We calculate the expected branching fraction of the second-class-current decay tau -> pi eta 'nu(tau), motivated by a recent experimental upper-limit determination of this quantity. The largest contribution to the branching fraction is due to the intermediate a(0)(980) scalar meson, assuming it is a (u) over bard state. Smaller contributions arise from a(0)(1450), rho(770), and rho(1450). Our calculated values are substantially below the experimental upper limit, and are smaller still if the a(0)(980) is a four-quark state, as often suggested. Thus, a precise measurement or tight upper limit has the potential to determine the nature of the a(0)(980), as well as provide information about new scalar interactions.
Nussinov, Shmuel, and Abner Soffer. "An estimate of the branching fraction of τ→ π η′ ν τ." Physical Review D 80.3 (2009): 033010. doi: 10.1103/PhysRevD.80.033010
American Physical Society