Edit: As noticed above in the comment, let's define BBN. Big Bang Nucleosynthesis is a process of formation of light nuclei from primordial protons and neutrons in the Early Universe. Standard BBN theory is extremely successful in predicting the abundances of multiple nuclei and is very sensitive to a number of parameters.
Let's see how it holds.
Below you can see predictions of Standard BBN for different elements (coloured curves), experimental measurements (horizontal bands) and the observed value of the cosmological parameter $\Omega_B$ (vertical band). So, in best theory all those things intersect perfectly. And they almost do! The difference with lithium is also known as "Lithium deficiency" and is an open problem for BBN, but it is amazing how everything else holds.
Especially, when you consider the details of the process:
First, you need to specify what does it mean "to participate in BBN". This question goes deep into the theory of this phenomenon first developed by George Gamow.
I will leave out lots of things and will attempt to focus instead on the main ideas. Unfortunately, I cannot estimate your knowledge of cosmology and particle physics, so only questions will help to avoid confusion.
A little background
The main feature of BBN is that this is a short-term non-equilibrium process. "Non-equilibrium" here is opposed to the thermodynamical equilibrium in which the whole state of the system can be described by a handful of parameters (e.g., temperature, volume, pressure). In the expanding Universe the equilibrium is possible only if energy transfer rate between particle species and among same particles is higher than the rate of expansion.
In general case the whole system does not necessarily enter the equilibrium state — parts of it can "decouple". This is precisely the key point of BBN theory. If the whole Universe was in equilibrium all the time, the Universe today would contain mostly Iron (as it has the biggest binding energy per nucleon).
In reality, during the expansion, some of the weak ($\approx$ slow) reactions decoupled and particles like neutron and neutrinos lost connection with fast-interacting electromagnetic plasma. In case of neutrinos, they formed an ancestor of CMB — the Cosmic Neutrino Background (which we unfortunately cannot detect nowadays and, probably, ever). Regarding neutrons... The process of their mutual conversion with protons became negligibly slow, but they still could decay:
$$
n \to p^+ + \overline{\nu}_e + e^-
$$
Shortly after that the conditions became favourable for nuclear reactions to occur, but the supply of the neutrons was limited by their lifetime and affected by the time between their decoupling and the beginning of the nuclear reactions. Few minutes later, the Universe did not contain any neutrons and was too cold to forge heavy elements from the positively charged nuclei.
How to participate?
So, who plays role in the BBN? Obviously, all those particles that you can find in the endless nuclear reactions chains: protons, neutrons, all the elements — and, of course, neutrinos and photons.
On the other hand, the interplay of the temperature of the plasma and the expansion rate is very important for the total number of neutrons you have: in equilibrium the neutron-to-proton density ratio exponentially depends on the temperature and every additional moment before decoupling of neutrons significantly changes their number. So, obviously, any change in the composition of the Universe would affect its expansion rate (but in the case of radiation-dominated epoch when BBN happens, only radiation species are important).
And there is yet another way to spoil everything. Since neutrons and neutrinos exited thermodynamical equilibrium, they effectively lost all collective behaviour and if anything was interacting with them (even ever so slowly), it left an imprint in the momentum distribution. (Notably, precisely this effect is responsible for the fact that the number of neutrino species estimated from CMB assuming the Standard Model is not 3, but 3.046; see, https://www.wikiwand.com/en/Cosmic_neutrino_background#/Indirect_mathematical_evidence_for_the_C.CE.BDB and http://resonaances.blogspot.nl/2013/01/how-many-neutrinos-in-sky.html)
So, basically, any particle that interacts with neutrinos or neutrons and is abundant at temperatures of ~3 MeV and below, might affect the abundances of the elements.
So who participates?
Here we have to assume Standard Model, otherwise things will get out of hand. As a rule of thumb, in the Early Universe, at some given temperature $T$ (say, 1 MeV), present only those particles that have $m \lesssim T$ (e.g., electrons with $m=0.5$ MeV) or those protected by conserved charges (like protons and neutrons — their total number is constant).
So, at the moment of neutrino decoupling (~3 MeV) there would be:
- photons and neutrinos (duh)
- electrons and positrons (other leptons are too heavy and are not abundant)
- protons and neutrons (about $10^9$ times less than photons)
Every other Standard Model particle does not work here directly (but one can always be annoying and say that without W/Z-bosons there would be no weak interaction and something similar about quarks/gluons and Higgs).
What about dark matter?
Although we do not know for sure, what kind of particle is dark matter, it is definite that dark matter does not interact electromagnetically, strongly or weakly (or is really-really bad at it). So, as a default option, we believe that dark matter does not affect BBN directly, but it of course carries energy density that increases expansion rate.
Moreover, we can use our understanding of BBN to extract constraints on dark matter and other particle physics models (this is what I do for life, yay!)
References
If you want to know more, you should read some book on particle physics in cosmology and the original (and very short) papers.
- Kolb, Turner "The Early Universe" (has especially good although outdated chapters on BBN)
- Original papers by George Gamow and collaborators (e.g., Alpher, R., Bethe, H., & Gamow, G. (1948). The Origin of Chemical Elements Physical Review, 73 (7), 803-804 DOI: 10.1103/PhysRev.73.803)
- Images were take from http://www.astro.ucla.edu/~wright/BBNS.html
