## Riding the wave to new physics

Article title: “Particle physics applications of the AWAKE acceleration scheme”

Authors: A. Caldwell, J. Chappell, P. Crivelli, E. Depero, J. Gall, S. Gninenko, E. Gschwendtner, A. Hartin, F. Keeble, J. Osborne, A. Pardons, A. Petrenko, A. Scaachi , and M. Wing

Reference: arXiv:1812.11164

On the energy frontier, the search for new physics remains a contentious issue – do we continue to build bigger, more powerful colliders? Or is this a too costly (or too impractical) an endeavor? The standard method of accelerating charged particles remains in the realm of radio-frequency (RF) cavities, possessing an electric field strength of about 100 Megavolts per meter, such as that proposed for the future Compact Linear Accelerator (CLIC) at CERN aiming for center-of-mass energies in the multi-TeV regime. Such a technology in the linear fashion is nothing new, being a key part of the SLAC National Accelerator Laboratory (California, USA) for decades before it’s shutdown around the early millennium. However, a device such as CLIC would still require more than ten times the space of SLAC, predicted to come in at around 10-50 km. Not only that, the walls of the cavities are based on normal conducting material and so tend to heat up very quickly and so are typically run in short pulses. And we haven’t even mentioned the costs yet!

Physicists are a smart bunch, however, and they’re always on the lookout for new technologies, new techniques and unique ways of looking at the same problem. As you may have guessed already, the limiting factor determining the length required for sufficient linear acceleration is the field gradient. But what if there were a way to achieve hundreds of times that of a standard RF cavity? The answer has been found in plasma wakefields – separated bunches of dense protons with the potential to drive electrons up to gigaelectronvolt energies in a matter of meters!

Wakefields of plasma are by no means a new idea, being proposed first at least four decades ago. However, most examples have demonstrated this idea using electrons or lasers to ‘drive’ the wakefield in the plasma. More specifically, this is known as the ‘drive beam’ which does not actually participate in the acceleration but provides the large electric field gradient for what is known as the ‘witness beam’ – the electrons. However, this has not been demonstrated using protons as the drive beam to penetrate much further into the plasma – until now.

In fact, very recently CERN has demonstrated proton-driven wakefield technology for the first time during the 2016-2018 run of AWAKE (which stands for Advanced Proton Driven Plasma Wakefield Acceleration Experiment, naturally), accelerating electrons to 2 GeV in only 10 m. The protons that drive the electrons are injected from the Super Proton Synchrotron (SPS) into a Rubidium gas, ionizing the atoms and altering their uniform electron distribution into an osscilating wavelike state. The electrons that ‘witness’ the wakefield then ‘ride the wave’ much like a surfer at the forefront of a water wave. Right now, AWAKE is just a proof of concept, however plans to scale up to 10 GeV electrons in the coming years could hopefully pave the pathway to LHC level proton energies – shooting electrons up to TeV energies!

In this article, we focus instead on the interesting physics applications of such a device. Bunches of electrons with energies up to TeV energies is so far unprecedented. The most obvious application would of course be a high energy linear electron-positron collider. However, let’s focus on some of the more novel experimental applications that are being discussed today, particularly those that could benefit from such a strong electromagnetic presence in almost a ‘tabletop physics’ configuration.

Awake in the dark

One of the most popular considerations when it comes to dark matter is the existence of dark photons, mediating interactions between dark and visible sector physics (see “The lighter side of Dark Matter” for more details). Finding them has been the subject of recent experimental and theoretical approaches, even with high-energy electron fixed-target experiments already. Figure 2 shows such an interaction, where $A^\prime$ represents the dark photon. One experiment based at CERN known as the NA64 already searches for dark photons through incident electrons on a target, utilizing interactions of the SPS proton beam. In the standard picture, the dark photon is searched through the missing energy signature, leaving the detector without interacting but escaping with a portion of the energy. The energy of the electrons is of course not the issue when the SPS is used, however the number of electrons is.

