A simple matter

Article title: Evidence of A Simple Dark Sector from XENON1T Anomaly

Authors: Cheng-Wei Chiang, Bo-Qiang Lu

Reference: arXiv:2007.06401

As with many anomalies in the high-energy universe, particle physicists are rushed off their feet to come up with new, and often somewhat often complicated models to explain them. With the recent detection of an excess in electron recoil events in the 1-7 keV region from the XENON1T experiment (see Oz’s post in case you missed it), one can ask whether even the simplest of models can even still fit the bill. Although still at 3.5 sigma evidence – not quite yet in the ‘discovery’ realm – there is still great opportunity to test the predictability and robustness of our most rudimentary dark matter ideas.

The paper in question considers would could be one of the simplest dark sectors with the introduction of only two more fundamental particles – a dark photon and a dark fermion. The dark fermion plays the role of the dark matter (or part of it) which communicates with our familiar Standard Model particles, namely the electron, through the dark photon. In the language of particle physics, the dark sector particles actually carries a kind of ‘dark charge’, much like the electron carries what we know as the electric charge. The (almost massless) dark photon is special in the sense that it can interact with both the visible and dark sector – and as opposed to visible photons, and have a very long mean free path able to reach the detector on Earth. An important parameter describing how much the ordinary and dark photon ‘mix’ together is usually described by $\varepsilon$ . But how does this fit into the context of the XENON 1T excess?

Fig 1: Annihilation of dark fermions into dark photon pairs

The idea is that the dark fermions annihilate into pairs of dark photons (seen in Fig. 1) which excite electrons when they hit the detector material, much like a dark version of the photoelectric effect – only much more difficult to observe. The processes above remain exclusive, without annihilating straight to Standard Model particles, as long as the dark matter mass remains less than the lightest charged particle, the electron. With the electron at a few hundred keV, we should be fine in the range of the XENON excess.

What we are ultimately interested in is the rate at which the dark matter interacts with the detector, which in high-energy physics are highly calculable:

$\frac{d R}{d \Delta E}= 1.737 \times 10^{40}\left(f_{\chi} \alpha^{\prime}\right)^{2} \epsilon(E)\left(\frac{\mathrm{keV}}{m_{\chi}}\right)^{4}\left(\frac{\sigma_{\gamma}\left(m_{\chi}\right)}{\mathrm{barns}}\right) \frac{1}{\sqrt{2 \pi} \sigma} e^{-\frac{\left(E-m_{\chi}\right)^{2}}{2 \sigma^{2}}}$

where $f_{\chi}$ is the fraction of dark matter represented by $\chi$ , $\alpha'=\varepsilon e^2_{X} / (4\pi)$ , $\epsilon(E)$ is the efficiency factor for the XENON 1T experiment and $\sigma_{\gamma}$ is the photoelectric cross section.

Figure 2 shows the favoured regions for the dark fermion explanation fot the XENON excess. The dashed green lines represent only a 1% fraction of dark fermion matter for the universe, whilst the solid lines are to explain the entire dark matter content. Upper limits from the XENON 1T data is shown in blue, with a bunch of other astrophysical contraints (namely red giants, red dwarfs and horizontal branch star) far above the preffered regions.

Fig 2: The green bands represent the 1 and 2 sigma parameter regions in the $\alpha' - m_{\chi}$ plane favoured by the dark fermion model in explaning the XENON excess. The solid lines cover the entire DM component, whilst the dashed lines are only a 1% fraction.

Fig 2: The green bands represent the 1 and 2 sigma parameter regions in the $\alpha' - m_{\chi}$ plane favoured by the dark fermion model in explaning the XENON excess. The solid lines cover the entire DM component, whilst the dashed lines are only a 1% fraction.

This plot actually raises another important question: How sensitive are these results to the fraction of dark matter represented by this model? For that we need to specify how the dark matter is actually created in the first place – with the two most probably well-known mechanisms the ‘freeze-out’ and the ‘freeze-in’ (follow the links to previous posts!)

Fig 3: Freeze-out and freeze-in mechanisms for producing the dark matter relic density. The measured density (from PLANCK) is $\Omega h^2 = 0.12$ , shown on the red solid curve. The best fit values are also shown by the dashed lines, with their 1 sigma band. The mass of the dark fermion is fixed to its best-fit value of 3.17 keV, from Figure 2.

Fig 3: Freeze-out and freeze-in mechanisms for producing the dark matter relic density. The measured density (from PLANCK) is $\Omega h^2 = 0.12$ , shown on the red solid curve. The best fit values are also shown by the dashed lines, with their 1 sigma band. The mass of the dark fermion is fixed to its best-fit value of 3.17 keV, from Figure 2.

The first important point to note from the above figures is that the freeze-out mechanism doesn’t even depend on the mixing between the visible and dark sector i.e. the vertical axes. However, recall that the relic density in freeze-out is determined by the rate of annihlation into SM fermions – which is of course forbidden here for the mass of fermionic DM. The freeze-in works a little differently since there are two processes that can contribute to populating the relic density of DM: SM charged fermion annihlations and dark photon annihilations. It turns out that the charged fermion channel dominates for larger values of $e_X$ and in of course then becomes insensitive to the mixing parameter $\varepsilon$ and hence dark photon annihilations.

Of course it has been emphasized in previous posts that the only way to really get a good test of these models is with more data. But the advantage of simple models like these are that they are readily available in the physicist’s arsenal when anomalies like these pop up (and they do!)

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