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The sigma meson

The Higgs boson and the $\sigma$ meson are the scalar particles which are relevant for mass generation through interaction with the electroweak and the strong interaction vacuum, respectively. Proton and neutron are the massive building blocks of atoms whereas the electrons of the electron cloud contribute less than 0.1$\%$. Proton and neutron consist of three quarks named up quark and down quark. The electric charge of the up quark amounts to +2/3 of the elementary charge, the corresponding quantity of the down quark is -1/3 of the elementary charge. The proton contains two up quarks and one down quark, corresponding to the charge +1 for the proton. The neutron contains two down quarks and one up quark, corresponding to the charge 0 for the neutron.

The mases of the quarks are generated through the combined action of the Higgs boson and the $\sigma$ meson. The Higgs boson mediates an electroweak mass-equivalent, or mass, of 5 MeV for the up quark and 9 MeV for the down quark. These masses correspond to $\approx$ 0.7 $\%$ of the mass of the proton, being 938.3 MeV. The mass of the down quark is larger than the mass of the up quark. This is the main reason for a larger mass of 939.6 MeV of the neutron. The $\sigma$ meson mediates the larger part of the quark masses by producing an additional contribution of 326 MeV. This leads to a mass of the up quark of 331 MeV and a mass of the down quark of 335 MeV. The mass of the nucleon is composed of the masses of the quarks supplemented by corrections due to binding energies from strong and electromagnetic interactions. The masses of the nucleons due to the hypothetical unbound quarks are 997 MeV for the proton 1001 MeV for the neutron. The strong-interaction binding energy amounts to 59 MeV for both nucleons. For the neutron there is an additional electromagnetic binding energy of 2 Mev. Taking these bindung energies together we arrive at the experimental values of the two nucleons \cite{schumacher14}.

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Martin Schumacher, Ann. Phys. (Berlin) {\bf 526}, 215 (2014), arXiv:1403.7804 [hep-ph].

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