{"id":3970,"date":"2016-08-25T03:11:50","date_gmt":"2016-08-25T03:11:50","guid":{"rendered":"http:\/\/www.particlebites.com\/?p=3970"},"modified":"2017-02-19T02:10:40","modified_gmt":"2017-02-19T02:10:40","slug":"the-delirium-over-beryllium","status":"publish","type":"post","link":"https:\/\/www.particlebites.com\/?p=3970","title":{"rendered":"The Delirium over Beryllium"},"content":{"rendered":"
Article: <\/strong>Particle Physics Models for the 17 MeV Anomaly in Beryllium Nuclear Decays
\nAuthors:<\/strong> J.L. Feng, B. Fornal, I.\u00a0Galon, S. Gardner, J. Smolinsky, T. M. P. Tait, F.\u00a0Tanedo
\nReference:<\/strong>\u00a0arXiv:1608.03591<\/a> (Submitted to Phys. Rev. D)
\nSee also this Latin American Webinar on Physics<\/a>\u00a0recorded talk.<\/div>\n
Also featuring the results from:<\/strong>
\n— Guly\u00e1s et al., “A pair spectrometer for measuring multipolarities of energetic nuclear transitions” (description of detector;\u00a01504.00489<\/a>;\u00a0NIM<\/a>)
\n— Krasznahorkay et al., “Observation of Anomalous Internal Pair Creation in 8Be: A Possible Indication of a Light, Neutral Boson” \u00a0(experimental result;\u00a01504.01527<\/a>;\u00a0PRL version<\/a>; note PRL version differs from arXiv)
\n— Feng et al., “Protophobic Fifth-Force Interpretation of the Observed Anomaly in 8<\/sup>Be Nuclear Transitions” (phenomenology;\u00a01604.07411<\/a>; PRL<\/a>)<\/div>\n

Editor’s note: the author is a co-author of the paper being highlighted.\u00a0<\/em><\/p>\n

Recently there’s some\u00a0press (see links below)\u00a0regarding\u00a0early hints\u00a0of a new particle\u00a0observed in a nuclear physics experiment.\u00a0In this bite,\u00a0we’ll\u00a0summarize the result that\u00a0has raised the eyebrows of some physicists,\u00a0and the hackles of others.<\/p>\n

A crash course on nuclear physics<\/h2>\n

Nuclei are bound states of protons and neutrons. They can have excited states analogous to the excited states of at lowoms, which are bound states of nuclei and electrons.\u00a0The particular nucleus of interest is beryllium-8, which has four neutrons and four protons, which you may know from\u00a0the triple alpha process<\/a>. There are three\u00a0nuclear states\u00a0to be aware of: the ground state, the 18.15 MeV excited state, and the 17.64 MeV excited state.<\/p>\n

<\/a>
Beryllium-8 excited nuclear states. The 18.15 MeV state (red) exhibits an anomaly. Both the 18.15 MeV and 17.64 states decay to the ground through a magnetic, p-wave transition. Image adapted from Savage et al. (1987).<\/figcaption><\/figure>\n

Most of the time the\u00a0excited states fall apart into a lithium-7 nucleus and a proton.\u00a0But sometimes, these excited states decay\u00a0into the beryllium-8 ground state\u00a0by emitting a photon (\u03b3-ray). Even more\u00a0rarely, these states can decay to the ground state by emitting an electron–positron pair from a virtual photon: this is called\u00a0internal pair creation <\/strong>and\u00a0it is these events\u00a0that\u00a0exhibit an anomaly.<\/p>\n

The beryllium-8 anomaly<\/h2>\n

Physicists\u00a0at the\u00a0Atomki nuclear physics institute<\/a> in Hungary\u00a0were\u00a0studying the nuclear decays of\u00a0excited\u00a0beryllium-8 nuclei. The team,\u00a0led by Attila J. Krasznahorkay,\u00a0produced\u00a0beryllium\u00a0excited states by bombarding a lithium-7 nucleus with protons.<\/p>\n

\"Preparation<\/a>
Beryllium-8 excited states are prepare by\u00a0bombarding\u00a0lithium-7 with protons.<\/figcaption><\/figure>\n

The proton beam is tuned to very specific energies\u00a0so that one can ‘tickle’ specific beryllium excited states.\u00a0When the protons have around 1.03 MeV of kinetic\u00a0energy, they excite lithium into the 18.15 MeV beryllium\u00a0state. This has two important features:<\/p>\n

