# Presentation: 855139

## Marc Vanderhaeghen
Jefferson Laboratory / College of William & Mary 

- Jefferson Laboratory / College of William & Mary

- August 2007 Hall C meeting
- JLab, August 9-10, 2007

- Nucleon  Structure Studies :
- Present and Future

## Slide 2

## proton e.m. form factor : status 

- proton e.m. form factor : status

**green : Rosenbluth data (SLAC, JLab)**

**JLab/HallA **
**recoil pol. data**

** ****new JLab/HallC recoil pol. exp. (2008) : extension up to Q****2 ****≈ 9 GeV****2**** **

## neutron e.m. form factor : status 

- neutron e.m. form factor : status

**JLab/CLAS**

**JLab/HallA**

**MAMI**

**JLab/HallC**

** ****new JLab/HallA double pol. exp. (spring 07) : extension up to Q****2 ****≈ 3.5 GeV****2 ****completed **

** ****new MIT-Bates (BLAST) data for both p and n at low Q****2**** **

## nucleon form factors : pion cloud

**Friedrich, Walcher  (2003)**

- phenomenological fit :
- “smooth” part
- (sum of 2 dipoles)
- + “bump”
- (gaussian)
- 6 parameter fit for each FF

- pronounced structure in all FF around Q  0.5 GeV/c

- pion cloud

## nucleon FF : lattice prospects

- nucleon FF : lattice prospects

_**state of art**_** :**
- connected diagrams
- -> OK for isovector quantities

- Pion masses down to less than 300 MeV

- chiral extrapolation to physical mass

**LHPColl.**

- √(r2)1V

- F1V

_**next step**_ :
- inclusion of disconnected diagrams

- full QCD lattice calculations

**Leinweber, Thomas, Young (2001)**

## Rosenbluth vs polarization transfer measurements of GE/GM of proton 

- Jlab/Hall A Polarization data
**Jones et al. (2000)**
**Gayou et al. (2002)**

- SLAC, Jlab
- Rosenbluth data

- Two methods, two different results ! 2γ exchange proposed as explanation

- Two-photon exchange effects

**Guichon, Vdh (2003)**

## Two-photon exchange calculations 

**Blunden, Melnitchouk, Tjon (2003, 2005)**

- N

- elastic contribution

**Chen, Afanasev, Brodsky, Carlson, Vdh (2003)**

- partonic calculation

- GPDs

## Generalized Parton Distributions

- x + ξ

- x - ξ

- P - Δ/2

- P + Δ/2

- *

- Qhard2  large

- t = Δ2

- low –t process : -t << Qhard2

- GPD (x, ξ ,t)

**Ji , Radyushkin**
**(1996)**

- at large Q2 : QCD factorization theorem       hard exclusive process can be described by 4 transitions (GPDs) :

- (x + ξ) and (x - ξ) : longitudinal momentum fractions of quarks

**Vector**  :  H (x, ξ ,t)
**Tensor**  :  E (x, ξ ,t)

**Axial-Vector**  :  H (x, ξ ,t)
**Pseudoscalar**  :  E (x, ξ ,t)

- ~

- ~

## known information on GPDs

- first moments : nucleon electroweak form factors

- ξ independence : Lorentz invariance

- Pauli

- Dirac

- axial

- pseudo-scalar

- forward limit : ordinary parton distributions

- unpolarized quark distr

- polarized quark distr

- :   do NOT appear in DIS          new information

## GPDs yield 3-dim quark structure of nucleon

**Elastic Scattering**
**transverse quark**
** ****distribution in **
**coordinate space**

**DIS**
**longitudinal**
**quark distribution**
**in momentum space**

**DES (GPDs)**
**f****ully-correlated**
**quark distribution in **
**both coordinate and **
**momentum space**

**   **

- GPDs yield 3-dim quark structure of nucleon

**Burkardt (2000, 2003)**
**Belitsky, Ji, Yuan (2004) **

## GPDs  :  Q2  dependence ( large Q2 )

- Input : forward parton distributions at  = 1 GeV2   (MRST2002 NNLO)

