# Presentation: 437681

## Physical Nucleon  Form Factors From Lattice QCD

**Hrayr H. Matevosyan,**
**Louisiana State University / JLab.**
**Anthony W. Thomas,**
**Thomas Jefferson Laboratory.**
**Gerald A. Miller,**
**University of Washington, Seattle.**

**Phys.Rev.C71:055204,2005; ArXiv:[nucl-th/0508049 ]**

- H.H. Matevosyan - PANIC 2005

## The Plan.

**Introduction.**
**Light Front Cloudy Bag Model.**
**Fits to the lattice data and extrapolations to the physical region. **
**Conclusions.**

- H.H. Matevosyan - PANIC 2005

**The recent advances in the lattice QCD provide us with form factor calculations over wide range of momentum transfer.**
- Problems:
_***Extrapolation of the lattice calculations to the physical quark mass region.***_
- Extrapolation of a **→ **0, V **→ **∞.
- Unquenching.

- Introduction.

- H.H. Matevosyan - PANIC 2005

## Motivation.

**Three problems to address: **
**Does the model describe lattice data? **
**Using the model to extrapolate the Form Factors to large values of ****Q****2**** for lattice values of ****m********. **
**Using the model to extrapolate the Form Factors to the physical ****m********.**

- H.H. Matevosyan - PANIC 2005

## The key features:
Respects  Lorentz Invariance.
Respects Chiral Symmetry.
Incorporates pion-cloud effects.
Reproduces the four nucleon electromagnetic form factors.
Is easily adaptable for calculations in high quark mass (“lattice”) regime.

- Respects  Lorentz Invariance.
- Respects Chiral Symmetry.
- Incorporates pion-cloud effects.
- Reproduces the four nucleon electromagnetic form factors.
- Is easily adaptable for calculations in high quark mass (“lattice”) regime.

- The Light Front Cloudy Bag Model (LFCBM). [G. Miller, Phys. Rev. C 66, 032201(R) (2002)]

- H.H. Matevosyan - PANIC 2005

##  LFCBM Wave-Function.

**In light-front dynamics four-vectors are**
- is similar to nonrelativistic kinetic energy form.
**The bare (pionless) nucleon wave function**:
-   - spin-isospin amplitude, u(pi) - Dirac spinors,  - momentum distribution wave function.
- ** ****is taken from ****F. Schlumpf, [arXiv:hep-ph/9211255].**
- where M is the constituent quark mass (_assumed constant_).

-  LFCBM Wave-Function.

- H.H. Matevosyan - PANIC 2005

**The Quark Core Contribution:**
-    In the Drell-Yan frame (q+=0), using light-front spinors

**Including The Pion Cloud:**

-  Nucleon EM Form Factors.

- H.H. Matevosyan - PANIC 2005

## Lattice Data Set.

**We fit the form factor calculations by QCDSF Collaboration.**
-  [M. Gockeler et al., Phys.Rev.D71:034508,2005.]
**The calculations were carried out using**** **_***quenched***_** ***Clover fermions*.
**The data range:**
- a    -  {0.093 fm, 0.067 fm, 0.051 fm},
-        V    -  {163x32,    243x48,    323x48},
- m  ~ {1.2 GeV,0.6GeV} ,
- MN ~ {2 GeV, 1.5 GeV },
- Q2 ~ {0.6 GeV2, 2.3 GeV2}.

- H.H. Matevosyan - PANIC 2005

**The Model Parameters:**
**M** - the Constituent Quark Mass
**** - the Nucleon Momentum Distribution WF Parameter – INSENSITIVE AT HIGH PION MASS
****  - the Nucleon Momentum Distribution WF Parameter
**** - the Pion-Nucleon Form Factor Parameter – INSENSITIVE AT HIGH PION MASS
**We need to extrapolate the Constituent Quark Mass**
** **
** **cmqphys=5.9 MeV**, and **M** is the constituent quark mass in the chiral limit.**    [I. Cloet *et. al*., Phys. Rev. C 65, 062201 (2002)]
**Our Fitting Parameters:**
** ** is varied for each m.
-  M is varied for each lattice a.

-  Fitting Parameters.

- H.H. Matevosyan - PANIC 2005

##  Fits to proton form factors.

- LFCBM fits to QCDSF data for proton GE (in units of e) and GM (in units of e/2MN) for a lattice spacing a=0.051 fm,MN=1.8 GeV and m=0.93 GeV.

-  Fits to proton form factors.

- H.H. Matevosyan - PANIC 2005

##  Extrapolation to high Q2 of calculated FF for different m for a=0.051 fm.

-  Extrapolation to high Q2 of calculated FF for different m for a=0.051 fm.

- H.H. Matevosyan - PANIC 2005

##  Extrapolation of the fitting parameters for a=0.051 fm.

-  Extrapolation of the fitting parameters for a=0.051 fm.

- H.H. Matevosyan - PANIC 2005

##  Physical Nucleon FF from LFCBM extrapolation for a= 0.051 fm.

-  Physical Nucleon FF from LFCBM extrapolation for a= 0.051 fm.

