The most correct ρ0(770) meson mass and width values

Erik Bartoš1, Stanislav Dubnička1,∗, Anna Z. Dubničková2, Robert Kamiński3, and Andrej Liptaj1 1Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 845 11 Bratislava, Slovak Republic 2Department of Theoretical Physics, Comenius University, Mlynská dolina F1, 842 48 Bratislava, Slovak Republic 3Henryk Niewodniczaňski Institute of Nuclear Physics, Polish Academy of Sciences, 31-342 Krakow, Poland

Further we demonstrated that the the mass and width values of the ρ 0 (770) meson following from the application of the Gounaris-Sakurai model to a description of these data are not trustworthy.

Analysis
The extensively quoted pion EM FF G.-S. model [4] has been constructed by assuming that for a wide energy of the elastic region up to t = 1 GeV 2 the P-wave isovector ππ scattering * e-mail: stanislav.dubnicka@savba.sk and takes the following form Its application to an optimal description of the unified BESIII-BaBaR data [1,2] at the elastic region (see Fig.1a) with χ 2 /nd f =40.6341 gives parameters m ρ = (775.73 ± 0.10)MeV (4) Γ ρ = (126.51 ± 0.13)MeV not in a coincidence with values presented by Review of Particle Physics [6].
On the other hand an application of the pion EM FF model (see Fig.1b) following from the first principles [7] to a description of the same data gives slightly lower values of parameters m ρ = (763.026 ± 0.10)MeV (6) Γ ρ = (144.233 ± 0.13)MeV than in [6].
Which of these three sets of ρ 0 meson parameters can be considered to be correct ones? For a solution of this problem the most accurate up to now P-wave isovector ππ scattering phase shift δ 1 1 (t) data [3] have been exploited. On the other hand, if fully solvable mathematical scheme through the phase representation of the pion EM FF elaborated in [9,10], is applied, a perfect description of δ 1 1 (t) data (see Fig.2b), by a model independent phase shift δ 1 1 (t) representation [8] δ 1 1 (q) = arctg with χ 2 /nd f = 0.0244 is achieved and the ρ 0 meson mass and width m ρ = (763.56 ± 0.51)MeV (10) Γ ρ = (143.09 ± 0.82)MeV. are found to be consistent with (6).
The same values of ρ 0 meson parameters are found also by a generalization of formula (5) to the region of the excited states of the ρ 0 meson [8], what can not be said about results obtained by a generalization of the pion EM FF G.-S. model [4] to the same region.
This all convinces us that the ρ 0 (770) meson mass and width values obtained by the Gounaris-Sakurai model can not be accepted as correct ones.