## From particlebites: “The Delirium over Helium”

January 4, 2020

Andre Frankenthal

Title: *New evidence supporting the existence of the hypothetic X17 particle*

Authors: A.J. Krasznahorkay, M. Csatlós, L. Csige, J. Gulyás, M. Koszta, B. Szihalmi, and J. Timár; D.S. Firak, A. Nagy, and N.J. Sas; A. Krasznahorkay

This is an update to the excellent *Delirium over Beryllium* bite written by Flip Tanedo back in 2016 introducing the Beryllium anomaly (I highly recommend starting there first if you just opened this page). At the time, the Atomki collaboration in Decebren, Hungary, had just found an unexpected excess on the angular correlation distribution of electron-positron pairs from internal pair conversion in the transition of excited states of Beryllium. According to them, this excess is consistent with a new boson of mass 17 MeV/c^2, nicknamed the “X17” particle. (Note: for reference, 1 GeV/c^2 is roughly the mass of a proton; for simplicity, from now on I’ll omit the “c^2” term by setting c, the speed of light, to 1 and just refer to masses in MeV or GeV. Here’s a nice explanation of this procedure.)

A few weeks ago, the Atomki group released a new set of results that uses an updated spectrometer and measures the same observable (positron-electron angular correlation) but from transitions of Helium excited states instead of Beryllium. Interestingly, they again find a similar excess on this distribution, which could similarly be explained by a boson with mass ~17 MeV. There are still many questions surrounding this result, and lots of skeptical voices, but the replication of this anomaly in a different system (albeit not yet performed by independent teams) certainly raises interesting questions that seem to warrant further investigation by other researchers worldwide.

**Nuclear physics and spectroscopy**

The paper reports the production of excited states of Helium nuclei from the bombardment of tritium atoms with protons. To a non-nuclear physicist, this may not be immediately obvious, but nuclei can be in excited states just as electrons around atoms. The entire quantum wavefunction of the nucleus is usually found in the ground state, but can be excited by various mechanisms such as the proton bombardment used in this case. Protons with a specific energy (0.9 MeV) were targeted at tritium atoms to initiate the reaction 3H(p, γ)4He, in nuclear physics notation. The equivalent particle physics notation is p + 3H → He* → He + γ (→ e+ e–), where ‘*’ denotes an excited state.

This particular proton energy serves to excite the newly-produced Helium atoms into a state with energy of 20.49 MeV. This energy is sufficiently close to the Jπ = 0– state (i.e. negative parity and quantum number J = 0), which is the second excited state in the ladder of states of Helium. This state has a centroid energy of 21.01 MeV and a wide “sigma” (or decay width) of 0.84 MeV. Note that energies of the first two excited states of Helium overlap quite a bit, so actually sometimes nuclei will be found in the first excited state instead, which is not phenomenologically interesting in this case.

Figure 1. Sketch of the energy distributions for the first two excited quantum states of Helium nuclei. The second excited state (with centroid energy of 21.01 MeV) exhibits an anomaly in the electron-positron angular correlation distribution in transitions to the ground state. Proton bombardment with 0.9 MeV protons yields Helium nuclei at 20.49 MeV, therefore producing both first and second excited states, which are overlapping.

With this reaction, experimentalists can obtain transitions from the Jπ = 0– excited state back to the ground state with Jπ = 0+. These transitions typically produce a gamma ray (photon) with 21.01 MeV energy, but occasionally the photon will internally convert into an electron-positron pair, which is the experimental signature of interest here. A sketch of the experimental concept is shown below. In particular, the two main observables measured by the researchers are the invariant mass of the electron-positron pair, and the angular separation (or angular correlation) between them, in the lab frame.

Figure 2. Schematic representation of the production of excited Helium states from proton bombardment, followed by their decay back to the ground state with the emission of an “X” particle. X here can refer to a photon converting into a positron-electron pair, in which case this is an internal pair creation (IPC) event, or to the hypothetical “X17” particle, which is the process of interest in this experiment. Adapted from 1608.03591.

