[PPT] - photons off transversely polarized protons (g9b-FROST) Lelia PowerPoint Presentation

SLIDE 1

¡ ¡

¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡August 22nd, 2017 Polarization observables in double charged pion photo-production with circularly polarized photons off transversely polarized protons (g9b-FROST)

Lelia Aneta Net

Research supported in parts by National Science Foundation NSF PHY-1505615

NSTAR 2017, Columbia, SC

SLIDE 2

Outline

The Theory and the Models
Double pion channel - Missing Resonances Problem
FROST Experiment (g9b)
Analysis: Extraction of polarization observables
Results for
Summary

2 ¡

I

J

, Px, Py, P

J x , P J y

SLIDE 3

THE THEORY AND THE MODELS ¡

Different models

predict different number of nucleon excited states

A QCD solution is not known at low energies

(of the order of the nucleon mass and its excited states)

(CQM) ¡

3 ¡

Experimental data will help confirm the

existence of these predicted resonances

SLIDE 4

Biggest contribution to the

photo-production cross section at higher energies

Branching ratio for N*

decay via double pion channel could be greater than 70% (e.g. N(1720))

Hagiwara et al., 2002

DOUBLE PION PHOTOPRODUCTION

4 ¡

SLIDE 5

POLARIZATION OBSERVABLES

Different helicity combinations of the initial nucleon,

final nucleon and the photon give rise to 8 complex transition amplitudes describing the reaction:

The cross section sums up the squares of these

transition amplitudes; polarization observables allows access to the amplitude’s phase; reveal more information about the reaction dynamics

This work focused on the extraction of 5 polarization
bservables: I

J

, Px, Py, P

J x , P J y

5 ¡

SLIDE 6

6 ¡

[Yuqing Mao, USC] ¡

PC

Z ¡

[Strauch, 2005]

Previous/Current Studies for Double Pion Photo-production with CLAS

SLIDE 7

FROST Experiment (g9 run) at Thomas Jefferson National Accelerator Facility (Newport News, VA)

7 ¡

h0p://www.phys.vt.edu/research/experiments/JLab-‑Aerial.jpg ¡

SLIDE 8

Electron beam: - longitudinally polarized:
beam energy: 3081.73 MeV
Photon beam: - circularly polarized

Eγ ≈ [0.5 − 3.0 GeV]

¯ Pe = 87%

δJ = ¯ Pe (4Eγ/Ee) − (Eγ/Ee)2 4 − (4Eγ/Ee) + (3Eγ/Ee)2

8 ¡

FROzen Spin Target (FROST) - transversely

polarized protons (C4H9OH)

Target polarization: 76% - 86%
Carbon target: unpolarized
Polyethylene target: unpolarized

BEAMS AND TARGETS

SLIDE 9

CLAS DETECTOR

8 < φ < 140 −25 < θ < 25

9 ¡

time and

momentum measurements

coverage:

