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

SLIDE 1

Role of Deck-like backgrounds in diffractive production

f π−π−π+ and π−π0π0 systems at COMPASS
D. Ryabchikov,on behalf of the COMPASS collaboration

E18 Technische Universit¨ at M¨ unchen

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 1 / 22

SLIDE 2

Quick introduction

(ππ) ↔ (ππ) amplitude: M = −8π m

q

l(2l + 1)Tl(m)Pl(cosθ)

is linear sum of amplitudes (ππ)S, ρ(770), f2(1260) and ρ3(1690) (πN) ↔ (πN) amplitude: TπN(sπN, t′) = sπN e−8t′ Pion propagator: P(tπ) = m2

πebtπ

m2

π−tπ

with b = 1.7 GeV −1 and mπ = mπc

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 2 / 22

SLIDE 3

Diagrams for π−π0π0 Deck

Pion propagator: P(tπ) = m2

πebtπ

m2

π−tπ

mπ = mπc for diagrams with (π0π0)π− topology mπ = mπ0 for diagrams with (π−π0)π0 topology

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 3 / 22

SLIDE 4

The method of Deck amplitude decomposition

Isobar model decay amplitudes: Ψi(τ, m) Quantum numbers i = JP CM ǫ[isobar]π L Deck amplitude decomposition: ΨDeck(τ, m, t′) ∼ Ci(m, t′)Ψi(τ, m)

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 4 / 22

SLIDE 5

Features of Deck amplitude decomposition

Both ΨDeck(τ, m, t′) and Ψi(τ, m) bose-symmetrized Different JP CM ǫ assumed orthogonal Building Deck model: using all componens of (ππ) ↔ (ππ) or adding them partly → the resulting decomposition can change

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 5 / 22

SLIDE 6

Deck model using (ππ) ↔ (ππ) without (ππ)S but with ρ(770), f2(1260) and ρ3(1690) is decomposed into set of 67 isobaric amplitudes in π−π−π+ and π−π0π0 systems

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 6 / 22

SLIDE 7

Deck total intensity π−π−π+ and π−π0π0

5 10 15 20 25 0.5 1 1.5 2 2.5 t=0.100-0.116 GeV2/c2 m(3π) (GeV/c2) 2.5 5 7.5 10 12.5 15 17.5 20 0.5 1 1.5 2 2.5 t=0.159-0.188 GeV2/c2 m(3π) (GeV/c2) 2 4 6 8 10 12 14 0.5 1 1.5 2 2.5 t=0.285-0.395 GeV2/c2 m(3π) (GeV/c2)

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 7 / 22

SLIDE 8

Deck components π−π−π+ and π−π0π0

2 4 6 8 10 12 14 16 18 0.5 1 1.5 2 2.5

150
100
50

50 100 150

150
100
50

50 100 150

150
100
50

50 100 150 r(chrg)=40% r(neutr)=43% m(3π) (GeV/c2)

1++0+ ρ(770) π S

0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5

150
100
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50 100 150

150
100
50

50 100 150

150
100
50

50 100 150 r(chrg)=5.5% r(neutr)=3% m(3π) (GeV/c2)

2-+0+ f2(1260) π S

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 1 1.5 2 2.5

150
100
50

50 100 150

150
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50

50 100 150

150
100
50

50 100 150 r(chrg)=1.6% r(neutr)=1.8% m(3π) (GeV/c2)

2++1+ ρ(770) π D

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 1 1.5 2 2.5

150
100
50

50 100 150

150
100
50

50 100 150

150
100
50

50 100 150 r(chrg)=2% r(neutr)=2.1% m(3π) (GeV/c2)

1-+1+ ρ(770) π P

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 8 / 22

SLIDE 9

1++0+(ππ)SπP Deck component π−π−π+ and π−π0π0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

150
100
50

50 100 150

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50 100 150

150
100
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50 100 150 r(chrg)=1.6% r(neutr)=2.2% m(3π) (GeV/c2) 1++0+ (ππ)S π P

Surprise to find amplitude with (ππ)S isobar reconstructed as (ππ)S scattering amplitude was excluded from Deck model !

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 9 / 22

SLIDE 10

The reason for “amplitude leakage”: possible effective distortion of isobar shapes by Deck kinematics → try free shape of (ππ)P in dominant 1++0+ρ(770)π S decay amplitude

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 10 / 22

SLIDE 11

Free Shape of (ππ)P in isobaric wave 1++0+(ππ)PπS

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.5 1 1.5 2 m(2π) (GeV/c2) I(ππ)P 20 40 60 80 100 120 140 160 180 0.5 1 1.5 2 m(2π) (GeV/c2) φ(ππ)P Low-t 0.2 0.4 0.6 0.8 1 1.2 1.4 0.5 1 1.5 2 m(2π) (GeV/c2) I(ππ)P 20 40 60 80 100 120 140 160 180 0.5 1 1.5 2 m(2π) (GeV/c2) φ(ππ)P High-t

