Can SKA--Phase 1 go much beyond the LHC in supersymmetry search?

We study the potential of the Square Kilometre Array in the first phase (SKA1) in detecting dark matter annihilation signals from dwarf spheroidals in the form of diffuse radio synchrotron. Taking the minimal supersymmetric standard model as illustration, we show that it is possible to detect such signals for dark matter masses about an order of magnitude beyond the reach of the Large Hadron Collider, with about 100 hours of observation with the SKA1.

Introduction: The upcoming low-frequency radio telescope, Square Kilometre Array Phase 1 (SKA1), can well surpass the Large Hadron Collider (LHC) reach in unveiling new physics responsible for dark matter (DM). This is shown for the minimal supersymmetric standard model (MSSM) where the lightest neutralino (χ 0 1 ) is the DM candidate. While the LHC is unlikely to see signatures of supersymmetry (SUSY) for (m χ 0 1 > ∼ )1 TeV, especially for coloured superparticle masses above 3 TeV [1,2], DM annihilation in dwarf spheroidal galaxies (dSph) can lead to radio synchrotron emission which clearly rises above the SKA1 detection threshold with 10-100 hours of observation, for m χ 0 1 up to at least 10 TeV. We scan the MSSM parameter space and predict the synchrotron radiation spectra for three such galaxies. for DM annihilation corresponding to the aforesaid SUSY breaking scales. Even with conservative parameter values, the SKA1 should see signals, for DM masses one order higher than the reach of the LHC with Ldt = 3000fb −1 [1,2].
The SKA1 is expected to address many important questions in astrophysics and cosmology [3]. It has relevance in the physics of elementary particles, too. Foremost in this context is the issue of DM, provided it is constituted of elementary particle(s). While there is no unique candidate theory yet, the MSSM shows a logically satisfactory way to obtain a stable neutral particle, especially the lightest neutralino (χ 0 1 ), which satisfies the requirements of DM. The LHC, however, has not found any signals of it so far, up to coloured new particle masses > ∼ 2 TeV [4]. On the other hand, spectra in the multi-TeV range can be phenomenologically allowed and satisfy all requirements of DM, if one defers judgements on the somewhat fuzzy issue of naturalness. While the LHC cannot see such heavy superparticles, and the fate of any future collider is uncertain, we show below that the SKA1 in its first phase itself can detect diffuse radio synchrotron signals of DM annihilation for such high m χ 0 1 . In dSphs and galactic clusters, DM-pairs annihilate into standard model (SM) particles such as bb, tt, W + W − , τ + τ − ..... The subsequent cascades produce copious e + e − pairs whose energy distribution is de-termined by the source function where m χ is the DM mass (m χ 0 1 in MSSM), σv and ρ χ are the DM annihilation rate in any aforementioned channel with fraction B f and DM density inside the galaxy respectively. Here we have used the NFW profile for Draco [5,6] and Ursa Major II [7], and the Einasto profile for Segue 1 [8], with the parameters of the profile chosen such that they are consistent with the kinematical observations of these galaxies. dN e f (E)/dE is the energy distribution of the e ± per annihilation.
Prediction of the synchrotron signal produced by these e + e − pairs requires tracking their propagation through galactic media. Accounting for the energy loss via various electromagnetic processes as well as diffusion, the steady state distribution dn/dE(E, r) of the e ± as a function of energy E and distance r from the centre of the galaxy can be obtained by solving the equation [6,9] where b(E) denotes the energy loss due to various radiative processes like the inverse Compton scattering, synchrotron radiation, Coulomb losses and bremsstrahlung. D(E) is the diffusion parameter which is assumed to have the Kolmogorov form D = D 0 E γ [5][6][7][8], D 0 being the diffusion coefficient. One finally obtains the frequency spectrum of observed photons by folding dn/dE with the synchrotron power spectrum, for which a simplified expression is available for frequencies above the gyro-frequency and plasma frequency [6,9,10]. Nearby ultra-faint dSphs are appropriate for studying such diffuse radio signals, as opposed to usual galaxies and clusters, as their low star formation rate minimises the uncertain contribution of astrophysical processes. Their relative proximity (most of them are satellites of the Milky Way) and high DM content, as inferred from the observed mass-to-light ratios within their halfradii, are of further advantage. Some of these dSphs have arXiv:1808.05793v1 [hep-ph] 17 Aug 2018 been observed using existing radio telescopes with the aim of recording such diffuse emission, although no signal has materialsed so far [7,8,11,12]. The ultra-faint nature of these galaxies necessitates a more sensitive telescope like SKA1 for detecting the radio synchrotron signal [13]. Here we predict the diffuse signal considering the parameters for Draco dSph (mainly because the various relevant parameters like the J-factor are better constrained for this object [14]), though even higher flux is expected out of the nearer dSphs such a Segue 1 and Ursa Major II, as shown later in this note.
