The last piece of the “Sigma-term Puzzle”

The explanation of the breaking of the Gell-Mann-Okubo relation completes the last piece of this long standing puzzle in hadron physics

The sigma-terms are quantities of great importance in physics since are related to the origin of the mass of the ordinary matter. Nowadays they are more popular because of their central role in detection of dark matter, what increased the demand of reliable and precise calculations of their values. On the other hand, the determination of the sigma-terms has been a long standing problem in hadron physics, where the accepted value for the pion-nucleon sigma-term (perhaps the most relevant one) has been moving in the range of 45 - 60 MeV in the last fifty years.

This situation seemed to change after the new experimental determination of the so-called pion-nucleon scalar-isoscalar scattering length, strongly correlated to the value of the pion-nucleon-sigma term, that pointed clearly to a value for the later of ~60 MeV. However, this value was confusing for the community, because seemed to imply a huge strangeness content (contribution of the strange quark) in the nucleon, what is disfavoured by experimental evidence. This calculation of the strangeness content is based on group-theoretical considerations (SU(3)-flavour symmetry), so to be sure whether a value of 60 MeV for the pion-nucleon sigma-term is problematic, it is important to calculate the corrections to the group-theoretical computation.

The size of these corrections brings into agreement a value of the pion-nucleon sigma-term of ~60 MeV with a negligible strangeness content in the nucleon

The estimation of the strangeness content via SU(3)-flavor symmetry was in general accepted by the community given the success of the Gell-Mann-Okubo mass formula, that allows to estimate the mass of one of the baryons in the octet in terms of the others with high accuracy. What we proved in our article is that the success of this mass relation is based on the fact that the bulk of the mass of the baryons is given by the singlet contribution, while the octet one provides just a small correction. However, if one focuses on the octet contribution, one observes important corrections to the SU(3)-flavour relation. The size of these corrections brings into agreement a value of the pion-nucleon sigma-term of ~60 MeV with a negligible strangeness content in the nucleon, which closes the long-standing "Sigma-term Puzzle".