Real Compton Scattering from the Proton in the Hard Scattering Regime
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Transcript of Real Compton Scattering from the Proton in the Hard Scattering Regime
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