${}^{16}\mathrm{O}$ spectral function from coupled-cluster theory: Applications to lepton-nucleus scattering

We calculate the ${}^{16}\mathrm{O}$ spectral function by combining coupled-cluster theory with a Gaussian integral transform and by expanding the integral kernel in terms of Chebyshev polynomials to allow for a quantification of the theoretical uncertainties. We perform an analysis of the spectral function and employ it to predict lepton-nucleus scattering. Our results well describe the ${}^{16}\mathrm{O}$ electron-scattering data in the quasielastic peak for momentum transfers $\left|\mathbf{q}\right|⪆500$ MeV and electron energies up to 1.2 GeV, extending, therefore, the so-called first-principles approach to lepton-nucleus cross sections well into the relativistic regime. To prove the applicability of this method to neutrino-nucleus cross sections, we implement our ${}^{16}\mathrm{O}$ spectral functions in the nuwro Monte Carlo event generator and provide a comparison with recently published T2K neutrino data.

Figure 1

The real part of optical potential for ${}^{16}\mathrm{O}$ as a function of the kinetic energy of the outgoing proton from Ref. [28].

Figure 2

Charge distribution (a) comparison between CCSD and SCGF calculations using the same interaction ${\mathrm{NNLO}}_{\mathrm{sat}}$. Momentum distribution (b) using CCSD. See text for details.

Figure 3

The integrated energy distribution $S\left(E\right)$ of the proton spectral function for various values of $\hslash \mathrm{\Omega }=12$–20 MeV. The chosen binning is also shown (arbitrary normalization).

Figure 4

${}^{16}\mathrm{O}$ spectral functions for protons (a) and neutrons (b). See text for details of spectral reconstruction. The theoretical uncertainty, not shown in this figure, is discussed in Sec. 4a.

Figure 5

Proton spectral function of ${}^{16}\mathrm{O}$ for three values of momentum $\left|\mathbf{p}\right|$. The uncertainty bars come from Eq. (24).

Figure 6

Electron-scattering differential cross section on ${}^{16}\mathrm{O}$ for different kinematics which correspond to the momentum transfer $\left|\mathbf{q}\right|\approx 320–650\mathrm{MeV}$. We show results obtained with CCSD without including the optical potential (dashed line) and after its inclusion (solid line). The uncertainty bands come from the uncertainty of the ChEK method. Experimental data were taken from Refs. [41, 42].

Figure 7

Electron-scattering cross section for ${}^{16}\mathrm{O}$ calculated within CCSD (continuous blue line) and within SCGF [15] (black dashed-dotted line) in comparison to experimental data from Ref. [42].

Figure 8

The double-differential cross section ${\nu }_{\mu }+{}^{16}\mathrm{O}\to {\mu }^{-}+X$ of $\mathrm{CC}0\pi$ events measured by the T2K experiment [43]. The momentum distribution $|{\mathbf{k}}^{\prime }|$ of outgoing ${\mu }^{-}$ was measured for five ranges of the scattering angle $cos\theta$. The results “SF” were obtained using our spectral function, while “$\mathrm{SF}+\mathrm{FSI}$” results include also the real part of the optical potential. In both cases we do not include theoretical uncertainties. Other mechanisms, predominantly MEC and resonance production (RES) give smaller contributions according to the model used in the simulation [43].

Figure 9

The same as Fig. 8, showing theoretical uncertainty coming from the reconstruction of spectral function. “$\mathrm{SF}+\mathrm{FSI}$ (low)” was obtained using the lower bound of the spectral reconstruction, while “$\mathrm{SF}+\mathrm{FSI}$ (high)” corresponds to the upper bound.