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Estimates of Sizes of Up
and Down Quarks of the
Three Different Types

Background

This is a follow-up to an alternate model of the quarkic structure of nucleons (protons and neutrons). The conventional theory ttreats quarks as point particles with the force of attraction between them being such that it became stronger the greater the distance between them. This conjecture became known as the bag model of quark confinement. On the other hand the conventional has the force between quarks going to zero as the separation distance between them goes to zero. This notion became known as asymptotic freedom.

Furthermore the conventional theory argues that there are three kinds of each type of quark. It denotes these kinds by color although these kinds have nothing to do with visual color. The conventional theory holds that any baryon contains one quark of each color and so it is color neutral, white. Stripped of the color terminology the conventional theory maintains that quarks can have one of three different attributes and any baryon contains one of each of the three attributes. These conjectures have become accepted as facts in physics.

Here is the standard representation of the radial distributions of electrostatic charge for a proton and a neutron.

This spherically symmetric distribution of charge is incompatible with any planar triangular arrangement of point particle quarks.

The alternate model of quarks considered here takes them to be spherical shells of charges, electrostatic and nucleionic (strong force).

Here is a visual depiction of nucleon structure.


Model of a Nucleon

The colors of the conventional model correspond to the radii of the shells. The spherically symmetric distribution of charge is compatible with nucleons being concentric spheres of charges. And it is obvious why in each nucleon there must be quarks of the three different attributes called color but actually correspond to radii.

The conventional notion of quarks identifies them with the centers of the charges and takes the charge distributions as things generated by these centers whereas the reality is that the charge distributions are the quarks and their centers are just incidental aspects of them.

Preliminary Estimates of Quark Sizes

The radius of the neutron, 1.1 fermi, corresponds to the outer radius of the large Down quar isk. Likewise the radius of the proton, 0.8 fermi, corresponds to the outer radius of the large Up quark. Note that the ratio of those two, 0.73, is about 3/4. The radial distribution of charge indicates that the outer radius of the small Up quark is 0.25 fermi. This would also be, at least approximately, the inner radius of the medium Down quark. The inner radius of both small quarks would be zero.

There is an analysis that indicates that the ratio of a radius of an Up quark to the corresponding radius of a Down quark of the same type is 3/4. This means that the outer radius of a small Down quark is about 0.33 fermi. This would also be the inner radius of a mediumDown quark.

There is a definite change in the slope of the charge distribution of the neutron at 0.85 fermi. That might be the outer radius of the medium Down quark and the inner radius of the outer Down quark. This would make the corresponding radii for the Up quarks 0.64 fermi. Because of the weakness of these estimates their values are put into italics. However the volume between R1 and R2 is proportional to R2²−R1³. For the Up quarks the ratio of the volume of the large type to that of the medium type is, very close to the value of 1.0 that it should be. However, the ratio of the correspondings volumes for the Down quark, 1.24, is not nearly as close.

Here these estimates are put into a table.

Estimates of Quark Radii
(fermi)
Quark
Small
Medium
Large
InnerOuterInnerOuterInnerOuter
Up0.00.250.250.640.640.8
InnerOuter InnerOuterInnerOuter
Down0.00.330.330.850.851.1

Geometric Estimates of Quark Radii
in a Neutron

A neutron contains (4/3) units of charge, positive and negative, contained within its 1.1 fermi radius. This establishes the charge density. The small Up quark at the center of a neutron contains (2/3) of a unit charge. The charge density establishes the volume of this Up quark and its radius of 0.8731 fermi.

Within the outer radius of the medium Down quark (and the inner radius of the large Down quark) there is contained 1=(2/3)+(1/3) unit of charge. That determins a radius of 0.9994 fermi. And of course there is (4/3) of a unit charge contained within the outer readius of the large Down quark.

Here these estimates put into a table.

Geometric Estimates of
Quark Radii in a Neutron
(fermi)
Quark
Small
Medium
Large
InnerOuterInnerOuterInnerOuter
Up0.00.8731
Down0.87310.994
Down0.9941.1

A proton contains (5/3)=(1/3)+(2/3)+(2/3) units of charge, positive and negative, contained within its 0.8 fermi radius. The small Down quark at the center of a proton contains (1/3) of a unit charge. The charge density establishes the volume of this Down quark and its radius of 0.468 fermi.

Within the outer radius of the medium Up quark (and the inner radius of the large Up quark) there is contained 1=(1/3)+(2/3) unit of charge. That determins a radius of 0.675 fermi. And of course there is (5/3) of a unit charge contained within the outer radius of the large Up quark which is the same as the radius of the proton.

Here these estimates put into a table.

Geometric Estimates of
Quark Radii in a Proton
(fermi)
Quark
Small
Medium
Large
InnerOuterInnerOuterInnerOuter
Down0.00.468
Up0.4680.675
Up0.6750.8

(To be continued.)

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