1 A model of 풏̅ annihilation in experimental searches for 풏 → 풏̅ transformations E. S. Golubeva1, J. L. Barrow2, C. G. Ladd2 1Institute for Nuclear Research, Russian Academy of Sciences, Prospekt 60-letiya Oktyabrya 7a, Moscow, 117312, Russia 2University of Tennessee, Department of Physics, 401 Nielsen Physics Building, 1408 Circle Drive, Knoxville, TN 37996, USA Searches for baryon number violation, including searches for proton decay and neutron-antineutron transformation (푛 → 푛̅), are expected to play an important role in the evolution of our understanding of beyond Standard Model physics. The 푛 → 푛̅ is a key prediction of certain popular theories of baryogenesis, and the experiments such as the Deep Underground Neutrino Experiment and the European Spallation Source plan to search for this process with bound- and free-neutron systems. Accurate simulation of this process in Monte Carlo will be important for the proper reconstruction and separation of these rare events from background. This article presents developments towards accurate simulation of the annihilation 12 process for use in a cold, free neutron beam for 푛 → 푛̅ searches from 푛̅퐶 annihilation, as 6퐶 is the target of choice for the European Spallation Source’s NNBar Collaboration. Initial efforts are also made in this 40 paper to perform analogous studies for intra-nuclear transformation searches in 18퐴푟 nuclei. 12 I. INTRODUCTION being allowed to hit a target of carbon ( 6퐶) foil A. Background (with a thickness of ~130 휇푚). This foil would have absorbed antineutrons, resulting in matter- As early as 1967, A. D. Sakharov pointed out [1] antimatter annihilation which was expected to that for the explanation of the Baryon Asymmetry yield a signal with a star-like topology made of of the Universe (BAU) there should exist several pions. Particle detectors and calorimeters interactions in which baryonic charge is violated surrounded the target to record such annihilation besides mere departures from thermal events, and was capable of reconstructing the equilibrium and 퐶푃 symmetry. Thus, vertex of the pion-star within the central plane of experimental searches for baryon number (퐵) the 12퐶 foil along with the visible energy. In total, violating processes, and in particular the baryon 6 the target received ~3 × 1018 neutrons, with no minus lepton (퐵 − 퐿) number violating process of recorded annihilation events, i.e. with zero neutron—antineutron oscillation (푛 → 푛̅), are of background. This was due to an analysis scheme great importance due to their possible requiring two or more tracks (푛̅-annihilation or connections to the explanations of the observed background-produced mesons, or their decay matter-antimatter asymmetry of the universe—as products) to be reconstructed in the detector as first laid out by V. A. Kuzmin [2] and followed in emanating from the 12퐶 foil. As a result, the developments by many authors, see e.g. recent 6 oscillation limit for free neutrons was established reviews [3-5]. to be Thus, the search for 푛 → 푛̅, along with nucleon 8 ( ) decay, remains one of the most important areas of 휏푛→푛̅ ≥ 0.86 × 10 푠. 1 modern physics, hopefully leading to an In the last two decades since obtaining this result, understanding of phenomena related to the BAU. there have been significant technological developments within the field which have The best lower limit on a measurement of the permitted the planning of another transformation oscillation period with free neutrons, 휏 , was 푛→푛̅ experiment, recently proposed at the currently attained at a reactor at the Institut Laue-Langevin under construction European Spallation Source (ILL) [6] in Grenoble, France, with a cold neutron (ESS) [5,7,8]. According to preliminary beam. These neutrons flew through an evacuated, estimates, such an experiment could explore this magnetically shielded pipe of 76 푚 in length process with 2 − 3 orders of magnitude higher (corresponding to a flight time of ~0.1 푠), until sensitivity than in [6], leading next generation 2 free neutron experiments to be sensitive to improvement in the separation of signal to 9 10 oscillation time range 휏푛→푛̅~10 − 10 푠. background in new experiments, it will be possible to improve the appearance limit, but Another way to detect 푛 → 푛̅ is through intra- impossible to claim any real discovery. This nuclear searches, and discovery is tantalizing contrasts the tantalizing figure that future possible. Searches for 휏푛→푛̅ can be performed in experiments in large underground detectors could experiments with large underground detectors improve the restrictions on processes where looking for any hints of the instability of matter. Δ퐵 = ±2 up to ~1033 − 1035 푦푟푠 [5] in the Within the nucleus, spontaneous 푛̅ production absence of background. An experiment possibly would lead to annihilation with another capable of such a search for 푛 → 푛̅ within the neighboring nucleon, resulting in the release of 40퐴푟 nucleus is currently under construction, ~2 퐺푒푉 of total energy. However, such intra- 18 using large liquid argon (40퐴푟) time projection nuclear transformations are significantly 18 chamber: the Deep Underground Neutrino suppressed compared to 푛 → 푛̅ in vacuum [5,9- Experiment (DUNE) [20]. 