This hadron tutorial is intended to make you familiar with the structural concepts and graphic
conventions of IPP’s drawings of mesons and baryons, so you can get the most out of them.
1) How IPP’s Graphic Convention For A Defect-Pair Is Derived
A: C-void planes with a solidly filled interior
B: C-void planes connected by a column of ECEs
C: C-void planes connected by a column of lattice cube
D: Final representation
2) Picturing Defect-Pairs Dynamically - The Collapse And Uncollapse Of Their C-voids
Defect-pairs form only in regions in which the lattice is fully collapsed.
Defect-pairs form only in regions of space in which there is enough
capturable shrinkage to fully collapse the lattice.
a hadron’s hovering lattice-density oscillation must have sufficient mass-energy to
saturate its central region during the peak density phase of its cycle. This requirement
accounts for the very brief moments when a defect-pair’s c-voids are fully uncollapsed,
as shown below.
3) Defect-Pair Spacings
A defect-pair's spacing is the distance in lattice units between the centers of its
c-voids. These spacings vary between 5ü to 15ü, usually increasing with the number of
defect-pairs clustered at the hadron’s center. Charged defect-pairs (those having odd
spacings) are distinguished by a single girder color (gold for + +, blue for - -).
Neutral defect-pairs (those having even spacings) have both girder colors, which meet
at the middle of the defect-pair. Below are four defect-pairs:
“A” and “B” are charged defect-pairs, spaced 7ü and 9ü. “C” and “D” are neutral
defect-pairs, spaced at 6ü and 8ü. (ü = one lattice unit).
4) Defect-Pair Mass-Energies
A compelling feature of IPP’s defect-pairs is that their individual mass-energies vs.
their spacings can be accurately calculated, and that these values hold precisely
throughout the whole spectrum of hadron particles. Here are the equations for calculating
these mass-energy values, in MeV, and graphs and tables showing the results of these
Odd defect-pair spacing mass-energy (MeV) =
Even defect-pair spacing mass-energy (MeV) =
5) Defect-Pair Slant
C-void defects can pair only when their zones of expansion & contraction are mutually
canceling (i.e., orthogonal), and when their centers are in cardinal lattice directions
from each other. If we call the direction of expansion of the two c-voids their “slant”,
we see immediately that there are two equally probable “slant” directions that permit
c-void pairing. We show these two forms, below, which we will distinguish by calling the
left figure, “L-slant”, and the right one, “R-slant”.
These labels take on meaning only when we specify two things: 1) the viewing location
(always from the particle center), and 2) the orientation of the eyes (e.g., in this case,
both eyes parallel to the x-z plane). The utility of these “slant” labels will become
evident as we proceed.
6) Slant Forms of Two-Defect-Pair Clusters
Orthogonal defect-pairs have two possible slant configurations. Below, left, we
show a two-defect-pair cluster with an x-axis L-slant defect-pair, and a z-axis R-slant
defect-pair. We refer to this mixed slant arrangement of orthogonal defect-pairs as A-slant
(for alternate slants). Below this is the other A-slant possibility (X=R, Z=L). Below,
right is a two-defect-pair cluster where both x-axis and z-axis defect-pairs have
L-slant. Below this is the other S-slant possibility (X=R, Z=R).
We refer to this slant arrangement of orthogonal defect-pairs as S-slant (for same
slant}. It should be obvious that S-slant neutral kaons have equal probability
of being created in either R-slant or L-slant configurations, and that A-slant
neutral kaons have equal probability of having L-slant or R-slant x-axis defect-pairs.
7) Slant Forms of Three-Defect-Pair Clusters
The slant forms of clusters of three mutually orthogonal defect-pairs (e.g., nucleons) can
in eight configurations (2x2x2). However, it is useful to think of these as just two basic
types, T-slant & M-slant. The two possible T-slant forms are shown below, left, and
two of the six possible M-slant forms is shown below, right. The planar slant relationships
for the three two-defect-pair subgroups in each form are shown as equal to A or S.
A refers to A-slant and S refers to S-slant. The T-slant form gets its name
from the tetrahedron produced by the projection of the axes of expansion of its six c-voids.
The M-slant form, or mixed form, gets its name from being produced merely by altering the
slant of one of the defect-pairs (in the case below, the Y defect-pair) of either of the
two T-slant forms. IPP is able to prove (see page 3-25 of online book)
that all nucleons (protons, neutrons, and antiprotons) exist only the two T-slant forms.
M-slant forms are apparently unstable, and occur only in certain kaon resonances.
8) Defect-Pair Bonding - IPP's Concept Of The Strong Force
Since the c-voids of defect-pairs are spaced apart, the mutual cancellation of their
orthogonal zones of expansion & contraction distortion is incomplete! Hence, there will
be residual expansion/contraction distortion extending from each end of defect-pairs. Thus,
when adjacent defect-pairs approach each other along a common pairing axis, with their
adjacent slants crossed (of opposite orientation), further cancellation of distortion
(mass-energy) can occur. This cancellation of mass-energy binds the two defect-pairs
together, and is termed a “paraxial strong-force bond”, or, more usually, a “paraxial bond”.
