Home | Jefferson Lab - Nucleon Form Fac...handbag: leading quark 06/07/10 JLab UM slide 7 EMFFs &12 GeV Bogdan Wojtsekhowski, JLab diagrams pQCD: 2-gluon exchange handbag: leading

Bogdan Wojtsekhowski, Jefferson Lab

Nucleon Form Factors��

-  Introduction of the form factors

-  The form factors in RCS

- The nucleon EM form factors

-  FOM and the design of experiment

-  The Hall A apparatus – Super Bigbite

Nucleon Form Factors��

Dirac, Pauli and Sachs Form Factors

J µhadron = ieN̄(pf) [γνF1(Q2) +iσµνqν2 M

F2(Q2)]N(pi)

dσ = dσNS{ε(GE)

2 + τ (GM )2}

· [1 + heA(GE , GM )]

A = A⊥ + A‖ =a·GE GM sin θ

! cos φ!

G2E

+c·G2M

+b·G2

Mcos θ!

G2E

+c·G2M

GE = F1(Q2) − Q2

4M2F2(Q2) GM = F1(Q2) + F2(Q2)

Jfi = 2E · F (−!q 2), !J = 0 ρ(r) = 1(2π)3∫

F (−!q 2)ei"q"rd3!q

Nucleon current, one-photon approximation, αem = 1/137, !Rosenbluth,1950

Cross section and asymmetry for electron-nucleon scattering

Sachs, 1962 Does a nucleon have a core ?

06/07/10 JLab UM EMFFs &12 GeV Bogdan Wojtsekhowski, JLab slide 3

The goal is understanding of the nucleon

from the D. Gross Nobel Lecture:

“It is sometimes claimed that the origin of mass is the Higgs mechanism that is responsible for the breaking of the electroweak symmetry that unbroken would forbid quark masses. This is incorrect. Most, 99%, of the proton mass is due to the kinetic and potential energy of the massless gluons and the essentially massless quarks, confined within the proton.”

Real photon Compton Scattering

RCS is the simplest exclusive process with a real photon

Expected to be a golden test of pQCD

The 1977 experiment at Cornell confirmed the pQCD prediction: the cross section scaling power

dσ/dt = C/sn; pQCD: n = 6

06/07/10 JLab UM slide 5 EMFFs &12 GeV Bogdan Wojtsekhowski, JLab

RCS process: p γ -> p γ , JLab E99-114

Kinematic range in s,-t


Exclusive high t/Q2 process RCS

pQCD: 2-gluon exchange

handbag: leading quark


diagrams

pQCD: 2-gluon exchange

handbag: leading quark


Exclusive high t/Q2 process RCS

dσ/dt

dσKN/dt= fV

[R2

V(t) +

−t4m2

R2T(t)

]+ (1 − fV )R2A(t)

RV (t) =∑

a

e2a

∫ 1

−1

dx

xHa(x, 0, t),

RA(t) =∑

a

e2a

∫ 1

−1

dx

xsign(x) Ĥa(x, 0, t),

F1(t) =∑

a

ea

∫ 1

−1dx Ha(x, 0, t)

Two-body kinematics

JLab RCS experiment

Mixed e/γ beam =>productivity 1300x higher than for “clean” γ

Two-body kinematics

JLab RCS experiment

A factor of 100 is due to a novel scheme of the experiment

Mixed e/γ beam

Two-body kinematics

1013 photons/sec

ep events RCS events

“pion” events

Two-body kinematics

1013 photons/sec

Mixed e/γ beam

Experimental results: cross section

For s = 11 GeV2

pQCD for αs = 0.3

E99-114

Form factors of RCS and helicity correlation


dσ/dt

dσKN/dt= fV

[R2

V(t) +

−t4m2

R2T(t)

]+ (1 − fV )R2A(t)

RV (t) =∑

a

e2a

∫ 1

−1

dx

xHa(x, 0, t),

RA(t) =∑

a

e2a

∫ 1

−1

dx

xsign(x) Ĥa(x, 0, t),

F1(t) =∑

a

ea

∫ 1

−1dx Ha(x, 0, t)

Experimental results: cross section scaling

[deg]cmθ60 80 100 1205

6

7

8

9JLabCornell

n=6 two gluon exchange

)cmθ

n( pQCD


Photon-proton helicity correlation


JLab E99-114

pQCD

Study of the nucleon should determine the nature of

1.  Light-quark confinement and dynamical chiral symmetry breaking (DCSB);

and provide understanding of

2. Nucleon structure and spectroscopy in terms of QCD's elementary degrees of freedom.


The DSE approach developed by C.Roberts et al provides consistent QCD description to the nucleon, which is in good agreement with the experimental FF.