**The measurement**

For this latest measurement, the researchers upgraded the spectrometer apparatus to include 6 arms instead of the previous 5. Below is a picture of the setup with the 6 arms shown and labeled. The arms are at azimuthal positions of 0, 60, 120, 180, 240, and 300 degrees, and oriented perpendicularly to the proton beam.

Figure 3. The Atomki nuclear spectrometer. This is an upgraded detector from the previous one used to detect the Beryllium anomaly, featuring 6 arms instead of 5. Each arm has both plastic scintillators for measuring electrons’ and positrons’ energies, as well as a silicon strip-based detector to measure their hit impact positions. Image credit: A. Krasznahorkay.

The arms consist of plastic scintillators to detect the scintillation light produced by the electrons and positrons striking the plastic material. The amount of light collected is proportional to the energy of the particles. In addition, silicon strip detectors are used to measure the hit position of these particles, so that the correlation angle can be determined with better precision.

With this setup, the experimenters can measure the energy of each particle in the pair and also their incident positions (and, from these, construct the main observables: invariant mass and separation angle). They can also look at the scalar sum of energies of the electron and positron (Etot), and use it to zoom in on regions where they expect more events due to the new “X17” boson: since the second excited state lives around 21.01 MeV, the signal-enriched region is defined as 19.5 MeV < Etot < 22.0 MeV. They can then use the orthogonal region, 5 MeV < Etot < 19 MeV (where signal is not expected to be present), to study background processes that could potentially contaminate the signal region as well.

The figure below shows the angular separation (or correlation) between electron-positron pairs. The red asterisks are the main data points, and consist of events with Etot in the signal region (19.5 MeV < Etot < 22.0 MeV). We can clearly see the bump occurring around angular separations of 115 degrees. The black asterisks consist of events in the orthogonal region, 5 MeV < Etot < 19 MeV. Clearly there is no bump around 115 degrees here. The researchers then assume that the distribution of background events in the orthogonal region (black asterisks) has the same shape inside the signal region (red asterisks), so they fit the black asterisks to a smooth curve (blue line), and rescale this curve to match the number of events in the signal region in the 40 to 90 degrees sub-range (the first few red asterisks). Finally, the re-scaled blue curve is used in the 90 to 135 degrees sub-range (the last few red asterisks) as the expected distribution.

Figure 4. Angular correlation between positrons and electrons emitted in Helium nuclear transitions to the ground state. Red dots are data in the signal region (sum of positron and electron energies between 19.5 and 22 MeV), and black dots are data in the orthogonal region (sum of energies between 5 and 19 MeV). The smooth blue curve is a fit to the orthogonal region data, which is then re-scaled to to be used as background estimation in the signal region. The blue, black, and magenta histograms are Monte Carlo simulations of expected backgrounds. The green curve is a fit to the data with the hypothesis of a new “X17” particle.

In addition to the data points and fitted curves mentioned above, the figure also reports the researchers’ estimates of the physics processes that cause the observed background. These are the black and magenta histograms, and their sum is the blue histogram. Finally, there is also a green curve on top of the red data, which is the best fit to a signal hypothesis, that is, assuming that a new particle with mass 16.84 ± 0.16 MeV is responsible for the bump in the high-angle region of the angular correlation plot.

The other main observable, the invariant mass of the electron-positron pair, is shown below.

Figure 5. Invariant mass distribution of emitted electrons and positrons in the transitions of Helium nuclei to the ground state. Red asterisks are data in the signal region (sum of electron and positron energies between 19.5 and 22 MeV), and black asterisks are data in the orthogonal region (sum of energies between 5 and 19 MeV). The green smooth curve is the best fit to the data assuming the existence of a 17 MeV particle.

