INTRODUCTION ρ 0 (770) MASS AND WIDTH FROM BESIII-BABAR DATA ON σ tot ( e + e − → π + π − ) ρ 0 (770) MASS AND WIDTH FROM δ 1 1 ( t ) DATA GENERALIZATION OF G.-S. AND U&A FF MODELS TO ρ 0 (1450), ρ 0 (1700) REGION CONCLUSIONS Thanks The most correct ρ 0 (770) meson mass and width values E.Bartos, S.Dubnicka , Anna Z.Dubnickova, R.Kaminski, A.Liptaj June 5, 2018 MESON18, Cracow, 7.-12. June 2018 The most correct ρ 0 (770) meson mass and width values S.Dubnicka
INTRODUCTION ρ 0 (770) MASS AND WIDTH FROM BESIII-BABAR DATA ON σ tot ( e + e − → π + π − ) ρ 0 (770) MASS AND WIDTH FROM δ 1 1 ( t ) DATA GENERALIZATION OF G.-S. AND U&A FF MODELS TO ρ 0 (1450), ρ 0 (1700) REGION CONCLUSIONS Thanks Outline INTRODUCTION 1 ρ 0 (770) MASS AND WIDTH FROM BESIII-BABAR DATA ON 2 σ tot ( e + e − → π + π − ) ρ 0 (770) MASS AND WIDTH FROM δ 1 1 ( t ) DATA 3 GENERALIZATION OF G.-S. AND U&A FF MODELS TO 4 ρ 0 (1450), ρ 0 (1700) REGION CONCLUSIONS 5 The most correct ρ 0 (770) meson mass and width values S.Dubnicka
INTRODUCTION ρ 0 (770) MASS AND WIDTH FROM BESIII-BABAR DATA ON σ tot ( e + e − → π + π − ) ρ 0 (770) MASS AND WIDTH FROM δ 1 1 ( t ) DATA GENERALIZATION OF G.-S. AND U&A FF MODELS TO ρ 0 (1450), ρ 0 (1700) REGION CONCLUSIONS Thanks INTRODUCTION The determination of ρ 0 (770) meson parameters m ρ , Γ ρ in C.Patrignani et al. (PDG) Chin. Phys. C40 (2016) 100001 comes from a description of data on σ tot ( e + e − → π + π − ) = πα 2 β 3 m 2 π | F I =1 ( t ) + Re i φ ω | 2 (1) π m 2 3 t ω − t − im ω Γ ω at the elastic region - to be considered up to 1 GeV 2 , where for the charged pion EM FF F I =1 ( t , m ρ , Γ ρ ) the Gounaris-Sakurai π (G.-S.) model m 2 2 π q ρ − m 2 ρ ln ( m ρ +2 q ρ m ρ π m ρ m 2 ρ + m ρ Γ ρ ( 3 ) + ρ ) π π q 2 2 m π π q 3 F GS π ( t ) = . m 2 q ρ ) 3 m ρ ρ − t )) − im ρ Γ ρ ( q ( m 2 ρ )( q 2 ( h ( t ) − h ( m 2 ρ )) + q 2 ρ h ′ ( m 2 ρ )( m 2 ρ − t ) + Γ ρ ( ρ √ t q 3 (2) has been used. The most correct ρ 0 (770) meson mass and width values S.Dubnicka
INTRODUCTION ρ 0 (770) MASS AND WIDTH FROM BESIII-BABAR DATA ON σ tot ( e + e − → π + π − ) ρ 0 (770) MASS AND WIDTH FROM δ 1 1 ( t ) DATA GENERALIZATION OF G.-S. AND U&A FF MODELS TO ρ 0 (1450), ρ 0 (1700) REGION CONCLUSIONS Thanks INTRODUCTION In this presentation it is clearly demonstrated - the G.-S. pion charged EM FF model is not enough accurate for a correct determination of the ρ 0 (770) meson parameters . For these investigations we utilize very precise measurements of σ tot ( e + e − → π + π − ) by BABAR J.P.Lees et al.(BABAR Collab.) Phys. Rev. D86 (2012) 032013 by BESIII M.Ablikin et al.(BESIII Collab.) Phys. Lett. B753 (2016) 629 and independently , also the most accurate up to now P-wave isovector ππ scattering phase shift δ 1 1 ( t ) data at the elastic region with theoretical errors, The most correct ρ 0 (770) meson mass and width values S.Dubnicka
