I was researching about structure functions and understand how it's a probability density function that describes the distribution of quarks inside hadrons. However, since mesons also have quark gluon interactions, I struggle to see why there can't be a structure function for mesons. Yet when I try to search and find it, only structure functions for hadronic currents come up. Therefore I just want to ask:
Can mesons have structure functions and if not, how could it be possible to describe the distribution and behaviour of quarks inside a meson?
Experimental knowledge of the partonic structure of mesons (the pion and kaon) is very limited due to the lack of a stable pion target! Our current knowledge of the pion structure function in the valence region is obtained primarily from pionic Drell-Yan scattering, and in the pion sea region at low Bjorken-x, from hard diffractive processes measured on e − p collisions at HERA. These data seem to indicate that the pion sea has approximately one-third of the magnitude of the proton sea, while from the parton model one expects the pion sea to be two-thirds of the proton sea. But...
at large Bjorken-x virtually nothing is known about the contribution of sea quarks and gluons.
The Electron-Ion Collider (EIC) with an acceptance optimized for forward physics has the potential for accessing pion and kaon structure functions over a large kinematic region through the Sullivan process, where one measures the contribution to the electron Deep Inelastic Scattering (DIS) of the meson cloud of a proton target: the nucleon parton distributions contain a component which can be attributed to the meson cloud.
Sullivan processes. In these examples, a nucleon’s pion cloud is used to provide access to the pion’s (a) elastic form factor and (b) parton distribution functions. $t = (k − k′)^2$ is a Mandelstam variable and the intermediate pion, $π^∗(P = k − k′)$, $P^2 = t$, is off-shell.