TARGET& TORUS&MAGNET& TIME&OF& FLIGHT& PADDLES& DRIFT& CHAMBERS& BEAM&LINE&

h0ps://www.jlab.org/Hall-‑B/int-‑web/clas_large1.jpg ¡

SLIDE 10

PHOTON SELECTION PARTICLE ID

t [ns] Δ

10
8
6
4
2

2 4 6 8 10

Counts

1000 2000 3000 4000 5000 6000

3

10 ×

Raw Data Final Selection

π

β Δ

0.1 -0.08 -0.06 -0.04 -0.02

0.02 0.04 0.06 0.08 0.1 Counts 1000 2000 3000 4000 5000 6000 7000 8000 9000

3

10 ×

= 0.033 σ Mean+3 = -0.029 σ Mean-3 Sigma = 0.010 Mean = 0.002

+

π

β Δ

0.1 -0.08 -0.06 -0.04 -0.02

0.02 0.04 0.06 0.08 0.1 Counts 1000 2000 3000 4000 5000 6000 7000 8000 9000

3

10 ×

= 0.038 σ Mean+3 = -0.036 σ Mean-3 Sigma = 0.01 Mean = 0.001

p

β Δ

0.1 -0.08 -0.06 -0.04 -0.02

0.02 0.04 0.06 0.08 0.1 Counts 2 4 6 8 10 12 14 16 18 20 22

6

10 ×

= 0.032 σ Mean+3 = -0.029 σ Mean-3 Sigma = 0.010 Mean = 0.002

∆β = βmeas − βcalc = βmeas − p p p2 + m2c2

∆t = tCLAS,vertex − tγ,vertex =

= tST − dST c · βcalc − h tT AGR + Z c i

10 ¡

SLIDE 11

γp → pπ+π−

Final State Composition: 2 positive charges and 1 negative charge

¡

~ ~ p → p⇡+⇡−(X) ~ ~ p → ⇡+⇡−(X) ~ ~ p → p⇡−(X) ~ ~ p → p⇡+(X)

Topology 1: Topology 2: Topology 3: Topology 4: ¡

p missing nothing missing π- missing π+ missing

REACTION SELECTION ¡

11 ¡

SLIDE 12

12 ¡

]

2

[GeV

X 2

M

0.1
0.05

0.05 0.1 0.15 0.2 0.25 0.3 Events 20 40 60 80 100 120 140 160 180 200 0.72 ± Scale factor= 9.79 0.02 ± Q value = 0.65

Carbon pre-fit Butanol fit Carbon scaled Carbon unscaled

Events ¡

M2

X[ GeV2]

Seed event M2

Q = Signal Signal + Background

i ¡

SIGNAL BACKGROUND SEPARATION: PROBABILISTIC WEIGHTING METHOD

Q value = the probability for a given event i to be a signal (Q=1) or a background event (Q=0)

SLIDE 13

13 ¡

Reaction plane

Figure ¡adapted ¡from ¡[Strauch, ¡2005] ¡

Polarization observables for circularly polarized photons off transversely polarized protons

* ¡

SLIDE 14

All the final expressions correct for the acceptance effects and for the fact that the target polarization is slightly different for different run groups.

¡ 14 ¡

Simplified observable extraction (for illustration)

¯ Px = 1 ¯ Λ P

i cos αi

P

i Qi cos2 αi

¯ Py = 1 ¯ Λ P

i sin αi

P

i Qi sin2 αi

¯ P

J x

= 1 ¯ Λ 1 ¯ δJ P

i Hi cos αi

P

i Qi cos2 αi

¯ P

J y

= 1 ¯ Λ 1 ¯ δJ P

i Hi sin αi

P

i Qi sin2 αi

SLIDE 15

15 ¡

Polarization Observables: Results

Observables fit functions:

PRELIMINARY ¡

I

J

g1c, ¡g9b ¡ comparison ¡

SLIDE 16

y

P

* [degrees] φ 90 180 270 360 y

P

0.5
0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5 W = 1450 - 1550 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 y

P

0.5
0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5 W = 1550 - 1650 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 y

P

0.5
0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5 W = 1650 - 1750 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 y

P

0.5
0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5 W = 1750 - 1850 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 y

P

0.5
0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5 W = 1850 - 1950 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 y

P

0.5
0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5 W = 1950 - 2050 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 y

P

0.5
0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5 W = 2050 - 2150 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 y

P

0.5
0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5 W = 2150 - 2250 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 y

P

0.5
0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5 W = 2250 - 2350 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 y

P

0.5
0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5 W = 2350 - 2450 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 y

P

0.5
0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5 W = 2450 - 2550 MeV

Data Even function fit

x

P

* [degrees] φ 90 180 270 360 x

P

0.3
0.2
0.1

0.1 0.2 0.3 W = 1450 - 1550 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 x

P

0.3
0.2
0.1

0.1 0.2 0.3 W = 1550 - 1650 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 x

P

0.3
0.2
0.1

0.1 0.2 0.3 W = 1650 - 1750 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 x

P

0.3
0.2
0.1

0.1 0.2 0.3 W = 1750 - 1850 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 x

