This material stems from a model of quarks being spherical shells of charge and mass. Hadrons are concentric spheres of 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 quarks in other particles.

This material is to investigate the characteristics of quarks in relation to those of hadrons which include a Bottom quark along with an Up or Down quark. These are called hyperons. There are also mesons containing Bottom quarks. These are called kaons or b--meson s. They include a Bottom quark and an anti-version of an Up quark or a Down quark.

A positive bottom sigma particle is composed of two up quarks and one Bottom quark. Another sigma particle is composed of two down quarks and one Bottom quark. The neutral sigma particle is composed of one up quark, one down quark and a strange quark. The Up quark has an electrostatic charge of +2/3 and a Bottom quark an electrostatic charge of −1/3. Therefore a positive sigma particle has an electrostatic charge of +1. A neutral sigma particle has a charge of zero. A sigma particle with two Down quarks and a Bottom quark has a charge of −1. But a particle consisting of a Down quark and two Bottom quarks would also have a charge of −1.

As mentioned above there are also mesons which contain a Bottom quark. The negative b--meson consists of a Bottom quark and an anti-Up quark. An anti-Up quark has the same characteristics as an Up quark exept its charge is the opposite. Thus a negative b--meson has a charge of −1.

A meson consisting of a Bottom quark and an anti-Down quark would have a charge of zero. A meson consisting of an Up quark and an anti-Bottom quark would have a charge of +1. It would be properly called a positive b--meson .

The Radial Distributions of
Charge in the Nucleons

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

The conventional model of the quarkic structure of nucleons is of quarks as 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 nucleon is 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 peceived 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.

In the concentric shells model of the quarkic structure of hadrons a quark is a spherical shell of electrostatic charge and mass.

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.

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.

In the conventional model of hadron structure 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 and mass their effects outside their boundaries is the same as if their charges and mass were concentrated at their centers.

An actual charged 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 Bottom Quarks

The mass of a positive bottom sigma particle Σ_b⁺ is 11,372.4071 electron masses (m_e). The question is the radial arrangement of the quarks The three possibilities are BUU, UBU and UUB, where the left represents the center of the particle. There is a rule for the linkage of particles that a particlle is linked to no more than one of the same kind and no more than one of the opposite kind. the arrangement UBU violates that rule.

The mass of a positive b-meson is 10,331.2916 electron masses (m_e). Its radial arrangement could be BU or UB. If the two arrangements are BU and BUU the the difference in the masses of the Σ_b⁺ and the positive b-meson should be the mass of a large Up quark. That difference is 1034.2661 m_e, but the mass of a large Up quark was previously estimated to be about 1565 m_e.

If the arrangements were UUB and UB then the difference should be the mass of the medium Up quark plus the difference between the mass of the large Bottom quark and the mass of the medium Bottom quark. It is plausible for that quantity to be 1034.2661 m_e.

The mass of a negative bottom sigma particle Σ_b⁻ consisting of two Down quarks and one Bottom quark is 11380.0391 m_e. The mass of a negative b-meson is 10,331.9178 m_e, The difference should be the mass of the medium Down quark plus the difference between the mass of the large Bottom quark and the mass of the medium Bottom quark. The difference is 1048.1213 m_e. The mass of a medium Downquark was previously estimated to be 223 m_e. Thus the difference between the mass of the large Bottom quark and the mass of the medium Bottom quark shou ld be about 825 m_e.

(To be continued.)

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 of 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.

A charged spherical shell within another charged spherical feels no force. The so-called colors of quarks are the radii of the spherical shells and this explains why a nucleon composed of three concentric quarkic shells needs one of each color.

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.

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

(To be continued.)