INTRODUCTION ρ 0 (770) MASS AND WIDTH FROM BESIII-BABAR DATA ON σ tot ( e + e − → π + π − ) ρ 0 (770) MASS AND WIDTH FROM δ 1 1 ( t ) DATA GENERALIZATION OF G.-S. AND U&A FF MODELS TO ρ 0 (1450), ρ 0 (1700) REGION CONCLUSIONS Thanks INTRODUCTION 160 140 120 100 (t) 80 1 1 δ 60 40 GKPY 20 0 0.2 0.4 0.6 0.8 1 1.2 2 t [GeV ] Figure : The most accurate up to now P-wave isovector ππ scattering phase shift δ 1 1 ( t ) data with theoretical errors. The most correct ρ 0 (770) meson mass and width values S.Dubnicka
INTRODUCTION ρ 0 (770) MASS AND WIDTH FROM BESIII-BABAR DATA ON σ tot ( e + e − → π + π − ) ρ 0 (770) MASS AND WIDTH FROM δ 1 1 ( t ) DATA GENERALIZATION OF G.-S. AND U&A FF MODELS TO ρ 0 (1450), ρ 0 (1700) REGION CONCLUSIONS Thanks INTRODUCTION to be generated from the existing inaccurate experimental information by the Garcia-Martin-Kaminski-Pelaez-Yndurain Roy-like equations . For more detail of these investigations see E.Bartos, S.Dubnicka, A.Liptaj, A.Z.Dubnickova, R.Kaminski, Phys. Rev. D96 (2017) 113004 The most correct ρ 0 (770) meson mass and width values S.Dubnicka
INTRODUCTION ρ 0 (770) MASS AND WIDTH FROM BESIII-BABAR DATA ON σ tot ( e + e − → π + π − ) ρ 0 (770) MASS AND WIDTH FROM δ 1 1 ( t ) DATA GENERALIZATION OF G.-S. AND U&A FF MODELS TO ρ 0 (1450), ρ 0 (1700) REGION CONCLUSIONS Thanks ρ 0 (770) MASS AND WIDTH FROM BESIII-BABAR DATA ON σ tot ( e + e − → π + π − ) First description of BESIII-BABAR σ tot ( e + e − → π + π − ) by G.-S. charged pion EM FF model (2) is carried out 3 10 ) − π + π → − e + 2 (e 10 tot σ GS model BESIII BaBar 10 0 0.2 0.4 0.6 0.8 1 1.2 2 t [GeV ] Figure : Description of the unified BESIII-BABAR data on σ tot ( e + e − → π + π − ) by pion GS FF model with χ 2 / ndf =40.634 The most correct ρ 0 (770) meson mass and width values S.Dubnicka
INTRODUCTION ρ 0 (770) MASS AND WIDTH FROM BESIII-BABAR DATA ON σ tot ( e + e − → π + π − ) ρ 0 (770) MASS AND WIDTH FROM δ 1 1 ( t ) DATA GENERALIZATION OF G.-S. AND U&A FF MODELS TO ρ 0 (1450), ρ 0 (1700) REGION CONCLUSIONS Thanks ρ 0 (770) MASS AND WIDTH FROM BESIII-BABAR DATA ON σ tot ( e + e − → π + π − ) It gives ρ 0 parameter values m ρ = (775 . 73 ± 0 . 10) MeV (3) Γ ρ = (126 . 51 ± 0 . 13) MeV . however, different (especially the width) from the parameter values m ρ = (775 . 26 ± 0 . 25) MeV (4) Γ ρ = (149 . 1 ± 0 . 8) MeV . quoted in C. Patrignani et al. (PDG), Chin. Phys. C40 (2016) 100001. The most correct ρ 0 (770) meson mass and width values S.Dubnicka
INTRODUCTION ρ 0 (770) MASS AND WIDTH FROM BESIII-BABAR DATA ON σ tot ( e + e − → π + π − ) ρ 0 (770) MASS AND WIDTH FROM δ 1 1 ( t ) DATA GENERALIZATION OF G.