My question is why are we colliding particles in LHC to produce new ones?
And these particles that they sometimes say live for a fraction of a second, how in space they exists then?
In space all these particle exist without smashing to each other, why do we need to smash them to produce them?
Physicists collide particles to study their behavior under extreme conditions. New unknown particles can be created in high energy collisions or new unknown processes may be observed. Our equations describing the particles are predicting certain behavior and physicists are testing if the particles really behave like that. And they are hoping to find a discrepancy to locate a problem in our theories and improve them.
The short lived particles are short lived not only in our laboratories, but also in space. They are created also in collisions, but not in accelerators. Certain processes in the space are powerful enough to accelerate and collide particles at much higher energies than our most powerful accelerator. If a short lived particle is created in such process, it decays quickly, like in the Earth laboratories. Long lived high energy particles (protons, neutrions, electrons) are flying through the space everywhere and they are even hitting the Earth. Every day there are lots of particles arriving to the Earth from the space that have much higher energy than protons in LHC.
The high energies of the LHC helps in a sense "reproduce" energetic eras of the universe right after the big bang, or even reproduce collisions of high energy particles in space.
During those periods of the universe, the energies were high enough for more massive particles to be produced (Recall the more mass a particle has, the more energy it needs to be produced via Einstein's famous $E = mc^2$ equation).
These particles are generally unstable and therefore decay very quickly to other lighter particles (which in turn might themselves decay into lighter particles).
The job of an LHC physicist is then to track these particles from the detectors and through a process of reverse engineering try to reconstruct which particles were produced initially.
Sometimes these reverse engineering methods helps in discovering new particles or even new physics.
In space there are phenomena leading to gigantic energies or temperatures. This can create such particles. In fact, there are collisions of high energy particles in space. We here on earth reproduce these effects using a collider like the LHC. But still the maximum energies per particle we meassure comming to us from space are far from reached with any man-build machines.
Edit: I am not talking about some global energy, most of the universe has a very low energy density. However, at certain points (stars for example) there is a high energy density. These localised areas in the universe emmit particles of high energy. These particles travel through space and we can meassure them. A great portion of these particles is already "destroyed", a few come through to us. But as they are still individual particles they rarely influence our day-to-day life. Most of them rarely even interact with us.