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 11 / 22

SLIDE 12

1++0+(ππ)SπP before and after free-isobarring (ππ)P

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 r(isob ρ)=1.6% r(free ρ)=0.056% m(3π) (GeV/c2) Low-t 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 r(isob ρ)=0.33% r(free ρ)=0.02% m(3π) (GeV/c2) High-t

before free-isobarring 1++0+ρ(770)πS after free-isobarring 1++0+(ππ)P πS

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 12 / 22

SLIDE 13

1++0+f2(1270)πP π−π−π+ and π−π0π0

0.05 0.1 0.15 0.2 0.25 0.5 1 1.5 2 2.5 r(charg)=0.3% r(neutr)=0.11% m(3π) (GeV/c2) Low-t 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.5 1 1.5 2 2.5 r(charg)=0.14% r(neutr)=0.098% m(3π) (GeV/c2) High-t 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.5 1 1.5 2 2.5 r(charg)=0.1% r(neutr)=0.07% m(3π) (GeV/c2) Low-t 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.5 1 1.5 2 2.5 r(charg)=0.12% r(neutr)=0.078% m(3π) (GeV/c2) High-t

Before free-isobarring of After free-isobarring of 1++0+ρ(770)πS 1++0+(ππ)P πS

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 13 / 22

SLIDE 14

The Data π−p → π−π−π+p π−p → π−π0π0p

)

2

(GeV/c

−

) π (3

m 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )

2

intensity (per 40 MeV/c 0.1 0.2 0.3 0.4 0.5

6

10 × p)

−

) π (3 → p

−

π COMPASS 2008 ( S π (770) ρ

+ + +

1 (scaled)

+

π

−

π

−

π , π π

−

π

2

/c

2

0.100 < t' < 0.116 GeV

2

/c

2

0.100 < t' < 0.113 GeV

Preliminary

)

2

(GeV/c

−

) π (3

m 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )

2

intensity (per 40 MeV/c 0.05 0.1 0.15 0.2 0.25 0.3

6

10 × p)

−

) π (3 → p

−

π COMPASS 2008 ( S π (770) ρ

+ + +

1 (scaled)

+

π

−

π

−

π , π π

−

π

2

/c

2

0.285 < t' < 0.395 GeV

2

/c

2

0.262 < t' < 0.326 GeV

Preliminary

Deck decomposition π−p → π−π−π+p π−p → π−π0π0p

2 4 6 8 10 12 14 16 18 0.5 1 1.5 2 2.5 t=0.100-0.116 GeV2/c2 m(3π) (GeV/c2) 1 2 3 4 5 6 0.5 1 1.5 2 2.5 t=0.285-0.395 GeV2/c2 m(3π) (GeV/c2)

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 14 / 22

SLIDE 15

The Data π−p → π−π−π+p π−p → π−π0π0p

)

2

(GeV/c

−

) π (3

m 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )

2

intensity (per 40 MeV/c 20 40 60 80 100

3

10 × p)

−

) π (3 → p

−

π COMPASS 2008 ( S π (1270)

2

f

+ + −

2

+

π

−

π

−

π , π π

−

π

2

/c

2

0.100 < t' < 0.116 GeV

2

/c

2

0.100 < t' < 0.113 GeV

Preliminary

)

2

(GeV/c

−

) π (3

m 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )

2

intensity (per 40 MeV/c 20 40 60 80

3

10 × p)

−

) π (3 → p

−

π COMPASS 2008 ( S π (1270)

2

f

+ + −

2

+

π

−

π

−

π , π π

−

π

2

/c

2

0.285 < t' < 0.395 GeV

2

/c

2

0.262 < t' < 0.326 GeV

Preliminary

Deck decomposition π−p → π−π−π+p π−p → π−π0π0p

0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5 t=0.100-0.116 GeV2/c2 m(3π) (GeV/c2) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 1 1.5 2 2.5 t=0.285-0.395 GeV2/c2 m(3π) (GeV/c2)

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 15 / 22

SLIDE 16

The Data π−p → π−π−π+p π−p → π−π0π0p

)

2

(GeV/c

−

) π (3

m 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )

2

intensity (per 40 MeV/c 20 40 60 80 100

3

10 × p)

−

) π (3 → p

−

π COMPASS 2008 ( D π (770) ρ

+

1

+ +

2

+

π

−

π

−

π , π π

−

π

2

/c

2

0.100 < t' < 0.116 GeV

2

/c

2

0.100 < t' < 0.113 GeV

Preliminary

)

2

(GeV/c

−

) π (3

m 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )

2

intensity (per 40 MeV/c 0.05 0.1 0.15 0.2 0.25 0.3

6

10 × p)

−

) π (3 → p

−

π COMPASS 2008 ( D π (770) ρ

+

1

+ +

2

+

π

−

π

−

π , π π

−

π

2

/c

2

0.285 < t' < 0.395 GeV

2

/c

2

0.262 < t' < 0.326 GeV

Preliminary

Deck decomposition π−p → π−π−π+p π−p → π−π0π0p

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 1 1.5 2 2.5 t=0.100-0.116 GeV2/c2 m(3π) (GeV/c2) 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.5 1 1.5 2 2.5 t=0.285-0.395 GeV2/c2 m(3π) (GeV/c2)

