New evaluation of the antiproton production cross section for cosmic ray studies

Theoretical predictions for the cosmic antiproton spectrum currently fall short of the corresponding experimental level of accuracy. Among the main sources of uncertainty are the antiproton production cross sections in cosmic ray inelastic interactions. We analyze existing data on antiproton production in $pp$ scattering, including for the first time the measurements performed by the NA49 Collaboration. We compute the antiproton spectrum finding that in the energy range where data are available (antiproton energies of about 4–550 GeV) different approaches lead to almost equivalent results, with an uncertainty of 10%–20%. Extrapolations outside this region lead to different estimates, with the uncertainties reaching the 50% level around 1 TeV, degrading the diagnostic power of the antiproton channel at those energies. We also comment on the uncertainties in the antiproton production source term coming from nuclei heavier than protons and from neutrons produced in $pp$ scatterings, and point out the need for dedicated experimental campaigns for all processes involving antiproton production in collisions of light nuclei.

Figure 1

The data on $d^3{\sigma }_{pp\to \overline{p}}/d{p}^3$ employed in our analysis are reported as a function of $E_{\overline{p}}^{\text{LAB}}$ (left panel) and in the $p_T-x_R$ space (right panel). For the data details, see Table 1.

Figure 2

Comparison of the source term for antiproton production in $pp$ collisions as obtained in [11] (see however text for a correction in their table) and in this work, by refitting the same data sets with the same functional form, with our nominal $3\sigma$ statistical error band. Vertical dot-dashed lines show the domain of energy actually covered by the experiments analyzed.

Figure 3

Comparison between NA49 data with the fitting function of Eq. (11) (see Table 3), with $3\sigma$ error bands. For clarity, the data and the theoretical curves at each $p_T$ value have been multiplied by a factor of $0.9^{n_{p_T}}$, where $n_{p_T}$ is the integer counting the $p_T$, from lower to higher (i.e. for $p_T=0.60\mathrm{GeV}/c^2$ the rescaling is $0.9^6$).

Figure 4

Comparison between the function Eq. (11) fitted to NA49 data, with $3\sigma$ error band (solid curve with cyan/blue shaded band), and interpolated curve (dashed red), with the interpolation envelope band, yellow/light shading. The dashed vertical lines correspond to the equivalent antiproton energy sampled by the NA49 experiment, where an interpolation is actually justified.

Figure 5

Differential cross section for antiproton production in $pp$ scattering, as a function of $x_R$, for different $p_T$ values. The curves refer to the $3\sigma$ uncertainty band around the best fit obtained with a fit of Eq. (13) to the data sets in Table 1. The data, from top left to bottom right, are from [14, 18, 19, 20, 21, 22, 23]. For the sake of clarity, the data from [19] and [14] and the relevant theoretical curves at each $p_T$ value have been rescaled by a factor $0.6^{n_{p_T}}$ and $0.9^{n_{p_T}}$, respectively, as described in Fig. 3.

Figure 6

Comparison between fitted function of Eq. (13) with $3\sigma$ band (solid curve with cyan/blue shaded band), of Eq. (12) with $3\sigma$ band (dot-dashed curve with green/light green shaded band) and interpolated curve (dashed red), with the interpolation envelope band (red/orange shading). The dashed vertical lines correspond to the equivalent antiproton energy sampled by the global data set, where an interpolation is in principle meaningful.

Figure 7

The best-fit and $3\sigma$ uncertainty band source term derived with the fit of Eq. (12) and Eq. (13) to all data sets in Table 1 is shown together with the source term obtained using [11, 12] cross section parametrizations.

Figure 8

Estimate of the uncertainties in the antiproton source term from inelastic $pp$ scattering. The blue band indicates the $3\sigma$ uncertainty band due to the global fit with Eq. (13), while the red band corresponds to the convolution of the uncertainties brought by fits to the data with Eq. (13), Eq. (12) and with the spline interpolation (see Fig. 6). The orange band takes into account the contribution from decays of antineutrons produced in the same reactions. Vertical bands as in Fig. 6. See text for details.