Real Compton Scattering from the Proton in the Hard Scattering Regime Alan M. Nathan SLAC...

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