A theoretical model is advanced to account for the 2nd and 3rd particle generations, associated production in quarks, type and number conservation in leptons, and the paralleling of generations between quarks and leptons. It's predicted that 2nd and 3rd generation quark flavors are conserved via transfer to respective generation neutrinos. An explanation is established for P violation in weak interactions, and the restoration of symmetry under the combined operations of parity and charge conjugation (CP). CP violation is also derived from the basic assumptions constituting the core of this model.

One of the longstanding puzzles of the Standard Model is the existence of two additional families of fundamental particles. The question of whether there are more families has recently been addressed¹. Evidence at two ends of the scale - astronomical and the particle level - persuasively fixes the number of additional families at precisely two¹.

The explanation for these duplications may lie in the existence of 'weak' magnetic pole charges that would constitute weak field analogues of Dirac monopoles². If the weak field accompanying an electron neutrino behaves as a local gauge field it automatically imposes the requirement that a secondary magnetic type field be associated with it (provided the neutrino possesses a finite mass). In contrast to the infinite range of the normal magnetic field this putative weak magnetic dipole field should reflect the weak force's intrinsicly short range, and its influence should not extend beyond about 10^-16 cm. It then follows that every fermion carrying a weak charge should possess this limited range weak magnetic bipolar field.

In analogy with the electric field surrounding a charged particle, which is polarized with particle-antiparticle pairs, it's assumed the vacuum surrounding the weak charges carried by left-handed fermions would possess weak magnetic pole-antipole pairs, that could materialize into real particles with sufficient energy input. On symmetry grounds it seems reasonable to assume that there would be two pole-antipole sets analogous with the electric field wherein virtual electron-positron and proton-antiproton pairs populate the vacuum. Thus, there would be a weak north-antinorth set and a weak south-antisouth set.

In normal low energy regimes these weak magnetic monopole pairs would remain unobserved since they would be confined to vacuum fluctuations. Only at higher energies would they be manifested, and then as components of the higher generation particles, where a pole charge would replace a normal weak charge. Or alternatively, a pole charge could form a discrete particle - either a muon neutrino or tau neutrino, or one of their antiparticles. (By "normal weak charge" it is meant the 'charge' carried by the electron neutrino or antineutrino, or any left-handed 1st generation fermion. The electron neutrino carries no electric charge, but the Standard Model assigns the electron neutrino with one quantum unit of weak charge. Considering the expectation that the intrinsic spin of the neutrino creates a bipolar weak magnetic field, the normal weak charge can, essentially, be thought of as a weak electric charge. (This distinction becomes highly significant as will be seen later).

One pole charge pair - the weak south-antisouth set - is arbitrarily assigned to the 2nd generation leptons and quarks. That is, strangeness and charm in the 2nd generation quarks, and muonness in 2nd generation leptons would be a manifestation of the same weak south pole charge, or weak antisouth pole charge present in what would normally be 1st generation particles. By convention, then, 3rd generation leptons and quarks would arise from the presence of a weak north or antinorth pole charge coupled to each member of this generation. Since there are only two poles in a dipole field the limit of two additional families is readily understood. Furthermore, it would be expected that the coupling forces between the electric charge in a quark (or charged lepton) and the weak magnetic charge of the weak monopole would be inherently unstable, and this may be the principal factor limiting the lifespans of the muon, tau, and the higher generation quarks.

Since the pole charges are assumed to exist in matter-antimatter sets this would account for associated production in quarks and the conservation of lepton number in the 2nd and 3rd generations. The muon neutrino and tau neutrino would constitute the 'bare' or quantitized south and north weak magnetic pole charges, respectively. Implicit in these arguments is that weak pole charge is conserved - implying the higher quark flavors are conserved. Where 2nd generation flavors disappear the theory proposes that it is carried off by either a muon neutrino or antineutrino corresponding to a weak south pole charge or weak antisouth pole charge, respectively. Third generation flavors, in turn, would be carried off by either a tau neutrino or antineutrino corresponding to a north weak pole charge or antinorth weak pole charge, respectively.

It has long been accepted that the 2nd and 3rd generation quark flavors are not conserved and the experimental evidence does not appear to contradict this belief. However, if neutrinos are carrying off the higher generation flavors their presence in a decay could only be discerned by direct detection or by their momentum contribution. In the former case the low reactivity of neutrinos makes direct observation exceedingly difficult, while in the latter case their momentum influence is likely to be obscured by the immense energies involved in higher generation hadronic production.

