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Spin, Mass and Size
Characteristics of Hyperons
Which Contain a Top Quark

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 Top quark along with one or two versions of an Up or Down quark or their antiparticle versions Such three quark particles are called topped sigma particles and the two particle versions are called mesons.

A double positive top sigma particle (Σt++) is composed of two Up quarks and one Top quark. Its mass has not yet been measured.

The mass of a meson composed of an Up quark and a Top quark also has not been measured. .

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 Σt++ were UTU, where the left represents the center of the particle, this rule would be violated. Therefore the radial arrangement has to be TUU or UUT.

The Up quark has an electrostatic charge of +2/3 and a Top quark also has an electrostatic charge of +2/3. Thus the charge of a Σt++ is indeedd +2.

The radial arrangement of a Top quark-containing meson could be TU or UT. For the radial arrangements of the Σt++ and the Top quark-containing meson particles to be consistent it would seem they would have to be TUU and TU, respectively.

There is another sigma particle is composed of two Down quarks and one Top quark. Its mass has not yet been measured.

A single positive topped sigma particle would be composed of one up quark, one down quark and a Top quark. The Up quark has an electrostatic charge of +2/3, a Down quark of −1/3 and a Top quark an electrostatic charge of +2/3. Therefore a single positive topped sigma particle has an electrostatic chargeof +1.

A neutral sigma particle has a charge of zero. A sigma particle with two Down quarks and a Top quark has a charge of 0.

A meson consisting of a Top quark and an ant-Down quark would have a charge of +1. A meson consisting of an Up quark and an anti-Top quark would have a charge of zero.

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 Top Quarks

The accepted mass of a Top quark is 338,552 electron masses. That is about 181 neutron masses or roughly the mass of an atom of Hafnium.

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.


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. There is however not enough measurements for particles containing a Top quark to apply the concentric shells model to the particles containing a Top quark.

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

(To be continued.)

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