Assuming one could work with the AWAKE scheme, one could achieve numbers of electrons on target orders of magnitude larger – clearly enhancing the reach for masses and mixing of the dark photon. The idea would be to introduce a high number of energetic electron bunches to a tungsten target with a following 10 m long volume for the dark photon to decay (in accordance with Figure 2). Because of the opposite charges of the electron and positron, the final decay products can then be separated with magnetic fields and hence one can ultimately determine the dark photon invariant mass.

Figure 3 shows how much of an impact a larger number of on-target electrons would make for the discovery reach in the plane of kinetic mixing $\epsilon$ vs mass of the dark photon $m_{A^\prime}$ (again we refer the reader to “The lighter side of Dark Matter” for explanations of these parameters). With the existing NA64 setup, one can already see new areas of the parameter space being explored for 1010 – 1013 electrons. However a significant difference can be seen with the electron bunches provided by the AWAKE configuration, with an ambitious limit shown by the 1016 electrons at 1 TeV.

Light, but strong

Quantum Electrodynamics (or QED, for short), describing the interaction between fundamental electrons and photons, is perhaps the most precisely measured and well-studied theory out there, showing agreement with experiment in a huge range of situations. However, there are some extreme phenomena out in the universe where the strength of certain fields become so great that our current understanding starts to break down. For the electromagnetic field this can in fact be quantified as the Schwinger limit, above which it is expected that nonlinear field effects start to become significant. Typically at a strength around 1018 V/m, the nonlinear corrections to the equations of QED would predict the appearance of electron-positron pairs spontaneously created from such an enormous field.

One of the predictions is the multiphoton interaction with electrons in the initial state. In linear QED, the standard $2 \rightarrow 2$ scattering of $e^- + \gamma \rightarrow e^- + \gamma$ for example is only possible. In a strong field regime, however, the initial state can then open up to $n$ numbers of photons. Given a strong enough laser pulse, multiple laser photons can interact with electrons and investigate this incredible region of physics. We show this in Figure 4.

The good and bad news is that this had already been performed as far back as the 90s in the E144 experiment at SLAC, using 50 GeV electron bunches – however unable to reach the critical field value in the electrons frame of rest. AWAKE could certainly provide highly energetic electrons and allow for different kinematic experimental reach. Could this provide the first experimental measurement of the Schwinger critical field?

Of course, these are just a few considerations amongst a plethora of uses for the production of energetic electrons over such short distances. However as physicists desperately continue their search for new physics, it may be time to consider the use of new acceleration technologies on a larger scale as AWAKE has already shown its scalability. Wakefield acceleration may even establish itself with a fully-developed new physics search plan of its own.

## Quark nuggets of wisdom

Article title: “Dark Quark Nuggets”

Authors: Yang Baia, Andrew J. Long, and Sida Lu

Reference: arXiv:1810.04360

Information, gold and chicken. What do they all have in common? They can all come in the form of nuggets. Naturally one would then be compelled to ask: “what about fundamental particles? Could they come in nugget form? Could that hold the key to dark matter?” Lucky for you this has become the topic of some ongoing research.

A ‘nugget’ in this context refers to large macroscopic ‘clumps’ of matter formed in the early universe that could possibly survive up until the present day to serve as a dark matter candidate. Much like nuggets of the edible variety, one must be careful to combine just the right ingredients in just the right way. In fact, there are generally three requirements to forming such an exotic state of matter:

1. (At least) two different vacuum states separated by a potential ‘barrier’ where a phase transition occurs (known as a first-order phase transition).
2. A charge which is conserved globally which can accumulate in a small part of space.
3. An excess of matter over antimatter on the cosmological scale, or in other words, a large non-zero macroscopic number density of global charge.

