david anez saint mary ’ s/dalhousie university december 10, 2012
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E08-010: 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
December 10, 2012
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 - December 10, 2012 2/30
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 - December 10, 2012 3/30
Motivation: Constituent Quark Model
Magnetic Dipole (M1 / ) Spin-flip Dominant
2/31M
David Anez - December 10, 2012 4/30
Electric quadrupole (E2 / ) Coulomb quadrupole (C2 / )
Only with virtual photons
Motivation: Constituent Quark Model
2/31E
2/31S
11 LqS
David Anez - December 10, 2012 5/30
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 - December 10, 2012 6/30
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 - December 10, 2012 7/30
World Data and Models
David Anez - December 10, 2012 8/30
World Data and Models
David Anez - December 10, 2012 9/30
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 - December 10, 2012 10/30
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 - December 10, 2012 11/30
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 - December 10, 2012 12/30
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 - December 10, 2012 13/30
The Experiment
Jefferson Lab, Hall A Feb 27th – Mar 8th, 2011 1160 MeV e− beam 4 & 15 cm LH2 target Two high resolution
spectrometers HRSe and HRSh
David Anez - December 10, 2012 14/30
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 - December 10, 2012 15/30
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 - December 10, 2012 16/30
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 - December 10, 2012 17/30
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%
David Anez - December 10, 2012 18/30
Calibrations – Beam Current
BCM Calibration Runs Kinematic 2, March 3rd
80 µA to 0.2 µA CODA Run 2252, MCC Run
170 Match Faraday Cup Current
to OLO2 Current CODA Run 2254, MCC Run
173 Match BCM Voltages to
OLO2 Current Bypassed Unser Coil
David Anez - December 10, 2012 19/30
Calibrations – Beam Position
BPM Calibration Runs Feb 19th – Runs 1579-1599 May 4th – Runs 4139-4149
BPM Code Determine pedestals Measure means Calculate coefficients Check calculations Determine raster constants
David Anez - December 10, 2012 20/30
Calibrations – Boiling Test
Boiling Test Runs Kinematic 12, Mar 6th Runs 2439-2447 10 µA to 80 µA, 4cm target
HAPPEX Luminosity Scintillators Downstream of target
David Anez - December 10, 2012 21/30
Calibrations – Vertical Drift Chambers
VDC Code Find maximum Find largest slope
David Anez - December 10, 2012 22/30
Calibrations – Mispointing
Target and Optical Survey JLab Alignment Group Feb 11th
BeO Target Runs Each kinematic
David Anez - December 10, 2012 23/30
Calibrations – RHRS Gas Cerenkov
Particle Identification – Electrons
David Anez - December 10, 2012 24/30
Calibrations – LHRS Pion Rejector
Particle Identification – Protons
David Anez - December 10, 2012 25/30
Calibrations – RHRS Shower/Preshower
Particle Identification – Electrons
David Anez - December 10, 2012 26/30
Coincidence Timing
Online Analysis Difference of BB T3 & T1
Offline Analysis Difference of LHRS T3 & T1 S2m Timing Difference
David Anez - December 10, 2012 27/30
Coincidence Timing
LHRS Double Peak Problem Due to S1 miswiring
RHRS Double Peak Problem Due to S2 miswiring
Both solved by subtracting local T1
David Anez - December 10, 2012 28/30
Coincidence Timing
Red: No other corrections, shifted +80 ns Green: Pathlength corrections Blue: Pathlength corrections and calibration offsets
David Anez - December 10, 2012 29/30
Still To Do
Cut Determination Process Raw Data Calculate Efficiencies Calculate Systematic Errors Produce Simulation Data Extract Cross Sections Thesis – Summer 2013 Paper – Summer 2013
David Anez - December 10, 2012 30/30
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
Motivation: Constituent Quark Model
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
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
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
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