Determination of dark matter properties at high-energy colliders

If the cosmic dark matter consists of weakly-interacting massive particles, these particles should be produced in reactions at the next generation of high-energy accelerators. Measurements at these accelerators can then be used to determine the microscopic properties of the dark matter. From this, we can predict the cosmic density, the annihilation cross sections, and the cross sections relevant to direct detection. In this paper, we present studies in supersymmetry models with neutralino dark matter that give quantitative estimates of the accuracy that can be expected. We show that these are well matched to the requirements of anticipated astrophysical observations of dark matter. The capabilities of the proposed International Linear Collider (ILC) are expected to play a particularly important role in this study.

Figure 1

Contours in a parameter space of supersymmetry models for the discovery of the missing-energy plus jets signature of new physics by the ATLAS experiment at the LHC. The three sets of contours correspond to levels of integrated luminosity at the LHC (in ${\mathrm{fb}}^{-1}$), contours of constant squark mass, and contours of constant gluino mass. From 26.

Figure 2

Four scenarios for decay chains observed at LHC. Each exhibits jets, hard leptons, and missing energy. Distinguishing between these cases by detailed study of energy distributions may not be possible with LHC alone.

Figure 3

Threshold behavior of pair-production cross sections for spin $1/2$ (KK muon) and spin 0 (smuon) counterpart to the standard model muon. These distributions are easily distinguished by an $e^{+}{e}^{-}$ collider.

Figure 4

Projected significance contours $(1,2,3,4\sigma )$ in the plane of WIMP mass versus cross section for an observation of dark matter by the SuperCDMS experiment (25 kg target, 2 yr dataset) [45, 111], compared to the determination of these parameters from data from the LHC. The projections are done using the model LCC3, to be defined in Sec. 3b.

Figure 5

(a) Suggested profiles of the dark matter mass density near the galactic center [69, 68]. (b) Corresponding values of $⟨J⟩$ at the galactic center, as a function of the angular resolution indicated as a circle size in sr.

Figure 6

Four neutralino annihilation reactions that are important in different regions of the MSSM parameter space: (a) annihilation to leptons, (b) annihilation to $W^{+}{W}^{-}$, (c) coannihilation with $\tilde{\tau }$, (d) annihilation through the $A^0$ resonance.

Figure 7

Particle spectrum for point LCC1. The lightest neutralino is predominantly $b$-ino, the second lightest neutralino and light chargino are predominantly $W$-ino, while the heaviest two neutralinos and heavy chargino are predominantly Higgsino.

Figure 8

Relic density measurement for point LCC1. Histograms in this and all following figures give the probability distribution $dP/dx$ of the quantity on the $x$ axis, given the three different sets of accelerator constraints. Where the $x$ axis is plotted logarithmically, the probability plotted is actually $dP/d{log}_{10}x$. All histograms integrate to unity. Results for the LHC make use of the assumption that the underlying physics model is supersymmetry. This might not be clear from the LHC data alone.

Figure 9

Scatter plots for point LCC1. (a) Inferred mass parameters $m_1$ and $\mu$ are shown to be well correlated in LHC data, with an uncertain overall scale. This reflects the fact that mass differences are measured more precisely than absolute masses. (b) The overall scale has a strong correlation with relic density. (c) For ILC-500, the mass of the $A^0$ boson is still unknown. For low values, there is a mild resonant enhancement to the neutralino annihilation cross section, and a corresponding reduction in relic density.

Figure 10

Relic density for point $\mathrm{SPS}1{\mathrm{a}}^{\prime }$. See Fig. 8 for description of histograms. In this case, the ILC-1000 provides no improvement in the relic density measurement over ILC-500.

Figure 11

Relic density for point $\mathrm{SPS}1{\mathrm{a}}^{\prime }$ at LHC. A dominant uncertainty at this point is the mass of the stau. Results of taking the stau-neutralino mass difference to have an error of 5 GeV are illustrated in red. Alternatively, results of taking the position of the tau-tau edge to have an error of 5 GeV (purple) and 1 GeV (blue) are also illustrated.

Figure 12

Scatter plot for point $\mathrm{SPS}1{\mathrm{a}}^{\prime }$. Relic density is plotted against neutralino mass, for points where the position of the tau-tau edge is measured to 1 GeV.

Figure 13

Scatter plot for point $\mathrm{SPS}1{\mathrm{a}}^{\prime }$. The $A^0$ mass is plotted against relic density, illustrating the small allowed region where $A^0$ resonance significantly decreases the relic density.

Figure 14

Annihilation cross section at threshold for point LCC1. See Fig. 8 for description of histograms.

Figure 15

Gamma-ray line annihilation cross section at threshold for point LCC1. See Fig. 8 for description of histograms.

Figure 16

Halo density profiles for point LCC1: (a) galactic center, (b) dark matter clump in the galactic halo. Angle-averaged $J$ values as measured by combining a 5-year all-sky dataset from GLAST with accelerator measurements are shown. See Fig. 8 for description of histograms.

