Tauriel and Kili relationship: Can a dwarf and an elf reproduce ?

The title sums it all, I just am seeking an answer in the Middle Earth world, not the Tolkien nor the Peter Jackson's world. I believe it is already a singularity to find a dwarf attracted to an elf and vice versa. So is it possible for the two breeds to reproduce? If it is, what can the outcome be? A hybrid, and dwarfish elf or an elvish dwarf? Please do excuse my lack of knowledge of the middle earth, I only watched the movies and didn't have the chance to read any written material about it, so if this is a redundant question, just let me know.