A central role of the dressed-quark mass function M(p2)


First Contents Back Conclusion

Frontiers of Nuclear Science:Theoretical Advances

S(p) =Z(p2)

iγ · p + M(p2)

0 1 2 3

p [GeV]

0

0.1

0.2

0.3

0.4

M(p

) [G

eV

]

m=0 (Chiral limit)

30 MeV70 MeV

for DSE-predicted

Hint of support in Lattice-QCD results

confinement signal

Mass from nothing.In QCD a quark’s effective mass

depends on its momentum. The

function describing this can be

calculated and is depicted here.

Numerical simulations of lattice

QCD (data, at two different bare

masses) have confirmed model

predictions (solid curves) that the

vast bulk of the constituent mass

of a light quark comes from a

cloud of gluons that are dragged

along by the quark as it

propagates. In this way, a quark

that appears to be absolutely

massless at high energies

(m = 0, red curve) acquires a

large constituent mass at low

energies.

Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 13/28

C.Roberts: the dressed-quark mass function M(p2)


First Contents Back Conclusion

Nucleon-Photon Vertex

M.Oettel, M. Pichowsky

and L. von Smekal, nu-th/9909082

6 terms . . .

constructed systematically . . . current conserved automatically

for on-shell nucleons described by Faddeev Amplitude

ii! !

Pff

P

Q ii! !

Pff

P

Q

ii! !

PPff

Q

"#

"

scalaraxial vector

ii! !

Pff

P

Q

µ

ii

X

! !Pf

f

Q

P "#

µi

i

X#

! !Pf

f

P

Q

"

Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 22/28

The goal is understanding of the nucleon C.Roberts: the dressed-quark mass function M(p2)

- What is a way to measure the dressed-quark mass function, M(p2)?

- What is a unique signature of the diquark configuration?



- What is a way to measure M(p2)?

The Compton scattering:

The polarized beam/polarized target asymmetry, ALL, is directly sensitive to the ratio mq/Eγ:




0 30 60 90 120 150 180photon scattering angle in Lab system

−1

−0.5

0

0.5

1

LL in QED

m/Eγ=1/1000m/Eγ=1/100m/Eγ=1/10m/Eγ=1/1

A


Interference between BH and CS is a key




0 30 60 90 120 150 180photon scattering angle in Lab system

−1

−0.5

0

0.5

1

LL in QED

m/Eγ=1/1000m/Eγ=1/100m/Eγ=1/10m/Eγ=1/1

A


Both the positron and electron beams are required for study of the quark CS

Sachs Form Factors of the nucleon

]2 [GeV2Q

0 5 10 15

DG

pµ/

p MG

0.7

0.8

0.9

1.0

1.1

1.2

Borkowski

Sill

Bosted

Walker

Andivahis

Diehl

Kelly

BBBA05

]2 [GeV2Q

0 5 10 15

DG

nµ/

n MG

0.4

0.6

0.8

1.0

1.2 RockLung

Markowitz

Anklin(1994)

Bruins

Anklin(1998)

Kubon

Lachniet

GPD

Kelly

BBBA05

]2 [GeV2Q

0 5 10 15

p M/G

p EG

pµ

0.0

0.5

1.0

GEp(1)

GEp(2)

GEp(3)

Diehl

Kelly

BBBA05

]2 [GeV2Q

n M/G

n EG

nµ

0.0

0.2

0.4

0.6

0.8

1.0

RCQM

GPD

VMD

Kelly

BBBA05

DSE

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

GEn

Sachs Form Factors of the nucleon

]2 [GeV2Q

0 5 10 15

DG

pµ/

p MG

0.7

0.8

0.9

1.0

1.1

1.2

Borkowski

Sill

Bosted

Walker

Andivahis

Diehl

Kelly

BBBA05

]2 [GeV2Q

0 5 10 15

DG

nµ/

n MG

0.4

0.6

0.8

1.0

1.2 RockLung

Markowitz

Anklin(1994)

Bruins

Anklin(1998)

Kubon

Lachniet

GPD

Kelly

BBBA05

]2 [GeV2Q

0 5 10 15

p M/G

p EG

pµ

0.0

0.5

1.0

GEp(1)

GEp(2)

GEp(3)

