Study of the processe+e−→π+π

Abstract

Study of the process e + e − → π + π − π 0 in the energy region √ s from 0.98 to 1.38 GeV. The cross section of the process e + e − → π + π − π 0 was measured in the Spherical Neutral Detector experiment at the VEPP-2M collider in the energy region √ s = 980 ÷ 1380 MeV. The measured cross section, together with the e + e − → π + π − π 0 and ωπ + π − cross sections obtained in other experiments, was analyzed in the framework of the generalized vector meson dominance model. It was found that the experimental data can be described by a sum of ω, φ mesons and two ω ′ and ω ′′ resonances contributions, with masses m ω ′ ∼ 1490, m ω ′′ ∼ 1790 MeV and widths Γ ω ′ ∼ 1210, Γ ω ′′ ∼ 560 MeV. The analysis of the π + π − invariant mass spectra in the energy region √ s from 1100 to 1380 MeV has shown that for their description one should take into account the e + e − → ωπ 0 → π + π − π 0 mechanism also. The phase between the amplitudes corresponding to the e + e − → ωπ and e + e − → ρπ intermediate states was measured for the first time. The value of the phase is close to zero and depends on energy. I. INTRODUCTIONThe cross section of hadron production in the e + e − annihilation in the energy region √ s < 1.03 GeV can be described within the vector meson dominance model (VDM) framework and is determined by the transitions of light vector mesons (ρ, ω, φ) into the final states. The light vector mesons have been studied rather well. They are quark-antiquark qq (q = u, d, s) bound states, and their masses, widths and main decays have been measured with high accuracy 1 . The cross section for hadron production above the φ(1020) resonance ( √ s ≃ 1.03-2 GeV) cannot be described in the conventional VDM framework (taking into account ρ, ω and φ mesons only) indicating the existence of states with vector meson quantum numbers I G (J P C ) = 1 + (1 −− ), 0 − (1 −− ) and with masses of about 1450, 1650 MeV. Parameters of these states are not well established due to inaccurate and conflicting experimental data. The nature of these states is not clear either. In some reviews of experimental data they are considered as a mixture of qq with 4-quark qqqq and hybrid qqg states 2-5 . On the other hand, the experimental data do not contradict *

Hadron production viae+e−collisions with initial state radiation

“…III it is clear that the cross section of the process e þ e À ! þ À 0 obtained by BABAR (Aubert et al, 2004b) is consistent with that of SND (Achasov et al, 2002) below ffiffi ffi s p ¼ 1:4 GeV, but is much higher than that at DM2 (Antonelli et al, 1992) above this energy. The energy dependence of the cross section observed by DM2 is also inconsistent with other measurements [see the discussion of this problem by Achasov et al (2002)] and the existence of the rather well-established !ð1420Þ and !ð1650Þ resonances.…”

“…23). The cross section below 1.4 GeV is in agreement with the SND measurement (Achasov et al, 2002), but at higher energies a large deviation from the DM2 results (Antonelli et al, 1992) is observed. The cross section in this region is fitted (see the inset in Fig.…”

“…10 shows the distribution of the integrated luminosities collected in some direct e þ e À experiments. At masses below 1:4 GeV=c 2 the statistics of the SND experiment (Achasov et al, 2002) recorded at the VEPP-2M collider is presented. This is the largest integrated luminosity collected in this mass region in a single experiment.…”

“…The solid curve shows "dL=dm for the B factory (2E 0 ¼ 10:58 GeV, L ¼ 500 fb À1 , tagged ISR photon), while the dashed curve shows the same function for the factory (2E 0 ¼ 1:02 GeV, L ¼ 240 pb À1 , untagged ISR photon). The histogram represents integrated luminosities collected in direct e þ e À experiments with the SND detector (Achasov et al, 2002) at the Novosibirsk VEPP-2M collider (below 1:4 GeV=c 2 ), and with the DM1 (Bisello et al, 1981) and DM2 (Antonelli et al, 1992) detectors at the Orsay DCI collider (above 1:4 GeV=c 2 ). masses below 0:8 GeV=c 2 the luminosity currently used for ISR analysis (Ambrosino et al, 2009) is comparable with that collected in direct e þ e À experiments.…”

A global treatment of VMD physics up to the φ: II. τ decay and hadronic contributions to g−2

“…On the other hand, the bin-to-bin correlated error has been treated as emphasized above for the τ data sets. For reasons already emphasized in [1], we have discarded the e + e − → π + π − π 0 data provided by [46,47].…”