Phenomenology of isospin-symmetry breaking with vector mesons

We study the effect of isospin-symmetry breaking in the framework of the extended linear <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>σ</a:mi></a:math> model in vacuum. In this model, several particles mix with each other at tree level, due to the three nonzero scalar condensates (nonstrange, strange, isospin). We resolve these mixings with the help of various field transformations. We compute all possible meson mixings and decay widths at tree level and perform a <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>χ</c:mi><c:mn>2</c:mn></c:msup></c:math> fit to PDG data. A very good fit is found if we exclude the (very small <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mo>∼</e:mo><e:mn>130</e:mn><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi>keV</e:mi></e:math>) <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>ω</g:mi><g:mo stretchy="false">→</g:mo><g:mi>π</g:mi><g:mi>π</g:mi></g:math> decay. We also investigate the violation of Dashen’s theorem.