Diehl

Kelly

BBBA05

]2 [GeV2Q

n M/G

n EG

nµ

0.0

0.2

0.4

0.6

0.8

1.0

RCQM

GPD

VMD

Kelly

BBBA05

DSE

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Fu

1 = 2 F1p + F1n

Fd

1 = 2 F1n + F1p

F1 =GE +τGM

1 + τ

F2 = −GE −GM1 + τ

From the Sachs FFs to the contributions of the u-/d-quarks

]2 [GeV2Q

0 5 10 15

p M/G

p EG

pµ

0.0

0.5

1.0

GEp(1)

GEp(2)

GEp(3)

Diehl

Kelly

BBBA05

]2 [GeV2Q

n M/G

n EG

nµ

0.0

0.2

0.4

0.6

0.8

1.0

RCQM

GPD

VMD

Kelly

BBBA05

DSE

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15


Flavor decomposition

]2 [GeV2Q

0 5 10 15

D/G

u 1F

2.0

2.5

3.0

Diehl

BBBA05

Kelly

]2 [GeV2Q

0 5 10 15

D/G

d 1F

-0.5

0.0

0.5

1.0 Diehl

BBBA05

Kelly

]2 [GeV2Q

0 5 10 15

D/G

d 2F

d-1!

0.0

0.5

1.0Diehl

BBBA05

Kelly

]2 [GeV2Q

0 5 10 15

D/G

u 2F

u-1!

0.0

0.2

0.4

0.6

0.8

1.0

Diehl

BBBA05

Kelly

F2/F1 and other ratios

]2 [GeV2Q

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

d 1/F

d 2F

d-1!

0.5

1.0

1.5

]2 [GeV2Q

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

u 1/F

d 1F

0.2

0.4

0.6

RCQM - Miller

Lattice

Diehl et al.

Galster fitq(qq) Faddeev&DSE

]2 [GeV2Q

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

u 2F

u-1!/

d 2F

d-1!

0.5

1.0

1.5

]2 [GeV2Q

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

u 1/F

u 2F

u-1!

0.0

0.1

0.2

0.3

0.4

0.5

- What is a unique signature of the diquark configuration?

]2 [GeV2Q

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

d 1/F

d 2F

d-1!

0.5

1.0

1.5

]2 [GeV2Q

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

u 1/F

u 2F

u-1!

0.0

0.1

0.2

0.3

0.4

0.5

Fu

1 = 2 F1p + F1n

Fd

1 = 2 F1n + F1p

F1 =GE +τGM

1 + τ

F2 = −GE −GM1 + τ

From Sachs FFs to the contributions of the u-/d-quarks


Results of E02-013 Hall A GEn

- A diquark configuration? - An effect of orbital motion?

]2 [GeV2Q

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

d 1/F

d 2F

d-1!

0.5

1.0

1.5

]2 [GeV2Q

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

u 1/F

u 2F

u-1!

0.0

0.1

0.2

0.3

0.4

0.5

Results of E02-013 Hall A GEn

Fu

1 = 2 F1p + F1n

Fd

1 = 2 F1n + F1p

F1 =GE +τGM

1 + τ

F2 = −GE −GM1 + τ

From Sachs FFs to the contributions of the u-/d-quarks


1.4 0.3

Two interesting observations: 1)  F2/F1 = R is constant in the Q2-range 1 - 3.5 GeV2 2)  The value of R for d-quark >> than R for u-quark

One- and Two-Arm experiments (O&TA)

The most productive experiments in the field belong to the category O&TA: Among them are DIS, SIDIS, FFs (GEP), RCS, DVCS, ....

The main advantage of the (e,e’) & (e,e’h/γ) is the simplicity of such processes for physics interpretation

FOM = L × Ω1(×Ω2)

Figure-of-Merit for O&TA experiments One-arm experiments: high L and large Ω (ΔQ2/Q2 ~ 0.1) :

The Super Bigbite Spectrometer is the best choice due to large solid angle Ω = 70 msr and detector rate capability

Two-arm experiments deal with elastic or quasi-elastic pm ~ 0.2 GeV/c for the nuclei; ~ 0.5-1 GeV/c for the nucleon The high Q2/t/ν experiment N(e,e’h) means ph ~ 2-8 GeV/c; 70 msr of SBS acceptance: the detector captures efficiently

events up to pm ~ ph/5 => one setting could be a whole experiment

FOM = L× Ωelectron = 1038 · 0.07 = 7× 1036electron/s× nucleon/cm2 × sr



Now we can formulate a detector configuration for productive one- and two-arm experiments