The invariant mass is constructed from the equation

where all relevant quantities refer to electron and positron observables: Etot is as before the sum of their energies, y is the ratio of their energy difference over their sum (y \equiv (E_{e^+} – E_{e^-})/E_{\textrm{tot}}), θ is the angular separation between them, and me is the electron and positron mass. This is just one of the standard ways to calculate the invariant mass of two daughter particles in a reaction, when the known quantities are the angular separation between them and their individual energies in the lab frame.

The red asterisks are again the data in the signal region (19.5 MeV < Etot < 22 MeV), and the black asterisks are the data in the orthogonal region (5 MeV < Etot < 19 MeV). The green curve is a new best fit to a signal hypothesis, and in this case the best-fit scenario is a new particle with mass 17.00 ± 0.13 MeV, which is statistically compatible with the fit in the angular correlation plot. The significance of this fit is 7.2 sigma, which means the probability of the background hypothesis (i.e. no new particle) producing such large fluctuations in data is less than 1 in 390,682,215,445! It is remarkable and undeniable that a peak shows up in the data — **the only question is whether it really is due to a new particle, or whether perhaps the authors failed to consider all possible backgrounds, or even whether there may have been an unexpected instrumental anomaly of some sort.**

According to the authors, the same particle that could explain the anomaly in the Beryllium case could also explain the anomaly here. I think this claim needs independent validation by the theory community. In any case, it is very interesting that similar excesses show up in two “independent” systems such as the Beryllium and the Helium transitions.

**Some possible theoretical interpretations**

There are a few particle interpretations of this result that can be made compatible with current experimental constraints. Here I’ll just briefly summarize some of the possibilities. For a more in-depth view from a theoretical perspective, check out Flip’s “Delirium over Beryllium” bite.

The new X17 particle could be the vector gauge boson (or mediator) of a protophobic force, i.e. a force that interacts preferentially with neutrons but not so much with protons. This would certainly be an unusual and new force, but not necessarily impossible. Theorists have to work hard to make this idea work, as you can see here.

Another possibility is that the X17 is a vector boson with axial couplings to quarks, which could explain, in the case of the original Beryllium anomaly, why the excess appears in only some transitions but not others. There are complete theories proposed with such vector bosons that could fit within current experimental constraints and explain the Beryllium anomaly, but they also include new additional particles in a dark sector to make the whole story work. If this is the case, then there might be new accessible experimental observables to confirm the existence of this dark sector and the vector boson showing up in the nuclear transitions seen by the Atomki group. This model is proposed here.

However, an important caveat about these explanations is in order: so far, they only apply to the Beryllium anomaly. I believe the theory community needs to validate the authors’ assumption that the same particle could explain this new anomaly in Helium, and that there aren’t any additional experimental constraints associated with the Helium signature. As far as I can tell, this has not been shown yet. In fact, the similar invariant mass is the only evidence so far that this could be due to the same particle. An independent and thorough theoretical confirmation is needed with high-stake claims such as this one.

**Questions and criticisms**

n the years since the first Beryllium anomaly result, a few criticisms about the paper and about the experimental team’s history have been laid out. I want to mention some of those to point out that this is still a contentious result.

First, there is the group’s history of repeated claims of new particle discoveries every so often since the early 2000s. After experimental refutation of these claims by more precise measurements, there isn’t a proper and thorough discussion of why the original excesses were seen in the first place, and why they have subsequently disappeared. Especially for such groundbreaking claims, a consistent history of solid experimental attitude towards one’s own research is very valuable when making future claims.

Second, others have mentioned that some fit curves seem to pass very close to most data points (n.b. I can’t seem to find the blog post where I originally read this or remember its author – if you know where it is, please let me know so I can give proper credit!). Take a look at the plot below, which shows the observed Etot distribution. In experimental plots, there is usually a statistical fluctuation of data points around the “mean” behavior, which is natural and expected. Below, in contrast, the data points are remarkably close to the fit. This doesn’t in itself mean there is anything wrong here, but it does raise an interesting question of how the plot and the fit were produced. It could be that this is not a fit to some prior expected behavior, but just an “interpolation”. Still, if that’s the case, then it’s not clear (to me, at least) what role the interpolation curve plays.