-  regge slopes :                  determined from rms radii

-              determined from F2 / F1 at large -t

- Drell-Yan-West relation : exp(- α ́ t ) -> exp(- α ́ (1 – x) t)   M. Burkardt (2001)

-  parameters :

- future constraints : moments from lattice QCD

- GPDs  :  Q2  dependence ( large Q2 )

- -t = Q2

## connection  large Q2 of FF <-> large x of GPD

- “Drell-Yan-West” relation for PDF/GPD :
- at large Q2  :  I is dominated by its behavior around x -> 1

- at large Q2  :  integral dominated by maximum of f(x,Q2), remainder region is exp. suppressed  (method of steepest descent)

- f(x,Q2) reaches maximum for :

## electromagnetic form factors

- modified  Regge GPD parametrization

- PROTON

- NEUTRON

- world data (2006)

**Guidal, Polyakov, Radyushkin, Vdh (2005)**

- 1 :  Regge slope -> proton Dirac (Pauli) radius
- 2, 3 : large x behavior of GPD Eu, Ed ->  large Q2 behavior of F2p, F2n

**also**** Diehl, Feldmann, Jakob, Kroll (2005)**

- 3-parameter fit

## proton Dirac & Pauli FFs :

- modified  Regge GPD model

- PQCD

**Belitsky, Ji, Yuan (2003)**

- GPD framework

**Guidal, Polyakov, Radyushkin, Vdh (2005)**

- data : SLAC

- data : JLab/HallA

- data : JLab/HallA

## GPDs : 3D quark/gluon imaging of nucleon

- Fourier transform of GPDs  :
- simultaneous distributions of quarks w.r.t. longitudinal momentum x P and transverse position b

- ( Burkardt )

## GPDs : transverse image of the nucleon (tomography)     

- GPDs : transverse image of the nucleon (tomography)

- Hu(x, b? )

- x

-     b? (fm)

## nucleon densities in transverse plane

## proton FFs and transverse densities

- proton FFs and transverse densities

- GPD parameterization

- phenom. BBBA05 fit

- Guidal, Polyakov, Radyushkin, Vdh (2005)

- Bradford, Bodek, Budd, Arrington (2006)

- Miller (2007)

## neutron FFs and transverse densities

- GPD parameterization

- phenom. BBBA05 fit

- Guidal, Polyakov, Radyushkin, Vdh (2005)

- Bradford, Bodek, Budd, Arrington (2006)

- Miller (2007)

## neutron Dirac & Pauli FFs at large Q2

- neutron Dirac & Pauli FFs at large Q2

## N -> Δ DVCS and GPDs

- N -> Δ DVCS and GPDs

- *

- x + ξ

- x - ξ

- Q2  >>

- t = Δ2

- N

- Δ

- low –t process : -t << Q2

- HM, HE, HC, H4  (x, ξ ,t)

- Jones-Scadron
- N -> Δ form factors

## N -> Δ magnetic dipole form factor

- modified  Regge model

- Regge model

- large Nc limit

## scaling behavior of N and N -> Δ  F.F.

- modified  Regge model

- Guidal, Polyakov, Radyushkin, Vdh (2005)

- PQCD

- + collinear quarks

- F1 p  ~  1/Q4

- F2 p / F1 p  ~  1/Q2

- GM*  ~  1/Q4

- GPD

- N

- N, Δ

## N -> Δ E2 and C2 form factors

- Buchmann, Hester, Lebed (2002)

-  large Nc limit of QCD :

-  Nc = 3

-  EXP :      rn2 = - 0.113 (3)  fm2

-  large Nc :   Qp -> Δ+  = - 0.080   fm2

-  EXP :         Qp -> Δ+  = - 0.085 (3)   fm2

-  finite (low) Q2 :

- Pascalutsa, Vdh (2006)

