Skyrmion vibrational energies with a generalized mass term

We study various properties of a one parameter mass term for the Skyrme model, originating from the works of Kopeliovich, Piette and Zakrzewski, through the use of axially symmetric solutions obtained numerically by simulated-annealing. These solutions allow us to observe asymptotic behaviors of the B=2 binding energies that differ to those previously obtained. We also decipher the characteristics of three distinct vibrational modes that appear as eigenstates of the vibrational Hamiltonian. This analysis further examine the assertion that the one parameter mass term offers a better account of baryonic matter than the traditional mass term.Comment: 12 pages, 8 figure

Near-BPS Skyrmions: Constant baryon density

Although it provides a relatively good picture of the nucleons, the Skyrme Model is unable to reproduce the small binding energy in nuclei. This suggests that Skyrme-like models that nearly saturate the Bogomol'nyi bound may be more appropriate since their mass is roughly proportional to the baryon number A. For that purpose, we propose a near-BPS Skyrme Model. It consists of terms up to order six in derivatives of the pion fields, including the nonlinear and Skyrme terms which are assumed to be relatively small. For our special choice of mass term, we obtain well-behaved analytical BPS-type solutions with constant baryon density configurations, as opposed to the more complex shell-like configurations found in most extensions of the Skyrme Model. Fitting the four model parameters, we find a remarkable agreement for the binding energy per nucleon B/A with respect to experimental data. These results support the idea that nuclei could be near-BPS Skyrmions.Comment: Matches version to bepublished in Nucl.Phys. B. arXiv admin note: substantial text overlap with arXiv:1205.141

Anarchy and Neutrino Physics

The neutrino sector of a seesaw-extended Standard Model is investigated under the anarchy hypothesis. The previously derived probability density functions for neutrino masses and mixings, which characterize the type I-III seesaw ensemble of $N\times N$ complex random matrices, are used to extract information on the relevant physical parameters. For $N=2$ and $N=3$, the distributions of the light neutrino masses, as well as the mixing angles and phases, are obtained using numerical integration methods. A systematic comparison with the much simpler type II seesaw ensemble is also performed to point out the fundamental differences between the two ensembles. It is found that the type I-III seesaw ensemble is better suited to accommodate experimental data. Moreover, the results indicate a strong preference for the mass splitting associated to normal hierarchy. However, since all permutations of the singular values are found to be equally probable for a particular mass splitting, predictions regarding the hierarchy of the mass spectrum remains out of reach in the framework of anarchy.Comment: 1+22 pages, 8 figures, typos fixed, added referenc

Near-BPS Skyrmions: Non-shell configurations and Coulomb effects

The relatively small binding energy in nuclei suggests that they may be well represented by near-BPS Skyrmions since their mass is roughly proportional to the baryon number $A.$ For that purpose, we propose a generalization of the Skyrme model with terms up to order six in derivatives of the pion fields and treat the nonlinear $\sigma$ and Skyrme terms as small perturbations. For our special choice of mass term (or potential) $V$, we obtain well-behaved analytical BPS-type solutions with non-shell configurations for the baryon density, as opposed to the more complex shell-like configurations found in most extensions of the Skyrme model . Along with static and (iso)rotational energies, we add to the mass of the nuclei the often neglected Coulomb energy and isospin breaking term. Fitting the four model parameters, we find a remarkable agreement for the binding energy per nucleon $B/A$ with respect to experimental data. These results support the idea that nuclei could be near-BPS Skyrmions.Comment: Correction of minors errors, references adde

The Stability of the Weak Skyrmions

We consider a set of gauge invariant terms in higher order effective Lagrangians of the strongly interacting scalar of the electroweak theory. The terms are introduced in the framework of the hidden gauge symmetry formalism. The usual gauge term is known to stabilize the skyrmion but only in the large vector mass limit. We find that adding higher-order gauge terms is insufficient to insure stability. We then proceed to analyze other gauge invariant interaction terms. Some of the conclusions also apply to QCD skyrmions.Comment: 3 pages, revtex v3, (optional), LAVAL-PHY-11-9

On the electromagnetic form factors of the proton from generalized Skyrme models

We compare the prediction of Skyrme-like effective Lagrangians with data for electromagnetic form factors of proton and consider the possibility of fixing the parameters of these higher-order Lagrangians. Our results indicate that one or two-parameter models can lead to better agreement with the data but more accurate determination of the effective Lagragian faces theoretical uncertainties.Comment: 8 pages, 2 figures, revte

Probability Density Functions for CP-Violating Rephasing Invariants

The implications of the anarchy principle on CP violation in the lepton sector are investigated. A systematic method is introduced to compute the probability density functions for the CP-violating rephasing invariants of the PMNS matrix from the Haar measure relevant to the anarchy principle. Contrary to the CKM matrix which is hierarchical, it is shown that the Haar measure, and hence the anarchy principle, are very likely to lead to the observed PMNS matrix. Predictions on the CP-violating Dirac rephasing invariant $|j_D|$ and Majorana rephasing invariant $|j_1|$ are also obtained. They correspond to $\langle|j_D|\rangle_\text{Haar}=\pi/105\approx0.030$ and $\langle|j_1|\rangle_\text{Haar}=1/(6\pi)\approx0.053$ respectively, in agreement with the experimental hint from T2K of $|j_D^\text{exp}|\approx0.032\pm0.005$ (or $\approx0.033\pm0.003$) for the normal (or inverted) hierarchy.Comment: 1+15 pages, 2 figure