Blast from the past II: Constraints on heavy neutral leptons from the BEBC WA66 beam dump experiment

We thank the Reviewer for appreciating our result. Our responses to the comments are interleaved below:

1) At the beginning of the paper, the author mentioned inverse seesaw mechanism as the theoretical context for HNL. In fact, a HNL with a mixing with the active neutrino of interest to this work, could occur in a broader class of theories, such as the type-I seesaw mechanism, as well as neutrino portal dark sector models where the HNL is a Dirac fermion. It will be worth commenting on these possibilities. Indeed the HNLs under consideration have broad motivation - as discussed in some of the reviews we cited. Our focus here is on obtainingmodel-independent bounds on the mixing with active neutrinos, so we did not feel that a comprehensive discussion of theoretical models is warranted.

However we take the Reviewer’s point about not just mentioning one specific mechanism so have replaced the opening paras:

Neutrinos have small but non-zero masses, the origin of which is unknown. An attractive explanation involves extending the Standard Model (SM) by adding to it right-handed neutrinos, thus generating small masses for the left-handed neutrinos e.g. by the ‘inverse-seesaw’ mechanism [1]. Such models have open parameter space where the heavy neutral leptons (HNL) mix only with a single flavour of active neutrinos [2]; our goal in this work is to bound the currently least constrained possibility of mixing between HNLs and the tau neutrino.

In this simple model, an HNL N has a mass mN and mixes with the ντ with a strength given by Uτ N . This mixing arises from one of the few renormalisable operators — the so-called neutrino portal — that may consistently be added to the Standard Model to couple it to a ‘dark sector’, so is a promising target in the search for new physics beyond the electroweak scale [3]

[1] R. N. Mohapatra and J. W. F. Valle, Neutrino Mass and Baryon Number Nonconservation in Superstring Models, Phys. Rev. D 34, 1642 (1986), doi:10.1103/PhysRevD.34.1642. [2] I. Cordero-Carrion, M. Hirsch and A. Vicente, General parametrization of Majorana neutrino mass models, Phys. Rev. D 101(7), 075032 (2020), doi:10.1103/PhysRevD.101.075032, 1912.08858 [3] G. Lanfranchi, M. Pospelov and P. Schuster, The Search for Feebly Interacting Particles, Ann. Rev. Nucl. Part. Sci. 71, 279 (2021), doi:10.1146/annurev-nucl-102419-055056, 2011.02157.

by:

Neutrinos have small but non-zero masses, the origin of which is unknown. An attractive explanation involves extending the Standard Model (SM) by adding to it right-handed neutrinos, thus generating small masses for the left-handed neutrinos. The most popular is the ‘seesaw’ mechanism for Majorana masses which has many variants [1]. Such models have open parameter space where the heavy neutral leptons (HNL) mix only with a single flavour of active neutrinos [2]. Our goal in this work is to bound the currently least constrained possibility of mixing between HNLs and the tau neutrino. In this simple model, an HNL N has a mass mN and mixes with the ντ with a strength given by Uτ N . This mixing arises from one of the few renormalisable operators — the so-called neutrino portal — that may consistently be added to the Standard Model to couple it to a ‘dark sector’, so is a promising target in the search for new physics beyond the electroweak scale [3]. Our bounds also apply to neutrino portal dark sector models where the HNL is a Dirac fermion [4].

1] R. N. Mohapatra et al., Theory of neutrinos: A White paper, Rept. Prog. Phys. 70, 1757 (2007), doi:10.1088/0034-4885/70/11/R02, hep-ph/0510213. [2] I. Cordero-Carrion, M. Hirsch and A. Vicente, General parametrization of Majorana neutrino mass models, Phys. Rev. D 101(7), 075032 (2020), doi:10.1103/PhysRevD.101.075032, 1912.08858 [3] G. Lanfranchi, M. Pospelov and P. Schuster, The Search for Feebly Interacting Particles, Ann. Rev. Nucl. Part. Sci. 71, 279 (2021), doi:10.1146/annurev-nucl-102419-055056, 2011.02157. [4] A. Y. Smirnov, Neutrino Mixing via the Neutrino Portal, In Prospects in Neutrino Physics (2019), 1905.00838.

2) In the resulting Figures 4 and 5, I suggest the authors to show the reach of a few upcoming experiments such as FASER2 and NA62. Although they are commented in the main text, it would be useful to see how the BEBC limit found here compare with the future probes. We agree this would be useful so have now indicated the projected sensitivities for FASER/FASER2 and NA62 as requested by the Reviewer

Additionally, we have added to the discussion following Eq.(2) as below, in order to respond to the Comment received:

We take 4σ(pN → Ds + X) = 2σ(pN → D+D− + X) = σ(pN → D0 ̄D0 + X) in accordance with data from the Fermilab E769 experiment [30], so that all cross-sections in the denominator above are proportional to each other. If all the production cross sections σ(pN → X) in the numerator too are proportional (to be justified when we identify the Pi that appear in this equation), then the hadronic dependence drops out modulo the proportionality constants, thus simplifying the calculation considerably and yielding a robust constraint. In the WA66 experiment, it was estimated that 4.1 × 10−4 muon neutrinos were produced via D decays per proton on target [22], which allows for direct calculation of Nνℓ . The above procedure minimises systematic uncertainties in the overall flux normalisation when the angular distribution is known.

1. Changed introductory paragraph in response to reviewer
2. Added additional projections to Figures 4 + 5.
3. Below equation 2, we have clarified the normalisation in response to reviewer.
4. Added HNL contribution from tau decay to vector boson for completeness, and corrected typo in branching ratio of tau decay to pseudoscalars; (slight) improvement to bounds at low masses.