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Article: Particle Physics Models for the \(17\MeV\) Anomaly inwards Beryllium Nuclear DecaysRecently there’s some press (see links below) regarding early on hints of a novel particle observed inwards a nuclear physics experiment. In this bite, we’ll summarize the final result that has raised the eyebrows of some physicists, together with the hackles of others.
Authors: J.L. Feng, B. Fornal, I. Galon, S. Gardner, J. Smolinsky, T. M. P. Tait, F. Tanedo
Reference: arXiv:1608.03591 (Submitted to Phys. Rev. D)
Also featuring the results from:
- Gulyás et al., “A pair spectrometer for measurement multipolarities of energetic nuclear transitions” (description of detector; 1504.00489; NIM)
- Krasznahorkay et al., “Observation of Anomalous Internal Pair Creation inwards 8Be: Influenza A virus subtype H5N1 Possible Indication of a Light, Neutral Boson” (experimental result; 1504.01527; PRL version; banknote PRL version differs from arXiv)
- Feng et al., “Protophobic Fifth-Force Interpretation of the Observed Anomaly inwards 8Be Nuclear Transitions” (phenomenology; 1604.07411; PRL)
A crash course of study on nuclear physics
Nuclei are outpouring states of protons together with neutrons. They tin give the axe pick out excited states analogous to the excited states of atoms, which are outpouring states of nuclei together with electrons. The particular nucleus of involvement is beryllium-8, which has 4 neutrons together with 4 protons, which y'all may know from the triple alpha process. There are 3 nuclear states to move aware of: the solid set down state, the \(18.15\MeV\) excited state, together with the \(17.64\MeV\) excited state.
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| Beryllium-8 excited nuclear states. The \(18.15\MeV\) nation (red) exhibits an anomaly. Both the \(18.15\MeV\) together with \(17.64\MeV\) states decay to the solid set down through a magnetic, \(p\)-wave transition. Image adapted from Savage et al. (1987). Click at images to zoom in. |
Most of the fourth dimension the excited states autumn apart into a lithium-7 nucleus together with a proton. But sometimes, these excited states decay into the beryllium-8 solid set down nation yesteryear emitting a photon (γ-ray). Even to a greater extent than rarely, these states tin give the axe decay to the solid set down nation yesteryear emitting an electron-positron pair from a virtual photon: this is called internal pair creation together with it is these events that exhibit an anomaly.
The beryllium-8 anomaly
Physicists at the Atomki nuclear physics institute inwards Republic of Hungary were studying the nuclear decays of excited beryllium-8 nuclei. The team, led yesteryear Attila J. Krasznahorkay, produced glucinium excited states yesteryear bombarding a lithium-7 nucleus amongst protons.
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| Beryllium-8 excited states are prepared yesteryear bombarding lithium-7 amongst protons. |
The proton beam is tuned to real specific energies so that i tin give the axe ‘tickle’ specific glucinium excited states. When the protons pick out about \(1.03\MeV\) of kinetic energy, they excite lithium into the \(18.15\MeV\) glucinium state. This has 2 of import features:
- Picking the proton release energy allows i to solely hit a specific excited nation so i doesn’t pick out to worry most contamination from decays of other excited states.
- Because the \(18.15\MeV\) glucinium nucleus is produced at resonance, i has a real high yield of these excited states. This is real practiced when looking for real rare decay processes similar internal pair creation.
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| Expected distribution of opening angles for ordinary internal pair creation events. Each trace of piece of employment corresponds to nuclear transition that is electrical (E) or magnetic (M) amongst a given orbital quantum number, \(\ell\). The glucinium transitions that we’re interested inwards are generally M1. Adapted from Gulyás et al. (1504.00489). |
Instead, the Atomki squad constitute an excess of events amongst large electron-positron opening angle. In fact, fifty-fifty to a greater extent than intriguing: the excess occurs about a particular opening angle (140 degrees) together with forms a bump.
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| Number of events (\({\rm d}N/{\rm d}\theta\)) for different electron-positron opening angles together with plotted for different excitation energies (\(E_p\)). For \(E_p=1.10\MeV\), at that spot is a pronounced bump at 140 degrees which does non appear to move explainable from the ordinary internal pair conversion. This may move suggestive of a novel particle. Adapted from Krasznahorkay et al., PRL 116, 042501. |
Here’s why a bump is peculiarly interesting:
- The distribution of ordinary internal pair creation events is smoothly decreasing together with so this is real unlikely to hit a bump.
- Bumps tin give the axe move signs of novel particles: if at that spot is a new, lite particle that tin give the axe facilitate the decay, i would aspect a bump at an opening angle that depends on the novel particle mass.
