The CERN Courier of 2 May 2019 carries an article *The flavour of new physics *https://cerncourier.com/the-flavour-of-new-physics/.

My post here explores that suspicion of a faint possibility (less than 5 sigma significance) of new physics using the details in my Preon Model#6 given at http://vixra.org/abs/1505.0076 .

The CERN article shows at the far right of its Figure 1 one path for the decay of

b –> c τ ν’ that is

bottom quark –> charm quark & tau & tau-antineutrino

An intermediary in the decay is the LQ or Leptoquark, which is a relative newcomer and appears to be acting as if it were a force carrier and would be a particle beyond the Standard Model, were it to exist. My aim here is to try to specify the exact structure of the Leptoquark in Figure 1 in terms of my Preon Model #6.

First, according to my preon model, each Standard Model particle is composed of a number of preons. Also, the left- and right-handed forms of particles are structurally different from one another; at least, in my model, they are different. The structure in terms of actual named preons will be shown later but for the moment it is only necessary to know the total number of preons in each particle and the summary qualities in each particle. Below is a list of these qualities for the particles used in this post. The higgs is also shown in this list as I believe the higgs has a role in this bottom decay.

Parentheses indicate (electric charge, spin, weak isospin, colour charge).

LH = left-handed form of the particle; RH = etc…

bottom LH = (-1/3, -0.5, -0.5, red) 20 preons (where red could alternatively be green, or blue, as desired)

bottom RH = (-1/3, 0.5, 0, red) 20 preons

charm LH = (2/3, -0.5, +0.5, red) 12 preons

charm RH = (2/3, 0.5, 0, red) 12 preons

tau LH = (-1, -0.5, -0.5, 0) 20 preons

tau RH = (-1, 0.5, 0, 0) 20 preons

tau-antineutrino LH = (0, -0.5, 0, 0) 20 preons which does not occur in the Standard Model as it is the antiparticle of the sterile or RH neutrino

tau-antineutrino RH = (0, 0.5, -0.5, 0) 20 preons

higgs LH = (0, 0, -0.5, 0) 16 preons

higgs RH = (0, 0, 0.5, 0) 16 preons

Some liberties are taken with the definition of handedness here. Normally LH refers to negative spin. This has been extended here to have LH referring to negative weak isospin, but only when spin is zero. This only applies to the higgs and the leptoquark and is for my convenience only and also is not strictly correct as weak isospin has connection with electric charge or hypercharge rather than spin.

A simple totaling of the numbers of particles before and after decay shows that there are more preons outputted into c τ ν’ (52) than are inputted by b (20). This discrepancy is due to extra preons inputted from the vacuum. In other decays described by my preon model it is normally a higgs boson which is taken from or given up to the vacuum. Also, spontaneous random decay is anathema to my model and the interactions in my model are exactly balanced before and after the interaction, as with a chemical reaction. To do this the model has two particles inputted and two outputted for each interaction vertex. So the b –> c τ ν’ decay is re-modeled, by me, here as two separate interactions:

bottom + higgs –> tau + leptoquark

20 +16 –> 20+ 16 preons

followed by the interaction

leptoquark + higgs –> charm + tau-antineutrino

16 + 16 –> 12 + 20 preons

Both of these interactions balance in numbers of preons in and out, which means that the leptoquark has 16 preons as does the higgs. In my model the gluon also has sixteen preons so the leptoquark is in this way in step with force carriers. In my model, the force carriers have 4 or 8 or 16 preons and are allocated to (my) three generations of forces while the fermions have 4 or 12 or 20 preons as in the Standard Model’s three generations.

Taking the first interaction: bottom + higgs –> tau + leptoquark ,

each of these four particles comes in LH and RH forms. It is not shown here but all of the permutations of these variants have been checked for elegibility and consistency and the outcome is that the Leptoquark has 16 preons and has the qualities:

LH Leptoquark (electric charge = 2/3, spin = 0, weak isospin = -1/2, colour [= R or G or B])

RH Leptoquark (electric charge = 2/3, spin = 0, weak isospin = 1/2, colour [= R or G or B])

These properties appear in the interactions as follows:

LH bottom + RH Higgs –> LH tau + RH leptoquark

(-1/3, -1/2, -1/2, Red) + (0, 0, 1/2, 0) –> (-1, -1/2, -1/2, 0) + (2/3, 0, 1/2, Red)

followed by

RH leptoquark + LH higgs –> LH charm + RH tau-antineutrino

(2/3, 0, 1/2, Red) + (0, 0, -1/2, 0) –> (2/3, -1/2, 1/2, Red) + (0, 1/2, -1/2, 0)

Where the numbers of preons balance into and out of the interactions and the particle qualities of charge, spin, weak isospin and colour balance into and out of the interactions.

Next, the exact preon structures of the leptoquarks are sought. If the interaction

LH bottom + RH Higgs –> LH tau + RH leptoquark

is written out as exact preons, we get

AC’g’ Cr C’b’ x^9 + A’B’CC x^6 –> AC x^9 + RH leptoquark

Cancelling on both sides of the interaction by the 20 preons in AC x^9 gives

RH leptoquark = A’B’C C’g’ Cr C’b’ x^6 which has 16 preons

where C’g’ Cr C’b’ is equivalent to one preon as C’g’ is a sub-preon which is a coloured (antigreen) one-third slice of preon C and so three such sub-preons make up the equivalent of a whole preon, at least in quantity of matter contained. This aggregate of three coloured sub-preons causes the net colour Red. The twelve preons in x^6 are completely neutral in properties as each x is a pair comprising a preon and an antipreon, for example, AA’ where A’ is the antipreon of preon A.

Next the interaction for the RH bottom quark is investigated.

RH bottom + LH higgs –> RH tau + LH leptoquark

(-1/3, 1/2, 0, Red) + (0, 0, -1/2, 0) –> (-1, 1/2, 0, 0) + (2/3, 0, -1/2, Red)

followed by the interaction

LH leptoquark + RH higgs –> RH charm + LH tau-antineutrino

(2/3, 0, -1/2, Red) + (0, 0, 1/2, 0) –> (2/3, 1/2, 0, Red) + (0, -1/2, 0, 0) {NB this is the sterile antineutrino which could mean that the RH charm is not produced, or at least not detected, in this interaction}

Next, the exact preon composition of the LH leptoquark is sought. If the interaction

RH bottom + LH higgs –> RH tau + LH leptoquark is written down as exact preons we get

B C’g’ Cr C’b’ x^9 + ABC’C’ x^6 –> BC x^9 + LH leptoquark

Cancelling on both sides of the interaction by the 20 preons in BC x^9 gives

LH leptoquark = ABC’C’C’ C’g’ Cr C’b’ x5 which contains 16 preons.

x refers to a preon-antipreon pair so that one of the x pairs on the input side of the interaction equation needs to be CC’ and is therefore usable in the cancellation step to supply the C preon, on the input side of the interaction, to be cancelled.

8 May 2019

Manchester

England