Figure 17

Spin-independent neutralino-proton direct detection cross section for point LCC1. See Fig. 8 for description of histograms.

Figure 18

Spin-dependent neutralino-neutron direct detection cross section for point LCC1. See Fig. 8 for description of histograms.

Figure 19

Scatter plot of the spin-independent direct detection cross section vs. $m(A)$ for point LCC1. The strong dependence of the direct detection cross section on the $A^0$ mass is clearly seen.

Figure 20

Effective local WIMP flux ${\Phi }_{\mathrm{local}}/{\Phi }_0$ at the Earth for point LCC1. The results assume the SuperCDMS measurement described in the text. See Fig. 8 for description of histograms.

Figure 21

Annihilation cross section at threshold for point LCC1. A direct detection constraint from 2 years of a 25 kg SuperCDMS is applied. Compared with Fig. 14, it is clear that the direct detection constraint significantly improves the measurement of the annihilation cross section in advance of ILC-1000. See Fig. 8 for description of histograms.

Figure 22

LCC1 heavy Higgs mass $m_A$, before and after a direct detection constraint is applied. The constraint allows a crude measurement of the $A^0$ mass in advance of the ILC-1000, which directly produces the $A^0$. See Fig. 8 for description of histograms.

Figure 23

Particle spectrum for point LCC2. All neutralinos and charginos are mixed. The most $b$-inolike neutralino is the lightest one, and the most $W$-inolike neutralino is the heaviest one. All scalars are above about 2 TeV.

Figure 24

Relic density for point LCC2. There are two overlapping very high peaks at ${\Omega }_{\chi }{h}^2<0.01$, with maxima at $dP/dx=122$ and 165, due to the $W$-ino and Higgsino solutions to the LHC constraints. See Fig. 8 for description of histograms.

Figure 25

Scatter plots for point LCC2. (a) $m_1$ vs $\mu$ distribution for LHC, illustrating multiple solutions. Left to right, these are $b$-ino (correct), $W$-ino, and Higgsino. (b) $m_A$ vs ${\Omega }_{\chi }{h}^2$, showing the influence of resonant annihilation.

Figure 26

Scatter plots of the LHC data for LCC2 illustrating the effects of $e^{+}{e}^{-}$ cross sections in defining the relic density. The $W$-ino and Higgsino islands in Fig. 25a are mapped to the lines on the left side of the figures at very low values of ${\Omega }_{\chi }{h}^2$. Thus they are removed by the $e^{+}{e}^{-}$ cross section constraints.

Figure 27

Annihilation cross section at threshold for point LCC2. The $W$-ino and Higgsino solutions giving very high cross section are clearly visible. See Fig. 8 for description of histograms.

Figure 28

Gamma-ray line annihilation cross section at threshold for point LCC2. The $W$-ino and Higgsino solutions are clear. See Fig. 8 for description of histograms.

Figure 29

Halo density profiles for point LCC2: (a) galactic center, (b) dark matter clump in the galactic halo. Angle-averaged $J$ values as measured by combining a 5-year all-sky dataset from GLAST with accelerator measurements are shown. The influence of the incorrect solutions is clearly seen as subsidiary peaks at low $J$ values. See Fig. 8 for description of histograms.

Figure 30

Spin-independent neutralino-proton direct detection cross section for point LCC2. The $W$-ino and Higgsino solutions have large cross sections, easily seen. See Fig. 8 for description of histograms.

Figure 31

Spin-dependent neutralino-neutron direct detection cross section for point LCC2. See Fig. 8 for description of histograms.

Figure 32

Effective local WIMP flux at the Earth for point LCC2. The results assume the SuperCDMS measurement described in the text. The second peak at low effective flux is due to the high cross section $W$-ino and Higgsino solutions. See Fig. 8 for description of histograms.

Figure 33

Scatter plot of annihilation cross section against relic density for point LCC2. Given ILC-1000 data, the two quantities are very well correlated.

Figure 34

Particle spectrum for point LCC3. The stau-neutralino mass splitting is 10.8 GeV. The lightest neutralino is predominantly $b$-ino, the second neutralino and light chargino are predominantly $W$-ino, and the heavy neutralinos and chargino are predominantly Higgsino.

Figure 35

Relic density measurement for point LCC3. The $W$-ino peak at very small relic density is clear. See Fig. 8 for description of histograms.

Figure 36

Scatter plot of $\mu$ vs $m_1$ for LHC data at point LCC3. The F structure indicates the fact that the lightest neutralino is either $b$-ino or $W$-ino, while the second could be anything.

Figure 37

Scatter plots of both $\tan \beta$ and ${\Gamma }_A$ vs relic density for point LCC3. There is a significant correlation, which can be resolved at ILC-1000. In fact, the correlation between $\tan \beta$ and ${\Gamma }_A$ is quite close.

Figure 38

Scatter plot of $m_{\tilde{\tau }}-m_{{\chi }_1^0}$ for point LCC3, ILC-1000 sample. A correlation exists, but it is not strong.

