<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>η</mml:mi> <mml:mi mathvariant="normal">w</mml:mi> </mml:msub> </mml:math> -meson from topological properties of the electroweak vacuum

We further scrutinize the evidence for a recently suggested pseudoscalar particle, the electroweak <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>η</a:mi> <a:mi mathvariant="normal">w</a:mi> </a:msub> </a:math> meson. Its existence is demanded by matching the removal of the weak vacuum angle <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:msub> <d:mi>θ</d:mi> <d:mi mathvariant="normal">w</d:mi> </d:msub> </d:math> by the anomalous <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>B</g:mi> <g:mo>+</g:mo> <g:mi>L</g:mi> </g:math> symmetry with a massive pole in the topological susceptibility of the vacuum. We specifically focus on the possibility of the emergence of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mi>η</i:mi> <i:mi mathvariant="normal">w</i:mi> </i:msub> </i:math> as a collective excitation of the phase of the condensate of the ’t Hooft fermion determinant, generated by the electroweak instantons, which breaks the <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mi>B</l:mi> <l:mo>+</l:mo> <l:mi>L</l:mi> </l:math> symmetry spontaneously. We argue that the generation of the ’t Hooft vertex is in one-to-one correspondence with its nonzero vacuum expectation value which is cutoff insensitive. We outline certain puzzles about the nature of the emergent <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:msub> <n:mi>η</n:mi> <n:mi mathvariant="normal">w</n:mi> </n:msub> </n:math> which require further investigation.