Yes, under certain conditions, quarks can emit photons. However, it's important to note that quarks themselves are never observed as isolated particles due to confinement, a property of the strong nuclear force. Quarks are always found in bound states called hadrons, such as protons and neutrons.
In the context of a high-energy environment, such as a quark-gluon plasma (QGP), which is a state of matter where quarks and gluons are deconfined, interactions involving quarks can give rise to photon emission.
In a QGP, the high energy density and temperature can lead to intense interactions among quarks and gluons. These interactions can result in a variety of processes, including the annihilation of quark-antiquark pairs and the scattering of quarks off each other. In some of these interactions, photons can be emitted as a result of electromagnetic interactions between charged particles.
Regarding the specific case of up and down quarks, they carry electric charge (2/3 and -1/3 of the elementary charge, respectively), which means they can interact electromagnetically. Therefore, in a high-energy collision involving up and down quarks, there is a possibility of photon emission as a consequence of these electromagnetic interactions.
It's worth noting that the precise details and probabilities of such processes in a QGP are complex and require sophisticated theoretical models and experimental studies to fully understand. The study of QGP and its properties is an active area of research in high-energy physics, particularly in the field of heavy-ion collisions conducted at particle accelerators such as the Large Hadron Collider (LHC).