Progress and simulations for intranuclear neutron-antineutron transformations in ${}_{18}{}^{40}\mathrm{Ar}$

With the imminent construction of the Deep Underground Neutrino Experiment (DUNE) and Hyper-Kamiokande, nucleon decay searches as a means to constrain beyond standard model extensions are once again at the forefront of fundamental physics. Abundant neutrons within these large experimental volumes, along with future high-intensity neutron beams such as the European Spallation Source, offer a powerful, high-precision portal onto this physics through searches for $\mathcal{B}$ and $\mathcal{B}-\mathcal{L}$ violating processes such as neutron-antineutron transformations ($n\to \overline{n}$), a key prediction of compelling theories of baryogenesis. With this in mind, this paper discusses a novel and self-consistent intranuclear simulation of this process within ${}_{18}{}^{40}\mathrm{Ar}$, which plays the role of both detector and target within the DUNE’s gigantic liquid argon time projection chambers. An accurate and independent simulation of the resulting intranuclear annihilation respecting important physical correlations and cascade dynamics for this large nucleus is necessary to understand the viability of such rare searches when contrasted against background sources such as atmospheric neutrinos. Recent theoretical improvements to our model, such as the first calculations of the ${}_{18}{}^{40}\mathrm{Ar}$ intranuclear radial annihilation probability distribution and the inclusion of a realistic $\overline{n}A$ potential, are discussed. A Monte Carlo simulation comparison to another publicly available $n\to \overline{n}$ generator within GENIE is shown in some detail. The first calculation of ${}_{18}{}^{40}\mathrm{Ar}$’s $n\to \overline{n}$-intranuclear suppression factor, an important quantity for future searches at the DUNE, is also completed, finding $T_R^{\mathrm{Ar}}\sim 5.6\times {10}^{22}{\mathrm{s}}^{-1}$.

Figure 1

The $\overline{n}$ radial distribution (red), arbitrarily rescaled to fit the figure, as compared to the nominal neutron distribution (blue) for the deuteron.

Figure 2

The $\overline{n}$ radial distribution (red), arbitrarily rescaled to fit the figure, as compared to the nominal neutron distribution (blue), and the annihilation density of (5), also arbitrarily rescaled (dashed black), for the $1d_{5/2}$ shell of ${}_{18}{}^{40}\mathrm{Ar}$.

Figure 3

Same as for Fig. 2, but for the $1f_{7/2}$ shell.

Figure 4

Antineutron densities for the shells of ${}_{18}{}^{40}\mathrm{Ar}$.

Figure 5

The relative change to the width of the $1d_{5/2}$ shell is shown when a factor $f_r$ is applied to the real potential, and $f_i$ to the imaginary part.

Figure 6

The factor $\gamma$ multiplying the width of the $1d_{5/2}$ shell when a factor $1+0.4\exp (-20(r-r_c))$ ($r$ is in fm) is applied to the absorptive potential.

Figure 7

The momentum distribution for ${\pi }^{+}$ emitted from $\overline{p}\mathrm{C}$ annihilation at rest. The dashed red histogram shows the distribution generated from calculation $\#1$ mentioned in Table 3, while the solid black shows calculation $\#2$. All points are taken from experimental data in [68, 71].

Figure 8

The new (solid line) and old (dashed line) total energy available to annihilating (anti-) nucleons (and generated mesons) is plotted.

Figure 9

The old (dashed line) and new (solid line) total $\overline{n}N$ pair (or generated meson) momentum is plotted.

Figure 10

The new (top) and old (bottom) total mesonic initial parameter space is shown for extranuclear $\overline{n}C$ annihilation.

Figure 11

The new (top) and old (bottom) total mesonic/pionic/photonic final state parameter space is shown for extranuclear $\overline{n}C$ annihilation.

Figure 12

Two plots are shown for various generator assumptions. In blue, we see the naive intranuclear radial position of annihilation probability distribution generated by a WS, as presented in GENIE. In orange, we see the modern, quantum-mechanically derived, shell-averaged, true intranuclear radial position of annihilation probability distribution as developed in Sec. 2, present in our generator. Probability distributions are normalized to the same arbitrary integral for a direct comparison, and the scale is arbitrary.

Figure 13

The distributions of total initial annihilation meson energy are shown for this work (solid line) and GENIEv3.0.6 (dashed line) using local Fermi gas models. Via conservation, each of these is equivalent to the distributions of the annihilating $\overline{n}N$ pair.

Figure 14

Top: This work, showing the initial (anti-) nucleon momentum distributions, using a zoned local Fermi gas model with an additional $\overline{n}$ potential. Bottom: the same for the GENIEv3.0.6, showing a local Fermi gas model and the default nonlocal Bodek-Ritchie model.

Figure 15

Two-dimensional $\overline{n}$ and $n$ momentum-radius correlation plots for this work (top two plots, using a zoned local Fermi gas and zoned Woods-Saxon annihilation position distribution) alongside GENIEv3.0.6’s local Fermi gas and nonlocal Bodek-Ritchie single (anti-) nucleon momentum nuclear models (bottom two plots, also with a smooth Woods-Saxon initial $\overline{n}$ annihilation position distribution).

Figure 16

The distributions of total initial annihilation meson momentum are shown for this work (solid line) and GENIEv3.0.6 (dashed line) using local Fermi gas models.

Figure 17

The initial mesonic parameter space (total momentum versus invariant mass) is compared for multiple generators: top, this work; bottom, GENIEv3.0.6. The no resonances phrase refers to a GENIE Mother particle status code cut which removes virtual contributions to invariant mass.

Figure 18

The final state mesonic/pionic parameter space (total momentum versus invariant mass) after intranuclear transport is compared for multiple generators: top, this work; middle and bottom, GENIEv3.0.6 local Fermi gas and nonlocal Bodek-Ritchie, respectively. Differences in these may lead to different detector signal efficiencies.

Figure 19

The outgoing ${\pi }^{+}$ momentum spectrum is shown for several local Fermi gas models.

Figure 20

The outgoing $p$ momentum spectrum is shown for several local Fermi gas models.