  Magnetic analysis with “vertical bend”   Moderate solid angle   Independent arms   Small angle capability   Space for segmented PID


Now we can formulate a detector configuration for productive one- and two-arm experiments

  Magnetic analysis with “vertical bend” => protected detector   Moderate solid angle => high luminosity   Independent arms => full range of angles   Small angle capability => high x, t   Space for segmented PID => RICH counter


Hall A GEn experiment Beam

Target Neutron arm

Electron arm

Super Bigbite Spectrometer in GEp


Parameters of SBS

Solid angle =>

Resolution:

Momentum =>

Angular =>

Momentum acceptance =>

Target length (y)

σpP

= 0.0029 + 0.0003 × p[GeV]σθ = 0.14 + 1.3/p [GeV], mrad

unlimited above 1-2 GeV/c

50 cm


Parameters of SBS

Solid angle =>

Resolution:

Momentum => σpP

= 0.0029 + 0.0003 × p[GeV]


The Committee [ Mecking’s Review 2010] finds that the SBS experimental design has a very high probability of meeting the experimental requirements. The high rate and high resolution capability of the GEM detectors make them the ideal solution for this application. The SBS Collaboration has the required expertise to carry out the project within the time schedule presented.

Optimization of the experimental setup Hadron Arm

Beam

Target

Electron Arm

.

.

17 m

Neutron Magnetic Form Factor

GEM

BigBenBNL

BigBiteGasCher

ECalo

HCalo

48D48

Electron Arm

Beam

.

.

Target

Proton form factors ratio, GEp(5): E12−07−109

Proton Arm

Lead−glassCalorimeter

BNLINFN

HCalo

Al filter

48D48

GEM

GEM

GEM

BigBenGEM

Beam

Target

Hadron Arm

Electron Arm

.

.

17 m

HCalo

48D48

BigBenBNL

BigBiteGasCher

ECalo

Neutron form factors, E12−09−016 and E12−09−019

GEM

Proton Magnetic Form Factor

Neutron form factors ratio, GEn(2):E12-09-016


Neutron/proton form factors ratio: E12-09-019

Proton magnetic form factor: E12-07-108

The cross section of H(e,e’)p.

By using two existing Hall A High Resolution Spectrometers with several new ideas for improved control of systematic.

It requires a total beam time of a 31-day run (25 days approved)

Moffit, Gilad, Arrington, and BW

12 GeV GMp experiment


]2

[GeV2

Q

0 10 20 30

DG

pµ/

p MG

0.8

1.0

Andivahis

BartelBerger

Janssens

Litt

Sill

Walker

Projected in this experiment


2 in GeV2Q

0 5 10 15

p M/G

p EG

p!

-0.5

0.0

0.5

1.0

GEp(1)

GEp(2)

GEp(3)

GEp(5) E12-07-109, SBS

VMD - E. Lomon (2002)

VMD - Bijker and Iachello (2004)

RCQM - G. Miller (2002)

DSE - C. Roberts (2009)

= 300 MeV!, 2)/Q2!/2(Q2 ln" 1

/F2

F

Brash, Jones, Khandaker, Pentchev, Perdrisat, Punjabi, and BW

12 GeV GEp experiment

CLAS 12 BigBite + SBS


)2 (GeV2Q0 2 4 6 8 10 12 14 16 18 20

DG

nµ/

n MG

0.2

0.4

0.6

0.8

1

1.2

BBBA FitKelly FitAlberico FitCLAS dataSLAC data

Hall A E12-09-19

value on BBBA fit

Hall B E12-07-104

value shifted to 1.1

Gilman, Quinn, and BW

12 GeV GMn experiment


Cates, Riordan, and BW

]2 [GeV2Q

n M/G

n EG

n!

0.0

0.5

1.0RCQM - Miller

GPD - Diehl

VMD - Lomon (2005)

Faddeev&DSE - Roberts = 300 MeV!,

1/F2F

Passchier, NIKHEFHerberg, MAMI

Ostrick, MAMI

Meyerhoff, MAMI

Golak, MAMI

Bermuth, MAMI

Plaster, JLab

Zhu, JLab

Warren, JLab

Glazier, MAMI

Geis, BATES

E02-013

E12-09-016, Hall A

2 4 6 8 10 12 14 16 18 20

12 GeV GEn experiment

DIS with Super Bigbite and BigBite

Inclusive electron scattering: high x (0.3-0.8); u/d; pol. u;d;