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| Schematic of the Atomki experiment together with novel particle (\(X\)) interpretation of the anomalous events. In summary: protons of a specific release energy bombard stationary lithium-7 nuclei together with excite them to the \(18.15\MeV\) beryllium-8 state. These decay into the beryllium-8 solid set down state. Some of these decays are mediated yesteryear the novel \(X\) particle, which so decays inwards to electron-positron pairs of a certainly opening angle that are detected inwards the Atomki pair spectrometer detector. Image from 1608.03591. |
As an exercise for those amongst a background inwards special relativity, i tin give the axe role the relation \((p_{e^+}+p_{e^-})^2 = m_X^2\) to essay the result:\[
m_X^2 = \zav{ 1 - \zav{\frac{E_{e^+}\!-\!E_{e^-}}{E_{e^+}\!+\!E_{e^-}}}^{\!2} } (E_{e^+}\!+\!E_{e^-})^2 \sin^2 \frac\theta 2
\] This relates the majority of the proposed novel particle, \(X\), to the opening angle \(\theta\) together with the energies \(E\) of the electron together with positron. The opening angle bump would so move interpreted every bit a novel particle amongst mass of roughly \(17\MeV\). To tally the observed issue of anomalous events, the charge per unit of measurement at which the excited glucinium decays via the \(X\) boson must move \(6\times 10^{-6}\) times the charge per unit of measurement at which it goes into a γ-ray.
The anomaly has a significance of 6.8σ. This agency that it’s highly unlikely to move a statistical fluctuation, every bit the \(750\GeV\) diphoton bump appears to pick out been. Indeed, the conservative bet would move some not-understood systematic effect, akin to the \(130\GeV\) Fermi γ-ray line.
The glucinium that cried wolf?
Some physicists are concerned that glucinium may move the ‘boy that cried wolf,’ together with betoken to papers yesteryear the piece of cake Fokke de Boer every bit early on every bit 1996 together with all the way to 2001. de Boer made strong claims most evidence for a novel \(10\MeV\) particle inwards the internal pair creation decays of the \(17.64\MeV\) beryllium-8 excited state. These claims didn’t pan out, together with inwards fact the instrumentation paper yesteryear the Atomki experiment rules out that master copy anomaly.
The proposed evidence for “de Boeron” is shown below:
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| The de Boer claim for a \(10\MeV\) novel particle. Left: distribution of opening angles for internal pair creation events inwards an E1 transition of carbon-12. This transition has similar release energy splitting to the beryllium-8 \(17.64\MeV\) transition together with shows practiced understanding amongst the expectations; every bit shown yesteryear the apartment “signal – background” on the bottom panel. Right: the same analysis for the M1 internal pair creation events from the \(17.64\MeV\) beryllium-8 states. The “signal – background” forthwith shows a wide excess across all opening angles. Adapted from de Boer et al. PLB 368, 235 (1996). |
When the Atomki grouping studied the same \(17.64\MeV\) transition, they constitute that a primal background component—subdominant E1 decays from nearby excited states—dramatically improved the fit together with were non included inwards the master copy de Boer analysis. This is the final boom inwards the coffin for the proposed \(10\MeV\) “de Boeron.”
However, the Atomki grouping also highlight how their novel anomaly inwards the \(18.15\MeV\) nation behaves differently. Unlike the wide excess inwards the de Boer result, the novel excess is concentrated inwards a bump. There is no known way inwards which additional internal pair creation backgrounds tin give the axe contribute to add together a bump inwards the opening angle distribution; every bit noted above: all of these distributions are smoothly falling.
The Atomki grouping goes on to suggest that the novel particle appears to fit the neb for a dark photon, a reasonably well-motivated re-create of the ordinary photon that differs inwards its overall strength together with having a non-zero (\(17\MeV\)?) mass.
Theory component subdivision 1: Not a nighttime photon
With the Atomki final result was published together with peer reviewed inwards Physics Review Letters, the game was afoot for theorists to sympathise how it would fit into a theoretical framework similar the nighttime photon. Influenza A virus subtype H5N1 grouping from UC Irvine, University of Kentucky, together with UC Riverside constitute that actually, dark photons pick out a hard fourth dimension plumbing equipment the anomaly simultaneously amongst other experimental constraints. In the visual linguistic communication of this recent ParticleBite, the province of affairs was this:
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| It turns out that the minimal model of a nighttime photon cannot simultaneously explicate the Atomki beryllium-8 anomaly without running afoul of other experimental constraints. Image adapted from this ParticleBite. |
The main argue for this is that a nighttime photon amongst majority together with interaction strength to fit the glucinium anomaly would necessarily pick out been seen yesteryear the NA48/2 experiment. This experiment looks for nighttime photons inwards the decay of neutral pions (\(\pi^0\)). These pions typically decay into 2 photons, but if there’s a \(17\MeV\) nighttime photon around, some fraction of those decays would larn into dark-photon — ordinary-photon pairs. The non-observation of these unique decays rules out the nighttime photon interpretation.
