Which software application did they use to create LHC data processing animation?
This can be achieved with almost any 3D suites out there.
Your options are 3Ds Studio Max, Cinema 4D, Blender (free and open source), Maya, Lightwave etc. etc.
These are all software suites that enable you to model, animate and render videos like this one.
Ontop of that they used a 2D animation software like After Effects for scenes like the earth overview animation at second 251.
Though the 3D scenes are very likely one single render without much post processing (except for the text overlay).

The style is simple, you have a rather flat shading without much reflections with Ambient Occlusion turned up a notch to get these shadows in the corners.

Going by these particle effects I'm rather convinced that they used Cinema 4D for the 3D animations, though they could have also made those with After Effects and a plugin called Particular from RedGiant Software, a very popular tool for particle animations.
Though Cinema 4D is very popular for motion graphic animations like this one, so it's likely they used that.