[PPT] - Hadronic Decays of the Meson Lena Heijkenskj old Uppsala PowerPoint Presentation

SLIDE 1

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Hadronic Decays of the ω Meson

Lena Heijkenskj¨

ld

Uppsala University

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 1 / 31

SLIDE 2

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Standard Model

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 2 / 31

Three fundamental forces Strong Weak Electro- Magnetism Quantum Chromo Dynamics Electro-Weak theory Prevailed a multitude of test

SLIDE 3

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Standard Model

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 2 / 31

Three fundamental forces Strong Weak Electro- Magnetism Quantum Chromo Dynamics Electro-Weak theory Prevailed a multitude of test Hint of physics beyond SM: anomalous magnetic moment of the muon aµ · ·= gµ−2

2

aexp

µ

=116592091(54)(33) × 10−11 aSM

µ

= aQED

µ

+ aEW

µ

+ aHad

µ

=116591803(1)(42)(26) × 10−11 3.6σ discrepancy → physics beyond the standard model

SLIDE 4

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Hadron Physics

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 3 / 31

Calculations in the lower energy (Q) regime Q Perturbative QCD applicable Phenomenological models and Effective Field Theories

r Lattice QCD

Elementary particles Hadrons

QCD αs(Mz) = 0.1181 ± 0.0013

pp –> jets e.w. precision fits (NNLO) 0.1 0.2 0.3

αs(Q2)

1 10 100

Q [GeV]

Heavy Quarkonia (NLO) e+e– jets & shapes (res. NNLO) DIS jets (NLO)

October 2015

τ decays (N3LO) 1000

(NLO

pp –> tt (NNLO)

)

(–)

SLIDE 5

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Hadron Physics

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 3 / 31

Calculations in the lower energy (Q) regime Q Perturbative QCD applicable Phenomenological models and Effective Field Theories

r Lattice QCD

Elementary particles Hadrons

QCD αs(Mz) = 0.1181 ± 0.0013

pp –> jets e.w. precision fits (NNLO) 0.1 0.2 0.3

αs(Q2)

1 10 100

Q [GeV]

Heavy Quarkonia (NLO) e+e– jets & shapes (res. NNLO) DIS jets (NLO)

October 2015

τ decays (N3LO) 1000

(NLO

pp –> tt (NNLO)

)

(–)

Quark Model Composite objects: Baryons - qqq Mesons - q¯ q Classification in Y and I3 JP = 0− JP = 1− η π0 η’ K 0 K + π− π+ K − ¯ K 0 ω ρ0 φ K ∗0 K ∗+ ρ− ρ+ K ∗− ¯ K ∗0 I3

1

1 I3

1

1 Y

1

1

SLIDE 6

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

This thesis

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 4 / 31

The ω meson I G (JPC ) = 0−(1−−) mω= 782.65(12) MeV, Γω = 8.49(8) MeV ω → Γi/Γω π+π−π0 89.2(7)% π0γ 8.28(28)% π+π− 1.53+0.11

−0.13 %

10

8

10

7

10

6

10

5

10

4

10

3

10

2

1 10 10

2 ω ρ φ ρ′ J /ψ ψ(2S)

Υ Z

σ(e+e− → Hadrons) σ [mb] √s [GeV]

SLIDE 7

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

This thesis

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 4 / 31

The ω meson I G (JPC ) = 0−(1−−) mω= 782.65(12) MeV, Γω = 8.49(8) MeV ω → Γi/Γω π+π−π0 89.2(7)% π0γ 8.28(28)% π+π− 1.53+0.11

−0.13 %

10

8

10

7

10

6

10

5

10

4

10

3

10

2

1 10 10

2 ω ρ φ ρ′ J /ψ ψ(2S)

Υ Z

σ(e+e− → Hadrons) σ [mb] √s [GeV] Thesis outline Part I: ω → π+π−π0 Dalitz plot study with WASA-at-COSY Theory, WASA experiment, Analysis, Results Part II: Additional ω studies – Search for ω → π+π− signal with WASA-at-COSY – Simulation study of π0π0 interference for ω Dalitz plot measurement using KLOE data

SLIDE 8

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 5 / 31

Part I: ω → π+π−π0 Dalitz plot study with WASA-at-COSY

Z

00.1 0.20.30.40.50.60.70.80.9 1

Φ

3
2
1

1 2 3 0.02 0.04 0.06 0.08 0.1

6

10 ×

SLIDE 9

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

What is a Dalitz plot?

