Multi-fermion states for heavy fermions bound via Higgs exchange

Understand

A possibility to produce bound states of several heavy fermions, which are bound together due to the Higgs exchange, is examined.

• It is shown that for 12 fermions, 6 fermions and 6 antifermions, occupying the lowest S_{1/2} shell this bound state cannot exist if the fermion mass is below the critical value, which depends on the Higgs mass and is found to be restricted to 320 < m_{cr} < 410 Gev/c^2 for the Higgs mass in the interval 100 < m_{H}< 200 Gev/c^2.
• This estimate is derived in the relativistic mean field approximation.
• The corrections are estimated to be not able to reduce significantly the critical value for the fermion mass.