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
David Anez – June 9th, 2011 3/19
Motivation: Constituent Quark Model
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
David Anez – June 9th, 2011
Motivation: Constituent Quark Model
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
David Anez – June 9th, 2011 6/19
Multipole Amplitudes
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
David Anez – June 9th, 2011 7/19
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
David Anez – June 9th, 2011 10/19
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
David Anez – June 9th, 2011 11/19
High Resolution Spectrometers
Vertical drift chambers Particle tracking
Scintillators Timing information Triggering DAQ
Gas Cerenkov detectors Particle identification
Lead glass showers Particle identification
David Anez – June 9th, 2011 12/19
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
David Anez – June 9th, 2011 13/19
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
David Anez – June 9th, 2011 14/19
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
David Anez – June 9th, 2011 16/19
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
David Anez – June 9th, 2011 17/19
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
David Anez – June 9th, 2011 18/19
Work Still to Do
Calibration Analysis: May 2011 Data Analysis: January 2012 Doctoral Thesis: December 2012 Published Paper: 2014?
David Anez – June 9th, 2011 19/19
Motivation: Constituent Quark Model
One-body interactions
Two-body interactions
i
iiii
iii rzerYreQ 223
1
20
2]1[ 3
5
16ˆ
3
1]2[ 3ˆ
jijijzizieBQ
David Anez – June 9th, 2011
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
David Anez – June 9th, 2011
Kinematics – Electronic Vertex
Momentum transfer, Q2
)( 2222 qqQ
2sin4 22 eEEQ
David Anez – June 9th, 2011
Kinematics – Hadronic Vertex
Recoil proton Energy Ep
Momentum pp
Angle θpq
Recoil pion Energy Eπ
Momentum pπ
Angle θπ
Not detected
pp
p
David Anez – June 9th, 2011
Kinematics – Planes
Scattering plane – ki and kf
Recoil plane – pp and pπ
Azimuthal angle – pq
ik
fk
pp
p
David Anez – June 9th, 2011
Multipole Amplitudes
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
David Anez – June 9th, 2011
Response Functions
Unpolarized cross section made up of four independent partial cross sections
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
David 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
David Anez – June 9th, 2011
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
Original Phase Space PlotsQ2 = 0.090 (GeV/c)2 (θpq
* = 40°)
W vs θpq*
W vs Q2
Q2 vs θpq*
Q2 vs θpq*
W ± 5MeV
Original Phase Space PlotsQ2 = 0.125 (GeV/c)2 (θpq
* = 30°)
W vs θpq*
W vs Q2
Q2 vs θpq*
Q2 vs θpq*
W ± 5MeV
Original Phase Space PlotsQ2 = 0.125 (GeV/c)2 (θpq
* = 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
Revised Phase Space PlotsQ2 = 0.090 (GeV/c)2 (θpq
* = 45°)
W vs θpq*
W vs Q2
Q2 vs θpq*
Q2 vs θpq*
W ± 5MeV
Revised Phase Space PlotsQ2 = 0.125 (GeV/c)2 (θpq
* = 30°)
W vs θpq*
W vs Q2
Q2 vs θpq*
Q2 vs θpq*
W ± 5MeV