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 6 / 31

3-body decay 1 2 3 M given by two independent variables → 2D representation, e.g. M(s12, s23)

d2Γ ds12ds23 = 1 (2π)3 1 32m3 |M|2

sij = |Pi + Pj|2

]

2

[GeV

12

s

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

]

2

[GeV

23

s

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

SLIDE 10

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

What is a Dalitz plot?

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 6 / 31

3-body decay 1 2 3 M given by two independent variables → 2D representation, e.g. M(s12, s23)

d2Γ ds12ds23 = 1 (2π)3 1 32m3 |M|2

sij = |Pi + Pj|2

]

2

[GeV

12

s

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

]

2

[GeV

23

s

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Common choice of variables when m1 = m2

X

1
0.5

0.5 1

Y

1
0.5

0.5 1

X = √ 3 T ∗

1 − T ∗ 2

Q Y = (2m1 + m3)T ∗

3

(m1Q) −1

Z

0.2 0.4 0.6 0.8 1

Φ

3
2
1

1 2 3

Z =X 2 + Y 2 Φ = tan−1 X Y

SLIDE 11

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

ω → π+π−π0 dynamics - 1

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 7 / 31

Dalitz plot density distribution ∼ |M(s12, s23)|2, |M|2 = 1 : Phase space Restrictions from quantum numbers ω : I(JP) = 0(1−) J3π = 1 and J2π = 1 P - wave phase space |M|2 = P ∝ |¯ pi × ¯ pj|2

X

1
0.5

0.5 1

Y

1
0.5

0.5 1 0.02 0.04 0.06 0.08 0.1

6

10 ×

Z

00.1 0.20.30.40.50.60.70.80.9 1

Φ

3
2
1

1 2 3 0.02 0.04 0.06 0.08 0.1

6

10 ×

SLIDE 12

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

ω → π+π−π0 dynamics - 2

1C. Terschl¨

usen, B. Strandberg, S. Leupold, F. Eichst¨ adt Eur.Phys.J. A49 (2013) 116 2S.P. Schneider, et al., Eur.Phys.J. C72 (2014) 2012 and Danilkin, et al. Phys. Rev. D91 (2015) 094029

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 8 / 31

π − π interactions Intermediate ρ π − π rescattering ω π ρ π π |M|2 / P

1 Lagrangian approach1

ω π ρ π π

2 Dispersion approach2

πV → ππ ↓ V → πππ Predictions of

d2Γ ds12ds23

SLIDE 13

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

ω → π+π−π0 dynamics - 2

1C. Terschl¨

usen, B. Strandberg, S. Leupold, F. Eichst¨ adt Eur.Phys.J. A49 (2013) 116 2S.P. Schneider, et al., Eur.Phys.J. C72 (2014) 2012 and Danilkin, et al. Phys. Rev. D91 (2015) 094029

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 8 / 31

π − π interactions Intermediate ρ π − π rescattering ω π ρ π π |M|2 / P

1 Lagrangian approach1

ω π ρ π π

2 Dispersion approach2

πV → ππ ↓ V → πππ Predictions of

d2Γ ds12ds23

Experiment - Theory comparison Parametrisation F(Z, Φ) × P F(Z, Φ) = 1 + 2αZ + 2βZ 3/2 sin(3Φ) + 2γZ 2 + 2δZ 5/2 sin(3Φ) + O(Z 3) Fits are performed on theory predictions.

SLIDE 14

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Why study ω → π+π−π0 dynamics?

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 9 / 31

Previous measurement Largest previous statistics for study of the dynamics - 4200 events. Unable to distinguish ρ onset.

SLIDE 15

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Why study ω → π+π−π0 dynamics?

