Here is an attempt at a less jargon-filled summary: Nuclei have energy levels that arise from how the protons and neutrons oscillate against each other. Nuclei generally prefer to be at lower energy levels, and the transitions between levels are dictated by rules having to do with properties of the levels like spin and parity. The group used a proton accelerator to populate a particular level in a particular nucleus that is forbidden from decaying by emitting a gamma ray. They observed electrons and their antimatter counterparts coming out, which often suggests that some neutral particle produced them. Gamma rays can do this too through "pair production," but gamma rays are mass-less and carry very little momentum compared to a heavy particle of the same energy. This is where the angular correlations come in, because they are ultimately influenced by the mass of the intermediate particle. They also measured the energy of the pairs and found it to be comparable to the mass energy of the proposed X17 particle.
I think this is really interesting, and I'm not a theorist, but I don't think I'm convinced that this is necessarily evidence of a fifth fundamental force. The transition they used in 4He is really convenient from an experimental standpoint, since tritium is commonly used as a proton target to make neutrons for other experiments.
Abridged from the article: "The mysterious X17 subatomic particle is indicative of a fifth force of nature. Four fundamental forces of nature: gravity, electromagnetism, the strong nuclear force, and the weak nuclear force. The discovery of a fifth force of nature could help explain the mystery of dark matter, which is proposed to make up around 85 percent of the universe's mass."
It's hard to observe particles directly (they're very small) so much particle physics involves using conservation laws to observe indirectly.
If you imagine for a moment that particles are integers and "total count" is a conserved property, then if I slammed a "2" and a "3" together and directly observed a "4" coming out, I could infer that there was also an "1" particle somewhere, since 2+3=4+1 (and wouldn't claim that there was a "2" and a "-1", because we already know we can observe "2"s.)
Real experiments use a variety of conserved quantities such as: mass/energy, linear momentum, angular-momentum/spin, charge, lepton number, etc.
This paper describes looking at spontaneous electron/positron pair emission. Electrons and positrons exactly cancel each out for some conserved quantities (charge, lepton number) where they have opposite signs but not for others (mass/energy), so its possible for things in general to lose some energy and generate an e/p pair.
This experiment observes the transition of 'high energy' Helium (He4') atoms to 'low energy' (He4) Helium where the excess energy created an e/p pair.
The reported observations show a high concentration of e/p pairs generated in such a way ("angular correlation") that implies that there was an intermediate particle created with a specific energy. The authors assert that this is evidence for the existence of the X17 boson, which they also assert might be a carrier for a 5th fundamental force (in the way that photons are the carrier for electromagnetic forces).
This is the second experiment they claim has found evidence of the same kind of hypothetical particle. The previous experiment used the transition from "high energy" Beryllium (Be8') to low energy (Be8) that also generates e/p pairs.
If true, this would be a big deal as it implies physics outside of "the standard model" of particle physics. That's what gets people talking about dark matter (which is also outside the standard model).
More likely (IMO), there's some experimental issue (i.e. they recorded bad data).
My understanding of the abstract is simply that they had previously postulated a new particle of a particular mass to explain a prior set of data, and that a new set of data from a different experiment gives evidence a missing particle with a similar mass.
https://news.ycombinator.com/item?id=21616381