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arXiv · 1610.03494

The decay $η\to 3 π$: study of the Dalitz plot and extraction of the quark mass ratio $Q$

Gilberto Colangelo·Stefan Lanz·Heinrich Leutwyler·Emilie Passemar
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Abstract

The $η\to 3 π$ amplitude is sensitive to the quark mass difference $m_u-m_d$ and offers a unique way to determine the quark mass ratio $Q^2 \equiv (m_s^2-m_{ud}^2)/(m_d^2-m_u^2)$ from experiment. We calculate the amplitude dispersively and fit the KLOE data on the charged mode, varying the subtraction constants in the range allowed by chiral perturbation theory. The parameter-free predictions obtained for the neutral Dalitz plot and the neutral-to-charged branching ratio are in excellent agreement with experiment. Our representation of the transition amplitude implies $Q = 22.0 \pm 0.7$.

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Gilberto Colangelo, Stefan Lanz, Heinrich Leutwyler, Emilie Passemar. 2017-01-20. The decay $η\to 3 π$: study of the Dalitz plot and extraction of the quark mass ratio $Q$. https://doi.org/10.1103/physrevlett.118.022001

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