The previous ideas were devoted mainly to the search of interactions weaker than gravitational or in the gap between the electromagnetic and gravitational force [1-3]. That seems like the cheapest and most under-investigated direction of research (for ultra low weight particles, ultra weak forces which may only reveal itself on the cosmic scales [4]).
However, there is a second more common direction of research in fundamental physics - towards the higher energies, as high as possible. The recent success of Standard Model instantly posed a question - what is next, where to go further? I already generated couple of ideas in this direction [5,6] and now it is time for the next one.
Assuming the Standard Model is valid in the areas the predictions coincide with experiment (on quark level) the fundamental electric charge (one of the oldest discoveries in physics) is not actually integer of charge of electron, but rather 1/3 (because quarks have charges 2/3, 1/3, positive and negative). Even artificial intelligence agrees with me, if asked through Google [7]:
"Fractional quark charges (like +2/3e or -1/3e) are more fundamental in describing particle substructure..."
They can not be seen outside the elementary particle like proton, this is true, but the presence of such fractional charges even inside the proton means that 1/3 and 2/3 charges are more primal compare to integer and possibly any integer is in essence combination of those fractions. That instantly means that electron is not elementary particle (because most probably it consists of some parts with 1/3 or 2/3 charge, despite most probably those constituents can not be separated similar to quarks). Of course, it is necessary to emphasize that the known quarks can not be inside the electrons (they have much higher mass and the whole Standard Model would fell apart if this is possible). That idea, however, is exactly New Physics - it is obviously goes beyond the known fundamental physics, does not contradict it (electron and muon are considered as elementary particles merely as a fit, as an approximation toward more general theory exactly like proton and neutron were considered as elementary particles 100 years ago). For example the neutron decay involves the conversion in charge from fractional number (in quarks) to the whole number (in electron) through the virtual W- boson, which is very heavy (so may easily consists of many particles inside) and responsible for conversion down quark to up quark (manipulation with fractional charges) so it is a strong hint that in reality it is also a composite particles with constituents having charge 1/3, 2/3 and it is not split yet merely because it demands too much energy. The particle W- boson is electron and most probably the fractional charges inside this boson is transferred to electron creating the unified charge of -1, being actually presented inside electrons like combination of -1/3, -1/3, -1/3 or -2/3, -2/3, +1/3 or even more complex. While nature is bizarre in it's laws and may have after all both fractional (1/3, 2/3) and integer numbers (-1, +1) being fundamental, there is a strong hint from history of science that only one variant predominates and electron, muon and other charged "elementary" particles are not really elementary, they only look elementary (because the fractional charge is more fundamental than integer).
Why such discovery is not yet made? The answer is in experiment - during the rotation of charged particles in the synchrotron the energy loss due to synchrotron radiation is inversely proportional to non-relativistic mass in the power of four [8]. Since proton is 1800 times more heavy it is dramatically easier to accelerate it in a classical circle accelerator compare to electron. While electrons are successfully accelerated in linear accelerators they can not yet reach the energies of TeV already reached for protons.
There is a serious push for even larger accelerator in the high energy community now and this hint toward discovery of internal structure of electron (muon actually should be easier to crack because of higher mass and possibly less "rigid" structure inside) may stir community interest toward linear accelerators of enormous power instead of more classical circles. In any case the money involved are huge and from my perspective much cheaper way to find New Physics stays in the opposite direction (toward as low energies as possible, see [1-4]
References.
2.https://www.morebooks.de/shop-ui/shop/product/9786205529867
3.https://www.researchgate.net/publication/375517684_Tired_light_hypothesis_possibly_got_confirmation_by_direct_observation_of_light_scattering
5.Tipikin: Quantum vacuum application to gravity: the Higgs boson antigravitational particle predicted
8.Lecture 9a Synchrotron Radiation.ppt