Back in the 1980s, before much work was done in the field of lattice quantum chromodynamics (lQCD), Edward Witten put forward the idea that the Standard Model QCD sector could in fact accommodate such an exotic form of matter. Quite simply this would occur at the early phase of the universe when the quarks undergo color confinement to form hadrons. In particular Witten’s were realized as large macroscopic clumps of ‘quark matter’ with a very large concentration of baryon number, $N_B > 10^{30}$. However, with the advancement of lQCD techniques, the phase transition in which the quarks become confined looks more like a continuous ‘crossover’ (i.e. a second-order phase transition), making the idea in the Standard Model somewhat unfeasible.

Theorists, particularly those interested in dark matter, are not confined (for lack of a better term) to the strict details of the Standard Model and most often look to the formation of sometimes complicated ‘dark sectors’ invisible to us but readily able to provide the much needed dark matter candidate.

Dark QCD?

The problem of obtaining a first-order phase transition to form our quark nuggets need not be a problem if we consider a QCD-type theory that does not interact with the Standard Model particles. More specifically, we can consider a set of dark quarks, dark gluons with arbitrary characteristics like masses, couplings, numbers of flavors or numbers of colors (which of course are quite settled for the Standard Model QCD case). In fact, looking at the numbers of flavors and colors of dark QCD in Figure 1, we can see in the white unshaded region a number of models that can exist with a first-order phase transition, as required to form these dark quark nuggets.

As with normal quarks, the distinction between the two phases actually refers to a process known as chiral symmetry breaking. When the temperature of the universe cools to this particular scale, color confinement of quarks occurs around the same time, such that no single-color quark can be observed on its own – only in colorless bound states.

Forming a nugget

As we have briefly mentioned so far, the dark nuggets are formed as the universe undergoes a ‘dark’ phase transition from a phase where the dark color is unconfined to a phase where it is confined. At some critical temperature, due to the nature of first-order phase transitions, bubbles of the new confined phase (full of dark hadrons) begin to nucleate out of the dark quark-gluon plasma. The growth of these bubbles are driven by a difference in pressure, characteristic of the fact that the unconfined and confined phase vacuums states are of different energy. With this emerging bubble wall, the almost massless particles from the dark plasma scatter from the wall containing heavy dark (anti)baryons and hence a large amount of dark baryon number accumulates in this phase. Eventually, as these bubbles merge and coalesce, we would expect local regions of remaining dark quark-gluon plasma, unconfined and stable from collapse due to the Fermi degeneracy pressure (see reference below for more on this). An illustration is shown in Figure 2. Calculations with varying energy scales of confinement estimate their masses are anywhere between $10^{-7}$ to $10^{23}$ grams with radii from $10^{-15}$ to $10^8$ cm and so can truly be classed as macroscopic dark objects!

How do we know they could be there?

There are a number of ways to infer the existence of dark quark nuggets, but two of the main ones are: (i) as a dark matter candidate and (ii) through probes of the dark QCD model that provides them. Cosmologically, the latter can imply the existence of a dark form of radiation which ultimately can lead to effects on the Cosmic Microwave Background Radiation (CMB). In a similar vein, one recent avenue of study today is the production of a steady background of gravitational waves emerging from the existence of a first-order phase transition – one of the key requirements for dark quark nugget formation. More importantly, they can be probed through astrophysical means if they share some coupling (albeit small) with the Standard Model particles. The standard technique of direct detection with Earth-based experiments could be the way to go – but furthermore, there may be the possibility of cosmic ray production from collisions of multiple dark quark nuggets. Among these are a number of other observations over the massive range of nugget sizes and masses shown in Figure 3.

To conclude, note that in such a generic framework, a number of well-motivated theories may predict (or in fact have unavoidable) instances of quark nuggets that may serve as interesting dark matter candidates with a lot of fun phenomenology to play with. It is only up to the theorist’s imagination where to go from here!