The theorists so decided to “break” the nighttime photon theory inwards club to endeavour to larn inwards fit. They generalized the types of interactions that a novel photon-like particle, \(X\), could have, allowing protons, for example, to pick out completely different charges than electrons rather than having exactly contrary charges. Doing this does gross violence to the theoretical consistency of a theory—but they goal was just to meet what a novel particle interpretation would pick out to aspect like. They constitute that if a novel photon-like particle talked to neutrons but non protons—that is, the novel strength were protophobic—then a theory mightiness handgrip together.
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| Schematic description of how model-builders “hacked” the nighttime photon theory to fit both the glucinium anomaly spell beingness consistent amongst other experiments. This hack isn’t pretty—and indeed, comes at the toll of potentially invalidating the mathematical consistency of the theory—but the exercise demonstrates the target for how to a consummate theory mightiness pick out to behave. Image adapted from this ParticleBite. |
Theory appendix: pion-phobia is protophobia
Editor’s note: what follows is for readers amongst some physics background interested inwards a technical detail; others may skip this section.
How does a novel particle that is allergic to protons avoid the neutral pion decay bounds from NA48/2? Pions decay into pairs of photons through the well-known triangle-diagrams of the axial anomaly. The decay into photon–dark-photon pairs move along through similar diagrams. The goal is so to brand certainly that these diagrams cancel.
Influenza A virus subtype H5N1 cute way to aspect at this is to assume that at depression energies, the relevant particles running inwards the loop aren’t quarks, but rather nucleons (protons together with neutrons). In fact, since solely the proton tin give the axe utter to the photon, i solely needs to consider proton loops. Thus if the novel photon-like particle, \(X\), doesn’t utter to protons, so there’s no diagram for the pion to decay into \(\gamma X\). This would move non bad if the story weren’t completely wrong.
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| Avoiding NA48/2 bounds requires that the novel particle, \(X\), is pion-phobic. It turns out that this is equivalent to \(X\) beingness protophobic. The right way to meet this is on the left, making certainly that the contribution of up-quark loops cancels the contribution from down-quark loops. Influenza A virus subtype H5N1 slick (but naively completely wrong) calculation is on the right, disceptation that effectively solely protons run inwards the loop. |
The right way of seeing this is to care for the pion every bit a quantum superposition of an up–anti-up together with down–anti-down outpouring state, together with so brand certainly that the \(X\) charges are such that the contributions of the 2 states cancel. The resulting charges plow out to move protophobic.
The fact that the “proton-in-the-loop” moving painting gives the right charges, however, is no coincidence. Indeed, this was exactly how Jack Steinberger calculated the right pion decay rate. The primal hither is whether i treats the quarks/nucleons linearly or non-linearly inwards chiral perturbation theory. The relation to the Wess-Zumino-Witten term—which is what genuinely encodes the low-energy interaction—is carefully explained inwards chapter 6a.2 of Georgi’s revised Weak Interactions.
Theory component subdivision 2: Not a spin-0 particle
The to a higher house considerations focus on a novel particle amongst the same spin together with parity every bit a photon (spin-1, parity odd). Another final result of the UCI study was a systematic exploration of other possibilities. They constitute that the glucinium anomaly could non move consistent amongst spin-0 particles. For a parity-odd, spin-0 particle, i cannot simultaneously conserve angular momentum together with parity inwards the decay of the excited beryllium-8 state. (Parity violating effects are negligible at these energies.)
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| Parity together with angular momentum conservation prohibit a “dark Higgs” (parity fifty-fifty scalar) from mediating the anomaly. |
For a parity-odd pseudoscalar, the bounds on axion-like particles at \(20\MeV\) suffocate whatever reasonable coupling. Measured inwards damage of the pseudoscalar–photon–photon coupling (which has dimensions of inverse \({\rm GeV}\)), this interaction is ruled out downwardly to the inverse Planck scale.
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| Bounds on axion-like particles exclude a \(20\MeV\) pseudoscalar amongst couplings to photons stronger than the inverse Planck scale. Adapted from 1205.2671 together with 1512.03069. |
Additional possibilities include:
- Dark Z-bosons, cousins of the nighttime photon amongst spin-1 but indeterminate parity. This is real constrained yesteryear atomic parity violation.
- Axial vectors, spin-1 bosons amongst positive parity. These rest a theoretical possibility, though their unknown nuclear matrix elements larn inwards hard to write a predictive model. (See department II.D of 1608.03591.)
