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