Scrutinizing the evidence for dark matter in cosmic-ray antiprotons

Global fits of primary and secondary cosmic-ray (CR) fluxes measured by AMS-02 have great potential to study CR propagation models and search for exotic sources of antimatter such as annihilating dark matter (DM). Previous studies of AMS-02 antiprotons revealed a possible hint for a DM signal which, however, could be affected by systematic uncertainties. To test the robustness of such a DM signal, in this work we systematically study two important sources of uncertainties: the antiproton production cross sections needed to calculate the source spectra of secondary antiprotons and the potential correlations in the experimental data, so far not provided by the AMS-02 Collaboration. To investigate the impact of cross-section uncertainties we perform global fits of CR spectra including a covariance matrix determined from nuclear cross-section measurements. As an alternative approach, we perform a joint fit to both the CR and cross-section data. The two methods agree and show that cross-section uncertainties have a small effect on the CR fits and on the significance of a potential DM signal, which we find to be at the level of $3\sigma$. Correlations in the data can have a much larger impact. To illustrate this effect, we determine possible benchmark models for the correlations in a data-driven method. The inclusion of correlations strongly improves the constraints on the propagation model and, furthermore, enhances the significance of the DM signal up to above $5\sigma$. Our analysis demonstrates the importance of providing the covariance of the experimental data, which is needed to fully exploit their potential.

Figure 1

Comparison of our best-fit proton and helium fluxes as a function of rigidity with AMS-02 and Voyager data. Both plots show the default setup without DM. In addition, we show the best fit before solar modulation (${\phi }_{\odot }=0$). The fit range is $R=5–300\mathrm{GV}$ (between the dotted lines).

Figure 2

Comparison of our best-fit antiproton-over-proton ratio as a function of rigidity with AMS-02 data. The left plot shows the default setup without DM, while the plot in the right panel shows the corresponding setup with DM. In addition, we show the tertiary component, the DM component, and the best fit before solar modulation (${\phi }_{\odot }=0$). The fit range is $R=5–300\mathrm{GV}$ (between the dotted lines).

Figure 3

Triangle plot with the fit parameters of the default fit which is the baseline for the following analyses. The black (red) contours show the $1\sigma$ to $3\sigma$ best-fit regions in the setup without (with) DM. On the diagonal the ${\chi }^2$ profiles are plotted for every fit parameter. The two additional plots show the ${\chi }^2$ profiles of the solar modulation potential of AMS-02 $p$, He and its difference to the potential of $\overline{p}$, respectively.

Figure 4

Residuals of the antiproton-over-proton ratio for different fit setups for the antiproton production cross section. The plot on the left-hand side originates from a fit setup without DM while the plot on the right-hand side is the corresponding setup including DM. From top to bottom the setups are changed compared to our default setup in the following way: (i) the parametrization of the antiproton production cross section is changed to param. MD, (ii) cross-section uncertainties are treated effectively by means of a covariance matrix imposed on the antiproton data using the MW parameterization, (iii) the cross-section uncertainties are treated effectively by means of a covariance matrix and the parametrization is changed to param. MD, and (iv) in addition to the CR parameters we fit a selection of cross-section parameters simultaneously to CR and cross-section data (joint fit).

Figure 5

Uncertainty contours ($1–3\sigma$) of the propagation parameters. The triangles show the effect of changing the cross-section parametrization from param. MW to param. MD (upper left), the effect of taking cross-section uncertainties into account by a covariance matrix within param. MW (upper right) and param. MD (lower left), and the effect of the joint fit (lower right).

Figure 6

Correlation of the CR propagation parameters with the antiproton production cross-section parameters in the joint fit without DM. The black contours show the $1\sigma$ to $3\sigma$ region. The plot on the very right contain the ${\chi }^2$ profiles of the cross-section parameters. The $y$ axis ranges from $\mathrm{\Delta }{\chi }^2=0$ to 10; cf. Fig. 7 for more details.

Figure 7

The three panels show the ${\chi }^2$ profiles of the cross-section parameter [cf. Eq. (15)] included in the joint fit of CR and cross-section data. The black solid (red dashed) line shows the profile from the fit without (with) DM. For comparison we show the ${\chi }^2$ profile from cross-section data only (blue dotted line).

Figure 8

Contours of the $1\sigma$ and $2\sigma$ best fit in the plane of DM mass and annihilation cross section. We overlay the result of the two different methods to treat cross-section uncertainties, the covariance matrix approach and the joint fit, with our default fit. For comparison we show the limit for the DM annihilation cross section derived from the observation of dwarf spheroidal galaxies [81] and the $2\sigma$ best-fit region of the GCE [82].

Figure 9

Triangle plots for the fit of a covariance matrix to proton, helium, and antiproton-over-proton data.

Figure 10

Residuals of the antiproton-over-proton ratio for different fit setups for different treatment of systematic uncertainties and its correlation. The plot on the left-hand side originates from a fit setup without DM while the plot on the right-hand side is the corresponding setup including DM. From top to bottom the setups are changed compared to our default setup in the following way: (i) The systematic uncertainty is taken to be uncorrelated 1% of the fluxes (or ratio), (ii) data-driven correlation approach with a correlation length of ${\ell }_{\mathrm{corr}}=0$, (iii) ${\ell }_{\mathrm{corr}}=5$, and (iv) ${\ell }_{\mathrm{corr}}=10$.

Figure 11

Uncertainty contours ($1–3\sigma$) of the propagation parameters corresponding to the four different treatments of systematic uncertainties and its correlation discussed in Sec. 5.

Figure 12

Contours of the $1–3\sigma$ best fit in the plane of DM mass and annihilation cross section. We show the result of the default fit and two benchmark scenarios for the correlations: 1% fixed systematic uncertainties and ${\ell }_{\mathrm{corr}}=5$. For comparison we show the limit for the DM annihilation cross section derived from the observation of dwarf spheroidal galaxies [81] and the $2\sigma$ best-fit region of the GCE [82].