Erratum: Interactions of astrophysical neutrinos with dark matter: a model building perspective

In ref. [1] we studied whether the neutrino-dark matter (DM) interactions can cause a suppression of astrophysical neutrino flux. We singled out the interactions which reduce the neutrino flux by & 1%, dubbed as ‘significant flux suppression’ throughout the paper. In light of the collider and electroweak precision constraints, we concluded that out of the eleven effective and three renormalisable neutrino-DM interactions studied in ref. [1], three could still lead to at least 1% suppression of astrophysical neutrino flux at IceCube. These three scenarios involve ultralight scalar DM interacting with neutrinos through (i) Topology I 3 from eq. (3.3), (ii) Topology III in section 3.3, and (iii) vector-mediated interaction in section 4.3.3 of ref. [1]. In this erratum we add that, as the Big Bang Nucleosynthesis (BBN) constraints forbid neutrinos to be in thermal equilibrium with light scalar DM after the neutrino decoupling epoch, two out of the aforementioned three scenarios fail to lead to any significant flux suppression. To be precise, Topology III in section 3.3 and vector-mediated interaction in section 4.3.3 cannot lead to significant neutrino flux suppression, while Topology I 3 still can. The BBN bounds on these three scenarios are discussed in a more detail in the next section. 1Now at: Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai, 400 076, India; karmakars@iitb.ac.in.


Introduction
In ref. [1] we studied whether the neutrino-dark matter (DM) interactions can cause a suppression of astrophysical neutrino flux. We singled out the interactions which reduce the neutrino flux by 1%, dubbed as 'significant flux suppression' throughout the paper. In light of the collider and electroweak precision constraints, we concluded that out of the eleven effective and three renormalisable neutrino-DM interactions studied in ref. [1], three could still lead to at least 1% suppression of astrophysical neutrino flux at IceCube. These three scenarios involve ultralight scalar DM interacting with neutrinos through (i) Topology I 3 from eq. (3.3), (ii) Topology III in section 3.3, and (iii) vector-mediated interaction in section 4.3.3 of ref. [1].
In this erratum we add that, as the Big Bang Nucleosynthesis (BBN) constraints forbid neutrinos to be in thermal equilibrium with light scalar DM after the neutrino decoupling epoch, two out of the aforementioned three scenarios fail to lead to any significant flux suppression. To be precise, Topology III in section 3.3 and vector-mediated interaction in section 4.3.3 cannot lead to significant neutrino flux suppression, while Topology I 3 still can. The BBN bounds on these three scenarios are discussed in a more detail in the next section.

JHEP11(2021)215 2 Details of BBN bounds on neutrino-DM interactions
To satisfy the Big Bang Nucleosynthesis (BBN) constraints on neutrino interactions with ultralight scalar DM Φ, the rate of νν ↔ ΦΦ at the neutrino decoupling temperature T ν ∼ 2 MeV must be less than Hubble expansion rate H. Thus, at T ν , the cross-section of νν ↔ ΦΦ has to be H/n ν ∼ 3.5 × 10 −34 eV −2 . For the interaction given by Topology I 3, the aforementioned bound translates to c the BBN bound reads C 1 c (9) l /Λ 2.5 × 10 −6 GeV −1 , which disfavours any significant flux suppression.
The BBN constraint on renormalisable vector mediated ν-DM interaction, 3) reads f l g 6 × 10 −8 for m Z ∼ 10 MeV. This does not allow for any significant change in the astrophysical neutrino flux. Though this interaction can still lead to changes in the flavour of astrophysical neutrinos passing through solitonic core of ultralight DM [2].
The key constraints on the effective and renormalisable interactions for light DM are summarised in tables 1 and 2 below. For DM with higher masses, the cosmological constraints such as, relic density, collisional damping, and N eff ensure that the mentioned interactions do not lead to any significant flux suppression, as shown in figure 5 of ref. [1].

Conclusion
In this erratum we point out, Topology III and the renormalisable vector-mediated model of neutrino-DM interactions are already too constrainted by BBN to show up at the IceCube neutrino observatory. Only Topology I 3 can lead to a suppression of astrophysical neutrino flux even after imposing the BBN bounds. Tables 1 and 2 are similar to tables 4 and 5 of ref. [1] respectively, but are improved with these BBN bounds.

JHEP11(2021)215
Topology Interaction Constraints Remarks Table 1. Summary of neutrino-DM effective interactions. c l and c e,µ,τ represent the coefficients of interactions for the gauge non-invariant and gauge-invariant forms respectively. The colour coding for the constraints is: Z → inv, LEP monophoton+ / E T , Z → µ + µ − , Z → τ + τ − , BBN and (g−2) e,µ . We also remark whether the interactions are favoured in context of the 1% flux suppression criteria.

Mediator
Interaction Constraints Remarks   Overall, our key conclusion remains the same: building effective and renormalisable models of neutrino-DM interactions which can lead to significant neutrino flux suppression at IceCube is rather hard when confronted with the existing precision, collider, astrophysical, and cosmological constraints.