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Real Compton Scattering from the Protonin the Hard Scattering Regime
Alan M. NathanSLAC Experimental Seminar
December 2, 2003
I. Compton Scattering from Nucleon at Large p
• Reaction Mechanisms
• Nucleon Structure
II. JLab E99-114
• the experiment
• preliminary results
III. Summary & OutlookPh.D. Students:
A. Danagoulian, D. Hamilton, V. Mamyan, M. Roedelbronn
Hard Scattering Regime (s, -t, -u >> m2)(p large)
Factorization:
amplitude hard soft
calculable in pQCD
nonperturbative structureprocess-independent
Real Compton Scattering on the Nucleonin the Hard Scattering Limit
Some Possible Factorization Schemes
• hard gluon exchange: *3 active quarks*2 hard gluons*3-body “form factor”
• handbag: *1 active quark*0 hard gluons*1-body form factor
The physics issues: • Which, if either, dominates at few GeV?• What does RCS teach us about nucleon structure?
I. Asymptotic (pQCD) Mechanism
Brodsky/LePage, Kronfeld, Vanderhaeghen, Dixon ...
• momentum shared by hard gluon exchange
• 3 active quarks
• valence configuration dominates
• soft physics in distribution amplitude (x1, x2, x3)
• constituent scaling: d/dt = f(CM)/s6
• dominates at “sufficiently high energy”
ydxdyyxKx
)φ(),()(φ
Constituent Scaling
ts
d
d6 s6d/dt
Cornell data approximately support scaling but...When is this the dominant mechamism?
Asymptotic (symmetric) DAx1 x2 x3
KS
COZCornell 1977 data
II. “Handbag” Mechanism
• One active parton—rest are spectators
• Momentum shared by soft overlap: GPD’s
• Central assumptions:
-- s,-t,-u >> m2
-- struck quark nearly real and ~co-linear with proton
• Formally power correction to leading-twist
-- asymptotically subdominant but ...
(Radyushkin; Diehl, Kroll, et al.)pQCD
Generalized PartonDistribution
Handbag Description of RCS
See Kroll, hep-ph/0110208
Various approximations improve
as s,-t,-u m2
• Factorization is simple product
• Hard scattering: Klein-Nishina (KN) from nearly on-shell parton
• Soft physics: form factors RV(t), RA(t)
|RV +/- RA|2 :
active quark spin parallel/antiparallel to proton spin
• Important feature: /KN ~ s-independent at fixed t
)(R)1()(Rd
dd
d 2A
2V
KN
tftftt VV
KN
Rv,RA,RT
0
0.005
0.01
0.015
0.02
0.025
8 9 10 11 12
d/dKN
s (GeV2)
-t = 4 GeV2
pQCD (x70)
handbag
RCS and Form Factors: GPD’s
2a
a
1 aa
( ) e ( , 0, )
( ) e ( , 0, )
( ) ( , 0,0)
V a
a
a a
dxR t H x t
x
F t H x t dx
q x H x
Generalized Parton Distributions
(GPD’s)
links among diverse processes
GPD x-1 moment x0 moment t=0 limit
Rv(t) F1(t) q(x)
RA(t) GA(t) q(x)
RT(t) F2(t) 2J(x)/x - q(x)
H (x, =0, t)
H (x, =0, t)
E(x, =0, t)
RCS sensitive to unskewed (=0) GPD’s at high –t, moderate x
• R ~ 1/t2 for -t = 3-10 GeV2 n 6 scaling (accidental!)
d/dt ~ s-2t-4
• Asymptotically R ~ 1/t4 n 10 scaling
ultimately subdominant (when?)• Handbag gives right order of magnitude for Cornell data
Scaling of Cross Sections at fixed CM :
d/dt ~ (1/s)2 R2(t)
-1
-0.5
0
0.5
1
0 40 80 120 160
ALL
CM
(deg)
handbag
pQCD
point
int A
V
R
Rpo
LL LL LLK A A
Polarization of Recoil Proton: Longitudinal
p
p
γ
γ
Robust prediction: depends only on ratio of form factors
-LT LTK A
2
1
2 2
LT T
LL V
K R Ft t
K M R M F
• RT : hadron helicity flip
• pQCD:
-t F2/F1 ~ constant
• JLab GEp expt:
-t½F2/F1 ~ constant
• Does RT/RV behave similarly?
