Equality of symmetrized tensors and the coordinate ring of the flag variety

In this note we give a transparent proof of a result of da Cruz and Dias da Silva on the equality of symmetrized decomposable tensors. This will be done by explaining that their result follows from the fact that the coordinate ring of a flag variety is a unique factorization domain.Comment: 5 page

Thick Braneworlds and the Gibbons-Kallosh-Linde No-go Theorem in the Gauss-Bonnet Framework

The sum rules related to thick braneworlds are constructed, in order to encompass Gauss-Bonnet terms. The generation of thick branes is hence proposed in a periodic extra dimension scenario, what circumvents the Gibbons-Kallosh-Linde no-go theorem in this context.Comment: 6 pages, to appear in the EPL. arXiv admin note: text overlap with arXiv:1406.632

A Short Proof of Gamas's Theorem

If \chi^\lambda is the irreducible character of the symmetric group S_n corresponding to the partition \lambda of n then we may symmetrize a tensor v_1 \otimes ... \otimes v_n by \chi^\lambda. Gamas's theorem states that the result is not zero if and only if we can partition the set {v_i} into linearly independent sets whose sizes are the parts of the transpose of \lambda. We give a short and self-contained proof of this fact

Maximum Entropy Inferences on the Axion Mass in Models with Axion-Neutrino Interaction

In this work we use the Maximum Entropy Principle (MEP) to infer the mass of an axion which interacts to photons and neutrinos in an effective low energy theory. The Shannon entropy function to be maximized is suitably defined in terms of the axion branching ratios. We show that MEP strongly constrains the axion mass taking into account the current experimental bounds on the neutrinos masses. Assuming that the axion is massive enough to decay into all the three neutrinos and that MEP fixes all the free parameters of the model, the inferred axion mass is in the interval $0.1\$eV$\ <m_{A}<0.2$ eV, which can be tested by forthcoming experiments such as IAXO. However, even in the case where MEP fixes just the axion mass and no other parameter, we found that $0.1$ eV $< m_A < 6.3$ eV in the DFSZ model with right-handed neutrinos. Moreover, a light axion, allowed to decay to photons and the lightest neutrino only, is determined by MEP as a viable dark matter candidate.Comment: 13 pages, 5 figures, typos corrected, figures update

Inferences on the Higgs Boson and Axion Masses through a Maximum Entropy Principle

The Maximum Entropy Principle (MEP) is a method that can be used to infer the value of an unknown quantity in a set of probability functions. In this work we review two applications of MEP: one giving a precise inference of the Higgs boson mass value; and the other one allowing to infer the mass of the axion. In particular, for the axion we assume that it has a decay channel into pairs of neutrinos, in addition to the decay into two photons. The Shannon entropy associated to an initial ensemble of axions decaying into photons and neutrinos is then built for maximization.Comment: Contributed to the 13th Patras Workshop on Axions, WIMPs and WISPs, Thessaloniki, May 15 to 19, 201