What is the Relationship Between Quark Size and Electric Charge?

[kurious]

When I use the following equation which assumes quarks are spheres of charge and compressing the spheres creates mass (by doing work):
mass of quark = integral of ( k q ^2 / r^2 c^ 2 ) d r

and input masses from the mass equation I arrived at by trial and error a few months ago

Mass = [12.50 x 10^3pi (n – 5) / 2 0] x ( n – 4 )^ 2 x 10^ 39 ( n – 3 ) / 2 x 10^57 x q ^n

I get radius of up quark,charm quark and top quark to be around 10^-18,
10^-19 and 10^-22 metres respectively.

If I am right this means that the assumption of quantum field theory that charges are pointlike is incorrect.However the integral only allows me to obtain the difference 1/r1 -1/r2 where r1 is initial radius and r2 is compressed radius of a sphere.Can anyone think of a way to get r1 for a quark?

 

[Antonio Lao]

The property of electric charge is related to the concept of a force as shown by Coulomb's law.

Coulomb's law is of the same form as Newton's law of universal gravitation and Biot-Savart law of magnetism. The form is the inverse square of distance.

When it comes to quarks (quarks are fractionally electric charges), a new kind of charge is needed, namely the color charges called gluons, to explain the interaction of quarks with each other. This is not of the same form as the inverse square laws mentioned above. This force law of the quarks is still much of an open question although many theories such as QCD and the Standard Model have good explanations.

But still, the quarks and the leptons remain as point-particles.

 

[kurious]

Nobody knows if the colour force dominates electricity at less than 10^-18 metres!

 

[Antonio Lao]

Do you have any idea by using the concepts of asymptotic freedom and infrared slavery? I will try to think about it.