Role of Deck-like backgrounds in diffractive production of + and - PowerPoint PPT Presentation

Role of Deck-like backgrounds in diffractive production of π − π − π + and π − π 0 π 0 systems at COMPASS D. Ryabchikov,on behalf of the COMPASS collaboration E18 Technische Universit¨ at M¨ unchen Role of Deck-like backgrounds in diffractive production of π − π − π + and π − π 0 π 0 systems at COMP D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18) 1 / 22

Quick introduction ( ππ ) ↔ ( ππ ) amplitude: M = − 8 π m � l (2 l + 1) T l ( m ) P l ( cosθ ) q is linear sum of amplitudes ( ππ ) S , ρ (770) , f 2 (1260) and ρ 3 (1690) ( πN ) ↔ ( πN ) amplitude: T πN ( s πN , t ′ ) = s πN e − 8 t ′ Pion propagator: P ( t π ) = m 2 π e btπ with b = 1.7 GeV − 1 and m π = m π c m 2 π − t π Role of Deck-like backgrounds in diffractive production of π − π − π + and π − π 0 π 0 systems at COMP D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18) 2 / 22

Diagrams for π − π 0 π 0 Deck π e btπ Pion propagator: P ( t π ) = m 2 m 2 π − t π m π = m π c for diagrams with ( π 0 π 0 ) π − topology m π = m π 0 for diagrams with ( π − π 0 ) π 0 topology Role of Deck-like backgrounds in diffractive production of π − π − π + and π − π 0 π 0 systems at COMP D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18) 3 / 22

The method of Deck amplitude decomposition Isobar model decay amplitudes: Ψ i ( τ, m ) Quantum numbers i = J P C M ǫ [ isobar ] π L Deck amplitude decomposition: Ψ Deck ( τ, m, t ′ ) ∼ � C i ( m, t ′ )Ψ i ( τ, m ) Role of Deck-like backgrounds in diffractive production of π − π − π + and π − π 0 π 0 systems at COMP D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18) 4 / 22

Features of Deck amplitude decomposition Both Ψ Deck ( τ, m, t ′ ) and Ψ i ( τ, m ) bose-symmetrized Different J P C M ǫ assumed orthogonal Building Deck model: using all componens of ( ππ ) ↔ ( ππ ) or adding them partly → the resulting decomposition can change Role of Deck-like backgrounds in diffractive production of π − π − π + and π − π 0 π 0 systems at COMP D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18) 5 / 22

Deck model using ( ππ ) ↔ ( ππ ) without ( ππ ) S but with ρ (770) , f 2 (1260) and ρ 3 (1690) is decomposed into set of 67 isobaric amplitudes in π − π − π + and π − π 0 π 0 systems Role of Deck-like backgrounds in diffractive production of π − π − π + and π − π 0 π 0 systems at COMP D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18) 6 / 22

Deck total intensity π − π − π + and π − π 0 π 0 25 t=0.100-0.116 GeV 2 /c 2 20 t=0.159-0.188 GeV 2 /c 2 17.5 20 15 12.5 15 10 10 7.5 5 5 2.5 0 0 0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5 m(3 π ) (GeV/c 2 ) m(3 π ) (GeV/c 2 ) t=0.285-0.395 GeV 2 /c 2 14 12 10 8 6 4 2 0 0.5 1 1.5 2 2.5 m(3 π ) (GeV/c 2 ) Role of Deck-like backgrounds in diffractive production of π − π − π + and π − π 0 π 0 systems at COMP D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18) 7 / 22

Deck components π − π − π + and π − π 0 π 0 1 ++ 0 + ρ (770) π S 2 -+ 0 + f 2 (1260) π S 2.5 18 150 150 150 150 150 150 16 r(chrg)=40% r(chrg)=5.5% 2 100 100 100 100 100 100 14 r(neutr)=43% r(neutr)=3% 12 50 50 50 50 50 50 1.5 10 0 0 0 0 0 0 8 1 -50 -50 -50 -50 -50 -50 6 -100 -100 -100 -100 -100 -100 4 0.5 2 -150 -150 -150 -150 -150 -150 0 0 0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5 m(3 π ) (GeV/c 2 ) m(3 π ) (GeV/c 2 ) 2 ++ 1 + ρ (770) π D 1 -+ 1 + ρ (770) π P 0.45 150 150 150 150 150 150 0.7 0.4 r(chrg)=1.6% r(chrg)=2% 100 100 100 100 100 100 0.35 r(neutr)=1.8% 0.6 r(neutr)=2.1% 0.3 50 50 50 0.5 50 50 50 0.25 0.4 0 0 0 0 0 0 0.2 0.3 -50 -50 -50 -50 -50 -50 0.15 0.2 -100 -100 -100 -100 -100 -100 0.1 0.1 0.05 -150 -150 -150 -150 -150 -150 0 0 0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5 m(3 π ) (GeV/c 2 ) m(3 π ) (GeV/c 2 ) Role of Deck-like backgrounds in diffractive production of π − π − π + and π − π 0 π 0 systems at COMP D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18) 8 / 22