13]. The limit on the 푛 → 푛̅ intra-nuclear transformation time (in matter) 휏푚 is associated Whether or not 푛 → 푛̅ is definitively observed with the square of the free transformation time [5] above background in intra-nuclear experiments through a dimensional suppression factor, 푅: depends critically upon the separability of signal from background and the energy scale at which 2 ( ) 휏푚 = 푅 ⋅ 휏푛→푛̅ 2 the new BSM mechanism will appear. In the case In the nucleus, this suppression is due to of an observation in intra-nuclear experiments the differences between the neutron and antineutron results will be of great importance for the nuclear potentials; however, in high mass understanding of fundamental properties of detectors, this suppression can be compensated matter, along with building a precise theoretical by the large number of neutrons available for model describing these properties. Although in investigation within the large detector volume. A the free neutron search [6] no background was number of nucleon decay search collaborations detected, the question of background separation have been involved in the search for 푛 → 푛̅ in might become essential with the planned increase nuclei, such as Frejus [14] and Soudan-2 [15] in in sensitivity in searches using both free neutrons 56 produced by spallation and bound neutrons in 26퐹푒, and IMB [16], Kamiokande [17], and 16 underground experiments, meriting further study Super-Kamiokande (SK) [18] in 8푂; there has also been a deuteron search performed at SNO beyond this work. [19]. In the Soudan-2 experiment, there is a limit Thus, one requires detailed information about the on the transformation time in iron nuclei of 휏퐹푒 ≥ processes during the annihilation of slow 7.2 × 1031 푦푟푠 [15], which is in line with the antineutrons on nuclei. The purpose of this work limit for the free transformation time of 휏푛→푛̅ ≥ is to create a model describing the annihilation of 8 12 1.3 × 10 푠. In SK, which extracted 24 푛 → 푛̅ a slow antineutron incident upon a 6퐶 nucleus candidate events while expecting a background for the upcoming transformation experiment count of 24.1 atmospheric neutrino events, these using a free neutron beam at ESS. Also, the first 32 limits were 휏푂 ≥ 1.9 × 10 푦푟푠 [18] and steps have also been taken towards a full, realistic 8 휏푛→푛̅ ≥ 2.7 × 10 푠, respectively. simulation of the annihilation resulting from 푛 → 푛̅ within 40퐴푟 nuclei for DUNE. The prevalence of background within SK and 18 other large underground detectors, possibly B. Past simulation for free and bound shrouding a true event, prioritizes the rigorous 풏 → 풏̅ searches modeling of both signal and background within an intra-nuclear context. Without any significant 3 In general, the experiment requires maximum C. This work and its goals efficiency for detection and reconstruction of Our goal is to create an adequately accurate incredibly rare antineutrons to be separated from generator, one which can serve as a platform to background. The development of Monte Carlo be used within all free and intra-nuclear 푛 → 푛̅ (MC) generators for 푛 → 푛̅ searches is not new, experiments. In this article, we present the main and has been an integral part of all past framework and approaches underlying the model, experiments. Sadly, the descriptions of these wherein the annihilation of an antineutron on the MCs, as known, are not always complete or target nucleus is considered to consist of several seemingly consistent, and are not easily sequential and independent stages. We use the accessible. Information about the generator approach originally undertaken in [24,25]. developed for the ILL experiment [6] is few and far between, unavailable [21], and lacking [22] in In the first stage of this approach, one defines the detailed explanation. absorption point of an antineutron by the nucleus in the framework of the optical model. Our Intra-nuclear searches have been completed far modeling was performed for more times than free neutron experiments, and so 10 푚푒푉 12 their accompanying generators are similarly antineutrons incident upon a 6퐶 nucleus [24,25]. 40 abundant. Never-the-less, many of their For 18퐴푟, 푛 → 푛̅ is assumed to occur within the descriptions are scattered throughout a multitude nucleus, where the nucleons have some Fermi of dissertations and are poorly defended within motion, and the present paper shows some first published works. Similarly, open access to these steps in this direction; the process of 푛 → 푛̅ 40 simulations is lacking. For instance, SK [18] cites within 18퐴푟 will be the focus of our future work. only three works in reference to their generator, After the point of these quite different initial one of which is a previous work of this paper’s conditions, all of the following stages of the 12 40 lead author, and two of which contain rather process for both 6퐶 and 18퐴푟 do not differ and ancient antiproton annihilation data; how exactly are considered within a unified approach.