conservation laws - Decay of elementary particle?

Many elementary particles decay, for instance a charm quark (according to wikipedia) will decay into a strange quark (and I assume some other elementary particles but I don't know what they are). Does this imply that on some fundamental level both charm quarks and strange quarks share composition?

My (probably naive) reasoning is that in chemistry if I have substance A isolated in a vacuum, and it decays into B and C, then A almost 100% composed of some ratio of B and C, as an example: $$\rm CaCO_3\rightarrow CaO + CO_2$$ which can be used to demonstrate that calcium carbide consists of the same substances that compose calcium oxide and carbon dioxide. Does this logic not apply on a quantum level?

Answer

In particle physics we have a list of "quantum numbers" that describe a particle. Different types of interactions may conserve, or may not conserve, different quantum numbers.

You give the example of decays which change quark flavor. Baryons and mesons (which we model as being made of quarks, even though individual quarks are confined) are assigned "flavor quantum numbers": the $D$ mesons have charm quantum number $C=\pm1$, the $K$ mesons have strangeness $S=\pm1$ but charm $C=0$, and so on. The strong and electromagnetic interactions do not change the flavor quantum numbers in a system, but the weak interaction does. So the stoichiometry skills that you learned in chemistry work for strong-interaction scattering, such as the strangeness-conserving production of hypernuclei, but not for weak decays which change those quantum numbers.

(In fact, you might say that it only makes sense for us to talk about flavor quantum numbers because the interaction that changes them is weak.)

A few of these quantum numbers are conserved by all known interactions. Those include

• electric charge: the number of positive charges minus the number of negative charges


• baryon number: the number of protons, neutrons, and hyperons, minus the number of antiprotons, antineutrons, and antihyperons. In the quark model, each quark has baryon number 1/3 (and antiquark $-$1/3), so you can use baryon stoichiometry to analyze reactions where mesons are produced.


• lepton number: the number of electrons, muons, taus, and neutrinos, minus the number of their antiparticles.

When you do chemical stoichiometry, like in your calcium carbonate decomposition reaction, you're conserving electric charge, the number of electrons, and the number of protons and neutrons. Your baryon number conservation is constrained because there's no interaction at the energies chemists care about which allows protons to change into neutrons or vice-versa, so you have to conserve proton and neutron numbers separately. Furthermore there's no interaction, at the energies that chemists care about, which allows a nucleon to hop from one nucleus to another, so you have to separately conserve the number of calciums, the number of carbons, etc.

It's tempting and useful to take these conservation laws and use them to conclude that a calcium nucleus is "made of" twenty protons and twenty-ish neutrons. But that approach breaks down when you start to consider the flavor-changing weak interactions. The muon decays by the weak interaction into a neutrino, an antineutrino, and an electron; but there's evidence against any model where the muon "contains" those decay products in the way that we can say a nucleus "contains" nucleons.