The plot thickens when i time also includes results from nuclear theory. Recent results from Saori Pastore, Bob Wiringa, together with collaborators betoken out a real of import fact: the \(18.15\MeV\) beryllium-8 nation that exhibits the anomaly together with the \(17.64\MeV\) nation which does non are genuinely closely related.
Recall (e.g. from the outset figure at the top) that both the \(18.15\MeV\) together with \(17.64\MeV\) states are both spin-1 together with parity-even. They differ inwards majority together with inwards i other primal aspect: the \(17.64\MeV\) nation carries isospin charge, spell the \(18.15\MeV\) nation together with solid set down nation hit not.
Isospin is the nuclear symmetry that relates protons to neutrons together with is tied to electroweak symmetry inwards the total Standard Model. At nuclear energies, isospin accuse is just about conserved. This brings us to the next puzzle:
If the novel particle has majority about \(17\MeV\), why hit nosotros meet its effects inwards the \(18.15\MeV\) nation but non the \(17.64\MeV\) state?Naively, if the novel particle emitted, \(X\), carries no isospin charge, so isospin conservation prohibits the decay of the \(17.64\MeV\) nation through emission of an \(X\) boson. However, the Pastore et al. result tells us that actually, the isospin-neutral together with isospin-charged states mix quantum mechanically so that the observed \(18.15\) together with \(17.64\MeV\) states are mixtures of iso-neutral together with iso-charged states. In fact, this mixing is genuinely rather large, amongst mixing angle of about 10 degrees!
The final result of this is that i cannot invoke isospin conservation to explicate the non-observation of an anomaly inwards the \(17.64\MeV\) state. In fact, the solely way to avoid this is to assume that the majority of the \(X\) particle is on the heavier side of the experimentally allowed range. The charge per unit of measurement for \(X\) emission goes similar the 3-momentum cubed (see department II.E of 1608.03591), so a little growth inwards the majority tin give the axe suppresses the charge per unit of measurement of \(X\) emission yesteryear the lighter nation yesteryear a lot.
The UCI collaboration of theorists went farther together with extended the Pastore et al. analysis to include a phenomenological parameterization of explicit isospin violation. Independent of the Atomki anomaly, they constitute that including isospin violation improved the fit for the \(18.15\MeV\) together with \(17.64\MeV\) electromagnetic decay widths inside the Pastore et al. formalism. The results of including all of the isospin effects destination upward changing the particle physics story of the Atomki anomaly significantly:
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| The charge per unit of measurement of \(X\) emission (colored contours) every bit a business office of the \(X\) particle’s couplings to protons (horizontal axis) versus neutrons (vertical axis). The best fit for a \(16.7\MeV\) novel particle is the dashed trace of piece of employment inwards the teal region. The vertical band is the share allowed yesteryear the NA48/2 experiment. Solid lines present the nighttime photon together with protophobic limits. Left: the instance for perfect (unrealistic) isospin. Right: the instance when isospin mixing together with explicit violation are included. Observe that incorporating realistic isospin happens to pick out solely a little outcome inwards the protophobic region. Figure from 1608.03591. |
The results of the nuclear analysis are hence that:
- An interpretation of the Atomki anomaly inwards damage of a novel particle tends to force for a slightly heavier \(X\) majority than the reported best fit. (Remark: the Atomki newspaper does non hit a combined fit for the majority together with coupling nor does it study the difficult-to-quantify systematic errors associated amongst the fit. This information is of import for understanding the extent to which the \(X\) majority tin give the axe move pushed to move heavier.)
- The effects of isospin mixing together with violation are of import to include; especially every bit i drifts away from the purely protophobic limit.
The theoretical construction presented to a higher house gives a framework to hit phenomenology: plumbing equipment the observed anomaly to a particle physics model together with so comparison that model to other experiments. This, however, doesn’t guarantee that a nice—or fifty-fifty self-consistent—theory exists that tin give the axe stretch over the scaffolding.
Indeed, a few challenges appear:
- The isospin mixing discussed to a higher house agency the \(X\) majority must move pushed to the heavier values allowed yesteryear the Atomki observation.
- The “protophobic” boundary is non apparently anomaly-free: just asserting that known particles pick out arbitrary charges does non generically hit a mathematically self-consistent theory.
- Atomic parity violation constraints require that the \(X\) couplet inwards the same way to \(3.5\keV\) together with \(130\GeV\), or penguins at LHCb—these are the signs that we’re making role of all of the information available to search for novel physics. Sometimes these hopes fizzle away, oftentimes they exit behind useful lessons most physics together with directions forward. Maybe i of these days an anomaly volition stick together with present us the way forward.
Further Reading
Here are some of the popular-level press on the Atomki result. See the references at the summit of this ParticleBite for references to the primary literature.
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