For a χ 0 1 DM in MSSM, the observed radio flux (obtained via the velocity averaged quantity σv (calculated using micrOMEGAs 4.3.1 [15])) depends on not only m χ 0 1 but also the particle spectrum and other MSSM parameters that determine the annihilation rates and branching ratios, and also the energy of e ± transported across the dSph. Some recent works [6,13,16] have treated m χ and σv as two free parameters, and studied the consequences of different 'dominant' annihilation channels. We instead select various MSSM benchmark regions, especially those with heavy superparticles undetectable at the LHC [1,2], and use the full dynamics of the model in terms of the emergent annihilation channels. These benchmarks are listed in Tables I and II. There are four broad classes. (A) has all squarks/gluinos and sleptons well above LHC detection limits, but with a hierarchy between squarks and sleptons. (B) includes somewhat lighter but still undetectable superparticles, but with no hierarchy between coloured and colourless ones. (C) and (D) have similar spectra as in (A) and (B) but with lighter top squarks in each case. (E) and (F) correspond to ultra-high χ 0 1 masses close to 10 TeV. These regions identify DM candidates beyond the commonly conceived domain of naturalness. Further categories within each class reflect different combinations of other MSSM parameters which drive annihilation in different channels. In addition, spectra with χ 0 1 beyond the LHC detection limit have been juxtaposed with relatively light ones for comparison. All benchmarks satisfy the constraints coming from collider [4,17] and direct DM searches [18], relic density [19], lightest neutral Higgs mass [20] (calculated at the two-loop level), flavour physics [21], (g − 2) µ [22] etc. Figure 1 shows the minimum σv required in various channels for detection with 100 hours (bandwidth = 300 MHz) at the SKA1, for the dSph Draco. The corresponding annihilation channel has to dominate in each case, for the lower limit to hold. We also indicate the model-independent upper limits on annihilation rates in these channels as functions of the DM particle mass, obtained from cosmic ray antiproton data [23]. The regions bounded by the upper and lower limits represent the area where DM annihilation in this galaxy can certainly be detected within 100 hours. For Draco, with the NFW profile and a galactic magnetic field (B) of   Table II) where m τ1 has been fixed at = 1.03 m χ 0 1 to emphasize the τ + τ − annihilation channel.  1.0 µG, D 0 = 3 × 10 28 cm 2 s −1 and γ = 0.3 [5], all of our benchmark points whose samples are shown as black spots (mostly beyond the LHC reach [1,2]) fall in the detectable range. Remarkably, this pushes the radio search limit up to m χ 0 1 ∼ 8.5 TeV. The reach goes up to even 10 TeV if there is substantial annihilation in the bb channel.
The frequency spectra of the predicted radio signals are shown in Figure 2. The expected SKA1 sensitivities in the frequency range 350 MHz -50 GHz [25] are also shown for observations over 10, 100 and 1000 hours. 1 Although the curves are drawn using the NFW profile   Table I, and the corresponding DM masses and annihilation channels.
for Draco, we have checked that the predictions remain very similar for other profiles such as Burkert and D05 [5]. Also, we have assumed no halo substructures which can in principle enhance the flux even further [10]. As per current understanding, significant radio signals from from astrophysical processes are unlikely, as dSphs are mostly devoid of gas and have almost no intrinsic sources of high energy e ± . The other possible sources of contamination are the astrophysical foregrounds, however, they too are expected to be sub-dominant for the SKA1 as the large baselines will help in resolving out these objects. On the whole, detection is almost certain for each case within 100 hours; there are several benchmark points where even 10 hours should suffice. Note that the flux depends on m χ 0 1 , σv and B f . Thus MSSM dynamics crucially decides detectability. Overall, the SKA1 clearly goes beyond the LHC in SUSY-DM search [1,2]. As Figure 1 shows, a neutralino DM with mass on the order of 10 TeV (or perhaps more) may be rendered visible in the process.
While the above results are presented for B = 1.0 µG (typical of a dSph like Draco where the magnetic field has visions in the sensitivity estimates. This should not affect our main conclusion, since the predicted signals are well above the sensitivity limits. been measured [26]), the predictions with other values, namely, B = 10.0 and 0.1 µG, are presented in Figure  3 (left). We thus see that even for the pessimistic value of 0.1 µG, the signals are detectable up to 10 3.4 (10 3.8 ) MHz for 100 (1000) hours of observation. Figure 3 (right) shows the effect of different D 0 . We once more include the 'unfavourable' value of D 0 = 3×10 29 cm 2 s −1 , γ = 0.3, for which detectability should be rather high in the range 10 2−4 MHz, for a neutralino mass ∼ 4 TeV, with the coloured particle masses at 10 TeV.
We finally show in Figure 4 some predictions for galaxies nearer than Draco, namely, Ursa Major II and Segue 1, with B = 1.0 µG, D 0 = 3 × 10 26 cm 2 s −1 , and appropriate values of γ [5][6][7][8]. Benchmark A1a is used for illustration. While detectability is much above threshold here, a comparison with Draco tells us that Segue 1 and Ursa Major II hold high hopes for DM annihilation detection, even with larger m χ 0 1 . Even if SKA1 succeeds in setting upper limits on the flux for for most of our benchmark points, it will be possible to probe and constrain regions of hitherto unexplored regions in the MSSM parameter space well. Observations of the signal in different wavebands, say, radio and γ-ray frequencies, from any dSph may enable also us to break the degeneracies between the MSSM parameters and B, D 0 .
We thus conclude that the SKA1, mostly with 100 hours of observation, should be able to detect radio  Table I and II) in the Draco dSph galaxy (D 0 = 3 × 10 28 cm 2 s −1 , B = 1 µG). The SKA1 sensitivity curves for 10, 100 and 1000 hrs are also shown for bandwidth = 300 MHz. of the LHC. Even neutralinoes below a TeV, which the LHC cannot probe due to overwhelming backgrounds, are covered by such observation. This holds even for conservative values of astrophysical parameters, and thus underscores a new potential of the SKA.