T/He-3 (e,e’) ; double pol. 3He(e,e’); ND3(e,e’); NH3(e,e’) -------------------------------------------------------------------------------------

Solid angle; momentum acceptance, luminosity 50 + 30-70 msr 100%; max available up to 1 x1038

========================================================================

•  A1n experiment will have FOM about 5000 times higher than was done with standard spectrometers (HRS, HMS …)

•  SIDIS measurement with SBS+BB (“high luminosity HERMES”)

Polarized DIS with SBS

BB+ SBS has an advantage over HMS+SHMS

by a factor of 12: a short run with precision results

GEM tracker

Averett, Cates, Liyanage, Rosner, Zheng, and BW

very good accuracy, x up to 0.75 the study of Q2 dependence


E12-06-122 SBS: 300 hours

SIDIS with Super Bigbite + BigBite

DOE

DOE DOE DOE

06/07/10 JLab UM EMFFs &12 GeV Bogdan Wojtsekhowski, JLab

The SBS+BB detector layout is close to the HERMES one

Cherenkov detector is from HERMES

It is a high luminosity continuation of HERMES

slide 47

Cates, Cisbani, Franklin, and BW e+3He↑→e’+π(K)±+X E12-09-018

Beam: 50 µA, E=8.8 and 11 GeV (80% long. Pol.) Target: 65% polarized 3He ⇐ GEn(2)/PR-09-016 Luminosity: 1.4×1037 cm-2s-1 , 50 msr

e+3He↑→e’+π(K)±+X

DOE

DOE DOE DOE

06/07/10 JLab UM EMFFs &12 GeV Bogdan Wojtsekhowski, JLab

The SBS+BB detector layout is close to the HERMES one

Cherenkov detector is from HERMES

It is a high luminosity continuation of HERMES

slide 48

Cates, Cisbani, Franklin, and BW E12-09-018


Beam: 50 µA, E=8.8 and 11 GeV (80% long. Pol.) Target: 65% polarized 3He ⇐ GEn(2)/PR-09-016 Luminosity: 1.4×1037 cm-2s-1 , 50 msr

BB: e-arm at 30o Ω = 45 msr GEM Tracker Gas Cherenkov Shower ⇐ GMn/E12-09-019 SBS: h-arm at 14o Ω = 50 msr GEM tracker excellent PID / RICH Hadron CALO

Event rate: ~104×HERMES 60 days of production expected stat. accuracy:

1/10 of proton HERMES

DOE

DOE DOE DOE


Cates, Cisbani, Franklin, and BW e+3He↑→e’+π(K)±+X E12-09-018


Summary

  Hall A Nucleon FF program will provide precision results for@ up to:

 GpE @ 14.5 GeV2  GpM @ 17.5 GeV2  GnE @ 10 GeV2  GnM @ 18 GeV2

  Super Bigbite spectrometer will be the almost ideal tool for experiments in hadron physics at large Q2


48D48 – 46x155 cm2 aperture and 2.5 Tesla*m

GEM chambers with 70 µm resolution

A

Target

Right yokeView to A ! A

Right yoke

92"

Left coil Right coil

Beam

14

6"

A

Beam line opening

- momentum resolution is 0.5% for 5 GeV/c - solid angle is 70 msr at angle 15o - angular resolution is 0.3 mr


Super Bigbite Spectrometer in GEp

Gas Electron Multiplier Technology Field

50 MHz/cm2

~ 2 times of max expected rate in SBS

Chamber gain vs. rate for LHCb project

GEM foil pictureChamber structure

track500 Volt


Isospin decomposition

]2 [GeV2Q

0 5 10 15

D/G

is 1F

0.6

0.8

1.0

1.2

1.4

Diehl

BBBA05

Kelly

]2 [GeV2Q

0 5 10 15

D/G

iv 1F

1.0

1.5

2.0

2.5

3.0

Diehl

BBBA05

Kelly

]2 [GeV2Q

0 5 10 15

D/G

is 2F

-0.4

-0.2

0.0

0.2

0.4 Diehl

BBBA05

Kelly

]2 [GeV2Q

0 5 10 15

D/G

iv 2F

0

1

2

3

4

Diehl

BBBA05

Kelly

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Home | Jefferson Lab - Nucleon Form Fac...handbag: leading quark 06/07/10 JLab UM slide 7 EMFFs &12 GeV Bogdan Wojtsekhowski, JLab diagrams pQCD: 2-gluon exchange handbag: leading