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 9 / 31

Previous measurement Largest previous statistics for study of the dynamics - 4200 events. Unable to distinguish ρ onset. Benchmark for meson transition form factors π0 ω ρ γ∗ γ∗ a part of π0 γ∗ γ∗ Probe of hadron structure Contribution to HLbL (muon g-2)

SLIDE 16

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Experimental setup

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 10 / 31

Wide Angle Shower Apparatus

EDDA

PAX WASA ANK E

Elec t ron c

oler

St

c

hast icc

oling

J ESSICA

Quadrupole Dipole RF c avit y Barrier buc k et c avit y Ex t rac t ion

TOF JULIC

COSY at Forschungszentrum J¨ ulich, Germany

SLIDE 17

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Experimental setup

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 10 / 31

Wide Angle Shower Apparatus

EDDA

PAX WASA ANK E

Elec t ron c

oler

St

c

hast icc

oling

J ESSICA

Quadrupole Dipole RF c avit y Barrier buc k et c avit y Ex t rac t ion

TOF JULIC

COSY at Forschungszentrum J¨ ulich, Germany

3He

π+ π− γ γ Collected data p + d →

3He +

ω

✲

π+ + π− + π0

✲

π0 + γ

✲

π+ + π− 4 weeks beam time in 2011 Tbeam = 1.45 GeV → 110h Tbeam = 1.50 GeV → 100h Trigger on 3He

SLIDE 18

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Event selection

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 11 / 31

3He

π+ π− γ γ

3He candidate

SLIDE 19

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Event selection

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 12 / 31

3He

π+ π− γ γ

3He candidate

π+π−γγ candidates

) [GeV] γ γ IM(

0.05 0.1 0.15 0.2 0.25 0.3 10000 20000 30000 40000 50000 60000

Experiment Fitted background

Charged tracks PID using drift chamber and solenoid ∼ 1 T ≥ 2 oppositely charged γ reconstruction in calorimeter ≥ 2 neutral

FWHM 40 MeV Mean 136 MeV

SLIDE 20

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Event selection

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 13 / 31

3He

π+ π− γ γ

3He candidate

π+π−γγ candidates π0 candidates

) [GeV] γ γ IM(

0.05 0.1 0.15 0.2 0.25 0.3 10000 20000 30000 40000 50000 60000

Experiment Fitted background

Charged tracks PID using drift chamber and solenoid ∼ 1 T ≥ 2 oppositely charged γ reconstruction in calorimeter ≥ 2 neutral

FWHM 40 MeV Mean 136 MeV

SLIDE 21

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Event selection

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 14 / 31

3He

π+ π− γ γ

3He candidate

π+π−γγ candidates π0 candidates Kinematic fit Constraint: Pin = Pout, Hypothesis: pd → 3Heπ+π−γγ Choose final track candidates Test pd → 3Heπ+π− hypothesis Cut on P(χ2)>0.05 Improve resolution for X Rec = T, θ, φ

) [GeV] π

π

+

π IM(

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1 2 3 4 5

3

10 × Reconstructed

Kin. fitted

SLIDE 22

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Event selection

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 15 / 31

Selected sample Tbeam = 1.45 GeV He) [GeV]

3

MM(

0.65 0.7 0.75 0.8 0.85 0.9 1000 2000 3000 4000 5000 6000

14630(220) Tbeam = 1.50 GeV He) [GeV]

3

MM(

0.65 0.7 0.75 0.8 0.85 0.9 1000 2000 3000 4000 5000

13450(210)

SLIDE 23

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Dalitz plot analysis - Creating the Dalitz plots

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 16 / 31

Bin size Z ∈ [0,1] and Φ ∈ [−π, π] 6×6 bins 1D-representation for comparison

Z

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Φ

3
2
1

1 2 3

1 2 3 4 5 6 1 2 3 4 5 6

Z bins bins Φ

1 1 2 1 3 1 4 1 5 1 6 1 1 2 2 2 3 2 4 2 5 2 6 2 1 3 2 3 3 3 4 3 5 3 6 3 1 4 2 4 3 4 4 4 5 4 6 4 1 5 2 5 3 5 100 200 300 400 500 600 700

3

10 ×

bin Φ Z bin

SLIDE 24

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Dalitz plot analysis - Creating the Dalitz plots

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 16 / 31

Bin size Z ∈ [0,1] and Φ ∈ [−π, π] 6×6 bins 1D-representation for comparison

Z

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Φ

3
2
1

1 2 3

1 2 3 4 5 6 1 2 3 4 5 6

Z bins bins Φ

1 1 2 1 3 1 4 1 5 1 6 1 1 2 2 2 3 2 4 2 5 2 6 2 1 3 2 3 3 3 4 3 5 3 6 3 1 4 2 4 3 4 4 4 5 4 6 4 1 5 2 5 3 5 100 200 300 400 500 600 700

