Three-pion decays of the tau lepton, the a_1(1260) properties, and the a_1-rho-pi Lagrangian

TL;DR

This paper models three-pion decays of the tau lepton using an a_1-rho-pi Lagrangian, fitting experimental data to determine properties of the a_1(1260) resonance and improve theoretical understanding.

Contribution

It introduces a two-component a_1-rho-pi Lagrangian with a mixing parameter and demonstrates its effectiveness in fitting multiple experimental data sets, refining the a_1(1260) resonance parameters.

Findings

Inclusion of the a_1(1640) resonance improves data fit to 100% confidence level.

The a_1(1260) mass is determined as 1233±18 MeV.

The mixing parameter sin(θ) is found to be 0.459±0.004.

Abstract

We show that the a_1-rho-pi Lagrangian is a decisive element for obtaining a good phenomenological description of the three-pion decays of the tau lepton. We choose it in a two-component form with a flexible mixing parameter sin(theta). In addition to the dominant a_1-> pho pi intermediate states, the a_1->pi sigma ones are included. When fitting the three-pion mass spectra, three data sets are explored: (1) ALEPH 2005 pi-pi-pi+ data, (2) ALEPH 2005 pi-pi0pi0 data, and (3) previous two sets combined and supplemented with the ARGUS 1993, OPAL 1997, and CLEO 2000 data. The corresponding confidence levels are (1) 28.3%, (2) 100%, and (3) 7.7%. After the inclusion of the a_1(1640) resonance, the agreement of the model with data greatly improves and the confidence level reaches 100% for each of the three data sets. From the fit to all five experiments [data set (3)] the following parameters of the a_1(1260) are obtained m_{a_1}=(1233+/-18) MeV, Gamma_{a_1}=(431+/-20) MeV. The optimal value of the Lagrangian mixing parameter sin(theta)= 0.459+/-0.004 agrees with the value obtained recently from the e+e- annihilation into four pions.