This would not be possible. The chain is way too slow and too small for the LHC. We are talking about hundreds of MB per second. Instead, we use a dedicated computing system, and decentralisation is not an option (too slow, too small in terms of space). We can only go with an expensive solution targeting the problem we need to solve (that is expensive because we need speed, space, backups, high-speed communication between universities and dedicated data centres from all over the world, etc.).
As I already mentioned it, blockchains are not suitable to solve any problem.