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3 Introduction Elastic scattering from spin ½ target (one photon exchange approx.) where: Use Bodek (Jour. Phys 110 (2008) ) for more realistic, more conservative estimate of count rates (Lagrange polynomial corrections to Kelly fit satisfying asymptotic quark-hadron duality constraints)
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PR10-005
Precision Measurement of the Neutron Magnetic Form Factor at
Q2=16 and 18 (GeV/c)2 by the Ratio Method
Brian Quinn/Carnegie Mellon Univ.Bogdan Wojtsekhowski/JLabRon Gilman/Rutgers Univ.
Carnegie Mellon/ JLab/ Rutgers/ William and Mary/ Santa Maria/ Norfolk/ Glasgow/ Ljubljana/ Richmond/ Kharkov/ U.N.H./ N.C. Central/ Saint Mary’s/ UVa/ Yerevan/ Florida International/ INFN/ Novosibirsk/
Tel Aviv/ Cal State/ MIT/ Edinburgh/ TempleThe Hall A Collaboration
2
Context‘Sister’ experiment to E12-09-019Two highest points not approved by PAC34Improved experiment with modified design:
BigHAND HCal – Higher luminosity– Higher (more uniform)
efficiency– Better spatial resolution– Reduced beam time
Efficient to run contiguously
2Q
( , ' )d e e N
3 Introduction
2 2MottE M
d G Gd
Elastic scattering from spin ½ target (one photon exchange approx.)
/2)(sin21
12
NME
21 1 2(1 )tan ( / 2)
22 4/ NMQwhere:
2
222
2( ) and ( ) are Sachs Electric and Magnetic form factors.
Scaling aproximation: G and G
where 1/ 1 / 0.71 GeV/c is empirical Dipole parameterization of
Nucleon:
p
E M
p nM D
D
MD n
pE
G Q G Q
G G
G Q G
Use Bodek (Jour. Phys 110 (2008) 082004) for more realistic, more conservative estimate of count rates(Lagrange polynomial corrections to Kelly fit satisfying asymptotic quark-hadron duality constraints)
4 Projected results(Projected E09-019 and present proposal plotted at Bodek prediction)
Proposed
5 MotivationTheory Review: The theoretical interest in extending this measurement to the highest possible is very general and unassailable.2Q• Among the simplest, most fundamental of hadronic observables• Helps provide definitive test of nucleon structure theory(With proton form factor, gives access to isovector form factor, which is ‘easy’ case for lQCD.)• Comparison of neutron magnetic form factor to proton magnetic form factor of particular interest
- Compare high scaling behavior- Extract magnetic form factor for each quark species
• Quark transverse charge density of neutron related to magnetic formfactor
• Sets sum rule for GPD measurements/predictions
2Q
01
12
1 1) where F( ) ( ( )2 E MdQ bQ F Q GQ GJ
6 TechniqueRatio Method:Measure quasi-elastic scattering from deuteron tagged by coincident nucleon: d(e,e’p) and d(e,e’n)
1
2 2Mott
( , ')
nEn
MG
dd
G
e ep
Many systematic effects (experimental and theory) cancel in ratio.
nucl.
corr.
( , ' ) ( , ')
( , ' ) ( , ')
''d dd d
d dd d
d e e e e
d e e e e
n
p p
nR
Expect very small correction for Electric because small form factor and large kinematic weighting of Magnetic
neutron
Electric
2
Mott/
( , ')
dd
Mn
e ep
GR
7 Nuclear CorrectionsCorrections to d(e,e’n) and d(e,e’p) almost identical cancel in ratioArenhovel (low Q2) finds small (<1% when wide-angle tail is cut)
corrections at 1 GeV/c and decreasing at larger Q2
Q2 (GeV/c) FSI corr.
1 0.99980
2 0.99971
3 0.99966
4 0.99962
5 0.99962
S. Jeschonnek found ratio of full calc (S. Jeschonnek and
J.W. Van Orden Phys. Rev. C 62 (2000) 044613) to PWIA calc. for Kinematics of earlier CLAS e5 measurements.Ratio almost identical for n and p tiny corrections
Additional nuclear effects due to Fermi motion manifest as PWIA calculation of coefficients a,b,c, and d:
PWIA
2 22 2
Free2 2 2 2 c.f.
n nn nM EM E
p p p pM E M E
G Ga G b GR R
c G d G G G
Q2 (GeV/c) PWIA corr.
16 1.0032
18 1.0046
Using Jechonnek’s code, found RPWIA/RFree (neglecting neutron Electric form factor) for planned kinematics and cuts. < 0.5%
8 Two-photon CorrectionsUsual complication of two-photon corrections is for separation of small form factor from large one. Small epsilon-dependence has big effects. We extract the larger Magnetic form factor.
2 2Mott( , ')
( , ') ( , ')
(1 )
(1 )En n
M
dGd
d dd d
Ge e
p pe e
n
e e
n
p
IR divergentp (full)n
Corrections may not tend to cancel in ratio (P.G. Blunden, W. Melnitchouk and J.A.Tjon,
Phys. Rev. C 72 (2005) 034612). Recent results at these kinematics: Q2=16 GeV2 n-p=-0.15% Q2=18 GeV2 n-p = 1.8 %Not specific to ratio technique, affect any elastic cross section measurement at these kinematics
9 SystematicsRatio Method is insensitive to:•Target thickness•Target density•Beam current•Beam structure•Live time•(electron) trigger efficiency•Electron track reconstruction•Electron acceptance
Important to understand:•Neutron efficiency/proton efficiency HCal almost ideal•Neutron acceptance/proton acceptance
( , ' )
( , ' )
''dd
dd
nd e e
d e pe
R
10 Kinematics Q2 (GeV/c)2
Ebeam (GeV)
e
(deg.)
