# The ESSnuSB Design Study: Overview and Future Prospects

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## Abstract

**:**

## 1. Introduction

## 2. CP Violation Measurement at the Second Oscillation Maximum

#### 2.1. Oscillations in Vacuum

#### 2.2. Matter Effects

#### 2.3. Summary

## 3. Neutrino Beam

## 4. Neutrino Detectors

#### 4.1. Near Detectors

#### 4.2. Far Detectors

## 5. Physics Reach

## 6. Future Developments

## 7. Conclusions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

CPV | Charge-parity violation |

ESS | European spallation source |

ESSnuSB | European spallation source neutrino super beam |

PMNS | Pontecorvo–Maki–Nakagawa–Sakata |

NC | Neutral current |

CC | Charged current |

QCD | Quantum chromodynamics |

QES | Quasi-elastic scattering |

RES | Resonant scattering |

DIS | Deep-inelastic scattering |

MEC | Meson-exchange current |

SFGD | Super fine-grained detector |

CH | Hydrocarbons |

PMT | Photomultiplier tube |

R&D | Research and development |

LEnuSTORM | Low-energy neutrinos from stored muons |

LEMNB | Low-energy monitored neutrino beam |

WC | Water Cherenkov |

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**Figure 1.**Dependence of ${\mathcal{A}}_{\mathrm{CP}}^{\mu \to e}$ on ratio $L/E$. The first maximum of the CPV amplitude is situated at L/E ≈ 585 km/GeV and the second at L/E ≈ 1534 km/GeV.

**Figure 2.**${\nu}_{\mu}\to {\nu}_{e}$ and ${\overline{\nu}}_{\mu}\to {\overline{\nu}}_{e}$ oscillation probabilities as a function of neutrino energy at the fixed distance of 360 km. The oscillation probabilities are shown for ${\delta}_{\mathrm{CP}}=0$ and ${\delta}_{\mathrm{CP}}=-\pi /2$. Full lines correspond to oscillations in vacuum and dashed lines to oscillations in matter.

**Figure 3.**Layout of the ESS accelerator including ESSnuSB modifications required for neutrino beam production and detection. The proposed modifications are show in color: the transfer line (blue), the accumulatior ring (red), the swithcyard (indigo), the neutrino target station (green), and the near detector hall (purple). Reprinted from [25,26].

**Figure 9.**CPV discovery potential as a function of true ${\delta}_{\mathrm{CP}}$ value, assuming the baseline of 360 km (Zinkgruvan mine) and run-time of 5 y in $\nu $ mode and 5 y in $\overline{\nu}$ mode. Different lines correspond to different normalization uncertainty assumptions. Reprinted from [25,26].

**Figure 10.**Coverage of the ${\delta}_{\mathrm{CP}}$ range for which the discovery potential is larger than 5 $\sigma $ as a function of run-time, assuming equal time in neutrino mode and antineutrino mode.

**Figure 11.**The expected 1 $\sigma $ precision for the measurement of the CPV parameter ${\delta}_{\mathrm{CP}}$ as a function of the true value of ${\delta}_{\mathrm{CP}}$, assuming the baseline of 360 km (Zinkgruvan mine) and run-time of 5 y in $\nu $ mode and 5 y in $\overline{\nu}$ mode. Different lines correspond to different bin-to-bin uncorrelated errors. A normalization error of 5% is applied on top of the bin-to-bin error. Reprinted from [25,26].

**Figure 12.**Layout of the proposed upgrades to the ESS linear accelerator, including those from ESSnuSB and ESSnuSB+. The ESSnuSB+ upgrades include a special target station, a muon storage racetrack ring (LEnuSTORM), a low-energy monitored neutrino beam (LEMNB) line, and a new near detector to be used both for LEnuSTORM and LEMNB. The ESSnuSB near detector will be used as a far detector for LEnuSTORM and LEMNB. The image has been reprinted from the ESSnuSB+ proposal.

Parameter | Best-Fit Value $\pm 1\text{}\mathit{\sigma}$ Range |
---|---|

${sin}^{2}{\theta}_{12}$ | $0.304\pm 0.012$ |

${sin}^{2}{\theta}_{13}$ | $0.02246\pm 0.00062$ |

${sin}^{2}2{\theta}_{23}$ | $0.9898\pm 0.0077$ |

$\Delta {m}_{21}^{2}$ | $\left(7.42\pm 0.21\right)\times {10}^{-5}$ eV${}^{2}$ |

$\Delta {m}_{31}^{2}$ | $\left(2.510\pm 0.027\right)\times {10}^{-3}$ eV${}^{2}$ |

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**MDPI and ACS Style**

Alekou, A.; Baussan, E.; Bhattacharyya, A.K.; Kraljevic, N.B.; Blennow, M.; Bogomilov, M.; Bolling, B.; Bouquerel, E.; Bramati, F.; Branca, A.;
et al. The ESSnuSB Design Study: Overview and Future Prospects. *Universe* **2023**, *9*, 347.
https://doi.org/10.3390/universe9080347

**AMA Style**

Alekou A, Baussan E, Bhattacharyya AK, Kraljevic NB, Blennow M, Bogomilov M, Bolling B, Bouquerel E, Bramati F, Branca A,
et al. The ESSnuSB Design Study: Overview and Future Prospects. *Universe*. 2023; 9(8):347.
https://doi.org/10.3390/universe9080347

**Chicago/Turabian Style**

Alekou, A., E. Baussan, A. K. Bhattacharyya, N. Blaskovic Kraljevic, M. Blennow, M. Bogomilov, B. Bolling, E. Bouquerel, F. Bramati, A. Branca,
and et al. 2023. "The ESSnuSB Design Study: Overview and Future Prospects" *Universe* 9, no. 8: 347.
https://doi.org/10.3390/universe9080347