    \n
  1. Picking the proton energy allows one to only produce a specific excited state\u00a0so one doesn’t have to worry about contamination from decays of other excited states.<\/li>\n
  2. Because\u00a0the 18.15 MeV beryllium\u00a0nucleus is produced at resonance<\/em>, one has a very high yield of these excited states. This is very good when looking for\u00a0very rare\u00a0decay processes like internal pair creation.<\/li>\n<\/ol>\n

    What one\u00a0expects<\/em> is that\u00a0most of the electron–positron pairs have small opening angle with\u00a0a\u00a0smoothly decreasing number as with larger opening angles.<\/p>\n

    \"Screen
    Expected distribution of opening angles for ordinary internal pair creation events.\u00a0Each line corresponds to\u00a0nuclear transition that is\u00a0electric (E) or magenetic (M) with a given orbital quantum number,\u00a0l<\/em>.\u00a0The beryllium\u00a0transitionsthat we’re interested in are mostly M1. Adapted from Guly\u00e1s et al. (1504.00489<\/a>).<\/figcaption><\/figure>\n

    Instead, the Atomki\u00a0team found an excess of events\u00a0with large electron–positron opening angle. In fact,\u00a0even more intriguing: the excess occurs around a particular opening angle (140 degrees) and forms a bump.<\/p>\n

    \"Adapted<\/a>
    Number of events (dN\/d\u03b8<\/em>) for different electron–positron opening angles and plotted for different excitation energies (Ep<\/sub><\/em>). For Ep<\/sub>=<\/em>1.10 MeV, there is a pronounced bump at 140 degrees which does not appear to be explainable\u00a0from the ordinary internal pair conversion. This may be suggestive of a new particle.\u00a0Adapted from Krasznahorkay et al., PRL 116, 042501<\/a>.<\/figcaption><\/figure>\n

    Here’s why\u00a0a bump is particularly interesting:<\/p>\n

      \n
    1. The distribution of ordinary internal pair creation events is smoothly decreasing and so this is\u00a0very unlikely to produce a bump.<\/li>\n
    2. Bumps can be signs of new particles: if there is a new, light particle\u00a0that can facilitate the decay, one would expect a bump at an opening angle that depends on the new particle mass.<\/li>\n<\/ol>\n

      Schematically, the\u00a0new particle interpretation\u00a0looks like this:<\/p>\n

      \"Schematic<\/a>
      Schematic of the Atomki experiment and new particle (X<\/em>) interpretation of the anomalous events. In summary: protons of a specific energy bombard stationary lithium-7 nuclei and excite them to the 18.15 MeV beryllium-8 state. These decay into the beryllium-8 ground state. Some of these decays are mediated by the new\u00a0X<\/em> particle, which then decays in to electron–positron pairs of a certain opening angle that are detected in the Atomki pair spectrometer detector. Image from 1608.03591<\/a>.<\/figcaption><\/figure>\n

      As an exercise for those with a background in special relativity, one can use the relation $latex (p_{e^+} + p_{e^-})^2 = m_X^2$ to prove the result:<\/p>\n

      $latex m_{X}^2 = \\left(1-\\left(\\frac{E_{e^+}-E_{e^-}}{E_{e^+}+E_{e^-}}\\right)^2\\right) (E_{e^+}+E_{e^-})^2 \\sin^2 \\frac{\\theta}{2}+\\mathcal{O}(m_e^2)$<\/p>\n

      This relates the mass of the proposed new particle,\u00a0X<\/em>, to the opening angle \u03b8 and the energies\u00a0E<\/em> of the electron and positron. The opening angle bump\u00a0would then be interpreted as a new particle with mass of roughly 17 MeV<\/strong>.\u00a0To match the observed number of anomalous events, the rate at which the excited beryllium decays via\u00a0the\u00a0X<\/em> boson must be 6\u00d710-6<\/sup> times the rate at which\u00a0it goes into a \u03b3-ray.<\/p>\n

      The anomaly has a significance of\u00a06.8\u03c3. This means that it’s highly unlikely to be a statistical fluctuation, as the 750 GeV diphoton bump<\/a> appears to have been. Indeed, the conservative bet would\u00a0be some not-understood systematic effect, akin to the 130 GeV Fermi \u03b3-ray line<\/a>.<\/p>\n

