# Why very cold neutrons could be useful for neutron-antineutron oscillation searches

#### Abstract

This note is based on a talk given at the “Workshop on Very Cold and Ultra Cold Neutron Sources for ESS”. It presents several arguments in favor of using very cold neutrons (VCN) for neutron – antineutron (

## 1.Introduction

The search for neutron – antineutron oscillations (

## 2.n and n ‾ guides for n − n ‾ oscillation experiments

An interesting option to simultaneously increase the sensitivity of such an experiment and decrease its cost is to implement the idea of a guide both for *n* and *n* guides have been in common use since the beginning of the neutron research, the idea of *n* with a surface [13]. Moreover, typical *n* and *A* of the nucleus, composing the material surface. The imaginary part *A*. The guide wall material should also have a large critical velocity for *n*, and should be suitable for building guides and/or coatings. Aside from these requirements, the choice of material for a relatively short neutron guide, in which the time of flight is significantly shorter than the *n* and

The idea of using the reflection of *n* energies, thus increasing statistics and, thereby, sensitivity; 2) point out conditions for suppressing the phase difference for *n* and *n* and 4) make certain choices for the nuclei composing the guide material.

Compared to the classical quasi-free-neutron method, our approach has certain advantages. For the same installation length, the advantages include smaller transversal sizes, lower costs, and larger statistics, i.e., higher sensitivity. For a longer installation, our approach provides a large gain in sensitivity. In terms of the oscillation probability, the gain increases quadratically with the length. For the particular case of a copper (Cu)

An experiment at the ESS would provide much higher sensitivity. Compared to the best experiment performed to-date [7], the gain factors include the possibilities of a significantly larger guide length and a significantly larger solid angle from which to extract neutrons. Each factor corresponds to a quadratic increase in sensitivity. Compared to a design that doesn’t use an

It is interesting to estimate the uncertainties in the experiment sensitivity associated with the uncertainty in the scattering length of

## 3.Advantages of very cold neutrons for n − n ‾ oscillations experiment

Such a hypothetical experiment would be entirely limited by statistics, and would have negligible systematics. Thus, one might try to further improve the statistical sensitivity even if systematic uncertainties increase. Roughly speaking, systematic and statistical uncertainties should be equal in a properly designed experiment. This argument, as well as the fact that the sensitivity to the

Let us assume for the sake of simplicity that the design of a *n* and

What is the optimum VCN velocity for such an experiment? One can profit from the

We now turn to an analyze of the main additional gain factor resulting from a larger phase-space density that can be achieved in a dedicated VCN source. The additional gain factor is simply proportional to the increase in the phase-space density.

## 4.A possible implementation of a dedicated VCN source at ESS

An optimization of the VCN

We propose the following implementation of the VCN source. In the current design, neutrons for the

##### Fig. 1.

## 5.Conclusion

We have motivated the use of very cold neutrons (VCN) for improving the sensitivity of

## Acknowledgements

This note summarizes the work done by my colleagues Aleksander Aleksenskii, Alexei Bosak, Artur Dideikin, Marc Dubois, Vladimir Gudkov, Esben Klinby, Ekaterina Korobkina, Egor Lychagin, Bernhard Meirose, David Milstead, Alexei Muzychka, Alexander Nezvanov, Konstantin Protasov, Nicola Rizzi, Valentina Santoro, William Michael Snow, Aleksander Strelkov, Alexei Voronin, Alexander Vul’, Albert Young, Luca Zanini and many others. The author is grateful to Tom Neulinger for his help in preparing this article.

This research is funded by ANR-20-CE08-0034.

## References

[1] | A. Addazi et al., New high sensitive searches for neutrons converting into antineutrons and/or sterile at the HIBEAM/NNBAR experiment at the European Spallation Source, J. Phys. G 48: ((2021) ), 070501. doi:10.1088/1361-6471/abf429. |

[2] | R. Allahverdi et al., A simple testable model of baryon number violation: Baryogenesis, dark matter, neutron-antineutron oscillation and collider signals, Phys. Lett. B 779: ((2018) ), 262. doi:10.1016/j.physletb.2018.02.019. |

[3] | A. Anghel et al., The PSI ultracold neutron source, Nucl. Instr. Meth. A 611: ((2009) ), 272. doi:10.1016/j.nima.2009.07.077. |

[4] | K. Babu et al., Neutrino mass hierarchy, neutron-antineutron oscillation from baryogenesis, Phys. Rev. D 79: ((2009) ), 015017. doi:10.1103/PhysRevD.79.015017. |

[5] | K.S. Babu et al., Post-sphaleron baryogenesis, Phys. Rev. Lett. 97: ((2006) ), 131301. doi:10.1103/PhysRevLett.97.131301. |

[6] | K.S. Babu et al., Post-sphaleron baryogenesis and an upper limit on the neutron-antineutron oscillation time, Phys. Rev. D 87: ((2013) ), 0115019. doi:10.1103/PhysRevD.87.115019. |