A total of ten flavor changing decays in which one unit of strangeness was dissapated were examined from old bubble chamber photos. Of these, six on initial inspection appeared as likely candidates for possible momentum disparity. Two more were suggestive of momentum discrepancies. One event was inconclusive since neutral particles were among the decay products complicating the analysis. The final event displayed no obvious evidence of momentum imbalance. The absense of evidence in this case may simply imply that the momentum vector of the proposed neutrinos closely coincided with the mean axis of momentum of the visible decay particles. All events where a quantitative assessment of momentum was obtainable directly from the photographic plate were evaluated and revealed varying degrees of momentum inconsistencies. The analysis of one of these events is detailed below.

Figure 1(a-c) illustrates a lambda decay arising from the reaction K^- + p → Λ + π⁰. The lambda originating at (A) decomposes to a pion and proton at (B) in diagram 1(b). In the process one unit of strangeness is lost. With the track of the neutral lambda serving as the reference line (vertical axis in diagram 1(c) ) for all angular measurements it is seen that the proton's initial track section subtends an angle of about 3.25° counterclockwise from the lambda's track. The pion's initial track subtends an angle of 160° clockwise from the lambda's trajectory. This information combined with the relative momenta of these two decay products allows an assessment of the momentum vectors of these particles.

The momentum of a charged particle in a magnetic field can be inferred from the radius of the particle’s curvature in the field. The degree of this curvature is given by mV/qB where m is the mass of the particle, V it’s velocity, q the charge on the particle, and B the magnetic field strength. Since q and B are the same magnitude for each particle we need only concern ourselves with the vector products m₁V₁ and m₂V₂ for the pion and proton, respectively. The magnitudes of these vectors are proportional to the curvature radius of each particle's track. The measured radius of curvature of the early part of the proton's trajectory is about 329 mm, while the curvature radius for the pion is about 96 mm.

Since the deflection field B, and the individual charges carried by each particle are not considered, the total momentum values of 96 and 329 (for the pion and proton respectively) constitute dimensionless numbers. Taking the sine of the pion's deflection angle from the lambdas trajectory (160°), and multiplying it by its dimensionless total momentum value (96), gives the transverse component of momentum for the pion, which works out to -32.83. In turn, multiplying the sine of the deflection angle for the proton (3.25°) by its dimensionless total momentum value (329) gives the proton's transverse momentum component, which comes out to 18.63.

It is immediately apparent that the transverse momentum component for the pion is far greater in magnitude than that for the proton - 32.83 versus 18.63; which means that momentum may not be conserved with respect to these two particles alone. The transverse components should be exactly equal, assuming no other particles are departing the decay vertex, since the originating lambda has no transverse component to its motion in the reference frame chosen.

It's tempting to suppose that a neutral unobserved particle (or particles) are carrying off the uncorrelated momentum. However, since these measurements are derived from a single camera perspective the 3-D structure of the particle tracks is not being taken into account. It would be desirable, therefore, to reconstruct the tracks of similar decays using stereoscopic techniques of the greatest possible precision.

Since the departure of a single extra fermion in flavor changing reactions would add 1/2 unit of spin it would appear the law of spin conservation is violated. But, recall that it is assumed the weak magnetic pole charges carried by 2nd and 3rd generation particles substitute for a regular weak charge. Therefore, in the transition of the higher generation quark back to a 1st generation quark, an electron neutrino or antineutrino must also be emitted to balance weak charge accounts. It follows that one must always be a particle and the other an antiparticle, so their spins cancel since neutrinos and antineutrinos of any generation have fixed spins with opposite helicity. The net spin of any higher generation quark transition is thus not altered. The higher generation quark decays must therefore parallel the 2nd and 3rd generation leptonic decays where a neutrino/antineutrino pair is emitted - one of 1st generation, while the other corresponds to the generation of the original charged lepton.

A mechanism is also provided for explaining parity (P) violation in weak interactions and the restoration of symmetry under the combined operations of charge conjugation and parity (CP). Robert K. Adair of Yale University has proposed a thought experiment in which a proton traverses a curved path through the magnetic field created by capacitor plates charged with Dirac monopoles³. In such a configuration the reversal of time reverses the direction of the proton's travel, but not the polarity of the magnetic field created by the monopoles. As a result the proton's path is not retraced and it is seen that the conditions defining the experiment are not invariant with respect to time reversal. But, time invariance (T) is essentially equivalent to CP invariance, so a condition that involves the mixing of electric and magnetic pole charges would appear to automatically lead to CP violation.

This situation is exactly what is entailed in the weak monopole scenario, except that it is the mixing of weak electric and weak magnetic pole charges that is involved. In principle, we then have a viable mechanism to explain CP violation. But this explanation needs to be qualified somewhat. If the cloud of virtual weak monopole pairs were distributed uniformly about every quantum particle the effect should be to balance out the CP violating forces, and the overall system would be CP conserving. This result follows from straightforward geometric arguments applied to Adairs's original conception.

