Mixing the strong and EW Higgs sectors

After noting the well-known similarity of the minimal electro-weak Higgs sector with the linear sigma model for the pion and the sigma, it is found that a small mixing term between the two models generates a pion mass. Although the custodial SU(2)L×SU(2)R, and the gauged SU(2)L×U(1) symmetry for the whole model remains intact, the mixing breaks the relative chiral symmetry between the two sectors. The mixing should be calculable from light quark masses as a quantum correction. This simple mechanism of “relative symmetry breaking” is believed to have applications for other forms of symmetry breaking.