Role of nucleon strangeness in supernova explosions

Recent hydrodynamical simulations of core-collapse supernova (CCSN) evolution have highlighted the importance of thorough control over the microscopic physics responsible for such internal processes as neutrino heating. In particular, it has been suggested that modifications to the neutrino-nucleon elastic cross section can potentially play a crucial role in producing successful CCSN explosions. One possible source of such corrections can be found in a nonzero value for the nucleon's strange helicity content $\mathrm{\Delta }s$. In the present analysis, however, we show that theoretical and experimental progress over the past decade has suggested a comparatively small magnitude for $\mathrm{\Delta }s$, such that its sole effect is not sufficient to provide the physics leading to CCSN explosions.

Figure 1

A summary of $\mathrm{\Delta }s$ determinations in this analysis. Experimental and phenomenological findings subsequent to Ref. [5] (solid, black square, $\left[a\right]$) are contained in the lower rectangle. These include the averaged results in Ref. [15] $\left[b\right]$, Ref. [21] $\left[c\right]$, the extrapolation and DSSV-based methods of Ref. [23] [$d$ and $e$, respectively], and the average of Refs. [24] and [27] $\left[f\right]$. The lower inverted triangle represents the mean of these measurements: $\mathrm{\Delta }s=-0.087\pm 0.009$. Modern theoretical calculations are given in the top rectangle, including the averaged small-$\mathrm{\Delta }s$ lattice calculations [28, 29, 30, 31, 32] $\left[g\right]$, the AWI-based computation of Ref. [26] $\left[h\right]$, and Refs. [33] $\left[i\right]$ and [34] $\left[j\right]$. The upper inverted triangle depicts the theory average: $\mathrm{\Delta }s=-0.032\pm 0.005$, while the vertical dot-dashed line represents the value used in Ref. [6].

Figure 2

Parameter scans for the Ref. [34] model consistent with $\mathrm{\Delta }s=-0.20\pm 0.01$. Results using wave functions with Gaussian (dots) and dipole-like (squares) momentum dependence are displayed. Parameter combinations satisfying $\mathrm{\Delta }s\sim -0.2$ require large wave-function normalizations, generating the lower bound $x{S}^{+}\ge 0.062$. This substantially overshoots the range (vertical band) for $x{S}^{+}$ determined by CTEQ [37]. The large disk near $(x{S}^{+},x{S}^{-})=(0.09,0.002)$ represents the model used for the strange PDFs plotted in Fig. 3.

Figure 3

$x[s\left(x\right)+\overline{s}\left(x\right)]$ consistent with $\mathrm{\Delta }s=-0.2$ according to the model of Ref. [34]. The model parameters leading to the above correspond to the large dot at $x{S}^{+}\sim 0.09$ in Fig. 2. The model has been evolved from $Q_0^2=1{\mathrm{GeV}}^2$ (solid line) to $Q^2=2.5{\mathrm{GeV}}^2$ (dot-dashed line) for comparison with HERMES [39] (red circles). A model constrained to $\left|\mathrm{\Delta }s\right|$ comparable to that of Ref. [6] thus hugely overestimates the strange PDF — especially for $x\gtrsim 0.1$.