References - Bogoliubov Laboratory of Theoretical Physics - JINR

〈r 2 ch 〉≈1fm2 . Now with Eqs. (5, 3), let us actually evaluate the mean square charge
radius:
� �
2 6
rch = −
F1(0)
dF1(Q 2 )
dQ 2
�
�
�
�
� Q 2 →0
= − 6 ∂
F1(0) ∂Q2 � 3 d κ
(2π) 3
�
1+ κ2 − (Q/2) 2
4 〈κ0 〉 2
� �
ϕ κ + Q
� �
ϕ κ −
2
Q
�
2
� �
���Q→0
= a 2
�
3
2 +
�
1
. (8)
1+ 8〈κ0 〉 2 a 2
3
Another constraint on the model parameters comes from the proton magnetic moment,
which in our additive quark model with charges eu = 2
3 ep, ed = − 1
3 ep appears to equal
μp
ep
= μq
eq
= 1
2 〈κ0 〉 F2(0) = 1
2 〈κ0 � 3 d κ
〉 (2π) 3 ϕ2 (κ) = 1
2 〈κ0 〉 1+
1
3
8〈κ 0 〉 2 a 2
. (9)
Together, constraints (8-9) may determine both free parameters of the wave function.
With the experimental values μp/ep ≈ 2.79
2MN , 〈r2 ch 〉≈(0.9fm)2 [1], Eqs. (8, 9) are, strictly
speaking, mutually inconsistent (see Fig. 1). But within our accuracy 30 ÷ 40% they are
sufficiently consistent, yielding a =0.55 ÷ 0.85 fm and 〈κ 0 〉 =50÷ 250 MeV. Similar
values for a were found by other authors [3]. 3 As for 〈κ 0 〉, it is about twice smaller than
typical quark mass in non-relativistic constituent models [1].
Valence quark distribution function. The constructed model should also be able to
describe valence quark distribution at Bjorken x150 MeV
look rather unrealistic. At 〈κ0 〉�50 MeV our xqv(x) holds within the declared 30 ÷ 40%
accuracy with the MRST, CTEQ pdf fits. It seems interesting that the constituent quark
“mass” 〈κ0 〉 = 50 ÷ 100 MeV gets already commensurable with the pion mass scale
mπ ≈ 140 MeV.
�
3However, if instead of (4) one took a model ϕ ∝ 1+ a2κ 2
�−α 2α with α