P

0.3
0.2
0.1

0.1 0.2 0.3 W = 1850 - 1950 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 x

P

0.3
0.2
0.1

0.1 0.2 0.3 W = 1950 - 2050 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 x

P

0.3
0.2
0.1

0.1 0.2 0.3 W = 2050 - 2150 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 x

P

0.3
0.2
0.1

0.1 0.2 0.3 W = 2150 - 2250 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 x

P

0.3
0.2
0.1

0.1 0.2 0.3 W = 2250 - 2350 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 x

P

0.3
0.2
0.1

0.1 0.2 0.3 W = 2350 - 2450 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 x

P

0.3
0.2
0.1

0.1 0.2 0.3 W = 2450 - 2550 MeV

Data Odd function fit

16 ¡ PRELIMINARY ¡ W=1450-2550 MeV

SLIDE 17

x

P

* [degrees] φ 90 180 270 360 x

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 1450 - 1550 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 x

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 1550 - 1650 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 x

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 1650 - 1750 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 x

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 1750 - 1850 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 x

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 1850 - 1950 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 x

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 1950 - 2050 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 x

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 2050 - 2150 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 x

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 2150 - 2250 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 x

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 2250 - 2350 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 x

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 2350 - 2450 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 x

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 2450 - 2550 MeV

Data Even function fit

y

P

* [degrees] φ 90 180 270 360 y

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 1450 - 1550 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 y

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 1550 - 1650 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 y

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 1650 - 1750 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 y

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 1750 - 1850 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 y

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 1850 - 1950 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 y

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 1950 - 2050 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 y

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 2050 - 2150 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 y

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 2150 - 2250 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 y

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 2250 - 2350 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 y

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 2350 - 2450 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 y

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 2450 - 2550 MeV

Data Odd function fit

17 ¡ PRELIMINARY ¡ W=1450-2550 MeV

SLIDE 18

y

P

* [degrees] φ 90 180 270 360 y

P

0.5
0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5 * = [-1.00 , -0.75] Θ cos W = 1550 - 1650 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 y

P

0.5
0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5 * = [-0.75 , -0.50] Θ cos W = 1550 - 1650 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 y

P

0.5
0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5 * = [-0.50 , -0.25] Θ cos W = 1550 - 1650 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 y

P

0.5
0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5 * = [-0.25 , 0.00] Θ cos W = 1550 - 1650 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 y

P

0.5
0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5 * = [0.00 , 0.25] Θ cos W = 1550 - 1650 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 y

P

0.5
0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5 * = [0.25 , 0.50] Θ cos W = 1550 - 1650 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 y

P

0.5
0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5 * = [0.50 , 0.75] Θ cos W = 1550 - 1650 MeV

Data Even function fit

* [degrees] φ 90 180 270 360 y

P

0.5
0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4 0.5 * = [0.75 , 1.00] Θ cos W = 1550 - 1650 MeV

Data Even function fit

x

P

* [degrees] φ 90 180 270 360 x

P

0.3
0.2
0.1

0.1 0.2 0.3 * = [-1.00 , -0.75] Θ cos W = 1450 - 1550 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 x

P

0.3
0.2
0.1

0.1 0.2 0.3 * = [-0.75 , -0.50] Θ cos W = 1450 - 1550 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 x

P

0.3
0.2
0.1

0.1 0.2 0.3 * = [-0.50 , -0.25] Θ cos W = 1450 - 1550 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 x

P

0.3
0.2
0.1

0.1 0.2 0.3 * = [-0.25 , 0.00] Θ cos W = 1450 - 1550 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 x

P

0.3
0.2
0.1

0.1 0.2 0.3 * = [0.00 , 0.25] Θ cos W = 1450 - 1550 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 x

P

0.3
0.2
0.1

0.1 0.2 0.3 * = [0.25 , 0.50] Θ cos W = 1450 - 1550 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 x

P

0.3
0.2
0.1

0.1 0.2 0.3 * = [0.50 , 0.75] Θ cos W = 1450 - 1550 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360 x

