Nucleon EM form factors
in a quark-gluon core
model
余先桥
西南大学
outline

Introduction to EM form factors
 The idea of quark-gluon core model
 Our work
 Summary
1. Introduction to EM form factors
来自质子的贡献分为两部分：1.
电场贡献。2. 磁矩贡献。
F_1 和F_2 是独立形状因子，但它们中的每一个都不单独对应磁矩
散射和电散射
我们重新定义一对形状因子，使它们分别直接对应磁矩散
射和电散射
其中G_M 称为磁形状因子，G_E称为电形状因子
在新的形状因子表述下，电子－质子弹性散射截面为
High accuracy experimental data in recent years indicate that nucleon
electromagnetic from factros can be well fitted by a simple dipole formula at low
Q^2:
当大动量转移时，形状因子会偏离偶极子公式，为什么？这激发了人们
重新讨论核子结构图像的兴趣。
2. The idea of quark-gluon core model
The spin-independent interaction between one
valence quark and the gluon nucleus take the
follwing form:
Where, alpha is a positive constant and V_conf
is the confining potential.
We assume that the mass of the gluon cluster is much larger than that of the
quark, in this case, setting the gluon nucleus at the origin of coordinate, we write
the non-relativistic Hamiltonian for the system as
where
is the hyperfine interaction which is spin-dependent.
3. Our work
Using this picrure we derive nucleon EM dipole form factors at
low Q^2 and the deviation from the dipole form at high Q^2.
The eigenstates of the Hamiltonian H_0 are well known. For nucleon, all
the three valence quarks in the 1s state, the ground state wave function is
It is impossible to solve accurately the eigen-wave function of Hamiltonian H; we
assume that the approximate ground state wave function of Hamiltonian H has the
same form as that of Hamiltonian H_0, that is
The electric charge and magnetic moment density distribution in nucleon are
After carrying through Fourier transformation
We get nucleon EM form factors
有效耦合常数alpha’ 及夸克质量m的确定
比较
和
得
4b^2=0.71GeV^2 （1） 这里
另外由夸克能级公式
假定核子N(939)处于基态，N(1440)为有一个夸克激发
到2s轨道，则有
E_2-E_1=1440MeV-939MeV （2）
联立方程（1）和（2）得
m＝133MeV
核子能谱的讨论
预言，如果有一个夸克被激发到3s轨道，则其质量为
m＝E_3-E_1+939MeV=1533MeV
我们可以认为其对应N(1535)
观察核子能谱
N(939)
N(1440)
N(1520)
可以由库仑势描述
N(1535)
N(1650)
N(1675)
N(1680)
N(1720)
N(2190)
N(2220)
N(2250)
可以由谐振子禁闭势描述
中子电形状因子的进一步讨论
然而近年来的高精度试验数据表明，中子的电形状因子虽然很小，但不为零，
如何解释？
我们发现，在这个模型中，中子电形状因子对零的偏离可以解释为是u
夸克和d夸克质量和相互作用的微小差异造成的
严格的，中子的电形状因子为
前面得到
m＝133MeV
如果令
则我们得到中子的电形状因子为
大动量转移时形状因子的讨论
电荷和磁矩密度分布的Fourier变换对应电磁形状因子只对小动量转移成
立，在大动量转移时，由于相对论效应，这个关系不再成立。
我们称
为内禀形状因子
在低Q^2, 内禀形状因子就是电磁形状因子G_E(Q^2)和G_M(Q^2)(called Sachs
FFs in the literature)
在高Q^2，内禀形状因子与Sachs形状因子的关系不明确，文献中常利用如
下公式进行唯象研究
其中\lambda 是一个模型相关的常数
To account for the asymptotic 1/Q^4 FFs obtained by perturbative QCD at very
large Q^2, Mitra and Kumari proposed the choice \lambda _E= \lambda _M=2.
我们也取\lambda _E= \lambda _M=2，计算了在高Q^2时的核子电磁形
状因子，如下图所示
可以看出，在高Q^2，
这和目前已经存在的试验数据
（for G^p_M/\mu_pG_D）在动
量转移从Q^2=19.5到31.3GeV^2
范围内是一致的。
4. Summary
1. We study the nucleon EM form factors in a quark-gluon core model framwork,
which can be viewed as an extension of the Isgur-Karl model of baryons.
2. Using this picture we derive nucleon EM dipole form factors at low Q^2
and the deviation from the dipole form at high Q^2, that are consistent with the
existing experimental data.
3. If we consider the gluon core inside nucleon as a quasi-particle, we ask:what
is its spin? The answer to this question may be helpful for solving the
proton spin crisis.