Where all those particles come from - proton proton collision I was reading an article about the "Higgs factory" China is planning to build  and it got me thinking about what happens when two protons collide.
I am an engineer so I have a good understanding of the laws of physics in the macroscopic scale, but is hard to imagine what happens with subatomic particles like protons so I have some questions:
If protons are made up of 3 quarks and those quarks are bonded with the exchange of gluons, why so many particles arise in a proton-proton collision? If the total energy is conserved, are those particles the transformation of the kinetic energy to matter?
 A: Here is an experimental  particle physicist's answer:

If protons are made up of 3 quarks  and those quarks are bonded with the exchange of gluons, why so many particles arise in a proton-proton collision?

It is mainly because of special relativity, the equivalence of mass and energy tied up in the $E^2-p^2=m^2$ rule of four dimensional space.

If the total energy is conserved, are those particles the transformation of the kinetic energy to matter?

Elementary particles are described by their mass and their quantum numbers. The same is true for composites of elementary particles, like the proton and neutron and all the resonances and the leptons. When the energy is available particles and resonances are created as long as the rest of the quantum numbers are conserved. For example there is conservation of baryon number, conservation of lepton number , in addition to angular momentum and momentum conservation. 
So if the quantum numbers are conserved and the energy threshold for creating specific combinations of particles is reached , a probability exists that these particles will be created when scattering protons on protons at that energy, in addition with all the lower mass particles . This probability is calculated using the standard model mathematics using Feynman  diagrams and quantum field theory .
The higher the projectile energy , thresholds for new particles can be reached and that is why higher and higher scattering energies are the goal in particle physics. Maybe new quantum numbers will be reached, i.e. theories beyond the standard model.
A: 
If the total energy is conserved, are those particles the transformation of the kinetic energy to matter?

Exactly!
To understand how this happens you have to understand how quantum field theory describes particles. For every type of particle there is a quantum field that pervades all of spacetime. Particles are excitations of these fields, so for example adding energy to the electron field creates an electron, or taking energy out of the electron field destroys an electron.
When two quarks collide in the LHC they have a huge kinetic energy, and this kinetic energy can be transferred into many different types of quantum field where it appears as new particles. That'show new particles are created at the LHC.
This approach to describing particles may seem strange to the newcomer to quantum field theory, but it elegantly explains how matter and energy can be transformed into each other. The rules for which particles can be transformed to what other particles are described by the Standard Model.
