VbvNeuE-001

Chapter 2
Is it possible to construct a
proton from quarks with an
integer charge [4]
Gell-Mann, when creating his theory, proceeded from the assumption that both
- proton and neutron - are elementary particles with different quark sets.
Because of this, the main purpose of his model was to explain the process of
conversion of neutron into proton on the quark level.
The solution of this problem required the introduction of quarks with fractional
charges that are not experimentally observed and are not intended for
predicting of nucleons properties.
However, if we take into account the electromagnetic nature of neutron [3],
it turns out that a explanation of the conversion of neutron into proton is
unnecessary and it is quite possible to model basic properties of proton using a
set of quarks with integer charges.
To calculate the basic properties of proton let’s construct it out of quarks
with integer charge (+e, -e). We assume that, as in Gell-Mann’s model, the
proton consists of three quarks. We also assume that own spin of the quarks
is absent, and their quantum motion is expressed in their rotation around a
common center of circle of radius R (Fig.(2.1)).
Let the value of the radius R is determined by the fact that the length of
the circumference 2πR is equal to length of de Broglie waves of quark λ D :
2πR = λ D = 2π
p q
, (2.1)
where p q is quark momentum.
For simplicity, we will assume that quarks have the same momentums p q
and rotate in a single circle, so that equality (2.1) reduces to equation
p q R = . (2.2)
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