Analysis of discrepancies in Dalitz plot parameters in eta to 3 pion decay

Abstract

We analyze the Dalitz plot parameters of eta to 3 pion decay in the framework of resummed chiral perturbation theory. This approach allows us to keep the uncertainties in the NNLO and higher orders under better control and estimate their influence. We cannot confirm the suspected discrepancy in the case of the charged decay parameter b, where even small uncertainties in higher orders could accommodate the difference. On the other hand, we find the experimental value of the neutral decay parameter alpha incompatible with an assumption of good convergence properties in the center of the Dalitz plot. We calculate pion-pion rescattering bubble corrections up to three loops and show that these might explain the discrepancy, especially for a low value of the pseudoscalar decay constant in the chiral limit. However, that could indicate a failure of convergence of the chiral series in this channel already at low energies around 500MeV.

Presented at "Hadron Structure 2011", Tatranska Strba, Slovakia, June 2011. 4 pages, 1 figure

References in corpus (7)

• Review of lattice results concerning low energy particle physics
• $\eta \to 3\pi$ at Two Loops In Chiral Perturbation Theory
• Cusps in K_L --> 3 pi decays
• Rescattering effects in eta {\to} 3pi decays
• Determination of the Dalitz plot parameter alpha for the decay eta->3pi^0 with the Crystal Ball at MAMI-B
• Measurement of the Slope Parameter for the eta->3pi0 Decay in the pp->pp eta Reaction
• Low-energy pi-pi and pi-K scatterings revisited in three-flavour resummed chiral perturbation theory

Cited by in corpus (3)

• The mass of the two lightest quarks
• Convergence properties of $\eta \to 3\pi$ decays in chiral perturbation theory
• Determination of the $m_u$ and $m_d$ quark masses from $\eta \to 3\pi$ decay