Figure 6. Sum of electron and positron energies distribution produced in the decay of Helium nuclei to the ground state. Black dots are data and the red curve is a fit.

Third, there is also the background fit to data in Figure 4 (black asterisks and blue line). As Ethan Siegel has pointed out, you can see how well the background fit matches data, but only in the 40 to 90 degrees sub-range. In the 90 to 135 degrees sub-range, the background fit is actually quite poorer. In a less favorable interpretation of the results, this may indicate that whatever effect is causing the anomalous peak in the red asterisks is also causing the less-than-ideal fit in the black asterisks, where no signal due to a new boson is expected. If the excess is caused by some instrumental error instead, you’d expect to see effects in both curves. In any case, the background fit (blue curve) constructed from the black asterisks does not actually model the bump region very well, which weakens the argument for using it throughout all of the data. A more careful analysis of the background is warranted here.

Fourth, another criticism comes from the simplistic statistical treatment the authors employ on the data. They fit the red asterisks in Figure 4 with the “PDF”:

where PDF stands for “Probability Density Function”, and in this case they are combining two PDFs: one derived from data, and one assumed from the signal hypothesis. The two PDFs are then “re-scaled” by the expected number of background events (N_{Bg}) and signal events (N_{sig}), according to Monte Carlo simulations. However, as others have pointed out, when you multiply a PDF by a yield such as N_{Bg}, you no longer have a PDF! A variable that incorporates yields is no longer a probability. This may just sound like a semantics game, but it does actually point to the simplicity of the treatment, and makes one wonder if there could be additional (and perhaps more serious) statistical blunders made in the course of data analysis.

Fifth, there is also of course the fact that no other experiments have seen this particle so far. This doesn’t mean that it’s not there, but particle physics is in general a field with very few “low-hanging fruits”. Most of the “easy” discoveries have already been made, and so every claim of a new particle must be compatible with dozens of previous experimental and theoretical constraints. It can be a tough business. Another example of this is the DAMA experiment, which has made claims of dark matter detection for almost 2 decades now, but no other experiments were able to provide independent verification (and in fact, several have provided independent refutations) of their claims.

I’d like to add my own thoughts to the previous list of questions and considerations.

The authors mention they correct the calibration of the detector efficiency with a small energy-dependent term based on a GEANT3 simulation. The updated version of the GEANT library, GEANT4, has been available for at least 20 years. I haven’t actually seen any results that use GEANT3 code since I’ve started in physics. Is it possible that the authors are missing a rather large effect in their physics expectations by using an older simulation library? I’m not sure, but just like the simplistic PDF treatment and the troubling background fit to the signal region, it doesn’t inspire as much confidence. It would be nice to at least have a more detailed and thorough explanation of what the simulation is actually doing (which maybe already exists but I haven’t been able to find?). This could also be due to a mismatch in the nuclear physics and high-energy physics communities that I’m not aware of, and perhaps nuclear physicists tend to use GEANT3 a lot more than high-energy physicists.

Also, it’s generally tricky to use Monte Carlo simulation to estimate efficiencies in data. One needs to make sure the experimental apparatus is well understood and be confident that their simulation reproduces all the expected features of the setup, which is often difficult to do in practice, as collider experimentalists know too well. I’d really like to see a more in-depth discussion of this point.

Finally, a more technical issue: from the paper, it’s not clear to me how the best fit to the data (red asterisks) was actually constructed. The authors claim:

*Using the composite PDF described in Equation 1 we first performed a list of fits by fixing the simulated particle mass in the signal PDF to a certain value, and letting RooFit estimate the best values for NSig andNBg. Letting the particle mass lose in the fit, the best fitted mass is calculated for the best fit […]*

When they let loose the particle mass in the fit, do they keep the “NSig” and “NBg” found with a fixed-mass hypothesis? If so, which fixed-mass NSig and which NBg do they use? And if not, what exactly was the purpose of performing the fixed-mass fits originally? I don’t think I fully got the point here.