Another possibility of distortion cancellation occurs when the two defect-pairs lie
parallel to each other, with their respective c-voids lying in the same cardinal plane and
in lattice face-diagonal direction from each other. Cancellations of mass-energy in this
configuration are termed, “diagonal strong-force bonds”, or, more usually, a “diagonal bond”.
We show examples of these two types of bonds, below:
An Example Of A Paraxial Bond - rho(770):
The rho(770) is the simplest example of a paraxial bond. In the upper example, the green
girder of 8ü length is the symbol for a paraxial bond between two 10ü defect-pairs whose
adjacent c-void defects are "crossed", and opposite in polarity. In the lower example,
where the bonded c-voids have the same polarity, the bond spacing will clearly be odd.
Charged rhos also
form, where one of the defect-pairs is charged, one neutral; and neutral rhos form, where
the two bonded defect-pairs have opposite charge. Double charge rhos evidently do not form,
probably because there is too much repulsion to permit the bond to form. Paraxial bond
spacings tend to scale inversely with the size of the bonded defect-pairs. This will
become clear as you study the numerous examples of meson and baryon resonances in our
An Example Of A Diagonal Bond - eta(547):
The eta(547) is the simplest example of a diagonal bond. In states 1 and 3, two neutral 8ü
defect-pairs of opposite slant site parallel to each other, such that their respective
c-void defects lie in face-diagonal directions from each other at spacing of 5ü/
(five face-diagonal lattice units, or 5v2). In states 2 and 4, opposite-charge 9ü defect-pairs site in the same geometry at the same spacing of 5ü/. The eta(547) alternates, by
charge-exchanges, between these two forms as it translates through the lattice. It is
characteristic of diagonal bonds that the bonded c-void defects have opposite polarity,
and that they occur dominantly in neutral resonances. With further study, you will
An Example Of Ring Diagonal Bonds - eta'(958):
The eta'(958) is the simplest example of ring diagonal bonds. Ring diagonal bonds
consist of four parallel defect-pairs sited equidistant from each other in face-diagonal
directions, with their "slants" alternating around the ring, as shown. The eta'(958)
closely resembles the eta(549), having 8ü defect-pairs spaced 5ü/ apart. It differs
only in not altering its defect-pair spacings to 9ü as it translates through the
lattice. Defect-pairs in a ring arrangement develop four diagonal bonds. However, IPP
defines a ring-diagonal bond as just two of these four bonds in its bond mass deficit
calculations, because in some particles only half a ring bond is formed. Ring diagonal
bonds are found in most meson resonances of higher mass-energy, and in all nuclei
except the deuteron.
An Example Of Multiple Bond Types - alpha particle:
Most particles possessing ring-bonded defect-pairs also have paraxial-bonded defect-pairs.
The two protons and two neutrons comprising the alpha particle are interconnected with
both types of bonds, as shown below.
9) Calculating Bond Mass-Deficits (in MeV)
Calculating the mass-deficits of strong force bonds between defect-pairs is
straightforward in IPP, because all the bond elements (defect-pair spacings
& bond spacings) are quantized. Here are the relevant equations in succinct
form. To learn how these are derived, see Chapter 2 of the online textbook.
Paraxial Bond Equation:
m1 and m2 are in MeV; d1, d2, d3 are
in lattice units; P = 1 / 294.17
Diagonal Bond Equation:
m1 and m2 are in MeV; f is in face-diagonal lattice units; S = 1 / 511.92
10) Defect-Pair Cluster Charge-Exchanging
What Is A Charge-Exchange?
IPP views a hadron charge-exchange as the process by which opposite-polarity c-voids
sited in face-diagonal directions from each other can move into each other's (approximate)
locations. Charge exchanges can take place only during the "void" state of a c-void's
hovering oscillation cycle, which, you will recall, is during the phase when the
surrounding ECEs have their lowest packing density. IPP calls this (lowest packing
state) "the central
rarefaction phase" of the hovering oscillator's lattice density oscillation.
How Are Charge-Exchanges Accomplished?
The means by which this charge-exchange is accomplished is through the synchronized
displacements of all the same-charge ECEs in two contiguous face-diagonal columns
of opposite-polarity extending between the before and after locations of the two
opposite-polarity c-voids. The effect of each column's displacement by one face-diagonal
toward the existing "void" is to annihilate it (by filling it), while the column's
displacement at the opposite end creates a "void" of the same polarity in that new site.
Both newly created "voids" immediately collapse into c-voids, as their synchronized
hovering cycles progress into their phase of higher central compaction. It is this
collapse that prevents the void exchange from developing into the continuous
back-and-forth oscillatory pattern of two bound isolated opposite-polarity voids
(IPP's concept of an electron neutrino).