Measurements using the inelasticity distribution of multi-TeV neutrino interactions in IceCube

Inelasticity, the fraction of a neutrino’s energy transferred to hadrons, is a quantity of interest in the study of astrophysical and atmospheric neutrino interactions at multi-TeV energies with IceCube. In this work, a sample of contained neutrino interactions in IceCube is obtained from five years of data and classified as 2650 tracks and 965 cascades. Tracks arise predominantly from charged-current ${\nu }_{\mu }$ interactions, and we demonstrate that we can reconstruct their energy and inelasticity. The inelasticity distribution is found to be consistent with the calculation of Cooper-Sarkar et al. across the energy range from $\sim 1$ to $\sim 100\mathrm{TeV}$. Along with cascades from neutrinos of all flavors, we also perform a fit over the energy, zenith angle, and inelasticity distribution to characterize the flux of astrophysical and atmospheric neutrinos. The energy spectrum of diffuse astrophysical neutrinos is described well by a power law in both track and cascade samples, and a best-fit index $\gamma =2.62\pm 0.07$ is found in the energy range from 3.5 TeV to 2.6 PeV. Limits are set on the astrophysical flavor composition and are compatible with a ratio of ${(\frac{1}{3}:\frac{1}{3}:\frac{1}{3})}_{\oplus }$. Exploiting the distinct inelasticity distribution of ${\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }$ interactions, the atmospheric ${\nu }_{\mu }$ to ${\overline{\nu }}_{\mu }$ flux ratio in the energy range from 770 GeV to 21 TeV is found to be ${0.77}_{-0.25}^{+0.44}$ times the calculation by Honda et al. Lastly, the inelasticity distribution is also sensitive to neutrino charged-current charm production. The data are consistent with a leading-order calculation, with zero charm production excluded at 91% confidence level. Future analyses of inelasticity distributions may probe new physics that affects neutrino interactions both in and beyond the Standard Model.

Figure 1

Two-dimensional distributions of atmospheric muon BDT score and NPE, after the outer-layer veto, for atmospheric muons (top left), cascadelike neutrinos (top right), tracklike neutrinos (bottom left), and 10% of the data (bottom right). Events above the black lines were accepted as signal events. To access $\sim 1\mathrm{TeV}$ neutrinos that typically produce $\sim 100\mathrm{PE}$, one must overcome muon background with a rate 1800 times higher.

Figure 2

The total event rate for data (black), atmospheric muons (red), cascadelike neutrinos (green), and tracklike neutrinos (orange) in the 10% testing sample as a function of the parameter $a$ appearing in Eq. (6) describing the elliptical cut. The chosen value of $a=0.75$ is shown with a vertical black line.

Figure 3

Top: The track purity and efficiency as a function of normalized BDT score ${\widehat{s}}_{\text{track}}$. Bottom: The signal-to-noise ratio as a function of ${\widehat{s}}_{\text{track}}$. A BDT track score cut ${\widehat{s}}_{\text{track}}\ge 0.52$ (black line) maximized the signal-to-noise ratio, yielding a 92% purity and 98% efficiency. The fluctuations in the purity curve are due to low statistics in that region.

Figure 4

Top: An event display showing the most energetic starting track found in the data. DOMs are represented by colored spheres with a radius corresponding to the number of photoelectrons detected and with a color showing the first photoelectron time going from red (earliest) to green (latest). The larger blue spheres show the reconstructed sequence of electromagnetic cascades along the track, and their size is proportional to the reconstructed energy of each cascade on a logarithmic scale. The event originates in the top half of the detector. Middle: The reconstructed energy loss profile as a function of distance along the reconstructed track. The detector boundaries are shown by green and red dashed lines. Energy losses outside the detector, shown in grey, are excluded from the energy and inelasticity reconstruction. Bottom: The cumulative fraction of the total deposited energy within the detector. Percentiles of the energy loss distribution, shown with blue points, are features for the random forest regression of cascade and muon energy. The cascade and muon energies are estimated to be $E_{\mathrm{casc}}=64\mathrm{TeV}$ and $E_{\mu }=724\mathrm{TeV}$, respectively, leading to $E_{\text{vis}}=788\mathrm{TeV}$ and $y_{\text{vis}}=0.08$ for the visible energy and inelasticity, respectively. The total deposited energy is 135 TeV, and the muon escapes the detector with most of the neutrino’s energy.

Figure 5

Joint distributions of reconstructed quantity vs true quantity for cascade energy, $E_{\mathrm{casc}}$; muon energy, $E_{\mu }$; total visible energy, $E_{\text{vis}}$; and visible inelasticity, $y_{\text{vis}}$. The RMS error for each quantity is shown at the top of each panel.