- H.H. Matevosyan - PANIC 2005

## Conclusion.

-  LFCBM gives _*quite accurate description of the lattice data points*_. It was used to both extrapolate in Q2  the calculated form factors, and with smooth quadratic extrapolation of the fitting parameters vs. m to _*extrapolate the form factors to the physical quark mass region*_.
-  We foresee the lattice calculated form factors as _*an alternative test of validity*_  for any model of the nucleon structure.
-  As new more accurate data at lower m and higher Q2 data will be available in the future, one _*will be able to have stricter tests and more accurate extrapolations to the physical mass region*_.

- H.H. Matevosyan - PANIC 2005

## Dirac F1 and Pauli F2 form factors:

Sachs Form Factors:

**Dirac F****1**** and Pauli F****2**** form factors:**
**Sachs Form Factors:**

-  Nucleon EM Form Factors.

- H.H. Matevosyan - PANIC 2005

## The Quark Core Contribution.

- The evaluation of the form factors is simplified by using the so-called Drell-Yan reference frame in which q+=0, so Q2=q**?**2=q12, K**0****?**** **= K**?**-q**?**.
- If light-front spinors for the nucleons are used, the form factors can be expressed in terms of matrix elements of the plus component of the current:
- The form factors are calculated using the "good" component of the current, J+, to suppress the effects of quark-pair terms.

- H.H. Matevosyan - PANIC 2005

## Including the Pion Cloud.

- H.H. Matevosyan - PANIC 2005

## Including the Pion Cloud.

- where g0 is the bare N coupling constant, and the renormalized
- coupling constant
- The N form factor is taken as [A. Dobrovolskaya, K. Ter-Martirosian, V. Zoller , Z.Phys.C53:263-268,1992 ]

- H.H. Matevosyan - PANIC 2005

##  Proton PGE/GM.

- H.H. Matevosyan - PANIC 2005

## Adaptation of LFCBM  to the lattice regime.

- The LFCBM is defined by choosing four free parameters: M, , , L so as to best reproduce the four experimentally measured electromagnetic form factors of the nucleon.
- The pion masses used in the lattice calculation are very large, and the resulting pion-loop contribution is very small. Therefore the value of L could not be determined from lattice data and its value was held fixed at L = 0.58 GeV taken from G. Miller’s fits to experimental data.
- Varying  did not change the description of the lattice data significantly, so it was held fixed at  = 0.607GeV/c taken from Schlumpf’s work.

- H.H. Matevosyan - PANIC 2005

## Fits to neutron form factors.

- LFCBM fits fit to QCDSF data for neutron GE (in units of e) and GM (in units of e/2MN) for a lattice spacing a=0.26GeV-1,MN=1.8 GeV and m=0.93 GeV.

- H.H. Matevosyan - PANIC 2005

## The best-fit values of the parameters.

- H.H. Matevosyan - PANIC 2005

##  Physical Neutron FF from LFCBM extrapolation for a=0.26GeV-1.

-  Physical Neutron FF from LFCBM extrapolation for a=0.26GeV-1.

- H.H. Matevosyan - PANIC 2005

##  Physical Nucleon FF from LFCBM extrapolation for a=0.26GeV-1.

-  Physical Nucleon FF from LFCBM extrapolation for a=0.26GeV-1.

- H.H. Matevosyan - PANIC 2005

## Physical Proton FF from LFCBM extrapolation for a=0.26GeV-1.

- H.H. Matevosyan - PANIC 2005

## The Extended Gari-Krumpelmann Model (GKex) [E. Lomon, Phys. Rev. C66: 045501, 2002]

- The key features:
- Is a generalized VMD model
- Predictions of nucleon GE, GM are in good agreement with the experiment.
- The high-Q2  behavior of the calculated form factors agrees with the PQCD prediction.
- Is easily adaptable for calculations in high quark mass (“lattice”) regime.

- H.H. Matevosyan - PANIC 2005

## The GKex model.

- In Gari-Krümpelmann model the “soft” photons couples to the “vector meson cloud” of the nucleon, while “hard” photons penetrate deep and couple to the “quark core” of the nucleon. The scale is set by a set of cut-off masses, which are found by fits to the data.

- M. Gari and W. Krumpelmann, Phys. Lett. B173, 10 (1986).

- In the GKex pole contributions of  the (782), (1020), **0**(1420),(770) and **0**(1450) mesons were included in order to achieve a good fit to the experimental  data available.

- H.H. Matevosyan - PANIC 2005

- 	Fits to the experimental data points were made using different sets of data, some of which excluded the controversial high proton GE/GM measured previously by Rosenbluth separation method. The fits with different data sets were labeled accordingly: GKex(01), GKex(01-), GKex(02S) and GKex(02L).
-         Rp, the ratio p GEp/GMp. Comparison of the models  GKex(01) [solid], GKex(02L) [dotted]
-          and GKex(02S ) [dash-dotted] with the data. [E. Lomon, arXiv:nucl-th/0203081 v3]

- The GKex model.

- GKex(01)

- GKex(02L)

- GKex(02S)

- H.H. Matevosyan - PANIC 2005

## Fits to the lattice proton form factors.

**GKex(01-) fit [solid] to QCDSF data for proton GE (in units of e) and GM (in units of e/2MN) for a lattice spacing a=0.26 GeV-1,MN=2.20 GeV and m********=1.24 GeV. LFCBM fits [dashed] are also shown for a comparison.**

- H.H. Matevosyan - PANIC 2005

## Table of the fitting parameters.

- H.H. Matevosyan - PANIC 2005