Meson spectroscopy at VES and COMPASS D. Ryabchikov Institute for - PowerPoint PPT Presentation

Meson spectroscopy at VES and COMPASS D. Ryabchikov Institute for High Energy Physics, Protvino; Technische Universit¨ at M¨ unchen D. Ryabchikov (IHEP, TUM E18) Meson spectroscopy at VES and COMPASS 27.02.2019 1 / 21

OUTLINE Two flagship reactions for VES and COMPASS experiments: π − N → π − π − π + N and π − N → π − π 0 π 0 N Methods of the analysis: The mass-independent PWA with established isobars Isospin relations between π − π − π + and π − π 0 π 0 amplitudes Two parametrizations of PWA density matrix: rank=1 and unlimited rank with extracting the Largest-Eigenvalue-Eigenvector (LEV) Resonance-model fits Analysis with free parametrization of ππ -isobars Results of the analysis: Mass-independent PWA for VES with established shapes of ππ -isobars, comparison of isospin relations between π − π − π + and π − π 0 π 0 (VES and COMPASS) Selected results for resonance model fits (COMPASS) Comparison of PWA with rank=1 and unlimited rank with extracting the Largest-Eigenvalue-Eigenvector (VES) Selected results for analysis with free parametrization of ππ -isobars (COMPASS) D. Ryabchikov (IHEP, TUM E18) Meson spectroscopy at VES and COMPASS 27.02.2019 2 / 21

The VES detector D. Ryabchikov (IHEP, TUM E18) Meson spectroscopy at VES and COMPASS 27.02.2019 3 / 21

The COMPASS detector D. Ryabchikov (IHEP, TUM E18) Meson spectroscopy at VES and COMPASS 27.02.2019 4 / 21

The measurement conditions, the statistics of 3 π states VES p beam = 29 GeV / c Nucleus Be target, no detection of the recoil particle Momentum transferred squared 0 < t ′ < 1 GeV 2 / c 2 87 x 10 6 events π − Be → π − π − π + Be 32 x 10 6 events π − Be → π − π 0 π 0 Be COMPASS p beam = 190 GeV / c LiH target, Recoil Proton Detector Momentum transferred squared 0 . 1 < t ′ < 1 GeV 2 / c 2 46 x 10 6 events π − p → π − π − π + p 3 . 5 x 10 6 events π − p → π − π 0 π 0 p D. Ryabchikov (IHEP, TUM E18) Meson spectroscopy at VES and COMPASS 27.02.2019 5 / 21

π − -beam dissociation on nucleon or nucleus target J PC M ε − (beam) π − (bachelor) π − 1 π X L ε = +: natural R ππ parity exchange 2 + π −: unnatural S ε = parity exchange target recoil Reggeon exchange, naturality η = P R ( − 1) J R p ∗ p ∗ p ∗ Gottfried-Jackson frame: SCM of X: Z GJ � � beam , Y GJ = [ � recoil x � beam ] Reflectivity basis for system of mesons: | JM ε > = | JM > − ε P ( − 1) J − M | J − M > At high beam energies: reflectivity ε equal to naturality η unpolarised target: ε = ± 1 states do not interfere D. Ryabchikov (IHEP, TUM E18) Meson spectroscopy at VES and COMPASS 27.02.2019 6 / 21

Brief introduction to mass-independent PWA Mass-independent PWA events density: 2 � � N r � � � � � I ( m , t ′ , τ ) = T ε i , r ( m , t ′ ) ψ ε i ( m , τ ) + FLAT � � � � � � ε = ± 1 r =1 i The decay amplitudes ψ ε i ( τ ) are enumerated by their quantum numbers i , ε = J PC M ε [ isobar ] π L and have no free parameters Transition amplitudes T ε ir ( m , t ′ ) fitted independently in each ( m , t ′ ) - bin Events density expressed through spin-density matrix: N r � � � I ( m , t ′ , τ ) = ρ ε i , j ( m , t ′ ) ψ ε i ( m , τ ) ψ ε ∗ ρ ε T ε i , r T ε ∗ j ( m , τ ) , i , j = j , r ε = ± 1 r =1 i , j For COMPASS data N r = 1 is chosen, for VES - two models are tried: N r = 1 and unlimited rank and extracting Eigenvector with Largest Eigenvalue D. Ryabchikov (IHEP, TUM E18) Meson spectroscopy at VES and COMPASS 27.02.2019 7 / 21