3

10 ×

bin Φ Z bin

Extracting the ω events Simulated distributions - Hω→3π and H3π F = ΛHω→3π + {a1 + a2x + a3x2}H3π Λ =

λ Imax

Imin

Hω→3π

λ = # signal events # events Tbeam = 1.45 GeV 13790(220) Tbeam = 1.50 GeV 12830(200)

He) [GeV]

3

MM(

0.65 0.7 0.75 0.8 0.85 0.9 1000 2000 3000 4000 5000

Experiment

Exp. signal

Fitted background Fitted background + signal Fit range Peak region

/d.o.f = 73 / 50

2

χ

0.65 0.7 0.75 0.8 0.85 0.9

Residuals

300
200
100

100 200 300

SLIDE 25

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Dalitz plot analysis - Creating the Dalitz plots

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 17 / 31

Efficiency correction Using simulated signal data ǫij =

Nfit

ij

Ntrue

ij

Bin-wise efficiency correction ˜ Nij =

Nij ǫij

1 1 2 1 3 1 4 1 5 1 6 1 1 2 2 2 3 2 4 2 5 2 6 2 1 3 2 3 3 3 4 3 5 3 6 3 1 4 2 4 3 4 4 4 5 4 6 4 1 5 2 5 3 5

Analysis efficiency

0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16

bin Φ Z bin

=1.45 GeV

beam

T =1.50 GeV

beam

T

SLIDE 26

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Dalitz plot analysis - Creating the Dalitz plots

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 17 / 31

Efficiency correction Using simulated signal data ǫij =

Nfit

ij

Ntrue

ij

Bin-wise efficiency correction ˜ Nij =

Nij ǫij

1 1 2 1 3 1 4 1 5 1 6 1 1 2 2 2 3 2 4 2 5 2 6 2 1 3 2 3 3 3 4 3 5 3 6 3 1 4 2 4 3 4 4 4 5 4 6 4 1 5 2 5 3 5

Analysis efficiency

0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16

bin Φ Z bin

=1.45 GeV

beam

T =1.50 GeV

beam

T

Resulting experimental Dalitz plots

1 1 2 1 3 1 4 1 5 1 6 1 1 2 2 2 3 2 4 2 5 2 6 2 1 3 2 3 3 3 4 3 5 3 6 3 1 4 2 4 3 4 4 4 5 4 6 4 1 5 2 5 3 5

Efficiency corrected bin content

2 4 6 8 10

3

10 ×

bin Φ Z bin

=1.45 GeV

beam

T

(scaled)

=1.50 GeV

beam

T

1 1 2 1 3 1 4 1 5 1 6 1 1 2 2 2 3 2 4 2 5 2 6 2 1 3 2 3 3 3 4 3 5 3 6 3 1 4 2 4 3 4 4 4 5 4 6 4 1 5 2 5 3 5

R

3
2
1

1 2 3 bin Φ Z bin

Compare the distributions: Rij =

˜ Nij − ˜ Mij

˜

σ2

Nij +˜

σ2

Mij

Unbinned ML fit of Gaussian: µ = −0.02 and σ = 0.93

SLIDE 27

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Dalitz plot analysis - Parametrisation

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 18 / 31

Parametrisation F(Z, Φ) × P F(Z, Φ) = 1 + 2αZ + 2βZ 3/2 sin(3Φ) + 2γZ 2 + 2δZ 5/2 sin(3Φ) + O(Z 3) Fit results

Parameters used in fit α × 103 β × 103 γ × 103 χ2/d.o.f . N 1N 2

84 / 40

N 1N 2α 153(42)

69 / 39

N 1N 2αβ 132(48) 55(63)

68 / 38

N 1N 2αγ 21(148)

232(252)

68 / 38

Sensitive to α parameter: Onset of ρ state

1 1 2 1 3 1 4 1 5 1 6 1 1 2 2 2 3 2 4 2 5 2 6 2 1 3 2 3 3 3 4 3 5 3 6 3 1 4 2 4 3 4 4 4 5 4 6 4 1 5 2 5 3 5