N
(deg.)
Escatt (GeV)
PN (GeV/c)
16 11 51.1 10.7 2.5 9.418 11 65.2 7.0 1.4 10.5
11 Apparatus BigBite Spectrometer
Instrumented with: -GEM planes from SBS-Electromagnetic Cal.-Gas Cerenkov-timing planesAllows high luminosity
38 22.8 10 / A /s/cm (44 A on d) L
12 Apparatus (2)Hadron Calorimeter (HCal) to be built for Super BigBite Spectrometer (SBS) provides ideal replacement for BigHAND stack• Iron/scintillator sampling calorimeter• 11X22 identical modules• High energy-deposition
- High threshold- High Luminosity
• Excellent spatial resolution
- Tight cut on nucleondirection (wrt q-vector)
• High efficiency for n and p
- Nearly equal (cancelin ratio)
Iron
Scintillator
13 Apparatus (3)
Hadron Calorimeter (HCal)
Background estimates (7 degrees)
50 MeV(ee) threshold<0.5 MHz (in 3X3 cluster)<0.5% accidental coincidence
14 Apparatus (4)
x=y=3 cm
Q2=16 (GeV/c)2
n=95.6n/p=0.988
Q2=18 (GeV/c)2
n=95.5n/p=0.990
Results from Geant4 Simulation(matches published results forCOMPASS calorimeter).Assume identical modules, 3X3 clustersize for hits
15 n/p identificationBig Ben dipole deflects protons so event-by-event displacement from q-vector direction is ~68 cm
Q2=16 (GeV/c)2
‘kick’=375 MeV/cQ2=18 (GeV/c)2
‘kick’=442 MeV/c
Simulated quasi-elastic neutron and proton hits (shown separately)
16 SimulationQuasi-elastic• On shell spectator(Struck nucleon off shell)• Boost to struck nucleon rest frame• Isotropic distribution
-Weighted by cross section (using Bodek parameterization)• Boost back to lab• Fold in resolution, make (weighted) increment of spectra
Inelastic• GENEV physics Monte Carlo (Genoa/CLAS)• On-shell initial nucleons (with Fermi momentum)• Boost to struck nucleon rest frame• Generate GENEV event (with boosted beam energy)• Boost back to lab• Fold in resolution, increment (un-weighted) spectra
Inelastic normalized empirically to quasi-elastic
17
Simulation Results
Q2 = 18 (GeV/c)2 results without cuts on pq
18
Simulation Results (2)
Q2 = 18 (GeV/c)2: W2 spectra for different cuts on pq
p
n
n n
p p
Assume 20% systematicerror on these estima
34%
tes(correlat
2
)
0%
ed
bs b
bs b
19 Error estimates. Q2 (GeV/c)2 16 18
Proton x-sect (%) 1.7 4.Neutron electric f.f. 0.89 0.39Nuclear (FSI and PWIA) - -Two-photon 1. 2.Accidental 0.16 0.11Target windows 0.2 0.2Acceptance 0.16 0.11Inelastic 4.7 5.4Nucleon mis-ID 0.5 0.5Hcal efficiency 0.5 0.5Statistical error on R(%) 2.5 4.1Total error on Gn
M(%) 2.8 4.1
Contributions(in %) to systematicerror on R
20 Beam RequestQ2 (GeV/c)2 16 18e (deg.) 45.1 65.2
N (deg.) 10.7 7.0
LD2 44A 96 192
Dummy 44A 8 16LH2 75A 6 12
LH2 37A 2 6
LH2 75A BigBen off 6 12
Total 118 238 356 hours Commissioning 01 Energy change 82 Angle changes 20
384hr (16 days)
21 Projected results(Projected E09-019 and present proposal plotted at Bodek prediction)
Proposed
22 Neutron statistics(Projected E12-09-019 and present proposal plotted at Bodek
prediction c.f. CLAS12 with Bodek or Alberico)
23 Backup Slides.
24
Simulation Results
Q2 = 16 (GeV/c)2 results without cuts on pq
25
Simulation Results
Q2 = 16 (GeV/c)2: W2 spectra for different cuts on pq
p
n
n n
p p
Assume 20% systematicerror on these estima
28%
tes(correlat
1
)
4%
ed
ss b
ss b
26
27 TechniqueRatio Method:Measure quasi-elastic scattering from deuteron tagged by coincident nucleon: d(e,e’p) and d(e,e’n)
nucl.
corr. 1
neutron
Electric
2 2Mott
2
Mott/
( , ' ) ( , ')
( , ' ) ( , ') ( , ')
( , ')
''
n nE M
d dGd d
d d dd d d
G
dd
M
d e e e e
d e e e ep e e
e e
p
n n
n
p
p
G
R
R
Many systematic effects (experimental and theory) cancel in ratio.Expect very small correction for Electric because small form factor and large kinematic weighting of Magnetic