What are the criteria for determining whether an elementary particle is elementary?
"What is an elementary particle?" This seemingly simple question has no clear answer; this seemingly unimportant question may be very important.
Weinberg says [1], "Giving this answer always makes me nervous. i would have to admit that no one really knows." in textbooks, the history of the discovery of particles is recounted. From atoms, electrons, protons, neutrons, up to neutrinos and quarks in the Standard Model, however, the definition of elementary particles is usually not given, and various particles are discussed directly, as in the literature [2][3], ignoring the concept of Elementary.
To answer this question, it is necessary to answer what is meant by "particle" and what is meant by "elementary".
"A particle is simply a physical system that has no continuous degrees of freedom except for its total momentum. "[1]. But obviously, whether this definition holds depends on the depth of the researcher's perspective. If we study only dust, then dust is a particle, even though it has a rich internal structure; if we study blackbody radiation, then a photon is a particle, even though we don't know if it has a structure ....... So the concept of "particle" depends only on our perspective and ability to focus.
"what is meant by elementary ?" Elementary is used in many contexts, not only as "elementary particle", but also as elementary fields, elementary electric charge, etc. Whatever the object of description, our understanding of elementary is that as long as the object it qualifies is irreducible, then that object is elementary. Does irreducible mean "nothing could be pulled or knocked out of it"? This is not a reliable answer, because we don't know at what energy level a composite particle would terminate its decomposition. If there are "Kerr black holes as elementary particles" [4], how do we break it up? And it has been found that different particles produce each other in collisions, so which is a composite of which [1]? even different things produce the same output, so "The difference between elementary and composite particles has thus basically disappeared. and that is no doubt the most important experimental discovery of the last fifty years." [Heisenberg 1975]. When we get to the QFT stage, "particles are not fundamental entities" [5], "There are no particles, there are only fields " [6]. "From the perspective of quantum field theory, the basic ingredients of Nature are not particles but fields; particles such as the electron and photon are bundles of energy of the electron and the electromagnetic fields."[1].
Although photons and electrons come from imagined different elementary fields*, they can nevertheless be converted into each other by the annihilation process e+e- → γ γ' and the pair creation process γ γ' → e+e- [7], with the consequent creation or disappearance of the properties of electrons (charge, spin, mass). Physics suggests that this process is not direct, but rather that photons γ γ' produced by electromagnetic fields excite electron fields, from which e+e- is produced. If we remove this intermediate process, the photon has a spacetime symmetry, which corresponds to the Lorentz invariance of SR in "flat spacetime", and the electron has a gauge-invariant Internal spacetime symmetry, which corresponds to the general covariance of GR in "curved spacetime"; the photon is a boson, the electron is a fermion; according to the supersymmetry theory [8], there is a symmetry relationship between bosons and fermions. Since it is a symmetry relation, they must be convertible to each other, that is, different states of one thing. So, shouldn't annihilation and pair production be a kind of supersymmetric transition relationship? Why don't we consider "annihilation" and "pair production" as verification experiments of supersymmetric relations? Do we have another theory and experiment to determine this symmetry relation? If we further define that particles that can be produced by photons through "pair production" are elementary particles, wouldn't that answer all the questions?
Weinberg said. "We will not be able to give a final answer to the question of which particles are elementary until we have a final theory of force and matter. " What does that really mean?
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Notes
* Space-time is filled with dozens of different fields, it is impossible to imagine their rationality and necessity.
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References
[1] Weinberg, S. (1996). "What is an elementary particle." See http://www. slac. stanford. edu/pubs/beamline/27/1/27-1-weinberg. pdf.
[2] Griffiths, D. J. (2017). Introduction to Elementary Particles, WILEY.
[3] Group, P. D. (2016). "Review of particle physics." Chinese Physics C 40(10): 100001.
[4] Arkani-Hamed, N., Y.-t. Huang and D. O’Connell (2020). "Kerr black holes as elementary particles." Journal of High Energy Physics 2020(1): 1-12.
[5] Fraser, D. (2021). Particles in quantum field theory. The Routledge Companion to Philosophy of Physics, Routledge: 323-336.
[6] Hobson, A. (2013). "There are no particles, there are only fields." American journal of physics 81(3): 211-223.
[7] https://www.researchgate.net/post/NO8_Are_annihilation_and_pair_production_mutually_inverse_processes
[8] Wess, J. (2000). From symmetry to supersymmetry. The supersymmetric world: the beginnings of the theory, World Scientific: 67-86.
The short answer to the main question is, No.
Regarding the criteria for when a particle is elementary, the answer is, if we can't find that it isn't.
The proton, neutron and electron were considered as elementary until the1960s. It was the deep inelastic scattering experiments at SLAC, that showed that the proton and neutron weren't elementary. Subsequent experiments were able to detrrmine the properties of the constituents of proton and neutron-two kinds of ``quarks"-and that quarks and electrons do behave as elementary up to LHC energies.
I don't see what more I can say. It isn't true that the process of annihilation is related to that of pair production by the action of supersymmetry generators. And whether either process can occur at all doesn't have anything to do with whether the particles involved are composite or not, but with relativistic kinematics and ``internal" conservation laws (such as of electric charge, baryon and lepton number conservation and so on).
Additional information: “What is a particle?”
”Indeed, when asked “What is a particle?”, many theoretical physicists like to smugly reply “An representation of the Poincar´e group”. This refers to the famous insight by Wigner and others that any mathematical property that we can assign to a quantum-mechanical object must correspond to a ray representation of the group of spacetime symmetries. “[1]
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[1] Tegmark, M. (2008). "The mathematical universe." Foundations of physics 38: 101-150.
In fact the representation of the Poincaré group describes the mass and the spin of a relativistic object; the further properties are described by the representation of the symmetry group that refers to the ``internal charges''.
Relativistic objects are described by representations of the group that is the direct product of the Poincaré group and the ``internal symmetry group''-that's what matters.
(For the leptons this is a representation of the SU(2) x U(1) group of the electroweak sector and for the quarks it's a representation of the the SU(3) x SU(2) x U(1) group, since the quarks are charged under all interactions.
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