K -> 3 pi Final State Interactions at NLO in CHPT and Cabibbo's Proposal to Measure a_0-a_2

Details K -> 3 pi Final State Interactions at NLO in CHPT and Cabibbo's Proposal to Measure a_0-a_2 K -> 3 pi Final State Interactions at NLO in CHPT and Cabibbo's Proposal to Measure a_0-a_2

2006-02-02

arxiv.org/abs/hep-ph/0602023v4

Eur.Phys.J.C50:405-422,2007

Physics

High Energy Physics

High Energy Physics - Phenomenology

31 pages, 8 figures. v2=v3 Added the full contributions to the cusp from the real part of the discontinuity. v4 Improved text.

Scientific paper

10.1140/epjc/s10052-006-0201-7

We present the analytical results for the K -> 3 pi final state interactions at next-to-leading order (NLO) in CHPT. We also study the recent Cabibbo's proposal to measure the pi-pi scattering lenghts combination a_0-a_2 from the cusp effect in the pi^0-pi^0 energy spectrum at threshold for K^+ -> pi^0 pi^0 pi^+ and K_L -> pi^0 pi^0 pi^0$, and give the relevant formulas to describe it at NLO. For that, we use the NLO CHPT expression to fit the real part of K -> 3 pi to data while the pi-pi scattering lenghts are treated non-perturbatively. Using them, we make a quantitative estimate of the theoretical uncertaintity of the a_0-a_2 determination at NLO in our approach and obtain that it is not smaller than 5 % if added quadratically and 7 % if linearly for K^+ -> pi^0 pi^0 pi^+. One gets similar theoretical uncertainties if the neutral K_L -> pi^0 pi^0 pi^0 decay data below threshold are used instead. For this decay, there are very large theoretical uncertainties above threshold due to cancellations and data above threshold cannot be used to get the scattering lenghts. All the numbers we present are in the isospin limit apart of two-pion phase space factors which are physical. We compare our results for the cusp effect with Cabibbo and Isidori's results and discuss the differences and agreements. We also comment on the apperance of the singularity at the K -> 3 pi pseudo-threshold s=(m_K-m_pi)^2 in the discontinuity that defines the cusp.

Affiliated with

Also associated with

No associations

Rating

K -> 3 pi Final State Interactions at NLO in CHPT and Cabibbo's Proposal to Measure a_0-a_2 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with K -> 3 pi Final State Interactions at NLO in CHPT and Cabibbo's Proposal to Measure a_0-a_2, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and K -> 3 pi Final State Interactions at NLO in CHPT and Cabibbo's Proposal to Measure a_0-a_2 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-123065