This material stems from a model of quarks being spherical shells of mass and charge and hadrons being concentric spheres of those quarks. A previous study established estimates of densities, volumes and masses for Up and Down quarks in their three different varieties of small, medium and large. These estimates are based upon the characteristics of nucleons and pi mesons such as magnetic moments. It is presumed that these characteristics are intrinsic properties of the quarks and carry over to those quarks in other particles.

This model provides an explanation of why the charged pi mesons composed of only two quarks have masses of only about 273 electron masses but the nucleons with three quarks have masses of almost two thousand electron masses.

The explanation is roughly that a nucleon has a spherical structure. Quarks are spherical shells of mass and a nucleon is three concentric quarkic spheres. A meson is two such concentric spherical shells. The quarks which make up a pi meson occupy a sphere of a radius that is about one half of the radius of a nucleon. They then occupy a volume which is about one eighth of the volume of the nucleon. If volume mass densities are the same then the meson would have one eighth the mass of a nucleon. Thus if the nucleon has a mass equal to two thousand electron masses then the meson would have a mass of 250=2000/8 electron masses. The full explanation, given below, is only a bit more complicated.

This material is to investigate the characteristics of quarks in relation to those of hadrons which include a Charm quark along with one or two versions of an Up or Down quark or their antiparticle versions Such three quark particles are called charmed sigma particles and the two particle versions are called D-mesons.

A double positive charmed sigma particle (Σ_c⁺⁺) is composed of two Up quarks and one Charm quark. It has a mass of 4802.3875 electron masses (m_e).

The D⁻ meson is composed of an Up quark and a Charm quark, Its mass is 3649.0 m_e.

The first question is what are the radial arrangements of quarks in these particles. There is a rule for spin pairing that a particle is linked to no more than one particle of its own kind and no more than one of the opposite kind. If the radial arrangement of quarks in the Σ_c⁺⁺were UCU, where the left represents the center of the particle, this rule would be violated. Therefore the radial arrangement has to be CUU or UUC.

The magnetic moment of the Σ_c⁺⁺ has been measured as +1.76 magnetons. The Up quark has an electrostatic charge of +2/3 and a Charm quark also has an electrostatic charge of +2/3. Thus the magnetic moment is consistent with the CUU radial arrangement and the UUC arrancement as well.

The radial arrangement of the D⁻ meson could be CU or UC. For the radial arrangements of the Σ_c⁺⁺ and the D⁻ particles to be consistent it would seem they would have to be CUU and CU, respectively.

This suggests that the mass of the Σ_c⁺⁺ baryon less the mass of the D⁻meson should be equal to the mass of a large Up quark. The difference is 1152.9875 electron masses whereas the mass of an Up quark was previously estimated to be 1565.5525 electron masses. The two figures definitely do not match except in order of magnitude, but they both might be valid estimates of the mass of a large Up quark..

So there is a problem with the model being investigated. The problem numerically is that the mass of the D-meson is too large compared with that of the Σ_c⁺⁺ baryon. That could be that the radial arrangement of the quarks in the D-meson is UC rather than CU as supposed above. This would mean that the mass for the meson includes the mass of a medium Charm quark but the mass of the baryon include the smaller mass of the small Charm quark. This makes the difference in the masses of the baryon and the meson equal to the mass of a large Up quark less the differnce in mass between a medium and small Charm quark. The figures suggest that difference in the masses of the medium and small Charm quark is about 412 electron masses.

Another sigma particle is composed of two down quarks and one Charm quark. Its mass is 4463.8 m_e. There is a CDmeson with a mass of 3649.0 m_e. Then the mass of the large Down quark might be 4463.8−3649.08 =814.8 m_e. The mass of a large Down quark was previously estimated to be 1563.0214 m_e. Thus from the above the difference in the masses of the medium and small Charm quark should be 1563.0214−814.8=748.2214 m_e.

The Radial Distributions of
Charge in the Nucleons

The radial distributions of electrostatic charge are found by sending electrons as probes against collections of positi and analyzing the deviations from a straight path. Here are the results of such experiments.

The conventional model of the quarkic structure of hadrons is of quarks as charged point particles in a plane rotating about their center of mass. The model being considered here is an alternative to that conventional model. In this model a quark is spherical shell of charge(s). A hadron is two or three concentric shells.

According to this concentric shell model there should be such radial distributions and they should appear the same in any radial direction. According to the conventional model there should be no such radial distribution. The perceived charge would depend upon the angle between the radial direction and the plane of point quarks.

