Step 1: Periosteal reaction is new bone laid down by the periosteum in response to inflammation or injury, and certain arthritides characteristically provoke it while others do not.
Step 2: Psoriatic arthritis, reactive arthritis (Reiter syndrome), and neuropathic arthropathy all typically show periosteal new bone formation on radiographs. The seronegative spondyloarthropathies in particular are known for fluffy or exuberant periostitis.
Step 3: Rheumatoid arthritis is an erosive arthropathy whose hallmarks are juxta-articular osteopenia, symmetrical marginal erosions, joint space narrowing and soft tissue swelling. Importantly it does NOT produce periosteal reaction, which helps distinguish it from the seronegative group.
Step 4: Since the other three options are associated with periostitis, rheumatoid arthritis is the one with no periosteal reaction and is the correct answer.