To postulate a basic particle would be to limit the characteristics of the universe. We have begun to realize that a particle may be nothing more than a convenient method of describing something of which we know almost nothing. We don't have an accurate model of the dimensional state of Space/time. We know that the 'particles' we recognize may, or may not exist simultaneously in several dimensions that we cannot perceive. The sheer quantity of ignorance about the 'quantum sponge' and the event horizon makes such discussion academic. Even Heisenberg noted that the path only comes into existence when we observe it. Quantum Mechanics can only deal in probabilities, and we must remember that if nothing is certain then nothing is impossible. A basic particle both exists and does not exist. This is a fundamental truth, if you don't understand it, go visit Schrdinger's cat. Since a quantum superposition is the combination of all the possible states of a system and the Universe is infinite, in a sense, then it would follow that all possible things can, and must, exist.
The non-zero value of the Planck constant is the reason why phenomena occurring in quantum physics display discrete behavior rather than assuming a continuous range of possible values. If this be true, and it is, we begin to realize that there is an absolute limit upon observation, a point at which the existence, or non-existence, of a particle can only be surmised by inference. We cannot know what exists beyond the limits of measure. If we determine a method of using a smaller particle to measure, it will perceive that which is too small to measure. From a Gluon's point of view, is everything larger, or are there a multitude of smaller things? Something is smaller, because the Gluon moves in response to it. A particle of gravity? What if gravity is only the tendency of the Space/time continuum to eject matter? Eject matter where? We once believed that Singularities were connected to an extra-dimensional space that ejected matter in the same way as they captured it, but that would mean that the Universe is emptying by gravitational influence, and that there used to be much more matter than there now is. Perhaps there are an exactly equal number of White Holes speaking in terms of Mass and the amount of energy transferred out of the Universe as we know it. Philosophers are the only persons who can debate the basic structure of Space/Time, inasmuch as it must be beyond knowing or the present theories need adjustment.
If we go back to classical Physics, and the time of Isaac Newton, we remember that it was believed his laws of motion were exact, in all situations. We eventually learned that this was untrue, especially at quantum levels. We now stand on another threshold, equally as great, wherein we see that what is right for the observations we have made may, in fact, be wrong on another scale or in another dimension. At present we do not even have terms for the environment that would be home to a 'basic particle' if such exist. The Atom turned out not to be indivisible, as did the electron, the proton, and probably every other particle we've discovered. It all falls down when you try to integrate waves and particles.
A wave-form is most easily understood as a string of particles that touch one another. As the stream is measured, we get first a space of little energy, then the particle cloud, which has energy that we can measure, and then another space of little energy. Charge and spin notwithstanding, we see a rise and fall of energy that we express as a waveform. This is the explanation most easily understood when we explain that everything has a frequency, or wave signature. Words do not adequately explain it and the Math would bore even me, so I'll just say that the difference in waves and particles lies in the measurement and properties which are observed by that measurement. I wish it were explainable, but it is not. Just as we cannot know, with certainty, anything about the quantum environment, so we cannot describe it in words. What goes on at the subatomic level has to defy description in order for the math to work. I know that I have been busy in this treatise, making all manner of non-circular objects into circles to simplify the math, but a discussion of something so unreal as a basic particle will cause that. If there be a basic particle, has it an imaginary twin? If so, then there is more than the basic particle. In order for a particle to be basic, it must be absolutely unique. Both real and imaginary, positive and negative, massless and having mass, a point which has shape. If you define a basic particle, then you soon realize that no single thing can act upon the universe according to the knowledge we now possess. Until such time as we are able to "see the path", it simply does not exist.
Einstein said "there is no space without field", and that would mean that the 'basic particle' is the stuff of which this field is composed. It becomes the canvas upon which the Universe is written, as well as the Medium from which it is designed. An analogy would be to say that it is the clay, the pottery stand, the glace used to decorate it, and in short everything but the Kiln and the Potter. Some scientists postulate that the Kiln should be included in the analogy and that there is no potter. Whatever, I simply wish to point out that we can't pet Schrdinger's cat until we know if it is alive, and then we violate the uncertainty principle. So long as we must use some form of energy to observe, we cannot know.