The lack of pain sensitivity on one side of the body is known as:

The term that describes the lack of pain sensitivity on one side of the body is hemianalgesia. This condition specifically refers to a diminished or loss of ability to feel pain on one side, typically resulting from neurological impairment or injury, affecting the sensory pathways.

In the context of the other terms provided, hematopoietic refers to the formation of blood cells, which is unrelated to pain sensitivity. Hemiplegia is a condition marked by paralysis on one side of the body, primarily affecting the motor function rather than sensory perception. Hemagglutination is a process in which particles, such as viruses, clump together, and it does not relate to pain sensitivity at all.

Thus, hemianalgesia accurately captures the essence of the lack of pain sensitivity on one side of the body, distinguishing it from the other terms that pertain to different medical concepts.