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New pathways in axion searches

Peering through telescopes we have found a deluge of evidence for dark matter. Given the speed that galaxies rotate, as well as theoretical calculations about the evolution of large-scale structure in the Universe, dark matter should make up 85% of the matter in the Universe. Despite considerable evidence in support of dark matter we still don’t know its substance. It remains one of the great mysteries of science today.

Until recently, there were strong motivations that dark matter (DM) is made out of particles with masses in the scale of 100 times the mass of the proton, the so-called WIMPs (Weakly Interacting Massive Particles). For many years, WIMP searches have dominated dark-matter research but without any clear evidence or hint appearing so far in one of our detectors. This is beginning to trigger a paradigm shift to another dark-matter candidate: a dainty particle called an axion, which could be more than a billion times lighter than an electron and much lighter than the WIMP. The physics of these particles has been considerably developed in recent years, and there are now useful guidelines and powerful motivations to attempt experimental detection.

In a recent seminar entitled “New ideas for the axion dark matter program” Nick Rodd (Miller fellow, UC Berkeley) outlined two key ideas that underpin and inform the future experimental programme in axion searches. “The field of dark matter searches is undergoing a transition to new ideas about the substance of dark matter based on axion or axion-like particles as good candidates”. Axions could also resolve another long-standing puzzle in physics: why do the quarks in a neutron arrange themselves to produce no observable electric dipole moment? In fact axions were first postulated through the Peccei-Quinn solution that addresses this so-called strong-CP problem. For Rodd, “it is encouraging that, as was noted over 40 years ago, a strong independent motivation for the existence of at least one axion comes from the theory of strong interactions. This “QCD axion” would explain why the laws of strong interactions are invariant under changing the direction of time.”

Given the strong theoretical motivation for axions, the experimental landscape is rapidly evolving, with many novel detection techniques and new experimental proposals. According to Rodd, “in the next decade we could have an answer as to whether the axion is DM or if we have been wrong in our guess. There are good reasons to be optimistic about the planned experimental programme” and adds “however this is also the time to reflect on how to maximize the research potential of the instruments that we are going to build. Questions about the possible signatures of DM axions or the amount of information contained in the data that we plan to collect are pertinent and should be addressed in parallel to experimental progress”.

Unlike the WIMP, which we conventionally think of as a particle that we could detect when it bumps into our detectors, the much lighter axion can be described as a wave. This means that our instruments could detect them as oscillating waves and in fact apply interferometry techniques that would give us a wealth of information about their source. “Axion interferometry proposes combining axion search results from different geolocations thus performing interferometry directly on the dark-matter wave”. The second idea Nick Rodd explored in his seminar is the search for relativistic axions that would form a residual Cosmic axion Background (CaB). “Existing searches at, for instance ADMX, are not yet sensitive to a cosmic relic, although if relativistic axions are produced in the late Universe, by for instance dark-matter decaying to axions, then this is a signal the experiments are already sensitive to, but would miss with existing analyses. Qualitatively the signal from CaB would be similar with that of Cosmic Microwave Background (CMB) and we should ensure that we don’t accidentally miss the axion discovery by not carefully analysing the data.”

Dark-Matter Interferometry: Exploiting the wave-like nature of axion

In order to move forward efficiently with axion DM searches we should look back and understand how well we have covered the parameter space available with our current instruments (haloscopes, helioscopes and other laboratory experiments exploiting different techniques). This is particularly important to map a search strategy with the next generation of technologies in DM axion searches which would give us access to masses and wavelengths beyond our present capabilities. Rodd says “It is wonderful to see all this effort on the instrumentation and experimental side which poses also a challenge for theorists to catch up and think on the opportunities offered by these new instruments”.

Fundamentally, a wave is described by its amplitude and phase. Interferometry could give us access to the  information contained in the phase of the wave that is related to its momentum. This can be seen by writing the equation for the wave-like Dark Matter as shown below:

Rodd notes: “Accessing information regarding the full axion momentum - which can only be done with interferometry - is very interesting as it could tell us more about the direction from which dark matter arrives at our instrument; in addition to the information about the particle energy that we get from its frequency. This opportunity will be integrated in the next generation of searches”.

We asked our interviewee whether having this information is also relevant/paves new ways in searches of streaming dark matter. “Our best guess at the moment is that the bulk of dark matter is like a gas moving all over the place in the rest frame of the Milky Way. Earth is streaming through this gas and although we don’t know for sure which direction it hits the Earth, our expectation is that it points to the constellation of Cygnus - though this could be wrong if the bulk of local dark matter is in streams. By performing axion DM interferometry and verifying that the signal points to the Cygnus constellation you will have another extremely important and non-trivial confirmation that your signal is related to DM and not an unexpected background”. This is particularly important when searching for such feeble signals. Rodd reminds me that “every new signal, even when it eventually turns out to be a discovery like the Higgs boson, starts with a small significance and our scientific attitude is to question it and perform tests to exclude that it could be a systematic error in our instruments or our analysis”. As new tools will offer much higher sensitivity - allowing us to explore a new regime in the parameter space where axions could live - we could see all sorts of things including unexpected backgrounds. This is why it is important to get more information from interferometry allowing us to verify that our signal is a DM axion. Furthermore, interferometry would prove to be particularly useful in the event that the local DM distribution is more complicated than we imagine. “Part of the DM near the Earth could be in an ultra coherent stream. In this case, we have no expectation as to where this stream might be coming from, and would only be able to test this using interferometry.”

