Addendum: the answer appears to be either "no" or "depends on what you mean". Most of the "depends" involve a meaning of "particle" that is clearly jargon. My question was motivated by meeting people who claimed it was not jargon but an essentially lumpish quasi classical particle. I selected the answer of ACuriousMind because it was most on topic and most informative and because I think that this has proved to be a controversial matter - it was not my interest to be the center of a controversy.
In an answer to this question from about 5 years ago,
Do particles exist according to quantum field theory?
the assertion was made that whatever the argument about fields and particles are - we observe particles. But, if by particles is meant an infinitesimal hard lump, how can they ever be observed? Average field properties can be observed. The Born interpretation can be used as well as path integrals, but none of those are experimental evidence that on observing a quantum system somehow a particle appears for a moment and then vanishes again.
Ethan Siegel on Facebook (FWIW) claims that deep inelastic scattering experiments in the 1970s prove that particles exist. But, again, that is just average properties of fields. Again, it seems to be just a matter of interpretation to see fundamental particle scattering to be small hard lumps bouncing off each other.
The core of my question is - what is the status of the assertion that particles actually exist in the current thinking in physics?
See also this related question:
Must Matter Particles Have A Hard Edge?
@ACuriousMind asked me to clarify "exists". I personally have no idea what the word means in a physical sense - this is a word used by others.
I only use it with a clear meaning in terms of being an implication of a mathematical theory - there exists a solution to an equation, that sort of thing. So, in the answer, I would ask that other people clarify what they mean by particle and by exists - as I am looking for others to clarify something that makes no sense to me in the theory of QM. What I say is that the Modern mathematics of the Standard Model does not imply little hard lumps. I interpret that as a sense of "particles do not exist in QM". Of course, there are other definitions of particles.
But, I am interested in the concept little hard lump particles that suddenly appear when you make an observation of a quantum system. I have yet to see anything other than -- localized quanta of energy, etc. If this is just terminology, it is terminology that quite a few people seem to think is vitally important.
Beyond this, we descend into semantics. Which is something I personally eschew.