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η→3π: Study of the Dalitz Plot and Extraction of the Quark Mass Ratio Q
Gilberto Colangelo1, Stefan Lanz1, Heinrich Leutwyler1
1Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland.
Abstract:
The η→3π 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}≡(m_{s}^{2}-m_{ud}^{2})/(m_{d}^{2}-m_{u}^{2}) from experiment. We calculate the amplitude dispersively and fit the KLOE Collaboration 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±0.7.
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