pQCD
-KLT
Polarization of Recoil Proton: Transverse
Goals of JLab E99-114
• Measure cross sections to 5% + 5% over broad kinematic range of s, t
--/KN vs. s @ fixed t
--1/sn @ fixed cm
--detailed comparison with handbag
• Measure KLL and KLT at s=7, -t=4
1
2
3
4
5
6
7
4 6 8 10 12
70o
90o
110o130o
s (GeV2)
-t (GeV2)
2
2
3.5 5.7 GeV
6 12 GeV
1.5 7 GeV
E
s
t
Experimental SetupKinematic Range:
e-
Experiment ran in Hall A in 2002
• mixed e- beam e-p/RCS discrimination needed background & calibrations
• good angular resolution• FPP
γ
Polarimeter
Proton Spectrometer
LH2e- Radiator
Deflection magnet Lead-Glass Calorimeter
e
e-
γ
Some Experimental Details
• e- beam: 5-40 A, 2.5-5.75 GeV, 75% polarization
• radiator: 6% Cu, 10 cm from target
• target: 15 cm LH2
• beam: 1013 sec-1 equivalent photons
• deflection magnet: 10 cm, 1 T
• calorimeter: 704 blocks, 4 cm x 4 cm x 40 cm lead glass
• proton spectrometer: HRS-L, =6 msr, Pp4.3 GeV/c
• proton polarimeter: 6 MWDC’s, 60 cm CH2, 60 cm C
Event Identification
RCSdeflected ep
0
e or
p
1/2 = m/E
'e'
RCS: p(,)pep: p(e,e)p
0: p(,0)p
t
y x
x vs E
RCS Event Identification
RCSep
0
0
RCS+ep
=270o • max sensitivity to L,T• no sensitivity to N
Analyzing the Recoil Proton Polarization:Proton Spin Precession
FPP
Analyzing the Recoil Proton Polarization:Focal Plane Polarimeter
spin-orbit interaction
•FPP calibration from ep•Transformation from Lab to CM
L and T get mixed•Dilution due to 0 background
easily measured
KLL consistent with single-quark mechanism with active quark carrying proton spin (RA Rv)
Longitudinal Polarization Transfer:Preliminary Result from E99-114…final results by Fall 2003
Kroll
-1
-0.5
0
0.5
1
0 40 80 120 160
ALL
CM
(deg)
handbag
pQCD
point
KLL
int A
V
R =
Rpo
LL LLK A
VanderhaeghenDixon
• K LL KRCSLL KKN
LL
• predicted by handbag• five more points measured but not yet analyzed (75o-130o)
Transverse Polarization Transfer:Preliminary Result from E99-114
pQCD
Conclusion:
RT/RV (0.50.4) F2/F1
= 0.21 0.152
T
V
Rt
M R
Calculation by Kroll
-KLT
Hard to draw any conclusions with this precision
this and the next few slides show preliminary cross sections(good to about 20%)
0.1
1
10
100
60 80 100 120 140
s6d/dt (b-GeV10)
cm
(deg)
s=7 s=9 s=11
asymptotic
KS
CZ
• s-6 scaling at fixed CM works only approximately• Leading twist still badly underestimates cross section
nCM s)f(θ
dt
dσ
0.001
0.01
0.1
2 3 4 5 6 7 8
d/dKN
-t (GeV2)
s=7
s=9
s=11
d/dKN
Prediction of s-independence at fixed t not well followedBut...
Preliminary Cross Sections
0.001
0.01
0.1
2 3 4 5 6 7 8
d/dKN
-t (GeV2)
s=7
s=9
s=11
s,-t,-u > 2.5 GeV 2
Preliminary Cross Sections
• Prediction of s-independence at fixed t not well followed• But...not so bad for data with s,-t,-u > 2.5 GeV2
• Higher energy data would be desirable
• For handbag, t4d/dKN nearly independent of s,t
• Data for s,-t,-u > 2.5 GeV2 in rough agreement
0
1
2
3
4
2 3 4 5 6 7
t4d/dKN
(GeV8)
-t (GeV2)
s=7
s=9
s=11
s,-t,-u > 2.5 GeV 2
Preliminary Cross Sections
Calculations by Kroll et al.
• Measure KLL,KLT,PN : confirm single-quark dominance
s = 7.0 ; -t: 1.3 - 5.1 ; -u: 3.0 - 0.1 [GeV]2
• Determine form factors:
RA/RV: Δu(x)/u(x) RT/RV: F2/F1
• Observe NLO effects
nonzero PN
A New Experiment: JLab E03-003:
Summary of Goals of E03-003
s = 7 GeV2
0
0.1
0.2
0.3
0.4
0.5
0.6
0 1 2 3 4 5 6
-t (GeV2/c2)
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5 6
RA/R
V
-t (GeV2/c2)
T2
V
R
4 R
t
m
A
V
R R
Summary and Outlook
• E99-114 successfully completed* KLL and KLT at s=7, -t=4
• KLL is “large” and positive
– Suggestive of single-quark mechanism
– Similar result for 0 photoproduction
– Consistent with handbag prediction
• KLT/KLL consistent with F2/F1, with poor statistics
* d/dt over broad kinematic range
• t4/KN roughly constant for s,-t,-u > 2.5 GeV2
• s-6 scaling at fixed CM works only approximately
* Lots of p(,0) to be mined
• Planned extension* JLab E03-003: angular distribution of KLL , KLT , PN at s=7
• Higher energy desirable