## The lighter side of Dark Matter

Article title: “Absorption of light dark matter in semiconductors”

Authors: Yonit Hochberg, Tongyan Lin, and Kathryn M. Zurek

 Reference: arXiv:1608.01994

Direct detection strategies for dark matter (DM) have grown significantly from the dominant narrative of looking for scattering of these ghostly particles off of large and heavy nuclei. Such experiments involve searches for the Weakly-Interacting Massive Particles (WIMPs) in the many GeV (gigaelectronvolt) mass range. Such candidates for DM are predicted by many beyond Standard Model (SM) theories, one of the most popular involving a very special and unique extension called supersymmetry. Once dubbed the “WIMP Miracle”, these types of particles were found to possess just the right properties to be suitable as dark matter. However, as these experiments become more and more sensitive, the null results put a lot of stress on their feasibility.

Typical detectors like that of LUX, XENON, PandaX and ZEPLIN, detect flashes of light (scintillation) from the result of particle collisions in noble liquids like argon or xenon. Other cryogenic-type detectors, used in experiments like CDMS, cool semiconductor arrays down to very low temperatures to search for ionization and phonon (quantized lattice vibration) production in crystals. Already incredibly successful at deriving direct detection limits for heavy dark matter, new ideas are emerging to look into the lighter side.

Recently, DM below the GeV range have become the new target of a huge range of detection methods, utilizing new techniques and functional materials – semiconductors, superconductors and even superfluid helium. In such a situation, recoils from the much lighter electrons in fact become much more sensitive than those of such large and heavy nuclear targets.

There are several ways that one can consider light dark matter interacting with electrons. One popular consideration is to introduce a new gauge boson that has a very small ‘kinetic’ mixing with the ordinary photon of the Standard Model. If massive, these ‘dark photons’ could also be potentially dark matter candidates themselves and an interesting avenue for new physics. The specifics of their interaction with the electron are then determined by the mass of the dark photon and the strength of its mixing with the SM photon.

Typically the gap between the valence and conduction bands in semiconductors like silicon and germanium is around an electronvolt (eV). When the energy of the dark matter particle exceeds the band gap, electron excitations in the material can usually be detected through a complicated secondary cascade of electron-hole pair generation. Below the band gap however, there is not enough energy to excite the electron to the conduction band, and so detection proceeds through low-energy multi-phonon excitations, with the dominant being the emission of two back-to-back phonons.

In both these regimes, the absorption rate of dark matter in the material is directly related to the properties of the material, namely its optical properties. In particular, the absorption rate for ordinary SM photons is determined by the polarization tensor in the medium, and in turn the complex conductivity, $\hat{\sigma}(\omega)=\sigma_{1}+i \sigma_{2}$ , through what is known as the optical theorem. Ultimately this describes the response of the material to an electromagnetic field, which has been measured in several energy ranges. This ties together the astrophysical properties of how the dark matter moves through space and the fundamental description of DM-electron interactions at the particle level.

In a more technical sense, the rate of DM absorption, in events per unit time per unit target mass, is given by the following equation:

$R=\frac{1}{\rho} \frac{\rho_{D M}}{m_{A^{\prime}}} \kappa_{e f f}^{2} \sigma_{1}$

• $\rho$ – mass density of the target material
• $\rho_{DM}$ – local dark matter mass density (0.3 GeV/cm3) in the galactic halo
• $m_{A'}$ – mass of the dark photon particle
• $\kappa_{eff}$ – kinetic mixing parameter (in-medium)
• $\sigma_1$ – absorption rate of ordinary SM photons

Shown in Figure 1, the projected sensitivity at 90% confidence limit (C.L.) for a 1 kg-year exposure of semiconductor target to dark photon detection can be almost an order of magnitude greater than existing nuclear recoil experiments. Dependence is shown on the kinetic mixing parameter and the mass of the dark photon. Limits are also shown for existing semiconductor experiments, known as DAMIC and CDMSLite with 0.6 and 70 kg-day exposure, respectively.

Furthermore, in the millielectronvolt-kiloelectronvolt range, these could provide much stronger constraints than any of those that currently exist from sources in astrophysics, even at this exposure. These materials also provide a novel way of detecting DM in a single experiment, so long as improvements are made in phonon detection.

These possibilities, amongst a plethora of other detection materials and strategies, can open up a significant area of parameter space for finally closing in on the identity of the ever-elusive dark matter!