Efficiency corrected bin content

2 4 6 8 10

3

10 ×

=1.45 GeV

beam

T Fitted function

bin Φ Z bin

Normalised residuals

4
3
2
1

1 2 3 4 1 1 2 1 3 1 4 1 5 1 6 1 1 2 2 2 3 2 4 2 5 2 6 2 1 3 2 3 3 3 4 3 5 3 6 3 1 4 2 4 3 4 4 4 5 4 6 4 1 5 2 5 3 5

Efficiency corrected bin content

2 4 6 8 10

3

10 ×

=1.50 GeV

beam

T Fitted function

bin Φ Z bin

Normalised residuals

4
3
2
1

1 2 3 4

SLIDE 28

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Dalitz plot analysis - Systematical checks

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 19 / 31

Test of fit procedure “True” data simulated with P-wave Fit with F(Z, Φ) × P

6
3

3 6 α ×10−3 χ2/ d.o.f. = 33/39

6
3

3 6 α β ×10−3 χ2/ d.o.f. = 32/38 ×

−

/ . . . ×

−

/ . . .

SLIDE 29

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Dalitz plot analysis - Systematical checks

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 19 / 31

Test of fit procedure “True” data simulated with P-wave Fit with F(Z, Φ) × P

6
3

3 6 α ×10−3 χ2/ d.o.f. = 33/39

6
3

3 6 α β ×10−3 χ2/ d.o.f. = 32/38

Test of signal extraction method Simulated dist. - Hω→3π (P-wave) and H3π Generate HGen ∼ HExp Extract signal events → Fill Dalitz plot

60
30

30 60 α ×10−3 χ2/ d.o.f. = 36/39

120
60

60 120 α β ×10−3 χ2/ d.o.f. = 35/38 31/19 37/19

SLIDE 30

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Dalitz plot analysis - Systematical checks

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 19 / 31

Test of fit procedure “True” data simulated with P-wave Fit with F(Z, Φ) × P

6
3

3 6 α ×10−3 χ2/ d.o.f. = 33/39

6
3

3 6 α β ×10−3 χ2/ d.o.f. = 32/38

Test of signal extraction method Simulated dist. - Hω→3π (P-wave) and H3π Generate HGen ∼ HExp Extract signal events → Fill Dalitz plot

60
30

30 60 α ×10−3 χ2/ d.o.f. = 36/39

120
60

60 120 α β ×10−3 χ2/ d.o.f. = 35/38

Test of efficiency correction Fit uncorrected Dalitz plots

50 100 150 200 250 Nominal Eff.Check α (x103)

χ2/d.o.f. 69/39 79/39 31/19 37/19

SLIDE 31

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Dalitz plot analysis - Systematical checks

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 19 / 31

Test of fit procedure “True” data simulated with P-wave Fit with F(Z, Φ) × P

6
3

3 6 α ×10−3 χ2/ d.o.f. = 33/39

6
3

3 6 α β ×10−3 χ2/ d.o.f. = 32/38

Test of signal extraction method Simulated dist. - Hω→3π (P-wave) and H3π Generate HGen ∼ HExp Extract signal events → Fill Dalitz plot

60
30

30 60 α ×10−3 χ2/ d.o.f. = 36/39

120
60

60 120 α β ×10−3 χ2/ d.o.f. = 35/38

Test of efficiency correction Fit uncorrected Dalitz plots

50 100 150 200 250 Nominal Eff.Check α (x103)

χ2/d.o.f. 69/39 79/39

Test of data set consistency Individual fits to the two Dalitz plots

50 100 150 200 250 Nominal Eff.Check Tbeam 1.45 Tbeam 1.50 α (x103)

31/19 37/19

SLIDE 32

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

ω → π+π−π0 Dalitz plot - Summary

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 20 / 31

3He

π+ π− γ γ p + d →

3He + ω

Tbeam = 1.45 and 1.50 GeV → ∼ 26600(300) events in the Dalitz plots Fit of parametrisation (1 + 2αZ) × P → α > 0 with ∼ 3.5 σ Theoretical predictions: Lagrangian approach (Uppsala) and Dispersive calculations (Bonn,JPAC)

