Velocity independent constraints on spin-dependent DM-nucleon interactions from IceCube and PICO

Adopting the Standard Halo Model (SHM) of an isotropic Maxwellian velocity distribution for dark matter (DM) particles in the Galaxy, the most stringent current constraints on their spin-dependent scattering cross-section with nucleons come from the IceCube neutrino observatory and the PICO-60 C 3 F 8 superheated bubble chamber experiments. The former is sensitive to high energy neutrinos from the self-annihilation of DM particles captured in the Sun, while the latter looks for nuclear recoil events from DM scattering oﬀ nucleons. Although slower DM particles are more likely to be captured by the Sun, the faster ones are more likely to be detected by PICO. Recent N-body simulations suggest signiﬁcant deviations from the SHM for the smooth halo component of the DM, while observations hint at a dominant fraction of the local DM being in substructures. We use the method of Ferrer et al. (2015) to exploit the complementarity between the two approaches and derive conservative constraints on DM-nucleon scattering. Our results constrain σ SD (cid:46) 3 × 10 − 39 cm 2 (6 × 10 − 38 cm 2 ) at (cid:38) 90% C.L. for a DM particle of mass 1 TeV annihilating into τ + τ − ( b ¯ b ) with a local density of ρ DM = 0 . 3 GeV / cm 3 . The constraints scale inversely with ρ DM and are independent of the DM velocity distribution.


INTRODUCTION
Based on inferences from observations of gravitational effects, it has long been believed that a significant fraction of the Universe is made up of dark matter (DM) (see van den Bergh et al. (1999)). However, very little is known about its properties and interactions. A weakly interacting massive particle (WIMP), whose relic abundance from a state of thermal equilibrium can make up DM has been the subject of considerable theoretical at- * Email: analysis@icecube.wisc.edu † now at Brookhaven National Laboratory ‡ now at Canadian Nuclear Laboratories § now at Argonne National Laboratory ¶ Email: analysis@picoexperiment.com * * also at National Research Nuclear University, Moscow Engineering Physics Institute (MEPhI), Moscow 115409, Russia tention and experimental focus (see Bertone et al. (2004) for a comprehensive review). Various complementary approaches have been pursued to detect the WIMPs that may constitute the DM halo of our Galaxy. Terrestrial direct detection (DD) experiments search for nuclear recoil events from the elastic scattering of WIMPs with the target nuclei of their detectors. Neutrino and gamma ray telescopes search for directional excesses over astrophysical backgrounds that may indicate the pair-annihilation of WIMPs, while collider searches look for the signatures of WIMPs being created in high-energy interactions of Standard Model particles.
Although the different search strategies have attained the sensitivity to probe the physically-motivated WIMP parameter space over the past few decades, they have failed to detect any signal. In the absence of a convincing detection, constraints have been derived on the interaction cross-sections of these hypothetical particles with Standard Model particles. Such an inference requires knowledge both of the density of DM ρ DM and of its velocity distribution function (VDF) f ( v).
In the Standard Halo Model (SHM) (Drukier et al. 1986), the DM of the halo is a collisionless gas in hydrostatic equilibrium with the stars, retaining the velocity distribution obtained during the formation of our Galaxy. An isotropic Maxwell-Boltzman velocity distribution in the Galactic rest frame is usually adopted.
Meanwhile, N-body simulations have hinted that a Maxwell-Boltzmann distribution does not accurately represent even the smooth component of the halo (Kuhlen et al. 2009;Lisanti et al. 2010;Mao et al. 2012). Recent observations point to the possibility that a dominant fraction of the DM in the Solar neighbourhood (Necib et al. 2018) may not yet have achieved dynamical equilibrium, perhaps due to the infalling tidal debris of a disrupted massive satellite galaxy of the Milky Way. New data also suggest that a substantial fraction of our stellar halo may lie in a strongly radially anisotropic population, the 'Gaia sausage' (Evans et al. 2019).
If so, constraints on WIMP-nucleon interactions derived assuming the SHM (from both direct and indirect searches) may be weakened. Direct detection experiments are preferentially sensitive to nuclear recoils from high velocity DM particles, while capture in the Sun is more likely for the slower fraction of the DM population. In this work we use the method of Ferrer et al. (2015), which is independent of the velocity distribution of the halo model to exploit this complementarity and derive conservative, upper limits on the spin-dependent DM-nucleon scattering cross-section by combining the results from  and Amole et al. (2017). Here the DM velocity distribution is taken to be a completely general superposition of individual 'streams' (delta functions in velocity), similarly to the halo-independent analysis of direct detection experiments (Frandsen et al. 2012). Although constraints from individual searches will now be dependent on the stream velocity, by exploiting the complementarity of the IceCube and PICO searches, constraints independent of the stream velocity can be obtained. This method also improves on previous assessments of halo model uncertainties on indirect DM detection (Choi et al. 2014), by allowing the velocity distribution to be anisotropic. The resulting constraints are a factor of 2 to 4 worse than the PICO SHM constraints at low DM masses and up to an order of magnitude worse at high DM masses, depending upon the annihilation channel, but are independent of the halo model.

