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How have we specifically proved that pions are mesons? Meaning what experiments or calculations have we done to prove that. In addition, how do we know that muons and taus are fundamental particles (not mesons). With such short lifetimes it is near impossible to measure them accurately so how have we come to this conclusion?

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    $\begingroup$ As a note - muons have a lifetime of microseconds, which is an eternity in the particle physics world. $\endgroup$
    – J. Murray
    Feb 14 '21 at 23:29
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Historicaly:

From theoretical considerations, in 1934 Hideki Yukawa predicted the existence and the approximate mass of the "meson" as the carrier of the nuclear force that holds atomic nuclei together. If there were no nuclear force, all nuclei with two or more protons would fly apart due to electromagnetic repulsion. Yukawa called his carrier particle the meson, from μέσος mesos, the Greek word for "intermediate", because its predicted mass was between that of the electron and that of the proton

italics mine.

All the experimental data that support the standard model of particle physics are a proof that the pion is not an intermediate of any fundamental interactions, so that the pion is not intermediate is firmly established experimentally.

In a dictionary, meson is:

a very small piece of matter that contains a quark and an antiquark

Again, all the experiments that led to the standard model have the pion as a meson, the first classification came with the eightfold way that led to the implication of the existence of quarks.

mesonocted

The meson octet. Particles along the same horizontal line share the same strangeness, s, while those on the same left-leaning diagonals share the same charge, q (given as multiples of the elementary charge).

The experiments that support this interpretation of the data are large in number.

The assignment of the title "fundamental" and the axiomatic entry into the table of fundamental particles of the standard model does not depend on lifetimes, although they can be measured accurately. They depend on observing interactions and the final classification of fundamental forces, and the quark model. The standard model is a mathematical model that fits successfully the majority of data gathered the last decades in particle experiments and is continually validated with new experiments.

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