50 100 150 200 250 This study Uppsala Bonn JPAC

α

×10−3

SLIDE 33

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 21 / 31

Part II: Additional ω studies

A search for the A simulation study of ω → π+π− signal in WASA π0π0 interference study with KLOE

[GeV]

π π

M

0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 200 250 300 350 400 450 500 550 600

0.94 0.96 0.98 1 1.02 1.04 1.06 1.08

Z

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Φ

3
2
1

1 2 3

SLIDE 34

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Introduction

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 22 / 31

Why search for ω → π+π− BR(ω → π+π−) = (1.53+0.11

−0.13)%

Isospin violating ρ − ω mixing assumed → Interference pattern in Mππ In WASA data ∼ 28000(300) ω → π+π−π0 events

SLIDE 35

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Introduction

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 22 / 31

Why search for ω → π+π− BR(ω → π+π−) = (1.53+0.11

−0.13)%

Isospin violating ρ − ω mixing assumed → Interference pattern in Mππ In WASA data ∼ 28000(300) ω → π+π−π0 events Previous observations π+p/d → Xπ+π− dip π−p → Xπ+π− peak K −p → Xπ+π− peak/“shoulder” Nγ → Nπ+π− “shoulder” e+e− → π+π− “shoulder”

SLIDE 36

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Introduction

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 23 / 31

ρ − ω mixing Sources of isospin violation: EM interactions, mu = md, . . . Common approach: |ρI ≡ |1, 0 and |ωI ≡ |0, 0 → |ρ = |ρI − ǫ |ωI |ω = |ωI + ǫ |ρI |ωI → π+π− often neglected

SLIDE 37

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Introduction

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 23 / 31

ρ − ω mixing Sources of isospin violation: EM interactions, mu = md, . . . Common approach: |ρI ≡ |1, 0 and |ωI ≡ |0, 0 → |ρ = |ρI − ǫ |ωI |ω = |ωI + ǫ |ρI |ωI → π+π− often neglected The role of production e+e−: known coupling γ∗ V hadronic: not known → mixing info from e+e−

ρ Aρ

+

ω Aω

+

ρ ω Aω = M2π

|M2π|2 =|W2s−1

ρ |2

|Aρ|2 + 2g(1 + ∆m2

0ℜ(s−1 ω ))|Aρ||Aω| cos(α)

−2g∆m2

0ℑ(s−1 ω )|Aρ||Aω| sin(α)

[GeV]

π π

M

0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84 0.86 200 250 300 350 400 450 500

°

= 0 α

[GeV]

π π

M

0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84 0.86 200 250 300 350 400 450 500

°

= 90 α

[GeV]

π π

M

0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84 0.86 200 250 300 350 400 450 500

°

= 180 α

[GeV]

π π

M

0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84 0.86 200 250 300 350 400 450 500 550

°

= 270 α

SLIDE 38

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Data analysis

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 24 / 31

Event selection

1

Selection of 3He, π+ and π−

2

Kinematical fit: choosing final tracks and suppress 3Heπ+π−π0

3

Cut on P(χ2)>0.1

)

2

χ P(

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

3

10

4

10

5

10

6

10

7

10

Experimental data

Reduction of non π+π− events

1

100 200 300 400 500

) [GeV]

+

π He

3

(

2

MM

0.4 -0.3 -0.2 -0.1

0.1 0.2 0.3 0.4 0.5

) [GeV]

π

He

3

(

2

MM

0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5

2

100 200 300 400 500

) [GeV]

+

π He

3

(

2

MM

0.4 -0.3 -0.2 -0.1

0.1 0.2 0.3 0.4 0.5

) [GeV]

π

He

3

(

2

MM

0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5

3

50 100 150 200 250 300

) [GeV]

+

π He

3

(

2

MM

0.4 -0.3 -0.2 -0.1

0.1 0.2 0.3 0.4 0.5

) [GeV]

π

He

3

(

2

MM

0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5

SLIDE 39

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Data analysis

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 25 / 31

The resulting π+π− mass distribution

He) [GeV]

3

MM(

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 200 400 600 800 1000 1200 1400 1600 1800 2000

He) [GeV]

3

MM(

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 200 400 600 800 1000 1200 1400 1600