**Where to go from here**

Despite the many questions surrounding the experimental approach, it’s still an interesting result that deserves further exploration. If it holds up with independent verification from other experiments, it would be an undeniable breakthrough, one that particle physicists have been craving for a long time now.

And independent verification is key here. Ideally other experiments need to confirm that they also see this new boson before the acceptance of this result grows wider. Many upcoming experiments will be sensitive to a new X17 boson, as the original paper points out. In the next few years, we will actually have the possibility to probe this claim from multiple angles. Dedicated standalone experiments at the LHC such as FASER and CODEX-b will be able to probe highly long-lived signatures coming from the proton-proton interaction point, and so should be sensitive to new particles such as axion-like particles (ALPs).

Another experiment that could have sensitivity to X17, and has come online this year, PADME (disclaimer: I am a collaborator on this experiment).

PADME stands for Positron Annihilation into Dark Matter Experiment and its main goal is to look for dark photons produced in the annihilation between positrons and electrons.

You can find more information about PADME here, and I will write a more detailed post about the experiment in the future, but the gist is that PADME is a fixed-target experiment striking a beam of positrons (beam energy: 550 MeV) against a fixed target made of diamond (carbon atoms). The annihilation between positrons in the beam and electrons in the carbon atoms could give rise to a photon and a new dark photon via kinetic mixing. By measuring the incoming positron and the outgoing photon momenta, we can infer the missing mass which is carried away by the (invisible) dark photon.

If the dark photon is the X17 particle (a big if), PADME might be able to see it as well. Our dark photon mass sensitivity is roughly between 1 and 22 MeV, so a 17 MeV boson would be within our reach. But more interestingly, using the knowledge of where the new particle hypothesis lies, we might actually be able to set our beam energy to produce the X17 in resonance (using a beam energy of roughly 282 MeV). The resonance beam energy increases the number of X17s produced and could give us even higher sensitivity to investigate the claim.

An important caveat is that PADME can provide independent confirmation of X17, but cannot refute it. If the coupling between the new particle and our ordinary particles is too feeble, PADME might not see evidence for it. This wouldn’t necessarily reject the claim by Atomki, it would just mean that we would need a more sensitive apparatus to detect it. This might be achievable with the next generation of PADME, or with the new experiments mentioned above coming online in a few years.

Finally, in parallel with the experimental probes of the X17 hypothesis, it’s critical to continue gaining a better theoretical understanding of this anomaly. In particular, an important check is whether the proposed theoretical models that could explain the Beryllium excess also work for the new Helium excess. Furthermore, theorists have to work very hard to make these models compatible with all current experimental constraints, so they can look a bit contrived. Perhaps a thorough exploration of the theory landscape could lead to more models capable of explaining the observed anomalies as well as evading current constraints.

**Conclusions**

The recent results from the Atomki group raise the stakes in the search for Physics Beyond the Standard Model. The reported excesses in the angular correlation between electron-positron pairs in two different systems certainly seems intriguing. However, there are still a lot of questions surrounding the experimental methods, and given the nature of the claims made, a crystal-clear understanding of the results and the setup need to be achieved. Experimental verification by at least one independent group is also required if the X17 hypothesis is to be confirmed. Finally, parallel theoretical investigations that can explain both excesses are highly desirable.

As Flip mentioned after the first excess was reported, even if this excess turns out to have an explanation other than a new particle, it’s a nice reminder that there could be interesting new physics in the light mass parameter space (e.g. MeV-scale), and a new boson in this range could also account for the dark matter abundance we see leftover from the early universe. But as Carl Sagan once said, extraordinary claims require extraordinary evidence.

In any case, this new excess gives us a chance to witness the scientific process in action in real time. The next few years should be very interesting, and hopefully will see the independent confirmation of the new X17 particle, or a refutation of the claim and an explanation of the anomalies seen by the Atomki group. So, stay tuned!

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