IceCube 3 year Solar WIMP search
IceCube is a cubic-kilometer neutrino detector installed in the ice at the geographic South Pole between depths of 1450 and 2450 m. It relies on photomultiplier tubes housed in pressure vessels known as digital optical modules (DOM) for the optical detection of Cherenkov photons emitted by charged particles traversing the ice. The principal IceCube array is sensitive to neutrinos down to ∼100 GeV in energy (Achterberg et al., 2006;Abbasi et al., 2009;. The central region of the detector is an infill array known as DeepCore optimized in geometry and DOM density for the detection of neutrinos at lower energies, down to ∼10 GeV (Abbasi et al., 2012).
Over a detector uptime of 532 days corresponding to the austral winters between May 2011 and May 2014, two non-overlapping samples of upgoing track-like events, dominated by muons from charged current interactions of atmospheric ν µ andν µ , were isolated (Aartsen et al. 2017). During austral summers, the Sun being above the horizon, is a source of downgoing neutrinos and the signal is overwhelmed by a background of muons originating in cosmic ray interactions in the upper atmosphere.
The first sample, consisting of events that traverse the principal IceCube array, is sensitive to neutrinos in the 100 GeV -1 TeV range in energy, while the second sample is dominated by events starting in and around the DeepCore infill array, and is sensitive down to neutrinos of ∼10 GeV in energy.
An unbinned maximum likelihood ratio analysis of the directions and energies of the events that make up the two samples was unable to identify a statistically significant excess of neutrinos from the direction of the Sun. This enabled 90% C.L. upper limits on the DM annihilation induced neutrino flux to be computed according to the prescription of Feldman & Cousins (1998) as presented in .
This can be interpreted as both a constraint on the annihilation rate of DM particles in the Sun, as well as on the scattering cross-section of DM with nucleons, although this has been usually done under the SHM assumption. In particle physics models where the DM couples to the spin of the nucleus and annihilates preferentially into SM particles that decay to produce a large number of high energy neutrinos (such as τ + τ − ), the resultant constraints are the most stringent for DM mass above ∼ 80 GeV (Particle Data Group 2018).

PICO
The PICO collaboration searches for WIMPs using superheated bubble chambers operated at temperature and pressure conditions which lead to being virtually insensitive to gamma and beta radiation (Amole et al. 2019). Events in PICO consist of the transition from liquid to gas phase, signalled by the nucleation of a bubble in the target material. This phase change is imaged by the cameras surrounding the active area, which trigger upon detecting the formation of a pocket of gas. Additional background suppression is achieved through the measurement of the acoustic signal generated by the event, allowing alpha particles to be discriminated from nuclear recoils. Details of the apparatus are available in Amole et al. (2015). The data used in this study were obtained from the PICO-60 detector, consisting of a 52.2±0.5 kg C 3 F 8 target, operated roughly two kilometres underground at SNOLAB in Sudbury, Ontario, Canada. The results used here come from an efficiency-corrected exposure of 1167 kg-days taken between November 2016 and January 2017 (Amole et al. 2017).
The response of the detector to WIMPs is dependent on the thermodynamic conditions, and is calibrated using in situ nuclear and electronic recoil sources. Additionally, the Tandem Van de Graaff facility at the University of Montreal was used to determine the detector response, using well-defined resonances of the 51 V(p,n) 51 Cr reaction to produce mono energetic neutrons at 61 and 97 keV. The combination of these measurements is simulated using differential cross-sections for elastic scattering on fluorine to produce the detector response.