1 ++ 0 + ( ππ ) S πP Deck component π − π − π + and π − π 0 π 0 0.8 1 ++ 0 + ( ππ ) S π P 150 150 150 r(chrg)=1.6% 0.7 100 100 100 r(neutr)=2.2% 0.6 50 50 50 0.5 0 0 0 0.4 0.3 -50 -50 -50 0.2 -100 -100 -100 0.1 -150 -150 -150 0 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 m(3 π ) (GeV/c 2 ) Surprise to find amplitude with ( ππ ) S isobar reconstructed as ( ππ ) S scattering amplitude was excluded from Deck model ! Role of Deck-like backgrounds in diffractive production of π − π − π + and π − π 0 π 0 systems at COMP D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18) 9 / 22

The reason for “amplitude leakage”: possible effective distortion of isobar shapes by Deck kinematics → in dominant 1 ++ 0 + ρ (770) π S decay try free shape of ( ππ ) P amplitude Role of Deck-like backgrounds in diffractive production of π − π − π + and π − π 0 π 0 systems at COMP D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18) 10 / 22

Free Shape of ( ππ ) P in isobaric wave 1 ++ 0 + ( ππ ) P πS 180 0.9 Low-t I( ππ ) P φ ( ππ ) P 0.8 160 140 0.7 0.6 120 100 0.5 0.4 80 0.3 60 0.2 40 0.1 20 0 0 0.5 1 1.5 2 0.5 1 1.5 2 m(2 π ) (GeV/c 2 ) m(2 π ) (GeV/c 2 ) 180 1.4 High-t I( ππ ) P φ ( ππ ) P 160 1.2 140 1 120 0.8 100 80 0.6 60 0.4 40 0.2 20 0 0 0.5 1 1.5 2 0.5 1 1.5 2 m(2 π ) (GeV/c 2 ) m(2 π ) (GeV/c 2 ) Role of Deck-like backgrounds in diffractive production of π − π − π + and π − π 0 π 0 systems at COMP D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18) 11 / 22

1 ++ 0 + ( ππ ) S πP before and after free-isobarring ( ππ ) P before free-isobarring 1 ++ 0 + ρ (770) πS 0.8 Low-t r(isob ρ )=1.6% r(free ρ )=0.056% 0.7 0.6 after free-isobarring 1 ++ 0 + ( ππ ) P πS 0.5 0.4 0.3 0.2 0.1 0 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 m(3 π ) (GeV/c 2 ) High-t r(isob ρ )=0.33% 0.07 r(free ρ )=0.02% 0.06 0.05 0.04 0.03 0.02 0.01 0 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 m(3 π ) (GeV/c 2 ) Role of Deck-like backgrounds in diffractive production of π − π − π + and π − π 0 π 0 systems at COMP D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18) 12 / 22

1 ++ 0 + f 2 (1270) πP π − π − π + and π − π 0 π 0 Low-t Low-t 0.25 0.045 r(charg)=0.3% r(charg)=0.1% 0.04 0.2 r(neutr)=0.11% r(neutr)=0.07% 0.035 0.03 0.15 0.025 0.02 0.1 0.015 0.01 0.05 0.005 0 0 0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5 m(3 π ) (GeV/c 2 ) m(3 π ) (GeV/c 2 ) 0.035 High-t High-t 0.035 r(charg)=0.14% r(charg)=0.12% 0.03 0.03 r(neutr)=0.098% r(neutr)=0.078% 0.025 0.025 0.02 0.02 0.015 0.015 0.01 0.01 0.005 0.005 0 0 0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5 m(3 π ) (GeV/c 2 ) m(3 π ) (GeV/c 2 ) Before free-isobarring of After free-isobarring of 1 ++ 0 + ρ (770) πS 1 ++ 0 + ( ππ ) P πS Role of Deck-like backgrounds in diffractive production of π − π − π + and π − π 0 π 0 systems at COMP D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18) 13 / 22

The Data π − p → π − π − π + p π − p → π − π 0 π 0 p π − → π − π − → π − × 6 × 6 COMPASS 2008 ( p (3 ) p) COMPASS 2008 ( p (3 ) p) 10 10 + + + + + + ) ρ π ) ρ π 2 1 0 (770) S 2 0.3 1 0 (770) S intensity (per 40 MeV/c intensity (per 40 MeV/c π − π π π − π − π + π − π π π − π − π + 0 0 0 0 , (scaled) , (scaled) 0.5 2 2 2 2 0.100 < t' < 0.116 GeV /c 0.285 < t' < 0.395 GeV /c 0.25 2 2 2 2 0.100 < t' < 0.113 GeV /c 0.262 < t' < 0.326 GeV /c Preliminary Preliminary 0.4 0.2 0.3 0.15 0.2 0.1 0.1 0.05 0 0 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2 2 m (GeV/c ) m (GeV/c ) π − π − (3 ) (3 ) Deck decomposition π − p → π − π − π + p π − p → π − π 0 π 0 p t=0.100-0.116 GeV 2 /c 2 t=0.285-0.395 GeV 2 /c 2 18 6 16 5 14 12 4 10 3 8 6 2 4 1 2 0 0 0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5 m(3 π ) (GeV/c 2 ) m(3 π ) (GeV/c 2 ) Role of Deck-like backgrounds in diffractive production of π − π − π + and π − π 0 π 0 systems at COMP D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18) 14 / 22