David Anez Saint Mary’s/Dalhousie University June 9, 2011

Measurement of the Coulomb quadrupole amplitude in the γ*p→Δ(1232) reaction in the low momentum transfer region

David Anez

Saint Mary’s/Dalhousie University

June 9, 2011

Introduction

Took measurements of the p(e,e′p)π0 (pion electroproduction) reaction In the low Q2 region where the pion cloud is expected

to dominate With center-of-mass energies near the Δ resonance to

look at the transition amplitudes between the nucleon and the delta

To better understand the Coulomb quadrupole transition amplitude behavior in this region and how it affects nucleon deformation

David Anez – June 9th, 2011 2/19

Motivation: Constituent Quark Model

Wave functions created

21

23

21

21 2,0,939 JLSaJLSaN DS

23

21

23

23 2,0,1232 JLSbJLSb DS



Magnetic Dipole (M1 / ) Spin-flip Dominant

David Anez – June 9th, 2011

2/31M

4/19

Electric quadrupole (E2 / ) Coulomb quadrupole (C2 / )

Only with virtual photons



2/31E

2/31S

11 LqS

5/19

Multipole Amplitudes

γN-Multipoles Initial State Excited State Final State πN-Multipoles

C, E, M N* I2I2J Δ Lℓ±, Eℓ±, Mℓ±

C0 0+ 1⁄2+ 1⁄2+ P11 P311⁄2+ 1+ L1−

C1,E1 1− 1⁄2+ 1⁄2− S11 S311⁄2+ 0− L0+, E0+

1⁄2+ 3⁄2− D13 D331⁄2+ 2− L2−, E2−

M1 1+ 1⁄2+ 1⁄2+ P11 P311⁄2+ 1+ M1−

1⁄2+ 3⁄2+ P13 P331⁄2+ 1+ M1+

C2, E2 2+ 1⁄2+ 3⁄2+ P13 P331⁄2+ 1+ L1+, E1+

1⁄2+ 5⁄2+ F15 F351⁄2+ 3+ L3−, E3−

M2 2− 1⁄2+ 3⁄2− D13 D331⁄2+ 2− M2−

1⁄2+ 5⁄2− D15 D351⁄2+ 2− M2+

L

Ns RJ

INs



E1+ and S1+ at same magnitude as background amplitudes

Measure ratio to dominant M1+

EMR =

CMR =

2

1

1*1

2/31

2/312/3 Re

Re

M

ME

M

EREM

2

1

1*1

2/31

2/312/3 Re

Re

M

MS

M

SRCM


World Data and Models





Q2 = 0.045 (GeV/c)2

New lowest CMR value θe = 12.5°

Q2 = 0.125 (GeV/c)2

Validate previous measurements

Q2 = 0.090 (GeV/c)2

Bridge previous measurements


The Experiment

Jefferson Lab, Hall A February 27th – March 8th,

2011 1160 MeV e− beam 4 & 15 cm LH2 target Two high resolution

spectrometers HRSe and HRSh


High Resolution Spectrometers

Vertical drift chambers Particle tracking

Scintillators Timing information Triggering DAQ

Gas Cerenkov detectors Particle identification

Lead glass showers Particle identification


Original Kinematic Settings# Q2 (GeV/c)2 W (MeV) (MeV/c) (MeV/c) I (µA) L (cm) Q (mC) Time (hrs)

1 0.041 1221 0 12.52 767.99 24.50 547.54 75 6 405 1.5

2 0.041 1221 30 12.52 767.99 12.52 528.12 75 6 540 2

3 0.041 1221 30 12.52 767.99 36.48 528.12 75 6 945 3.5

4 0.041 1260 0 12.96 716.42 21.08 614.44 75 6 405 1.5

5 0.090 1230 0 19.14 729.96 29.37 627.91 75 6 405 1.5

6 0.090 1230 40 19.14 729.96 14.99 589.08 75 6 810 3

7 0.090 1230 40 19.14 729.96 43.74 589.08 75 6 1215 4.5

8 0.125 1232 0 22.94 708.69 30.86 672.56 75 6 945 3.5

9 0.125 1232 30 22.94 708.69 20.68 649.23 75 6 1890 7

10 0.125 1232 30 22.94 708.69 41.03 649.23 75 6 1890 7

11 0.125 1232 55 22.94 708.69 12.52 596.43 75 6 945 3.5

12 0.125 1232 55 22.94 708.69 49.19 596.43 75 6 945 3.5

13 0.125 1170 0 21.74 788.05 37.31 575.57 75 6 810 3

14 0.125 1200 0 22.29 750.16 34.06 622.63 75 6 540 2

Configuration changes 17

Calibrations 8

Total: 72

*pq e eP p pP


Revised Kinematic Settings# Q2 (GeV/c)2 W (MeV) (MeV/c) (MeV/c) I (µA) L (cm) Q (mC) Time (hrs)

1 0.045 1221 0 12.5 805 25.5 552 50 4 608 3.5

2 0.045 1221 33 12.5 805 12.5 528 50 4 810 4.5

3 0.045 1221 33 12.5 805 38.5 528 50 4 1418 8

4 0.045 1260 0 13 755 22 618 50 4 608 3.5

5 0.090 1230 0 18 770 30 626 50 15 162 1

6 0.090 1230 45 18 770 13.5 576 50 15 324 2

7 0.090 1230 45 18 770 46 576 50 15 486 3

8 0.125 1232 0 22 750 31.5 670 50 15 378 2.5

9 0.125 1232 30 22 750 21 646 50 15 756 4.5

10 0.125 1232 30 22 750 41.5 646 50 15 756 4.5

11 0.125 1232 55 22 750 13 591 50 15 378 2.5

12 0.125 1232 55 22 750 50 591 50 15 378 2.5

13 0.125 1170 0 20.5 826 37.5 574 50 15 324 2

14 0.125 1200 0 21 789 34.5 621 50 15 216 1.5

*pq e eP p pP


Actual Kinematic Settings# Q2 (GeV/c)2 W (MeV) (MeV/c) (MeV/c) I (µA) L (cm) Q (mC) Time (hrs)