-S. AND U&A FF MODELS TO ρ 0 (1450), ρ 0 (1700) REGION CONCLUSIONS Thanks ρ 0 (770) MASS AND WIDTH FROM BESIII-BABAR DATA ON σ tot ( e + e − → π + π − ) Then description of the BESIII-BABAR unified data on σ tot ( e + e − → π + π − ) has been carried out by U & A charged pion EM FF model . S.Dubnicka and A.Z.Dubnickova, Acta Phys. Slovaca 60 (2010) 1 ( q ) = ( q − q Z )( q N − q P ) ( q N − q ρ )( q N − q ¯ ρ ) F EM , I =1 ρ ) ( f ρππ / f ρ ) . (5) π ( q − q P )( q N − q Z ) ( q − q ρ )( q − q ¯ It contains the right-hand unitary cut in t-plane, also a contribution of the left-hand cut from the II. Riemann sheet and generally it reflects all known theoretical properties of the charged pion EM FF . The most correct ρ 0 (770) meson mass and width values S.Dubnicka
INTRODUCTION ρ 0 (770) MASS AND WIDTH FROM BESIII-BABAR DATA ON σ tot ( e + e − → π + π − ) ρ 0 (770) MASS AND WIDTH FROM δ 1 1 ( t ) DATA GENERALIZATION OF G.-S. AND U&A FF MODELS TO ρ 0 (1450), ρ 0 (1700) REGION CONCLUSIONS Thanks ρ 0 (770) MASS AND WIDTH FROM BESIII-BABAR DATA ON σ tot ( e + e − → π + π − ) 3 10 ) − π + π → − e + 2 (e 10 tot σ AVMD model BESIII BaBar 10 0 0.2 0.4 0.6 0.8 1 1.2 2 t [GeV ] Figure : Description of the unified BESIII-BABAR data on σ tot ( e + e − → π + π − ) by U&A pion EM FF model with χ 2 / ndf =1.544 The most correct ρ 0 (770) meson mass and width values S.Dubnicka
INTRODUCTION ρ 0 (770) MASS AND WIDTH FROM BESIII-BABAR DATA ON σ tot ( e + e − → π + π − ) ρ 0 (770) MASS AND WIDTH FROM δ 1 1 ( t ) DATA GENERALIZATION OF G.-S. AND U&A FF MODELS TO ρ 0 (1450), ρ 0 (1700) REGION CONCLUSIONS Thanks ρ 0 (770) MASS AND WIDTH FROM BESIII-BABAR DATA ON σ tot ( e + e − → π + π − ) It provides m ρ = (763 . 03 ± 0 . 10) MeV (6) Γ ρ = (144 . 23 ± 0 . 13) MeV but also different (slightly lower) from the parameter values quoted in C. Patrignani et al. (PDG), Chin. Phys. C40 (2016) 100001. The most correct ρ 0 (770) meson mass and width values S.Dubnicka
INTRODUCTION ρ 0 (770) MASS AND WIDTH FROM BESIII-BABAR DATA ON σ tot ( e + e − → π + π − ) ρ 0 (770) MASS AND WIDTH FROM δ 1 1 ( t ) DATA GENERALIZATION OF G.-S. AND U&A FF MODELS TO ρ 0 (1450), ρ 0 (1700) REGION CONCLUSIONS Thanks ρ 0 (770) MASS AND WIDTH FROM δ 1 1 ( t ) DATA Which of three sets of ρ 0 meson parameters, - found by G.-S. FF model , - found by U & A FF model or - presented by newest PDG , can be considered to be correct one? The latter problem is solved by exploiting the most accurate up-to-now δ 1 1 ( t ) data ! The most correct ρ 0 (770) meson mass and width values S.Dubnicka
INTRODUCTION ρ 0 (770) MASS AND WIDTH FROM BESIII-BABAR DATA ON σ tot ( e + e − → π + π − ) ρ 0 (770) MASS AND WIDTH FROM δ 1 1 ( t ) DATA GENERALIZATION OF G.-S. AND U&A FF MODELS TO ρ 0 (1450), ρ 0 (1700) REGION CONCLUSIONS Thanks ρ 0 (770) MASS AND WIDTH FROM δ 1 1 ( t ) DATA The basis of G.-S.charged pion EM FF model is two parametric effective-range formula of Chew-Mandelstam type for δ 1 1 ( t ) q 3 1 ( t ) = a + bq 2 + q 2 h ( t ) √ t cot δ 1 (7) where √ t + 2 q h ( t ) = 2 q √ t ln ( ); (8) π 2 m π q = [( t − 4 m 2 π ) / 4] 1 / 2 . (9) The most correct ρ 0 (770) meson mass and width values S.Dubnicka
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