On the precise determination of the differences of ρ-meson family parameters

Unlike previous approaches to determine the known ρ-meson family parameters, we have proposed new phenomenological approach based on the exploiting experimental data on e+e− → π+π− and τ− → ππντ processes and on the Unitary and Analytic models of the corresponding electromagnetic and weak pion form factors.


Introduction
The rho-meson resonances, with quantum members J PC = 1 −− to be specified by their mass and decay width, exist in three charged states ρ 0 , ρ + and ρ − , whereby the cleanest processes of their demonstrations are, for neutral rho-mesons the e + e − annihilation processes and for charged rho-mesons τ − -decay into two-pions.While masses of charged rho-mesons have to be identical due to the CPT theorem, one can naturally expect that the mass of the neutral rho-mesons will be different from previous ones.
A lot of experimental determinations of masses and decay widths by employing various strong, electromagnetic and weak processes of the rho-mesons have been carried out [1] and the current values of the difference of ground state ρ(770) meson parameters have the following average values, m ρ 0 − m ρ ± = −0.7 ± 0.8 MeV and Γ ρ 0 − Γ ρ ± = 0.3 ± 1.3 MeV, revealing no difference between charged and neutral ρ(770) meson parameters.Similar estimates of a difference of excited ρ(1450) and ρ(1700) meson parameters do not exist up to now.
In this contribution, in connection with the updated e + e − → π + π − annihilation data [2,3] we determine ρ 0 meson parameters for all three ρ(770), ρ(1450) and ρ(1700) resonance families applying the Unitary and Analytic (U&A) model of the pion electromagnetic form factor (FF).Moreover, such approach allows us to determine also ρ ± parameters for all three ρ(770), ρ(1450) and ρ(1700) resonance families by using accurate weak pion FF data from the measurement of τ − -lepton decay into two pions [4] and the relation between pion electromagnetic FF and pion weak FF derived by conserved vector current (CVC) hypothesis in [5].Parameter

U&A models of pion FF
A phenomenological approach, based on the synthesis of the experimental fact of a creation of ρmeson family in e + e − annihilation into two pions, the asymptotic behavior ( f π = 92.4± 0.2MeV -weak pion decay constant, α s (t) -QCD running coupling constant) and the analytic properties, is still the most successful way of a reconstruction of the EM pion FF behavior.This approach leads to U&A model of EM pion FF represented by the expression with the conformal mapping q in +q+ √ q in −q , q = t−t 0 4 , q in = t in −t 0 4 of four-sheeted Riemann surface into one W-plane, W Z and W P the zero and the pole, by means of which a contribution of the left-hand cut on the II.Riemann sheet is simulated, f vππ and f v the vector-meson-pion and the universal vector-meson coupling constants, respectively, whereby a e-mail: erik.bartos@savba.skEPJ Web of C onferences Table 1.U&A model values of fitting parameters for the masses and decay widths of ρ 0 (for e + e − data) and ρ ± (for τ − -lepton decay data) mesons and their resonances.
The model is defined on four-sheeted Riemann surface with complex conjugate poles (corresponding to unstable ρ-resonances) on unphysical sheets, and reflecting all known properties of EM pion FF.It depends on 10 physically interpretable free parameters, t in , m ρ , Γ ρ , f ρππ / f ρ , m ρ , Γ ρ , m ρ , Γ ρ , W Z and W P .Conserved vector current hypothesis allows one to relate the isovector part of the weak spectral function v I=1 0 (s) characterizing the π + π − system (s is the invariant mass squared of such system) with the spectral function v − (s) of π − π 0 system.Because there also exists the dependence of the spectral function and pion form factor, one can relate F EM π -EM pion FF with F W π -the weak pion FF through the relation F W π = √ 2F EM π (see [5]).In such a way it is possible to use the same U&A model of EM pion FF for the description of the weak pion FF data from τ − -lepton decay.

Conclusions
In contrast to previous approaches to determine the rho-meson family parameters, we have proposed new phenomenological approach based on e + e − → π + π − and τ − → π − π 0 ν τ data analysis.The complex U&A models of EM and weak pion FF allow one to determine the masses and widths for neutral and charge rho-mesons and their excitations precisely, see Tab. 1.Our result for the difference m ρ 0 − m ρ ± = −3.37 ± 1.06 MeV is in the coincidence with the recently published values, see Fig. 1.
DOI: 10.1051/ C Owned by the authors, published by EDP Sciences,

Figure 1 .
Figure 1.The comparison of published values for mass difference of neutral ρ 0 and charged ρ ± mesons for the state ρ(770) with our result and PDG average value.