# Does either Quantum Field Theory or the Standard Model of Particle Physics predict the maximum number of particles or fields that can exist?

Perhaps since the Standard Model relies heavily on the symmetries of chosen groups do either or both theories demand a maximum number of particles or fields that are allowed to exist? My guess is that someone has asked this but I cannot find it in the "Similar Questions" section or the "Questions that may already have your answer" section.

• Nope. In fact a huge deal of modern theoretical physics is to randomly assume another bunch of particles and see what that would predict. – image Sep 24 '17 at 10:59
• I fear you have fallen into the trap of considering the SM as a perfect theory that came out of a received QFT text and "predicts" everything. It is a minimal, remarkable!, pragmatic fit of experimental facts, essentially a vehicle for systematic abuse of a terminology expressly invented for that very purpose. There is a standard theory involving the gauge groups (not a "model", but a solid theory, like the "theory of relativity"); however the representations and extensions of it are open-ended. So, e.g., new pieces like sterile neutrinos are neither predicted nor excluded by it. – Cosmas Zachos Sep 25 '17 at 15:55
• If experiment confirms them, (sterile neutrinos, singlet Higgses, BSM entities) so be it, but leave QFT predictions out of it: trying to model-build out of hyperbolic totemic QFT properties gives both QFT and model-building a bad name. – Cosmas Zachos Sep 25 '17 at 15:58
• A framework is incomplete, by definition. Nobody is trying to break anything--one looks for anything new that extends knowledge, like anywhere else in physics. If you actually read the books, instead of irresponsible science reporting you might appreciate the actual beauty and the gaps of the framework. – Cosmas Zachos Sep 26 '17 at 13:44
• Short answer, No. – Rexcirus Sep 26 '17 at 19:20

There is a limit on the number of flavors in Quantum Chromodynamics, behind that limit Color Confinement can no longer exist. The Beta-function that describes the interaction strength at different scales (at one loop) is:

$$\beta(g) = \frac{g^3}{16 \pi^2} \left( - \frac{11}{3} N_c + \frac{2}{3} N_f \right)$$

This is negative for $N_f = 6$ quark flavors and $N_c = 3$ colors which leads to the confinement phenomena. A positive value would mean that quarks must interact more at very small distances, which contradicts confinement.

Another interesting aspect of this is the unitarity of the CKM matrix. If there are more quark families than what is presently known, the measurements should eventually show violations of unitarity of this 3x3 matrix.

• The constraint from the $\beta$ function boils down to $N_f<11N_c/2$. Since $N_c$ has no apriori upper bound, neither does $N_f$. – user154997 Sep 23 '17 at 22:00
• Furthermore, I don't get your argument about unitary CKM: with a 4th family we would have a 4x4 matrix and we can require it to be unitary. – user154997 Sep 23 '17 at 22:07
• I might be wrong, but isn't $N_c$ fixed by our observations of hadron production? If $N_c$ would be bigger - wouldn't we see larger scattering rates in existing processes? – Darkseid Sep 23 '17 at 22:19
• @LucJ.Bourhis : the number of colors $N_{c}$ is fixed experimentally because of comparison the experimental neutral pion decay width with the SM prediction based on the chiral anomaly. – Name YYY Sep 23 '17 at 22:49
• I know $N_c\ne 3$ is falsified experimentally but we have a direct observational constraint on $N_f$ through $Z$ pole physics: by measuring the widths and computing $\Gamma(\text{invisible})=\Gamma_Z-3\Gamma(\text{leptons})-\Gamma(\text{hadron})=499.0\pm 1.5 \text{MeV}$, the number $N_\nu$ of neutrinos much lighter than the mass of $Z$ can then be fitted and the result is $N_\nu=2.992\pm0.007$. I.e. $N_f=3$. So as @ACuriousMind wrote, if we allow observations for one side of the coin, the OP game is over. – user154997 Sep 24 '17 at 5:02

It depends on what kinds of "Quantum Field Theory or the Standard Model of Particle Physics" you are focusing on.

Other than the familiar quarks+leptons+ gauge bosons+ Higgs particle sectors in the Standard Model, there could be other sectors that are topological, that could have extended objects like strings (Cosmic strings) or different kinds of topological defects, or anyon particles, or even anyonic strings (that are neither bosonic nor fermionic), for examples see Ref. 1 and Ref. 2. You can describe some of these topological objects by fields of higher form gauge fields, etc.

In general, you can imagine there are other Topological sectors that somehow couple to the underlying standard model in some way. And there is no limit but many many number of anyon particles that you can construct, and you can see for example Ref. 3.

It just if the mother Nature uses these topological sectors as fundamental as the known Standard Model, then the Nature must weave her puzzle in a non-contrived but elegant way.