conservation of energy and momentum
Roll one billiard ball into another and the second one shoots off while the first slows down. Nothing was created or destroyed: the 'oomph' of motion just got handed from one ball to the other. Two bookkeeping quantities capture this. Energy is, loosely, the total capacity to make things happen — including the energy locked up in mass. Momentum is mass-times-velocity, a measure of motion that also has a direction. In any closed system, both totals stay fixed: whatever you add up before a collision you get back after it.
In particle physics these two rules are merged into one and enforced absolutely. When particles smash together or a heavy particle decays, the total energy and the total momentum of everything coming in must equal the total of everything going out — added up as quantities that respect Einstein's relativity, where mass itself counts as a form of energy through E = mc^2. So a heavy particle sitting still can decay into lighter particles that fly apart at speed: the original mass-energy is shared out as the motion-energy and masses of the products, while the momenta of the products always add back to zero (since the parent was not moving).
These conservation laws are not optional extras; they are why a decay or collision is allowed at all. A particle can only decay into products whose combined rest masses are lighter than itself — otherwise there is not enough energy, and the decay is forbidden. Experimenters lean on this constantly: by measuring the energies and momenta of the visible debris from a collision and demanding the books balance, they can deduce that an invisible particle (like a neutrino) escaped, and even estimate its energy. Energy and momentum conservation follow, via Noether's theorem, from the fact that the laws of physics are the same at every time and in every place.
A heavy Z boson sitting at rest can decay into an electron and a positron flying off back-to-back. Their momenta are equal and opposite, so they add to zero — matching the motionless parent — and the sum of their energies equals the Z's mass-energy.
The decay products' momenta cancel and their energies sum to the parent's mass-energy.
Mass is not separately conserved in particle physics — only energy is, and mass is one form of it. A particle's rest mass can vanish into pure motion-energy and radiation, and energy can condense into the masses of brand-new particles.