      The beryllium that cried wolf?<\/h2>\n

      Some physicists are concerned that\u00a0beryllium may be the ‘boy that cried wolf<\/a>,’ and point to\u00a0papers by the late Fokke de Boer as early as\u00a01996<\/a>\u00a0and\u00a0all the way to 2001<\/a>. de Boer\u00a0made strong claims about\u00a0evidence for a new 10 MeV particle in the internal pair creation decays of the\u00a017.64 MeV beryllium-8\u00a0excited state. These claims didn’t pan out, and in fact\u00a0the instrumentation paper<\/a> by the Atomki\u00a0experiment rules out\u00a0that original anomaly.<\/p>\n

      The proposed\u00a0evidence for\u00a0“de Boeron” is shown below:<\/p>\n

      \"Beryllium\"<\/a>
      The de Boer claim for a 10 MeV\u00a0new particle.\u00a0Left: distribution of opening angles\u00a0for internal pair creation events in an E1 transition of carbon-12. This transition\u00a0has similar\u00a0energy splitting to the beryllium-8 17.64 MeV transition and shows good agreement with the\u00a0expectations; as shown by the flat “signal – background” on the bottom panel. Right: the same analysis for the M1 internal pair creation events from the\u00a017.64 MeV beryllium-8 states.\u00a0The “signal – background” now shows a broad excess across all opening angles. Adapted from de Boer et al. PLB 368, 235 (1996)<\/a>.<\/figcaption><\/figure>\n

      When the\u00a0Atomki group\u00a0studied the same 17.64 MeV transition, they found that a\u00a0key\u00a0background component—subdominant E1 decays from nearby excited states—dramatically improved the fit and were not included in the original de Boer analysis. This\u00a0is\u00a0the last nail in the coffin for the proposed 10 MeV “de Boeron.”<\/p>\n

      However, the Atomki group also\u00a0highlight how their new anomaly in the 18.15 MeV state behaves differently. Unlike the\u00a0broad excess in the de Boer result, the\u00a0new excess is concentrated in a bump.\u00a0There is no known way in which additional internal pair creation backgrounds can contribute to add a bump in\u00a0the opening angle distribution; as noted above: all of these distributions are smoothly falling.<\/p>\n

      The Atomki group goes\u00a0on to suggest that\u00a0the new particle appears to fit the bill for a dark photon<\/a>, a reasonably\u00a0well-motivated copy of the ordinary photon that differs in\u00a0its overall strength and having a non-zero (17 MeV?) mass.<\/p>\n

      Theory part 1:\u00a0Not a dark photon<\/h2>\n

      With\u00a0the Atomki result was published and peer reviewed in Physics Review Letters, the game was afoot for theorists to\u00a0understand\u00a0how it would fit into a theoretical framework like the dark photon. A group from UC Irvine, University of Kentucky, and UC Riverside found that actually, dark photons have a hard time fitting the anomaly<\/a> simultaneously with other experimental constraints. In the visual language of\u00a0this recent ParticleBite<\/a>, the situation was this:<\/p>\n

      \"Beryllium-8\"<\/a>
      It turns out that the minimal model of a dark photon cannot\u00a0simultaneously explain the Atomki beryllium-8 anomaly without\u00a0running afoul of other experimental constraints. Image adapted from this ParticleBite<\/a>.<\/figcaption><\/figure>\n

      The main reason for this is that a dark photon with mass and interaction strength to fit the beryllium anomaly would necessarily have\u00a0been seen by the NA48\/2 experiment<\/a>. This experiment looks for dark photons in the decay of neutral pions (\u03c00<\/sup>). These pions typically decay into two photons, but if there’s a 17 MeV dark photon around, some fraction of those decays would go into dark-photon — ordinary-photon pairs. The non-observation of these\u00a0unique decays\u00a0rules out the dark photon\u00a0interpretation.<\/p>\n

      The theorists\u00a0then decided to “break” the dark photon theory\u00a0in order to try to make it fit. They generalized the types of interactions\u00a0that a\u00a0new photon-like particle, X<\/em>,\u00a0could have, allowing protons, for example,\u00a0to have completely different charges than electrons rather than\u00a0having exactly opposite charges. Doing this does gross violence to the theoretical consistency of\u00a0a theory—but they goal was just to\u00a0see\u00a0what a new particle interpretation\u00a0would have to look like. They found that if a new photon-like particle\u00a0talked to neutrons but not protons—that is, the new force were protophobic<\/em>—then\u00a0a theory might hold together.<\/p>\n

