In the previous post [1] the idea of the internal structure of the electron is discussed (based on the already discovered for quarks fractional charges, what makes the idea of electron (muon) holding primal, most basic integer charge unit somewhat improbable. But what would be the energy necessary to see such an internal structure of the electron? Is it easier for muon (obviously the electron and muon would have similar structures with merely different "electronic quarks" being present, muon merely having heavier "electronic quarks"). This is the discussion topic here.
Obviously the constituents of the electron or muon can not be the same quarks as in proton or pion - they are way too heavy for this small (only 0.5 MeV for electron) particle. Let's call them "electronic quarks" to emphasize analogy to already discovered quarks - they most probably have the same fractional charges of 1/3, 2/3 as well. This also goes from pion known structure (consists of two quarks) and may go through W- boson to either muon or electron. Inside this W- boson the known quarks are converted into "electronic quarks" while keeping theirs primal basic charges thus transferring this integer charge (in reality combination of -2/3+(-1/3) or -2/3+(-2/3)+(1/3) or (-1/3)+(-1/3)+(-1/3) further to "elementary" particles like electron and/or muon). It is possible, of course that nature is so bizarre that after all it have two types of primal, most basic values of charges - both fractional and integer. As described in another blog, it is impossible to "outsmart" the nature [2] and every fundamental theoretical work only takes place after some small experimental result (like a hint in the correct direction), including the Standard Model, which was only possible after the high-energy particle experiments demonstrated some wrong results. For now the presence of fractional charges in quarks I consider as a hint that electron and muon are not elementary particles and may be split (at least the scattering experiments may reveal the complex nature of them because most probably the "electronic quarks" may not be isolated pretty much like already known quarks).
In order to make any evaluations of the energy and probability of splitting involved it would be necessary to switch to empirical consideration of the structure of electron. Instead of further development of Standard Model to include new types of "electronic quarks" (what would theoretician prefer) I would go to the concept of surface tension (similar to Aage Bohr [3]) (similar to liquid drop model [4]), because I am an experimentalist and very rough estimate is OK for me. The "surface tension" in composite (non-elementary) particles plays more and more important role as size becomes smaller and total energy larger since the smaller the size of the particle (and correspondingly the energy is larger) the more virtual particles may it excite from quantum vacuum (both discovered and undiscovered, either small energy or large energy, on all possible levels). In certain sense the quarks can not be separated because the force between them becomes larger with distance but because if somebody pumps the proton with energy in an attempt to split it the "surface layer" is becoming larger and larger and sorbing the energy inside, creating the bubble of virtual particles around those quarks preventing energy being delivered directly to quarks. In essence the properties of quantum vacuum as we know it preventing this event. It may be possible however, if the quantum vacuum around the proton is modified, if the event of strike takes place inside quark-gluon plasma, for example [5]. The importance of pure empirical "surface term" as size goes down may be demonstrated as follows:
A. Rydberg hydrogen atom considered as obtaining more energy through "surface term": diameter of around 1 micrometer [6] and added energy is 13.6 eV (ionization energy of hydrogen), the "surface term" energy would be E= - α*S, α=1.8*10exp(13) eV/m2
B. Nucleus of iron: radius is 4.6*10exp(-15) m and "surface term" from [4] is 17.23MeV*A2/3
what yields E= - β*S, β=1.44*10exp(37) eV/m2
C. W- boson being considered as non-elementary particles: energy is 80 GeV (for simplicity it is assumed all energy now is from "surface term", the other terms are neglected for evaluation). Radius may be only estimated as 10exp(-17) m [7] and the "surface term" would be:
E= - γ*S, γ=2.5*10exp(44) eV/m2
My way to explain why those "electronic quarks" are capable to be inside the particle like electron with mass only 0.5 MeV or muon with mass of 105.7 MeV is that they stay so tightly together, that the surface term due to minimization of size becomes very small too. Thus the size of "electron nucleus" may be estimated (from formula E= - γ*S) as 2.5*10exp(-20) m for electron and 3.7*10exp(-19) m for muon. Since electron is not considered here as elementary particle it may now have two sizes, similar to any atom which has Compton size of ~2.43*10exp(-12) m and Compton size of nucleus of ~1.32*10exp(-15) m. Now electron has the electric field determined Compton size of ~2.43*10exp(-12) m and "electronic quarks" determined size of 2.5*10exp(-20) m.
The only way to evaluate how much energy would be necessary to see the internal structure of electron and muon (since they both have one progenitor W- boson) is to use analogy: quarks were visible for proton when accelerators reached around 10-20 GeV, W- boson is 80 times heavier, so the lowest level would be 0.8-1.6 TeV for electron-positron, muon-muon, electron-electron etc. beams energy. The predecessor of BAC was only able to reach 200 GeV for electron-positron beam, way below what is necessary.
Another way to evaluate energy is to find at what energy ultra-relativistic particle would have the De-Broglie wavelength of 2.5*10exp(-20) m (for electron internal structure) or 3.7*10exp(-19) m (for muon). From formula λ=h/p=h*c/p*c=h*c/E, where h is Plank's constant, c is speed of light and E is energy of the ultra-relativistic particle it follows: for electron energy is 7.956*10exp(-6) J and for muon it is 5.38*10exp(-7) J. Corresponding energy in TeV would be 50 TeV for electron and "merely" 3.36 TeV for muon. Again for muon it seems to be easier to be split apart (sense internal structure), electron is by far tougher particle.
It is also enormously small probability of correct interaction in the beam - since the only way to see the structure is to see the scattering of nearly head to head collision, with size of only 2.5*10exp(-20) the scattering event would be very rare. Those accelerators will mainly generating the same stuff which was discovered on predecessor of BAC, possibly decades of experiment would be necessary to see such scattering, which would revealed the internal structure of electron and muon. It seems millions of times easier for muon, of course (since it is heavier, this energy may be reached in circular accelerator, much less energy loss due to synchrotronic radiation [1]; plus it is bigger, so the probability of correct strike is much higher). For electron the special linear accelerator is to be built, the expenses are expected to be enormous and such discovery may only prognosed for the next century (or may be 23d century).
As a conclusion - the hint from fractional charges of quarks means the shortest way for new physics in the higher energy direction includes electron or muon accelerator for 0.8-1.6 TeV (another evaluation 3.4-50 TeV) capable of working for decades in order to catch enormously rare event of scattering revealing the internal structure of those "elementary" particles. While it is possible from engineering point of view, such breakthrough would demand so enormous money that may be safely considered as sci-fi for now. Repeating [1] - new physics in the opposite direction (ultra-low energy particles, search for fifth force weaker than gravitational or in the gap between gravity and electromagnetism) would be much cheaper to reach.
References.
3.https://gymarkiv.sdu.dk/MFM/kdvs/mfm%2020-29/mfm-26-14.pdf
4.https://www.personal.soton.ac.uk/ab1u06/teaching/phys3002/course/04_liquiddrop.pdf