Figure 6

The distribution of the difference in zenith angle between the cascade and track reconstructions for tracks with $y_{\text{vis}}>0.75$. All reconstructions use the baseline SPICE Mie ice model. 192 events meeting this condition were found in the full 5-year data sample. The data (black) show a mismatch between cascade and track zenith angles, with cascades being reconstructed with a median angle of 8.1° more down going than the corresponding tracks. When events simulated using the SPICE Mie model are reconstructed (red), the median zenith angle difference is only 1.3°. This discrepancy may be caused by systematic errors in the ice model since the cascade reconstruction is much more sensitive to the ice model than the track reconstruction. Distributions for two separate simulations increasing the bulk ice scattering globally by $+10\%$ (blue) and increasing hole ice scattering by $+67\%$ (green) are shown. Increased bulk ice scattering and hole ice scattering produce a shift that can explain the down-going bias seen in the data.

Figure 7

The reconstructed visible inelasticity distribution in five different bins of reconstructed energy. Observed data are shown in black. Error bars show 68% Feldman-Cousins confidence intervals for the event rate in each bin [57]. The result of fitting the distribution to the parametrization of Eq. (10) is shown with dashed green lines. The prediction of the CSMS differential CC cross section are shown for neutrinos with solid blue lines and antineutrinos with dashed blue lines. The total CC charm contribution is shown in magenta, illustrating its flatter inelasticity distribution. The best-fit flux models of Table 2 are assumed for all predictions.

Figure 8

The mean inelasticity obtained from the fit to Eq. (13) in five bins of reconstructed energy. Vertical error bars indicate the 68% confidence interval for the mean inelasticity, and horizontal error bars indicate the expected central 68% of neutrino energies in each bin. The predicted mean inelasticity from CSMS is shown in blue for neutrinos and in green for antineutrinos. The height of the colored bands indicates theoretical uncertainties in the CSMS calculation. A flux-averaged mean inelasticity per the HKKMS calculation is shown in red.

Figure 9

Best-fit distributions with all neutrino flux and detector parameters. Top: The distribution of the reconstructed visible energy, visible inelasticity, and cosine zenith for the sample of starting tracks. Bottom: the distribution of the reconstructed energy and cosine zenith for the sample of cascades. Contributions of conventional atmospheric and astrophysical neutrinos are shown in blue and red, respectively, and the total predicted distribution is shown in maroon. The prompt atmospheric neutrino contribution is not shown since its best-fit value is zero. The black error bars show the data. The inclusion of detector parameters describing bulk and hole ice scattering substantially improves the model description of the cascade cosine zenith distribution. The best-fit parameters are shown in Table 2.

Figure 10

Confidence regions for the astrophysical power-law index, $\gamma$, and flux normalization, ${\mathrm{\Phi }}_0$. The blue contours show the confidence region for the joint fit of the cascade and starting track samples, which is the main result obtained here. The red contours show the confidence region for a fit of starting tracks only, and the green contours show the confidence region for a fit of cascades only, and all are consistent with each other. The confidence region from the IceCube analysis of through-going tracks [23] is shown in orange, which is in tension with the cascade confidence region. The contours from the starting track sample are consistent with both cascade and through-going samples.

Figure 11

Confidence regions for astrophysical flavor ratios $(f_e:f_{\mu }:f_{\tau }{)}_{\oplus }$ at Earth. The labels for each flavor refer to the correspondingly tilted lines of the triangle. Averaged neutrino oscillations map the flavor ratio at sources to points within the extremely narrow blue triangle diagonally across the center. The $\approx {(\frac{1}{3}:\frac{1}{3}:\frac{1}{3})}_{\oplus }$ composition at Earth, resulting from a ${(\frac{1}{3}:\frac{2}{3}:0)}_S$ source composition, is marked with a blue circle. The compositions at Earth resulting from source compositions of ${(0:1:0)}_S$ and ${(1:0:0)}_S$ are marked with a red triangle and a green square, respectively. The updated best-fit neutrino oscillation parameters from Ref. [61] are used here. Though the best-fit composition at Earth (black cross) is ${(0:0.21:0.79)}_{\oplus }$, the limits are consistent with all compositions possible under averaged oscillations.

Figure 12

The predicted fraction of ${\overline{\nu }}_{\mu }$ contributing to the total ${\nu }_{\mu }+{\overline{\nu }}_{\mu }$ event rate in bins of reconstructed energy and inelasticity. At energies below $\sim 10\mathrm{TeV}$, there are substantial differences in the inelasticity distribution that enable the atmospheric neutrino-to-antineutrino ratio to be measured. The bottom panel shows the fraction of atmospheric neutrinos contributing to the total event rate in bins of reconstructed energy. At energies above $\sim 100\mathrm{TeV}$ where astrophysical neutrinos begin to dominate the event rate, differences in the inelasticity distribution vanish, and it is not possible to measure the neutrino-to-antineutrino ratio for the astrophysical flux. An equal neutrino and antineutrino composition is assumed for the astrophysical flux here.

Figure 13

The predicted fractional contribution of all-flavor neutrino CC charm production events to the total event rate in bins of reconstructed visible energy and inelasticity. The increased charm production fraction at high visible inelasticity and high energy (up to 36%) provides a shape difference that allows the presence of charm production to be identified in a likelihood fit to the data.