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 16 / 22

SLIDE 17

The Data π−p → π−π−π+p π−p → π−π0π0p

)

2

(GeV/c

−

) π (3

m 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )

2

intensity (per 40 MeV/c 2 4 6 8 10

3

10 × p)

−

) π (3 → p

−

π COMPASS 2008 ( P π (770) ρ

+

1

+

1 (scaled)

+

π

−

π

−

π , π π

−

π

2

/c

2

0.100 < t' < 0.116 GeV

2

/c

2

0.100 < t' < 0.113 GeV

Preliminary

)

2

(GeV/c

−

) π (3

m 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )

2

intensity (per 40 MeV/c 2 4 6 8

3

10 × p)

−

) π (3 → p

−

π COMPASS 2008 ( P π (770) ρ

+

1

+

1 (scaled)

+

π

−

π

−

π , π π

−

π

2

/c

2

0.285 < t' < 0.395 GeV

2

/c

2

0.262 < t' < 0.326 GeV

Preliminary

Deck decomposition π−p → π−π−π+p π−p → π−π0π0p

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 1 1.5 2 2.5 t=0.100-0.116 GeV2/c2 m(3π) (GeV/c2) 0.1 0.2 0.3 0.4 0.5 0.5 1 1.5 2 2.5 t=0.285-0.395 GeV2/c2 m(3π) (GeV/c2)

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 17 / 22

SLIDE 18

The Data π−p → π−π−π+p π−p → π−π0π0p

)

2

(GeV/c

−

) π (3

m 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )

2

intensity (per 40 MeV/c 0.5 1 1.5 2 2.5 3 3.5 4

3

10 × p)

−

) π (3 → p

−

π COMPASS 2008 ( H π (770) ρ

+ + −

6 (scaled)

+

π

−

π

−

π , π π

−

π

2

/c

2

0.100 < t' < 0.116 GeV

2

/c

2

0.100 < t' < 0.113 GeV

Preliminary

)

2

(GeV/c

−

) π (3

m 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )

2

intensity (per 40 MeV/c 1 2 3 4 5 6 7 8

3

10 × p)

−

) π (3 → p

−

π COMPASS 2008 ( H π (770) ρ

+ + −

6 (scaled)

+

π

−

π

−

π , π π

−

π

2

/c

2

0.285 < t' < 0.395 GeV

2

/c

2

0.262 < t' < 0.326 GeV

Preliminary

Deck decomposition π−p → π−π−π+p π−p → π−π0π0p

0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.5 1 1.5 2 2.5 t=0.100-0.116 GeV2/c2 m(3π) (GeV/c2) 0.1 0.2 0.3 0.4 0.5 0.5 1 1.5 2 2.5 t=0.285-0.395 GeV2/c2 m(3π) (GeV/c2)

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 18 / 22

SLIDE 19

CONCLUSIONS

The method produces continuous intensities and flat phases depending on m(3π) for most of amplitudes Isobaric decomposition produces artifacts:

Leakage to 1++0+(ππ)SπP amplitude Low-mass leakage and distortion of 1++0+f2(1260)π

Remedy - free-isobarring of dominant isobaric amplitudes

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 19 / 22

SLIDE 20

COMPARISON with DATA

Data shows shifts of the mass spectrums with t′ for dominant 1++0+ρ(770)πS The mass shapes of high-spin waves is fully reproduced by Deck The JP CM ǫ = 1−+1+ exotic wave is has dominating contribution from Deck at low t′

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 20 / 22

SLIDE 21

OUTLOOK

Apply to different targets, t′-regions Develop the model

Off-shell behavior for ππ → ππ amplitiudes Understand I=2 (incl π−π0, π0π0, π+π−, π−π−)

Develop the methods

Make fits with non-linear parameters (as suggested by Adam Szczepaniak and Vincent Mathieu).

Other models: Bowler, Berger, 3-component Deck model ... Rescattered Deck.

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 21 / 22

SLIDE 22

BACKUP: The Data: relative phase of JPCM ǫ = 1−+1+ρπP

Phase (Degree)

150
100
50

50 100 150 )

2

System (GeV/c

+

π

π
π

Mass of the 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

p (COMPASS 2008)

+

π

π
π

→ p

π

preliminary

S π (770) ρ

+ + +

1

P

π (770) ρ

+

1

+ −

1

2

/c

2

0.128 GeV ≤ t' ≤ 0.113

2

/c

2

0.220 GeV ≤ t' ≤ 0.189

2

/c

2

0.326 GeV ≤ t' ≤ 0.262

2

/c

2

0.724 GeV ≤ t' ≤ 0.449

D. Ryabchikov,on behalf of the COMPASS collaboration (TUM E18)

Role of Deck-like backgrounds in diffractive production of π−π−π+ and π−π0π0 systems at COMP 22 / 22