SLIDE 40

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Data analysis

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 25 / 31

The resulting π+π− mass distribution

He) [GeV]

3

MM(

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 200 400 600 800 1000 1200 1400 1600 1800 2000

He) [GeV]

3

MM(

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 200 400 600 800 1000 1200 1400 1600

He) [GeV]

3

MM(

0.65 0.7 0.75 0.8 0.85 0.9 200 400 600 800 1000 1200 1400 1600 1800 2000

Experiment Fitted background Fit region

0.65 0.7 0.75 0.8 0.85 0.9

Residuals

300
200
100

100 200 300

He) [GeV]

3

MM(

0.65 0.7 0.75 0.8 0.85 0.9 200 400 600 800 1000 1200 1400 1600

Experiment Fitted background Fit region

0.65 0.7 0.75 0.8 0.85 0.9

Residuals

300
200
100

100 200 300

Fit to background using simulated distribution H2π F = {a1 + a2x + a3x2}H2π No convincing ρ − ω interference

SLIDE 41

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Data analysis

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 25 / 31

The resulting π+π− mass distribution

He) [GeV]

3

MM(

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 200 400 600 800 1000 1200 1400 1600 1800 2000 Experiment Estimated signal

He) [GeV]

3

MM(

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 200 400 600 800 1000 1200 1400 1600 Experiment Estimated signal

Estimation of # ω → π+π− events in final sample With assumption of no interference

SLIDE 42

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Summary

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 26 / 31

Data collected by WASA, 28000(300) ω → π+π−π0 events (BR=89%) Search for ω → π+π− signal (BR=1.53%) Observe ρ − ω signal in hadronic production

He) [GeV]

3

MM(

0.65 0.7 0.75 0.8 0.85 0.9 200 400 600 800 1000 1200 1400 1600 1800 2000

Experiment Fitted background Fit region

0.65 0.7 0.75 0.8 0.85 0.9

Residuals

300
200
100

100 200 300

He) [GeV]

3

MM(

0.65 0.7 0.75 0.8 0.85 0.9 200 400 600 800 1000 1200 1400 1600

Experiment Fitted background Fit region

0.65 0.7 0.75 0.8 0.85 0.9

Residuals

300
200
100

100 200 300

No visible interference Estimated # ω → π+π− small Size of ρ → π+π− signal unknown

SLIDE 43

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 27 / 31

Part II: Additional ω studies

A search for the A simulation study of ω → π+π− signal in WASA π0π0 interference study with KLOE

[GeV]

π π

M

0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 200 250 300 350 400 450 500 550 600

0.94 0.96 0.98 1 1.02 1.04 1.06 1.08

Z

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Φ

3
2
1

1 2 3

SLIDE 44

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Introduction

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 28 / 31

Previous study of e+e− → π0ω with KLOE ∼ 600 −1 pb √s ∈ [1000,1030] MeV e+e− → π0ω → π0π+π−π0 1349(2)·103 reconstructed events Could be used for Dalitz plot study!

KLOE DEA R

F I N U D A

Accumulator Storage rings LINAC 10 m DAΦNE

Drift Chamber Barrel EMC S.C. coil Yoke Endcap EMC QCal 7 m 6 m

KLOE

SLIDE 45

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Introduction

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 28 / 31

Previous study of e+e− → π0ω with KLOE ∼ 600 −1 pb √s ∈ [1000,1030] MeV e+e− → π0ω → π0π+π−π0 1349(2)·103 reconstructed events Could be used for Dalitz plot study!

KLOE DEA R

F I N U D A

Accumulator Storage rings LINAC 10 m DAΦNE

Drift Chamber Barrel EMC S.C. coil Yoke Endcap EMC QCal 7 m 6 m

KLOE

Why care about π0π0 interference?

1

Identify primary π0 in simulation Needed for ǫ = Reconstruced

True

No π0

Primary/Decay in simulation with interference

Can simulation without interference be used?

2

Effect of π0π0 interference in Dalitz plot Effect in simulation Effect in experiment ?