[7] | M. Baldo-Ceolin et al., A new experimental limit on neutron-antineutron oscillations, Z. Phys. C 63: ((1994) ), 409. doi:10.1007/BF01580321. |

[8] | C.J. Batty et al., Unified optical model approach to low energy antiproton annihilation on nuclei and to antiprotonic atoms, Nucl. Phys. A 669: ((2001) ), 721. doi:10.1016/S0375-9474(00)00608-4. |

[9] | K.G. Chetyrkin et al., On the possibility of an experimental search for n-nbar oscillations, Phys. Lett. B 99: ((1981) ), 358. doi:10.1016/0370-2693(81)90117-9. |

[10] | R. Cubitt et al., Quasi specular reflection of cold neutrons from nano-dispersed media at above-critical angles, Nucl. Instr. Meth. A 622: ((2010) ), 182. doi:10.1016/j.nima.2010.07.049. |

[11] | P.S.B. Dev et al., TeV scale model for baryon and lepton number violation and resonant baryogenesis, Phys. Rev. D 92: ((2015) ), 016007. doi:10.1103/PhysRevD.92.016007. |

[12] | A. Dolgov, Non-GUT baryogenesis, Phys. Rep. 222: ((1992) ), 309. doi:10.1016/0370-1573(92)90107-B. |

[13] | E. Fermi, Sul moto dei neutroni nelle sostanze idrogenate, Ric. Sci. 7: ((1936) ), 13. |

[14] | R. Golub et al., The interaction of ultracold neutrons (UCNs) with liquid helium and a superthermal UCN source, Phys. Lett. A 53: ((1975) ), 133. doi:10.1016/0375-9601(75)90500-9. |

[15] | R. Golub et al., Ultracold antineutrons (UCNBAR). The approach to the semi-classical limit, Nucl. Phys. A 501: ((1989) ), 869. doi:10.1016/0375-9474(89)90166-8. |

[16] | V. Gudkov et al., A possible neutron-antineutron oscillation experiment at PF1B at the Institut Laue Langevin, Symmetry 12: ((2021) ), 2314. doi:10.3390/sym13122314. |

[17] | M.V. Kazarnovski et al., On neutron-antineutron oscillations, JETP Lett. 32: ((1980) ), 82. |

[18] | V.A. Kuzmin, CP-non invariance and baryon asymmetry of the universe, JETP Lett. 12: ((1970) ), 228, |

[19] | E.V. Lychagin et al., Storage of very cold neutrons in a trap with nano-structured walls, Phys. Lett. B 679: ((2009) ), 186. doi:10.1016/j.physletb.2009.07.030. |

[20] | R.N. Mohapatra et al., Local B−L symmetry of electroweak interactions, Majorana neutrinos, and neutron oscillations, Phys. Rev. Lett. 44: ((1980) ), 1316. doi:10.1103/PhysRevLett.44.1316. |

[21] | V.V. Nesvizhevsky et al., A new operating mode in experiments searching for free neutron-antineutron oscillations based on coherent neutron and antineutron mirror reflections, Europ. Phys. J. Web of Conf. 191: ((2018) ), 01005. doi:10.1051/epjconf/201819101005. |

[22] | V.V. Nesvizhevsky et al., Fluorinated nanodiamonds as unique neutron reflector, Carbon 130: ((2018) ), 799. doi:10.1016/j.carbon.2018.01.086. |

[23] | V.V. Nesvizhevsky et al., Experimental approach to search for free neutron-antineutron oscillations based on coherent neutron and antineutron mirror reflection, Phys. Rev. Lett. 122: ((2019) ), 221802. doi:10.1103/PhysRevLett.122.221802. |

[24] | V.V. Nesvizhevsky et al., Comment on B.O. Kerbikov “The effect of collisions with the wall on neutron-antineutron transitions” |

[25] | V.V. Nesvizhevsky et al., Production of ultracold neutrons in a decelerating runaway trap, |

[26] | V.V. Nesvizhevsky et al., Implementations of neutron/antineutron ( |

[27] | D.G. Phillips et al., Neutron-antineutron oscillations: Theoretical status and experimental prospects”, Phys. Rept. 612: ((2016) ), 1. doi:10.1016/j.physrep.2015.11.001. |

[28] | K.V. Protasov et al., Theoretical analysis of antineutron-nucleus data needed for antineutron mirrors in neutron-antineutron oscillation experiments, Phys. Rev. D 102: ((2020) ), 075025. doi:10.1103/PhysRevD.102.075025. |

[29] | A.D. Sakharov, Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe, JETP Lett. 5: ((1967) ), 24, |

[30] | A. Saunders et al., Demonstration of a solid deuterium source of ultracold neutrons, Phys. Lett. B 593: ((2004) ), 55. doi:10.1016/j.physletb.2004.04.048. |