DM VELOCITY DISTRIBUTIONS AND IMPACT ON CONSTRAINTS: THE METHOD
Following the method of Ferrer et al. (2015), the velocity distribution of the DM (WIMP) population in the Solar system, f ( v) can be expressed as the superposition of streams with fixed velocity v 0 with respect to the Solar frame.
where v max is the maximum velocity at which WIMPs can be found, typically the escape velocity of the Galaxy. For every stream with velocity v 0 with respect to the Sun, upper limits can be derived from the null results of IceCube by requiring that the capture rate for the stream C v0 be less than or equal to C max , the upper limit on the capture rate from the results of the experiment. For a direct detection experiment, which sees the same stream with velocity v 0 − v E (t) with respect to the Earth, similar constraints can be derived for each stream velocity by requiring that the event rate for the stream R v0 be less than or equal to R max , the upper limit on the event rate from the results of the experiment. C v0 and R v0 are computed by evaluating the integrals of equations 2 and 3 of Ferrer et al. (2015). Since the PICO exposure period was too short for the Earth's velocity v E (t) to average out to zero, velocities are conservatively shifted by 30.29 km s −1 (the velocity of the Earth around the Sun at perihelion (Tollerud et al. 2017)) when computing R v0 . For the capture rates in the Sun, the integrals were evaluated using the density profile and nuclear abundances in the Sun for protons and nitrogen nuclei (the second most abundant species with nuclear spin) in the standard Solar model (Bahcall et al. 1988) as implemented in sunpy (SunPy Comm 2015). Nuclear form factors as implemented in dmdd (Gluscevic et al. 2015) for spin-dependent scattering, corresponding to the Σ 1M (Axial transverse electric response) and Σ 1M (Axial longitudinal response), table 1 of Fitzpatrick et al. (2013) were employed for the event rate calculations in PICO. Figure 1 demonstrates the evolution of the constraints on the spin-dependent DM-proton scattering crosssection from both IceCube and PICO as |v 0 | is varied. The individual constraints on the cross section are computed from the constraints on the capture rate in the Sun already derived in  as well as the constraint on the event rate within PICO presented in Amole et al. (2017). For a WIMP of mass M scattering off a nucleus of mass m, the maximum stream velocity at which capture is allowed is given by (Ferrer et al. 2015): where v esc is the escape velocity. Consequently, above certain threshold values of the stream velocity, capture by scattering off protons is kinematically impossible and only nitrogen nuclei contribute to the capture rate. Subsequently, the largest value of the scattering crosssection allowed by both IceCube and PICO, σ HI , can be determined at the velocity of least constraint, v LC , . This procedure is illustrated in Figure 1 for two specific models, 40 GeV and 700 GeV WIMPs annihilating to bb.

RESULTS AND CONCLUSIONS
The resultant DM velocity independent constraints are illustrated in Figure 2 and presented in Table 1. For the "hard" channels ( W + W − and τ + τ − ), which produce a relatively large number of neutrinos at energies just below the DM mass, the DM-velocity-independent constraints are in general worse only by a factor of 2 to 4 compared to the PICO SHM constraints. However, at a DM Mass of ∼250 GeV (∼700 GeV for bb), the constraints are significantly worse because the DM particle velocities just below the PICO threshold are still too high to be captured by scattering off protons in the Sun (see Figure 1). At immediately higher masses, the constraints improve because the IceCube sensitivity improves with the DM mass in this range. The constraints are in agreement with the findings by Ibarra et al. (2017). The IceCube constraints were recomputed with Monte-Carlo data sets under varying assumptions of all systematic uncertainties as described in . The dominant uncertainties were found to originate in the photodetection efficiency of the photomultiplier tubes that make up the DOMs, as well as the optical properties of the ice. Since these constraints correspond to the same annihilation rates of DM particles in the Sun reported in , captureannihilation equilibrium continues to be a valid assumption. The dominant uncertainties in the detector acceptance of PICO originate in the uncertainties of the neutron beam used in the calibration process. These are propagated to the final level and shown as shaded regions. Conservatively, the pessimistic efficiencies of PICO have been used to derive the constraints. While these constraints are robust with respect to any uncertainties in the velocity distribution of DM particles, they are still susceptible to uncertainties and/or fluctuations in the local density of DM, and are presented for the benchmark local density of ρ DM = 0.3 GeV cm −3 , and scale inversely with this quantity.