SLIDE 46

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Simulation studies

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 29 / 31

The reaction model |M|2 =|J+−00

ωπ0 |2

=

Gω[tω(pπ0

1 , pπ−, pπ+, pπ0 2 ) − tω(pπ0 1 , pπ+, pπ−, pπ0 2 )

−tω(pπ0

1 , pπ0 2 , pπ+, pπ−)] + (pπ0 1 ←

→ pπ0

2 )

2

=|J+−00

ωπ0

1

+ J+−00

ωπ0

2

|2 ω π0 ρ π π π

SLIDE 47

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Simulation studies

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 29 / 31

The reaction model |M|2 =|J+−00

ωπ0 |2

=

Gω[tω(pπ0

1 , pπ−, pπ+, pπ0 2 ) − tω(pπ0 1 , pπ+, pπ−, pπ0 2 )

−tω(pπ0

1 , pπ0 2 , pπ+, pπ−)] + (pπ0 1 ←

→ pπ0

2 )

2

=|J+−00

ωπ0

1

+ J+−00

ωπ0

2

|2 ω π0 ρ π π π The simulation procedure

1

Generate π0π+π−π0 at √s = 1 GeV with GENBOD → WPS

2

Calculate |M|2 → W = |M|2 · WPS Exclude interference |MI |2 = |J+−00

ωπ0

1

|2 → WI = |MI |2 · WPS

SLIDE 48

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Simulation studies - The results

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 30 / 31

Pion kinematics

) [GeV/c] π |p| (

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

10000 20000 30000 40000 50000

W

I

W

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

I

W / W

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

) [deg] π π Opening angle (

20 40 60 80 100 120 140 160 180

500 1000 1500 2000 2500 3000 3500

W

I

W

20 40 60 80 100 120 140 160 180

I

W / W

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

) [GeV]

π

+

π IM(

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

500 1000 1500 2000 2500 3000 3500

W

I

W

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

I

W / W

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

[GeV]

recoil

M

0.4 0.5 0.6 0.7 0.8 0.9

10000 20000 30000 40000 50000 60000

W

I

W

0.4 0.5 0.6 0.7 0.8 0.9

I

W / W

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

No drastic effect on simulation when excluding interference

SLIDE 49

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Simulation studies - The results

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 30 / 31

Pion kinematics

) [GeV/c] π |p| (

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

10000 20000 30000 40000 50000

W

I

W

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

I

W / W

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

) [deg] π π Opening angle (

20 40 60 80 100 120 140 160 180

500 1000 1500 2000 2500 3000 3500

W

I

W

20 40 60 80 100 120 140 160 180

I

W / W

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

) [GeV]

π

+

π IM(

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

500 1000 1500 2000 2500 3000 3500

W

I

W

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

I

W / W

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

[GeV]

recoil

M

0.4 0.5 0.6 0.7 0.8 0.9

10000 20000 30000 40000 50000 60000

W

I

W

0.4 0.5 0.6 0.7 0.8 0.9

I

W / W

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

No drastic effect on simulation when excluding interference Dalitz plot Select π0

Decay using |mω − IM(π+π−π0 i )|

W/WI

0.94 0.96 0.98 1 1.02 1.04 1.06 1.08

Z

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Φ

3
2
1

1 2 3

Noticeable effect from interference. Take care in analysis strategy

SLIDE 50

Introduction Part I: WASA Dalitz plot Part II: WASA ω → π+π− signal Part II: KLOE simulation study

Overall Summary

L. Heijkenskj¨
ld (Uppsala University)

Hadronic Decays of the ω Meson 31 / 31

ω → π+π−π0 Dalitz plot

50 100 150 200 250 This study Uppsala Bonn JPAC

α

×10−3

ω → π+π− signal search

He) [GeV]

3

MM(

0.65 0.7 0.75 0.8 0.85 0.9 200 400 600 800 1000 1200 1400 1600 1800 2000

Experiment Fitted background Fit region

0.65 0.7 0.75 0.8 0.85 0.9

Residuals

300
200
100

100 200 300

He) [GeV]

3

MM(

0.65 0.7 0.75 0.8 0.85 0.9 200 400 600 800 1000 1200 1400 1600

Experiment Fitted background Fit region

0.65 0.7 0.75 0.8 0.85 0.9

Residuals

300
200
100

100 200 300

π0π0 simulation study

0.94 0.96 0.98 1 1.02 1.04 1.06 1.08

Z

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Φ

3
2
1

1 2 3