P

0.3
0.2
0.1

0.1 0.2 0.3 * = [0.75 , 1.00] Θ cos W = 1450 - 1550 MeV

Data Odd function fit

18 ¡ PRELIMINARY ¡ W=1450-‑1550 ¡MeV ¡, ¡cosΘ*=[-‑1,1] ¡ W=1550-‑1650 ¡MeV ¡, ¡cosΘ*=[-‑1,1] ¡

SLIDE 19

y

P

* [degrees] φ 90 180 270 360 y

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 * = [-1.00 , -0.75] Θ cos W = 1550 - 1650 MeV

Data Model calculation Odd function fit

* [degrees] φ 90 180 270 360 y

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 * = [-0.75 , -0.50] Θ cos W = 1550 - 1650 MeV

Data Model calculation Odd function fit

* [degrees] φ 90 180 270 360 y

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 * = [-0.50 , -0.25] Θ cos W = 1550 - 1650 MeV

Data Model calculation Odd function fit

* [degrees] φ 90 180 270 360 y

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 * = [-0.25 , 0.00] Θ cos W = 1550 - 1650 MeV

Data Model calculation Odd function fit

* [degrees] φ 90 180 270 360 y

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 * = [0.00 , 0.25] Θ cos W = 1550 - 1650 MeV

Data Model calculation Odd function fit

* [degrees] φ 90 180 270 360 y

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 * = [0.25 , 0.50] Θ cos W = 1550 - 1650 MeV

Data Model calculation Odd function fit

* [degrees] φ 90 180 270 360 y

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 * = [0.50 , 0.75] Θ cos W = 1550 - 1650 MeV

Data Model calculation Odd function fit

* [degrees] φ 90 180 270 360 y

P

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 * = [0.75 , 1.00] Θ cos W = 1550 - 1650 MeV

Data Model calculation Odd function fit

The comparison between

d a t a a n d t h e m o d e l prediction shows rather a lack of agreement

The data will help further

constrain the model for a better agreement

MODEL CALCULATION - DATA COMPARISON Effective Lagrangean Model (A. Fix)

19 ¡

SLIDE 20

Summary

Overview
f the methods used to analyze

double pion photo-production with circularly polarized photon beam off transversely polarized protons and to extract the polarization observables

5 polarization observables were extracted for

W=1450-2550 MeV

Comparison with the model shows some similarities with

general features of the data; the data will help constrain the model for a better agreement

Data will enter PWA study to help identify missing nucleon

resonances

20 ¡

SLIDE 21

SLIDE 22

EXTRA SLIDES

SLIDE 23

SLIDE 24

MvrtZ [cm]

10
5

5 10 15 20 Counts 1000 2000 3000 4000 5000 6000 7000

MVRTZ MVRTZ

Butanol( Events( Carbon( Events(

Photon selection

Butanol events: -3 cm < mvrtZ < +3cm Carbon events: +6cm < mvrtZ <+11cm

βcalc = p p p2 + m2

∆β = βmeas − βcalc

|∆t| < 1 ns

∆t = tCLAS − tT AGR

Analysis: Event Pre-selection

Momentum ¡[GeV/c} ¡ βmeas ¡ Δt ¡[ns] ¡ Events ¡

mvrtZ[cm] ¡

Events ¡

SLIDE 25

SLIDE 26

Electron beam: - longitudinally polarized:

beam energy: 3081.73 MeV

Photon beam: - circularly polarized

TAGGING ¡SYSTEM ¡[B. ¡A. ¡Mecking ¡et ¡al, ¡2003} ¡

Eγ ≈ [20% − 95%Ee] Eγ ≈ [0.5 − 3.0 GeV]

E-counter resolution:

0.001E0

¯ Pe = 87%

δJ = ¯ Pe (4Eγ/Ee) − (Eγ/Ee)2 4 − (4Eγ/Ee) + (3Eγ/Ee)2

σδJ ≈ 3.0%

9 ¡

SLIDE 27

TARGETS

Repolarized for each run group
Polarization checked via NMR

measurements

Polarization uncertainty <3.5%
FROzen Spin Target (FROST) - transversely polarized protons