Isospin relations between π − π − π + and π − π 0 π 0 Decay amplitudes for I=1 of 2 π isobar (i.e. ρπ ) in case of I (3 π ) = 1 are connected: � � 2 ( 1 1 2 [( π − (1) π + ) π − (2) + ( π − (2) π + ) π − 1 2 ( 1 2 [( π − π 0 (1) ) π 0 (2) + ( π − π 0 (2) ) π 0 (1) ]) ↔ − (1) ]) √ √ Same dalitz-plot structure → N( π − π 0 π 0 ):N( π − π − π + )=1:1 Decay amplitudes for I=0 of 2 π isobar (i.e. f 0 π or f 2 π ) channels are always connected : � � (2) ) π − ) 3 ( 1 2 2 [( π − (1) π + ) π − (2) + ( π − (2) π + ) π − 1 3 (( π 0 (1) π 0 (1) ]) ↔ − √ Different Dalitz-plot structure. Narrow isobar and m (3 π ) >> m isob + m π → N( π − π 0 π 0 ):N( π − π − π + )=0.5:1 Case of broad, overlapping isobars for π − π − π + - ratio can be siginficantly larger or smaller than 0.5 All corresponding relative phases in π − π 0 π 0 and π − π − π + are equal - in case of appropriate choosing of directions of ”spin analyzers” - π − - direction in 2 π center-of-mass for both systems D. Ryabchikov (IHEP, TUM E18) Meson spectroscopy at VES and COMPASS 27.02.2019 8 / 21

J PC M ε = 1 ++ 0 + ρ (770) π S -intensity VES COMPASS π − → π − × 6 COMPASS 2008 ( p (3 ) p) 10 x 10 3 + + + ρ π Events/ 20 MeV ) 3 1 0 (770) S 2 intensity (per 40 MeV/c 4000 summed over t fit1 fit2 π − π π π − π − π + 0 0 , 2 2 0.100 < t' < 1.000 GeV /c 3500 2.5 (incoherent sum) Preliminary 3000 2 2500 1.5 2000 1 1500 1000 0.5 500 0 0 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 GeV 2 m (GeV/c ) − 1-(1++)0+ rho pi S π (3 ) D. Ryabchikov (IHEP, TUM E18) Meson spectroscopy at VES and COMPASS 27.02.2019 9 / 21

J PC M ε = 2 ++ 1 + ρ (770) π D -intensity VES COMPASS π − → π − × 6 COMPASS 2008 ( p (3 ) p) 10 + + + ρ π Events/ 20 MeV ) 2 2 1 (770) D 2 x 10 2 intensity (per 40 MeV/c summed over t fit1 fit2 π − π π π − π − π + 0 0 , 4000 2 2 0.100 < t' < 1.000 GeV /c (incoherent sum) 3500 1.5 Preliminary 3000 2500 1 2000 1500 0.5 1000 500 0 0 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 GeV 2 m (GeV/c ) − 1-(2++)1+ rho pi D π (3 ) D. Ryabchikov (IHEP, TUM E18) Meson spectroscopy at VES and COMPASS 27.02.2019 10 / 21

J PC M ε = 2 ++ 1 + ρ (770) π D -phase relative to 1 ++ 0 + ρπ S VES COMPASS π − → π − COMPASS 2008 ( p (3 ) p) φ + + + ρ π − + + + ρ π Degrees phase (degree) (2 1 (770) D 1 0 (770) S) t=0-0.015 GeV 2 200 150 150 100 100 50 50 0 0 -50 Preliminary -50 -100 -150 -100 π − π π π − π − π + 0 0 , 2 2 0.100 < t' < 0.116 GeV /c -200 2 2 -150 0.100 < t' < 0.113 GeV /c -250 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 GeV 2 m (GeV/c ) φ (1-(2++)1+ rho pi D - 1-(1++)0+ rho pi S π − (3 ) The relative phases between waves containing 3 π -resonances do not depend on beam energy and t ′ D. Ryabchikov (IHEP, TUM E18) Meson spectroscopy at VES and COMPASS 27.02.2019 11 / 21

The total intensity of ρ (770) π with ε = +1 VES COMPASS π − → π − × 6 COMPASS 2008 ( p (3 ) p) 10 x 10 3 ρ π ε Events/ 20 MeV ) 2 (770) spin total ( =+1) intensity (per 40 MeV/c 4500 summed over t fit1 fit2 π − π π π − π − π + 5 0 0 , 2 2 0.100 < t' < 1.000 GeV /c 4000 (incoherent sum) 3500 4 Preliminary 3000 3 2500 2000 2 1500 1000 1 500 0 0 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 GeV 2 m (GeV/c ) − rho pi Natur= + π (3 ) The ε = +1 dominates over ε = − 1 (latest also do not show isospin relations) D. Ryabchikov (IHEP, TUM E18) Meson spectroscopy at VES and COMPASS 27.02.2019 12 / 21

J PC M ε = 2 − + 0 + f 2 (1270) π S -intensity VES COMPASS π − → π − × 6 COMPASS 2008 ( p (3 ) p) 10 − + + π Events/ 20 MeV ) 2 0 f (1270) S 2 intensity (per 40 MeV/c x 10 2 summed over t fit1 fit2 2 π − π π π − π − π + 0 0 0.7 , 5000 2 2 0.100 < t' < 1.000 GeV /c 0.6 (incoherent sum) Preliminary 4000 0.5 0.4 3000 0.3 2000 0.2 0.1 1000 0 0 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 GeV 2 m (GeV/c ) − 1-(2-+)0+ f2 pi S π (3 ) D. Ryabchikov (IHEP, TUM E18) Meson spectroscopy at VES and COMPASS 27.02.2019 13 / 21