## N -> Δ E2 and C2 form factors

- N -> Δ E2 and C2 form factors

- Pascalutsa, Vdh (2006)
- hep-ph/0611050

- modified Regge model

- data :
- MAMI, BATES, JLab/CLAS, JLab/Hall A

-  large Nc limit

## Nucleon strangeness FFs

**G****M****s**** = 0.28 ± 0.20       **** **
**G****E****s**** = -0.006 ± 0.016****   **

- Q2  = 0.1 GeV2

- PV e-scattering

- APV =

**G****M****s**** = -0.01 ± 0.25       **** **
**G****E****s**** = +0.002 ± 0.018****   **

** ****re-analysis **
**Young et al. (2006)**

## Nucleon strangeness FFs : Q2 dependence

***Forward angle e-p data***

** ****Rapid variation at low Q****2**** unlikely**
** ****Await backward angle measurements from A4, G0**
** ****Deuterium running will provide constraints on G****A**** **
** ****One high precision point at Q****2****~0.6 (HAPPEX III: run in 2009)**

- Nucleon strangeness FFs : Q2 dependence

## Nucleon strangeness FFs : interpretation

- Nucleon strangeness FFs : interpretation

- Regge slope : α’ ≈ 0.95 GeV2

**Barone, Pascaud, Zomer (2000)**

**CCFR + NuTeV data (2001)**

**Vdh ( PAVI2002 )**

**data ****(Young et al.)**** : **
**0.002 ± 0.024**

- F1s

- GPD

- lattice

**G****M****s ****(0)   = -0.046 ± 0.019 ****μ****N****     ****    ****Leinweber et al. (2005)**
**G****E****s**** (0.1) = 0.001 ± 0.004 ± 0.004****   ****Leinweber et al. (2006)**** **

- + charge symm. constraints

## 
   Nucleon form factors :
      -> high precision data at low Q2  : map out pion cloud of nucleon 
    -> difference Rosenbluth vs polarization data GEp /GMp : 
         mainly understood as due to two-photon exchange effects  (new expt. planned)
    -> PV e-scattering : strangeness contributions to E and M distributions very small
    -> lattice QCD : state-of-art calculations go down to mπ  ~ 300 MeV, into the  
                              regime where chiral effects are important 

   GPDs :
    -> unifying theme in hadron physics (form factors, parton distributions)
   -> provide a tomographic image of nucleon
    -> access to angular momentum of quarks/gluons in nucleon 
    -> encouraging experimental results coming out of HERMES, H1/ZEUS, JLab@6 GeV
        indicating twist-2 dominance
    -> future programs : COMPASS, dedictated JLab@12 GeV, EIC...

    Nucleon excitation spectrum :
     -> precision data on NΔ form factors : shape of hadrons
    -> chiral EFT is used in dual role : 
        describe both observables and use in lattice extrapolations 
        strong non-analytic behavior in quark mass due to opening of πN decay channel    
         (interplay of scales)

-    **Nucleon form factors**** :**
-       -> high precision data at low Q2  : map out pion cloud of nucleon
-     -> difference Rosenbluth vs polarization data GEp /GMp :
-          mainly understood as due to two-photon exchange effects  (new expt. planned)
-     -> PV e-scattering : strangeness contributions to E and M distributions very small
-     -> lattice QCD : state-of-art calculations go down to mπ  ~ 300 MeV, into the
-                               regime where chiral effects are important
-    **GPDs ****:**
**    **-> unifying theme in hadron physics (form factors, parton distributions)
**   **-> provide a tomographic image of nucleon
-     -> access to angular momentum of quarks/gluons in nucleon
-     -> encouraging experimental results coming out of HERMES, H1/ZEUS, JLab@6 GeV
-         indicating twist-2 dominance
-     -> future programs : COMPASS, dedictated JLab@12 GeV, EIC...
-     **Nucleon excitation spectrum ****:**
-      -> precision data on NΔ form factors : shape of hadrons
-     -> chiral EFT is used in dual role :
-         describe both observables and use in lattice extrapolations
-         strong non-analytic behavior in quark mass due to opening of πN decay channel
-          (interplay of scales)

- Summary