# Structure functions for mesons

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.

Three informative refs are:

1. Aitkenhead, et al. "Determination of the pion and kaon structure functions." Physical Review Letters 45 (1980) 157 .

2. Collins, & Martin, "Hadron reaction mechanisms." Reports on Progress in Physics 45 (1982) 335. Section 6.1.

3. Aguilar et al, "Pion and kaon structure at the electron-ion collider" European Physical Journal A55 (2019) 1-15.