      <\/a>
      Schematic description of how model-builders “hacked” the dark photon theory to fit both the beryllium anomaly\u00a0while being\u00a0consistent with other experiments. This hack isn’t pretty—and indeed, comes at the cost of potentially invalidating the\u00a0mathematical\u00a0consistency of the theory—but the exercise demonstrates\u00a0the target for how to a complete theory might have to behave. Image adapted from this ParticleBite<\/a>.<\/figcaption><\/figure>\n

      Theory appendix:\u00a0pion-phobia is protophobia<\/h2>\n

      Editor’s note: what follows is for readers with some physics background interested in a technical detail; others\u00a0may skip this section.<\/em><\/p>\n

      How does a new\u00a0particle that is allergic to protons avoid the\u00a0neutral pion decay bounds from NA48\/2?\u00a0Pions decay into pairs of photons through the well-known triangle-diagrams of the axial\u00a0anomaly<\/a>. The decay into photon–dark-photon pairs proceed through similar diagrams.\u00a0The goal is then to make sure that these diagrams cancel.<\/p>\n

      A cute way to look at this is to assume that at low energies, the relevant particles running in the loop aren’t quarks, but rather nucleons (protons \u00a0and neutrons). In fact,\u00a0since only the proton can talk to the photon, one only needs to consider proton loops. Thus if the new photon-like particle,\u00a0X<\/em>, doesn’t talk to protons, then\u00a0there’s no diagram for the pion to decay into \u03b3X<\/em>. This would be great if the story weren’t completely wrong.<\/p>\n

      \"Avoiding<\/a>
      Avoiding NA48\/2 bounds requires that\u00a0the new particle,\u00a0X,\u00a0<\/em>is pion-phobic. It turns out that\u00a0this is equivalent to\u00a0X<\/em> being protophobic. The\u00a0correct way to see this is on the left, making sure that the contribution of up-quark loops cancels the contribution from down-quark loops.\u00a0A slick (but naively\u00a0completely wrong) calculation is on the right,\u00a0arguing that effectively only protons\u00a0run in the loop.<\/figcaption><\/figure>\n

      The correct way of seeing this is to treat the pion as a quantum superposition of an up–anti-up and down–anti-down bound state, and then make sure that the X<\/em> charges are such that the\u00a0contributions of the two\u00a0states cancel. The resulting charges turn out to be protophobic.<\/p>\n

      The fact that the “proton-in-the-loop” picture gives the correct charges, however, is no coincidence. Indeed, this\u00a0was\u00a0precisely how Jack Steinberger calculated the correct pion decay rate.\u00a0The key here is whether one\u00a0treats the\u00a0quarks\/nucleons linearly or non-linearly in\u00a0chiral perturbation theory. The relation to the Wess-Zumino-Witten term—which is what really encodes the low-energy interaction—is carefully\u00a0explained in chapter 6a.2 of Georgi’s revised\u00a0Weak Interactions<\/em><\/a>.<\/p>\n

      Theory part 2: Not\u00a0a\u00a0spin-0 particle<\/h2>\n

      The above considerations focus on a new particle with\u00a0the same spin and parity as a photon (spin-1, parity odd).\u00a0Another result of the UCI study was a systematic exploration of other possibilities. They found\u00a0that the beryllium anomaly could not be consistent with spin-0 particles.\u00a0For a\u00a0parity-odd, spin-0 particle, one cannot simultaneously conserve angular momentum and parity in the decay of the excited beryllium-8 state. (Parity violating effects are\u00a0negligible at these energies.)<\/p>\n

      \"Parity\"<\/a>
      Parity and angular momentum conservation prohibit a “dark Higgs” (parity even scalar) from mediating the anomaly.<\/figcaption><\/figure>\n

      For a parity-odd\u00a0pseudoscalar,\u00a0the\u00a0bounds on axion-like particles\u00a0at 20 MeV suffocate any reasonable\u00a0coupling. Measured in terms of the pseudoscalar–photon–photon coupling (which has dimensions of inverse GeV), this interaction is ruled out down to the inverse Planck scale.<\/p>\n

      \"Screen<\/a>
      Bounds on axion-like particles exclude a 20 MeV\u00a0pseudoscalar with couplings to photons stronger than the inverse Planck scale. Adapted from 1205.2671<\/a> and 1512.03069<\/a>.<\/figcaption><\/figure>\n

      Additional possibilities include:<\/p>\n