${\eta }_{\mathrm{w}}$-meson from topological properties of the electroweak vacuum

Abstract

We further scrutinize the evidence for a recently suggested pseudo-scalar particle, the electroweak ${\eta }_{\mathrm{w}}$-meson. Its existence is demanded by matching the removal of the weak vacuum angle ${\theta }_{\mathrm{w}}$ by the anomalous $B+L$ - symmetry with a massive pole in the topological susceptibility of the vacuum. We specifically focus on the possibility of the emergence of ${\eta }_{\mathrm{w}}$ as a collective excitation of the phase of the condensate of the 't Hooft fermion determinant, generated by the electroweak instantons, which breaks the $B+L$ - symmetry spontaneously. We argue that the generation of the 't Hooft vertex is in one-to-one correspondence with its non-zero vacuum expectation value which is cutoff insensitive. We outline certain puzzles about the nature of the emergent ${\eta }_{\mathrm{w}}$ which require further investigations.

Comments: 22 pages, 4 figures