Novel method for determining the light quark mass ratio using η ′ → η π π decays

We propose a novel approach for extracting symmetry breaking effects from symmetry conserving three-body decays. The method is based on mapping the Dalitz plot to a unit disk, and the difference of the disk distributions of two related decays isolates purely symmetry breaking effects. We demonstrate this method by extracting the fundamental parameter Q , an isospin breaking ratio of light quark masses defined as Q 2 ≡ ( m s 2 − m ^ 2 ) / ( m d 2 − m u 2 ) with m ^ the average of up and down quark masses, from the decays η ′ → η π + π − and η ′ → η π 0 π 0 . With the Dalitz plot distributions for these two decays reported by BESIII, we illustrate the method and obtain Q = 22.5 ± 1.0 , which is consistent with previous determinations and has a comparable uncertainty. With the full BESIII dataset, which is eight times larger than the one used here, a more precise determination of Q should become possible. This promising and novel method can be generalized to other three-body decays to extract symmetry breaking effects.