(C4H9OH)

Carbon target: unpolarized, L=0.15 cm, 6 cm downstream
Polyethylene target: unpolarized, L=0.35 cm, 16 cm

downstream

¡ 10 ¡

h0ps://www.jlab.org/highlights/images/physics/CutawayAnnotated-‑LG.jpg ¡

SLIDE 28

Hao ¡Jiang ¡

SLIDE 29

7 ¡

Reaction plane

Figure ¡adapted ¡from ¡[Strauch, ¡2005] ¡

Polarization observables for circularly polarized photons off transversely polarized protons

J y

= 2[(Y 0¯ Λ180 + Y 180¯ Λ0) − (Y 0

cos 2α¯

Λ180 + Y 180

cos 2α¯

Λ0)](Y +0

sin α − Y −0 sin α + Y +180 sin α − Y −180 sin α )−

δJ[(Y 0¯ Λ180 + Y 180¯ Λ0)2 − (¯ Λ180Y 0

sin 2α + ¯

Λ0Y 0

sin 2α)2 − (Y 0 cos 2α¯

Λ180 + Y 180

cos 2α¯

Λ0)2]

−(¯ Λ180Y 0

sin 2α + ¯

Λ0Y 180

sin 2α)(Y +0 cos α − Y −0 cos α + Y +180 cos α − Y −180 cos α )

δJ[(Y 0¯ Λ180 + Y 180¯ Λ0)2 − (¯ Λ180Y 0

sin 2α + ¯

Λ0Y 180

sin 2α)2 − (Y 0 cos 2α¯

Λ180 + Y 180

cos 2α¯

Λ0)2]

P

J x

= 2 (¯ Λ180Y 0

sin 2α + ¯

Λ0Y 180

sin 2α)(Y +0 sin α − Y −0 sin α + Y +180 sin α − Y −180 sin α )−

δJ[(¯ Λ180Y 0

sin 2α + ¯

Λ0Y 0

sin 2α)2 − (Y 0¯

Λ180 + Y 180¯ Λ0)2 + (Y 0

cos 2α¯

SLIDE 32

Target ¡polarizakon: ¡(NMR_sign ¡Holding_magnet_sign) ¡e.g. ¡(+ ¡+) ¡and ¡(-‑ ¡-‑) ¡means ¡pos.sign; ¡(+ ¡-‑) ¡ and ¡(-‑ ¡+) ¡means ¡neg.sign ¡

SLIDE 33

2 M−∗ 4

M+

2 M+∗ 4 )

SLIDE 34

SLIDE 35

Observables odd/even behavior fit check

SLIDE 36

SLIDE 37

Target polarization orientation angle

SLIDE 38

SLIDE 39

SLIDE 40

SLIDE 41

I

* [degrees] φ 90 180 270 360

I

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 1450 - 1550 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360

I

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 1550 - 1650 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360

I

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 1650 - 1750 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360

I

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 1750 - 1850 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360

I

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 1850 - 1950 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360

I

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 1950 - 2050 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360

I

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 2050 - 2150 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360

I

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 2150 - 2250 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360

I

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 2250 - 2350 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360

I

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 2350 - 2450 MeV

Data Odd function fit

* [degrees] φ 90 180 270 360

I

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 W = 2450 - 2550 MeV

Data Odd function fit

SLIDE 42

MODEL CALCULATION AND DATA COMPARISON Effective Lagrangean Model (A. Fix)

Nucleon and Delta Born terms, Resonances Δ(1232), N*(1440),

N(1520) , N(1535), Δ(1620), N(1675), N(1680), N(1700), N(1720)

[A.Fix, ¡H. ¡Arenhövel, ¡Eur.Phy. ¡J.A ¡25, ¡115 ¡(2005)] ¡

23 ¡

The model takes as an input the four momentum vectors of the

incident and the final state particles and calculates the differential cross-section in the center of mass frame

SLIDE 43

SYSTEMATIC UNCERTAINTIES

17 ¡