity values. Also, we confirm that the lifetime spent before the white dwarf stage increases with metallicity. Finally, we estimate the mean mass at the top of the white dwarf cooling curve for three globular clusters NGC 6397, M4 and 47 Tuc, around $0.53 M_{\odot}$, characteristic of old stellar populations. However, we found different values for the progenitor mass, lower for the metal poor cluster, NGC 6397, and larger for the younger and metal rich cluster 47 Tuc, as expected from the metallicity dependence of the initial$-$to$-$final mass relation.Comment: Accepted for publication in MNRA

On Negative Mass, Partition Function and Entropy

This work examines some aspects related to the existence of negative mass. The requirement for the partition function to converge leads to two distinct approaches. Initially, convergence is achieved by assuming a negative absolute temperature, which results in an imaginary partition function and complex entropy. Subsequently, convergence is maintained by keeping the absolute temperature positive while introducing an imaginary velocity. This modification leads to a positive partition function and real entropy. It seems the utilization of imaginary velocity may yield more plausible physical results compared to the use of negative temperature, at least for the partition function and entropy.Comment: A version of this manuscript was accepted for publication in Mod. Phys. Lett.