How gluons gain mass and why they never escape hadrons

Gluons—the particles that bind quarks together—shouldn't have mass according to conventional QCD, yet the authors show they can acquire it dynamically through a non-perturbative mechanism. Their renormalization program reveals that massive gluons cannot exist as free particles; they're confined to the vacuum or inside hadrons, resolving a long-standing puzzle about why we never observe them alone. The framework passes consistency checks, recovers the massless limit correctly, and provides equations ready for lattice simulations.