Rodd also emphasizes an interesting experimental fact as interferometry would give a very dramatic fluctuation in the signal even with a single day of data. “We don’t live in the reference frame of DM but in the reference frame of the Earth. So as the Earth rotates the separation between the two instruments is changing with respect to the incident direction of the DM. So the relative phase seen by the two instruments changes throughout the day so when you add the two instruments together the interference pattern changes hugely over the 24h period. This would be very strong evidence that what you see is DM”. This daily modulation, one of the hallmark features of DM interferometry, is shown in figure 2 below. 


Fig.3: A Mollweide projection of the Asimov test statistic for the location on the sphere of the boost velocity of the Sagitarrius stream. Brighter locations indicate those locations which are preferred by a likelihood analysis of the interference effect which arises in the analysis of axion direct detection data simultaneously collected at two spatially separated locations. By leveraging the daily modulation of the separation of the two detectors which are confined to the Earth's surface, an increasingly precise determination of the boost orientation can be made. Each frame shows the improvement to the localization based on an additional hour of data collection over a 24 hour collection period. This animation additionally compares the localization for configurations where the detectors are oriented along the East-West (North-South) direction with respect to one another in the left (right) panel. The North-South configuration leads to a better localization since there is a unique global maximum in the Asimov test statistic, whereas the East-West configuration produces an exact degeneracy between two global minima. For more details, see the main work. Copyright: 2020 Joshua Foster (MIT Press).

In the present funding climate it may sound utterly optimistic to hope for two detectors located in different positions for allowing interferometry. However, Rodd explains that “interferometry is an extremely interesting technique that can apply in the data from currently planned axion experiments. Competing groups could combine their data in order to apply interferometry techniques to extract more information from their data.” For Rodd, “This is more a long term vision of collaboration between different experiments rather than an argument for one collaboration building two identical detectors”. This proposal presents an analogy with the approach of the Event Horizon Telescope (EHT) leading to the first image of a black hole in 2020. “The different telescopes stored the data with extremely precise time measurements which allowed them to go back and analyse their data offline. This is what we have in mind when proposing DM axion interferometry. Experiments take the data and restore them with high timing precision using atomic clock accuracy, thus ensuring that there will be no time offsets that could wash out a signal. Each experiment could see a bump coming from the axion but by adding the signals you would see the bump with some wrinkles that give you extra information about the direction of the source”.

A cosmological window into the early Universe

In his seminar, Rodd also presented another key topic of his research, namely the idea of a Cosmic axion Background that could be one of the relics of the Big Bang. In models of particle physics and cosmology arising from compactifications of string theory, axions are a generic prediction. These axions could be produced in the early Universe, and would exist today as a homogeneous and isotropic background of relativistic axions, hence called the CaB.

There are a number of ways we could imagine producing the light axons that make up the CaB. Possible axion sources include thermal production, dark-matter decay, parametric resonance, and topological defect decay. Each of these sources would give a characteristic frequency spectrum that can be searched for in axion direct detection experiments, and if found would allow us to answer basic questions about the early history of our Universe, as shown in figure 4:

Fig. 4: The variation in the form of the CaB as a function of energy and density can be seen for four different scenarios for its production. Finding any one of these would help answer the fundamental questions listed. (Credit: Dror et al.)

Rodd clarifies that "While I hope that the axion is dark matter, axions are such well motivated particles that we should search for the possibility that they exist even if they aren't. The CaB provides a window for doing so." or Rodd and his collaborators, building these unbelievably sophisticated and advanced experiments for DM calls for a wider strategy for analysing the collected data. “We should try and obtain as much physics as possible from the instruments that will come online over the next decade. The key is to have an open mindset and expand the questions you pose when analysing your data otherwise you risk throwing out useful data and missing a potential discovery.”

The key insight in the work of Rodd and his collaborators is that the axions that make up the CaB would also create a signal in the same instruments searching for dark-matter axions. Yet critically, the signals would look quite different: whilst dark-matter is predicted to produce all its signal at almost a single frequency (determined by its mass), the CaB would deposit its power over a broad frequency range. Existing dark-matter searches would discard such broad distributions as a background, thereby potentially missing a discovery.

Looking forward

It is hard to predict what the future holds but it is clear that the planned facilities for axion and ALP searches trigger theoretical thinking; allowing new avenues to be thoroughly explored before detectors are put in place.

The discovery of one axion would boost our thinking that there are different types of axions, one of which could even constitute dark matter. Furthermore, the search for axions reminds us of the close ties between particle physics and cosmology.

DM axion interferometry and searches for relic axions are both well motivated and present new opportunities for the foreseen instruments currently being developed in different laboratories around the world. In a closing remark Rodd tells me “We want to make sure that we are not biased towards one signal and miss a discovery. The ongoing cross talk is needed as every year new instruments come online and each of them could bring a new discovery.”

Further Reading