Figure 39

Annihilation cross section at threshold for point LCC3. The $W$-ino solution giving very high cross section is clearly visible. See Fig. 8 for description of histograms.

Figure 40

Gamma-ray line annihilation cross section at threshold for point LCC3. The $W$-ino solution for LHC data at large cross section is clearly seen. See Fig. 8 for description of histograms.

Figure 41

Halo density profiles for point LCC3: (a) galactic center, (b) dark matter clump in the galactic halo. Angle-averaged $J$ values as measured by combining a 5-year all-sky dataset from GLAST with accelerator measurements are shown. For LHC, the $W$-ino peak at low $J$ is clearly visible. See Fig. 8 for description of histograms.

Figure 42

Spin-independent neutralino-proton direct detection cross section for point LCC3. See Fig. 8 for description of histograms.

Figure 43

Spin-dependent neutralino-neutron direct detection cross section for point LCC3. See Fig. 8 for description of histograms.

Figure 44

Effective local WIMP flux at the Earth for point LCC3. The results assume the SuperCDMS measurement described in the text. See Fig. 8 for description of histograms.

Figure 45

Measurements of $\tan \beta$ for point LCC3. Various astrophysical constraint sets are included. The relic density constraint improves even the ILC-1000 measurement, while the ILC-500 measurement is greatly helped by including both direct detection and relic density.

Figure 46

Particle spectrum for point LCC4. The lightest neutralino is predominantly $b$-ino, the second neutralino and light chargino are predominantly $W$-ino, and the heavy neutralinos and chargino are predominantly Higgsino.

Figure 47

Relic density measurement for point LCC4. The $W$-ino peak at very small relic density is clear. See Fig. 8 for description of histograms.

Figure 48

Scatter plot of the distance from the $A^0$ resonance vs relic density for point LCC4. The quantity plotted is actually the distance in widths, with true value 5.5.

Figure 49

Annihilation cross section at threshold for point LCC4. The $W$-ino solution giving very high cross section is clearly visible. See Fig. 8 for description of histograms.

Figure 50

Gamma-ray line annihilation cross section at threshold for point LCC4. Again, the $W$-ino solution at large cross section is clear. See Fig. 8 for description of histograms.

Figure 51

Halo density profiles for point LCC4: (a) galactic center, (b) dark matter clump in the galactic halo. Angle-averaged $J$ values as measured by combining a 5-year all-sky dataset from GLAST with accelerator measurements are shown. See Fig. 8 for description of histograms.

Figure 52

Spin-independent neutralino-proton direct detection cross section for point LCC4. See Fig. 8 for description of histograms.

Figure 53

Spin-dependent neutralino-neutron direct detection cross section for point LCC4. See Fig. 8 for description of histograms.

Figure 54

Effective local WIMP flux at the Earth for point LCC4. The results assume the SuperCDMS measurement described in the text. See Fig. 8 for description of histograms.

Figure 55

Annihilation cross section at threshold for point LCC4, including various astrophysical constraints. Direct detection reduces the weight of the $W$-ino solution, and relic density completely eliminates this possibility.

Figure 56

Spectra of gamma rays and positrons from neutralino annihilation at threshold for points LCC1-4. Solid curves are gammas, dashed curves are positrons, and dotted curves show the gamma spectrum of LCC4, scaled to each endpoint and total cross section. The scaled LCC4 spectrum is a good match in every case. The positron spectrum for LCC2 exhibits a shelf due to direct decays of gauge bosons, e.g. $\chi \chi \to W^{+}{W}^{-}\to e^{+}\nu \overline{u}d$.

Figure 57

Spectrum of positrons for all models after galactic propagation effects are accounted for. The “interstellar” spectrum is illustrated. Solar modulation is neglected. Above a few GeV solar modulation effects are negligible.

Figure 58

Positrons observed on earth, as a fraction of electrons, for LCC2. The HEAT data are plotted as well, indicating the possibility of an excess. The positron signal from a smooth halo has been boosted by a factor of 185 in order to fit the data.

Figure 59

Section of the Markov chain for $\tan \beta$ at LCC2-LHC. The repeated brief excursions to large values are clearly seen.

Figure 60

Fourier transform of the Markov chain for $\tan \beta$ at LCC2-LHC. A constant rolling into a power-law fit [97] is shown. This illustrates the white noise (flat) spectrum for low $k$ indicating decorrelation at large distances in the chain and the random walk ($k^{-2}$) spectrum at short distances (large $k$).

Figure 61

Illustration of MCMC bridging the gap between islands in parameter space. These are solutions for LCC2 with LHC data, as in Fig. 25. The true solution has the largest $b$-ino fraction $Z_{b1}$.

Figure 62

Illustration of MCMC exploring very different regions of parameter space. These regions are actually connected, as shown in Fig. 36, but allow vastly different properties for ${\chi }_2^0$, as shown here.