1 0.045 1221 0 12.5 805 25.5 552 15 4 636 19

2 0.045 1221 33 12.5 805 12.5 528 15 4 849 18

3 0.045 1221 33 12.5 805 38.5 528 20 4 1416 17

4 0.045 1260 0 13 755 22 618 50 4 0 0

5 0.090 1230 0 18 770 30 626 80 4 642 3

6 0.090 1230 45 18 770 13.5 576 40 4 1296 10

7 0.090 1230 45 18 770 46 576 80 4 1861 8

8 0.125 1232 0 22 750 31.5 670 80/40 4/15 914 5

9 0.125 1232 30 22 750 21 646 30 15 652 6

10 0.125 1232 30 22 750 41.5 646 50 15 758 5

11 0.125 1232 50 22 750 14.5 606 55 4 1436 8

12 0.125 1232 50 22 750 48 606 80 4 1365 6

13 0.125 1170 0 20.5 826 37.5 574 35 15 285 3

14 0.125 1200 0 21 789 34.5 621 35 15 220 2

*pq e eP p pP

85%

85%

15/19David Anez – June 9th, 2011

Response Functions

Unpolarized cross section made up of four independent partial cross sections

TTLTTLef q

k

dddk

d

0*

5

LSL R

TT R

** cossin12 pqpqLTSLT R

**2 2cossin pqpqTTTT R


Response Functions

1*1

2

12

11*01

*1

2

1

2

1

2

02

2

Recos124Recos2Re44 LLLLLLLLLLLQ

R cmL

111*0

2

111212

11212

0 3Recos232 MMEEMMEMMERT

2

111212

11212

1112 323cos MMEMMMME

1*1111

*10

*1

*1111

*02

2

cos623Resin ELMMELELLMMELQ

R cmLT

1*111

*1

2

1212

1232 Resin3 MMMMEMERTT


Response Functions

Truncated Multipole Expansion

Model Dependent Extraction Fit theoretical model to existing data Insert model values for background amplitudes

1*11

*1

2

1212

1*11

*0

2

12

23

1*0

2

125

Resin3

cos6Resin

cosRecos2

0

MMMEMR

MLMLR

MMEMR

R

TT

LT

T

L


Work Still to Do

Calibration Analysis: May 2011 Data Analysis: January 2012 Doctoral Thesis: December 2012 Published Paper: 2014?



One-body interactions

Two-body interactions

i

iiii

iii rzerYreQ 223

1

20

2]1[ 3

5

16ˆ

3

1]2[ 3ˆ

jijijzizieBQ



Pion Cloud


Kinematics – Electronic Vertex

Incoming electron Energy E Momentum ki

Scattered electron Energy E′ Momentum kf

Angle θe

Virtual photon Energy ω Momentum q Angle θq

ik

fk

q


Kinematics – Electronic Vertex

Momentum transfer, Q2

)( 2222 qqQ

2sin4 22 eEEQ


Kinematics – Hadronic Vertex

Recoil proton Energy Ep

Momentum pp

Angle θpq

Recoil pion Energy Eπ

Momentum pπ

Angle θπ

Not detected

pp

p


Kinematics – Planes

Scattering plane – ki and kf

Recoil plane – pp and pπ

Azimuthal angle – pq

ik

fk

pp

p



General form of πN Multipoles: X – type of excitation (M, E, S) I – isospin of excited intermediate state ℓ± – JΔ = ℓ ± 1⁄2

Magnetic dipole – M1 / Electric quadrupole – E2 / Coulomb quadrupole – C2 /

2/31E

2/31S

11 LqS

2/31M

IX


Response Functions


p

p

m

mWk

2

22

TTLTTLef q

k

dddk

d

0*

5

1

1

2 22 Q

k

k

k

i

f

1

22

2

2tan21

e

Q

q

22

222

4 m

W

mmWk p

W

mWq p

2

22

0

2

2

q

QS


Response Functions


TTLTTLef q

k

dddk

d

0*

5

LSL R

TT R

** cossin12 pqpqLTSLT R

**2 2cossin pqpqTTTT R


Original Phase Space PlotsQ2 = 0.041 (GeV/c)2 (θpq

* = 30°)

W vs θpq*

W vs Q2

Q2 vs θpq*

Q2 vs θpq*

W ± 5MeV


* = 40°)

W vs θpq*

W vs Q2

Q2 vs θpq*

Q2 vs θpq*

W ± 5MeV


* = 30°)

W vs θpq*

W vs Q2

Q2 vs θpq*

Q2 vs θpq*

W ± 5MeV


* = 55°)

W vs θpq*

W vs Q2

Q2 vs θpq*

Q2 vs θpq*

W ± 5MeV

Revised Phase Space PlotsQ2 = 0.045 (GeV/c)2 (θpq

* = 33°)

W vs θpq*

W vs Q2

Q2 vs θpq*

Q2 vs θpq*

W ± 5MeV


* = 45°)

W vs θpq*

W vs Q2

Q2 vs θpq*

Q2 vs θpq*

W ± 5MeV


* = 30°)

W vs θpq*

W vs Q2

Q2 vs θpq*

Q2 vs θpq*

W ± 5MeV


* = 55°)

W vs θpq*

W vs Q2

Q2 vs θpq*

Q2 vs θpq*

W ± 5MeV

Documents

David Anez Saint Mary’s/Dalhousie University June 9, 2011