An axially symmetric distribution of pole charges should obtain along the polar axis of any isolated weak charge. Just as virtual e+/e- pairs cluster around an ordinary electron and virtual p+/p- pairs cluster around a proton, so the weak pole pairs would cluster about their appropriate hemispheres. In short, these polar regions would serve as loci of their respective weak virtual pole charges, whose distribution would be axially symmetric. Since the tau neutrino (weak north monopole) is probably much heavier than the muon neutrino (weak south monopole) it will take more energy to create a given number of virtual weak north-antinorth monopole pairs. This obviously leads to an asymmetry in the degree of virtual weak monopole charge polarization between the two polar regions. This asymmetry, in turn, might well be the source of parity violation observed in processes mediated by the weak force by disrupting the delicately balanced forces that determine the choice of polar emergence (and hence the handedness) of secondary decay products. Thus, P violation in weak interactions could be traceable to the mass differential between a muon neutrino and tau neutrino. Most importantly, this idea provides a physical basis for asymmetry in fundamental particles, a precondition for parity violation.

Since the weak dipole field of a quantum particle should align with the normal magnetic dipole field of the particle (by virtue of Z₀ coupling between the electromagnetic and weak fields) it would be expected that the parity violating force would manifest most strongly along the particle's longitudinal axis. This is precisely what is observed in weak decays. In the classic parity testing experiment conducted by Wu et al.⁴ in 1957 a sample of radioactive Co₆₀ was cryogenically cooled to minimize thermal jiggling, and subjected to an intense magnetic field to align the Co₆₀ nucleii with the external magnetic field. It was found that a preponderance of beta particles emerged from the south magnetic hemisphere of the nucleii. Had the Co₆₀ in this experiment been replaced by its antimatter twin, the asymmetry in terms of handedness would be reversed; that is, the majority of positrons would be right-handed. Consequently, the decay of anti-Co₆₀ would appear as the mirror image of Co₆₀ decay, and beta decay is therefore CP conserving.

The virtual weak monopole concept can readily explain this restoration of symmetry when charge-conjugation is taken into account. In antimatter the reversal of charge reverses the sense of rotation needed to create the same direction of dipole field as observed in matter. However, the virtual weak monopole distribution is pole dependant so the majority of positrons would still emerge from the local south pole of the Co₆₀ nucleii. Since the relative spin of the anticobolt is reversed from that in cobolt the emerging positrons are imparted the opposite handedness as that of the electrons produced in Co₆₀ decay.

Most higher generation weak processes are believed to have a small CP violating component as a slight pertubation on the dominant parity violating component. This is exactly what would be expected since 2nd and 3rd generation particles (with the exception of the neutrinos) would be mixed assemblies of weak electric and weak magnetic pole charges. Also, unlike the situation for individual isolated weak charges the overall spatial distribution of weak electric and magnetic pole charges should contain significant asymmetries in composite particle structures creating the condition for CP violation.

CP violation was first observed in k₂ type neutral kaons in 1964 when it was demonstrated by Christenson et al.⁵ that they decayed to a pion pair with a branching ratio of about 2 × 10^-3. Since a neutral kaon is composed of a mixture of 1st and 2nd generation quarks it constitutes an asymmetric mixed weak pole charge assembly, and therefore would be expected to violate CP symmetry via the aforementioned Adair mechanism. More detailed analysis would be needed to explain why this proposed CP violating mechanism varies in strength from one weak interaction to another.

The mass spectrum observed between the three particle generations cannot be a direct function of the mass values of the weak pole charges since the upper mass limits established for the ν_μ and ν_τ are fractions of the masses of the 2nd and 3rd generation quarks and leptons. Instead these masses may derive from residual uncancelled mass-energy, if it is assumed that the weak charges constitute a component of some, as yet, unknown prequark substructure (prequark being used here in a generic sense to embrace a possible substructure to charged leptons as well).

The classical electron radius (r_e = 2.8 x 10^-13 cm.) precludes the possibility that the weak charges are the primary prequarks since conservation of angular momentum in such a confined space demands energies in the multi-Gev range for such hypothetical prequarks. This is much greater than the energy needed to produce 2nd or 3rd generation particles. A secondary role for weak charges in a prequark substructure is not ruled out, but it implies a more complex substructure than envisaged in contempory prequark theories such as the Rishon model⁶ proposed by Haim Harari.

In summary, it would be worthwhile to scrutinize existing archives of relevant flavor changing events to look for discrepancies in the momentum of the decay products that may have previously been overlooked. It should also be feasible to design experiments that would optimize conditions for detecting momentum anomalies in higher generation quark decays. Direct detection of the proposed flavor transition derived neutrinos would provide unabiguous confirmation of the weak monopole concept.

[1] Gary J. Feldman and Jack Steinberger, "The Number of Families of Matter", Scientific American, February, 1991.