New study of the interactions of the axion with mesons and photons using a chiral effective Lagrangian model

In this paper, we extend the results obtained in a previous work and investigate the most interesting decay processes involving axions, photons, and the lightest pseudoscalar mesons in the more general case in which the quarks (and, therefore, the mesons) may be charged under the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>1</a:mn><a:mo stretchy="false">)</a:mo></a:math> Peccei-Quinn symmetry, making use of a chiral effective Lagrangian model with <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>N</e:mi><e:mi>f</e:mi></e:msub><e:mo>=</e:mo><e:mn>3</e:mn></e:math> light quark flavors, which also includes the flavor-singlet pseudoscalar meson and implements the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>U</g:mi><g:mo stretchy="false">(</g:mo><g:mn>1</g:mn><g:mo stretchy="false">)</g:mo></g:math> axial anomaly of the fundamental theory. In particular, we compute the axion mass, the electromagnetic coupling of the axion to photons, and the amplitudes and widths of the decay processes <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>η</k:mi><k:mo>/</k:mo><k:msup><k:mi>η</k:mi><k:mo>′</k:mo></k:msup><k:mo stretchy="false">→</k:mo><k:mi>π</k:mi><k:mi>π</k:mi><k:mi>a</k:mi></k:math>.