In the standard model (SM) of particle physics, quarks come in three colors, red, green and blue. It’s not that the colors mean anything. They don’t, but just as the three primary colors mix to white, the three quark colors mix to neutral color, which many times is conveniently glossed over in discussing quarks. In Bilson -Thompson’s (BT) paper, his braids of three helons are uniquely ordered to represent the 3 possible colors for each of the four quarks. We adopt a similar arrangement, as shown in figure 1 below:
Figure 1. Three Colors of Quarks
To facilitate identification of the quark colors in the scheme, the S|T positions in the triplet have been numbered and the colors of the inner terms of the S|T units have been denoted as positive, negative, and neutral charges. Notice that, in the red column of quarks, the “odd-man-out” (S|T # 3) is to the right of the two like-color charges, while, in the green column, the “odd-man-out” (S|T # 2) is in the center, and it (S|T # 1) is to the left of the like-color charges in the blue column. This scheme is different than the BT scheme, but it correlates with our color convention of placing the color red “below,” to the left, of the color green, and the color blue “above,” to the right of the color red and green, just as 1 is lower than 2 and 3 is higher than both of them, so we put 1 to the left of 2, and 3 to the right of 2, to indicate the ascending order.
The first reaction to this concept of rearranging the locations of the colors in the triplet is that it is meaningless, since the orientation of the S|T units in the triplets is invariant under rotation, just as the geometric triangle is also. However, while this is true, it is also true that, relative to one another, the different positions have meaning; that is, while there is no absolute distinction, there is a relative one, which represents the relative orientation of the constituent S|T units of one triplet, relative to the orientation of the constituent S|T units in a second and a third triplet.
In the SM way of combining 3 quarks to form a first generation hadron, a proton or neutron, the resulting hadron must be color neutral. That is to say, one triplet in the hadron must have a “red” orientation, one a “green” orientation, and the third a “blue” orientation. In the braids of BT, this is accomplished by “stacking” the braids. He writes in his paper, A Topological Model of Composite Preons that the color interaction can be physically represented as a “‘pancake stack’ of braids” that can be added together as permutation matrices:
We may similarly represent colour interactions physically, this time as the formation of a “pancake stack” of braids. Each set of strands [in a braid] that lie one-above-the-other can be regarded as a “super-strand”, with a total charge equal to the sum of the charges on each of its component strands. If we represent braids as permutation matrices, with each non-zero component being a helon, we can easily represent the colour interaction between fermions as the sum of the corresponding matrices…Hadrons can therefore be regarded as a kind of superposition of quarks.
In our theory, we combine the three triplets as a double tetrahedron (see previous posts below). If we now introduce the quark color constraint that requires the hadron to be color neutral, we can combine them by summing the positions marked 1, 2, and 3 together; that is, we can sum the charges of the ones, twos, and threes of the three triplets, and, as shown in figure 2 below, the summed color charges in each position of the hadron are then sure to be identical.
Figure 2. First Generation Color-Neutral Hadrons
Notice that, while the color-charges add up to 1, positive, unit, in each position of the proton hadrons, they add up to 1, neutral, unit, in each position of the neutron hadrons, and that all three hadrons are color-neutral in each case, and, of course, that the electrical charges add up to positive 1 for the proton (udu), and neutral for the neutron (dud).
Figure 3 below shows the double tetrahedron form of the grb neutron of the top row of figure 2.
Figure 3. GRB Neutron Hadron as Double Tetrahedron (Top and Bottom View)
Here, the inner terms of the inner triplet are numbered in the clockwise direction also, from 1 to 3, and the inner terms of the outer triplet are denoted with a and b designations to indicate that they are one and the same terms in the top and bottom view. The top half of the double tetrahedron (shown on the left) depicts the red up quark combined with the green down quark, while bottom half (on the right) depicts the same red up quark combined with the blue down quark, placing the up quark between the two down quarks. It’s interesting to note that, while this “stacking” of quarks is similar to the stack of braids in the BT model, the physical binding of the quarks into hadronic triplets in our model, like the physical binding of the S|T units into quark and lepton triplets, is not contrived, but has an actual physical basis.
Moreover, since the double tetrahedron has five nodes, as opposed to the three nodes of a stack of three braids, two new degrees of freedom are introduced into these hadrons. The implications of this are now being investigated and the results will be discussed in a future article. Stay tuned!