The experimental radial charge distribution for a neutron, shown above, could not occur unless there is a radial separation of the Up quark and the Down quarks.

The radial distribution of charge for neutrons is entirely in keeping with the concentric shells model. However according to this alternative model there should also be radial range of negative charge for the proton. It may well be that the experimentalists who developed the above distribution for protons overlooked such negative charge density because they were not expecting it.

At SLAC it was found that some of the electrons in the probing of protons bounced back this was interpreted as evidence of electrons impinging upon the hard cores of quarks It could equally well be interpreted as electrons impinging upon a region of negative charge.

In the concentric shells model of the quarkic structure of hadons a quark is a spherical shell of electrostatic charges.

A hyperon in this model consists of three concentric rotating quarkic shells. There is thus three versions of each quark: The small, medium and large versions. It is impossible to separate them because any action taken againt the outer quark equally affects the other quarks in a nucleon. There may also be bindinding energies created by the spin pairing of quarks within the hadrons.

Conventionally each quark has another attribute that is callled color although it has nothing to do with visual color. A nucleon has quarks of each color so it is said to be color neutral white.

The attribute corresponding to color is the outer radius of the quark shell. It is obvious in this model why there must be quarks of three different attributes in each nucleon.

The force of attraction is zero between shells of opposite charge if one is located within another but becomes large positive if they are not concentric. However, if separated the force of attraction decreases with separation distance.

There is no mechanism that would account for the radial distributions of charge and their boundedness if quarks were point particles. On the other hand if quarks are bounded symmmetrical distributions of charge their effects outside their boundaries is the same as if their charges were concentrated at their centers.

An actual point particle would have infinite energy. There is not enough energy in the entire Universe to create even one charged point quark. That is to say, in attempting to create one point particle quark the the effort would fail even after all of the energy of the billions of stars in every one the billions of galaxies is used up. And there would be nothing left over for creating a second quark or any of the zillions upon zillions of other quarks in the Universe.

The Masses of
the Charm Quarks

The mass of a D⁻ meson with a radial arrangement UC is 3649.4 electron masses. The previously estimated mass of a sall Up quark is 50.2382 electron masses. These figures imply that the mass of a medium Charm quark is 3599,1618 electron masses.

To find the volume occupied by a medium Charm quark requires its density The densities the U quark and the Down quark have been estimated. It is plausible that the density of a quark is a function of its charge. If the density of a Charm quark is the same as that of an Up quark the the volume occupied by a medium Charm quark is (3599.1618)/(768.1684)=4.6854 f³. This value divided by (4/3)π gives the cube of the radius; i.e., 1.1186 ³ Hence the radius of a medium Charm quark should be 1.0381 fermi. This is about the radius of a large Down quark (the radius of a neutron). This would make the radius of a large Charm quark, if any such exists, surprisingly large.

Magnetic Moments

A magnetic moment is generated by spinning charged particles or charged particles in shells if flowing in a circular path. For some of the details llof the technicalities of magnetic moments see Studies.

A magnetic moment of a system composed of charged particles rotating about a center can arise in part from that rotation of charges. This is usually called a dipole moment. But it is thought that the magnet moment of a rotating particle structure can also come from the intrinsic magnetic moments of the particles. This latter phenomenon is usually deemed as being due to the spin of the particles. In 1922 the physicists Otto Stern and Walther Gerlach ejected a beam of silver atoms into a sharply varying magnetic field. The beam separated into two parts. This separation could be explained by the outer unpaired electrons of these atoms having a spin that is oriented in either of two directions. It has been long asserted that this so-called spin is not necessarily literally physial particle spin. However there is no evidence that it is not. Here it is accepted that the magnet moment of any particle is due to its actual spinning.

In the concentric shells model the concentricity of three spheres forces a closeness of their centers. Also if the spheres are subject to a force that drops off faster than distance squared then concentric spheres will line up their centers exactly. See Quarks for the details.

The experimentally determined radial distribution of charge density is compatible with the concentric shells model but not with the conventional model.

Conclusions

All in all the concentric shell model better explains the single fact, the absence of evidence of an isolated quark, explained by the conventional model and lends itself to further analysis that the conventional model doesn't.

For more on the quarkic spatial structure of nucleons see Sensible Model of Quarkic Structure of Nucleons.

(To be continued.)