Imaginary part of the right-handed neutrino self-energy at 5 GeV < T < 300 GeV

Jacopo Ghiglieri and Mikko Laine

The files below contain data for the imaginary part of the right-handed neutrino self-energy, as specified in 1605.07720. Data is presented for the quantity ImΠR(k) / T2, whose relation to physical quantities is described in sec. 2 of that paper. The purpose of these results is to fill the gap between previous results for the same quantity applicable at low and high temperatures, respectively. In addition, for the temperature range 160 GeV < T < 300 GeV, we have taken the opportunity to remove (phenomenologically) an unphysical dip that appeared in the previous high-temperature results in the regime k << T, M << T.

Before presenting the data it should be noted that, in the meanwhile, the results on this page have been generalized in a couple of respects. First, they have been generalized to include the dependence on lepton chemical potentials in 1703.06087. Second, they have been resolved into two separate helicity channels. For T > 130 GeV this was done in 1703.06087, whereas the case T < 130 GeV was discussed in 1703.06085. Numerical results corresponding to these generalizations can be found here.

Coming to the data, the file names indicate the value of the sterile neutrino Majorana mass M in GeV. In each case a grid of temperatures and momenta is considered. The columns of the files are:

1: T / GeV (203 values)
2: k / T (120 values)
3: ImΠR / T2 (full result)
4: ImΠR / T2 (direct 1+n <-> 2+n contribution)
5: ImΠR / T2 (direct 2 <-> 2 contribution)
6: ImΠR / T2 (indirect contribution)

We also tabulate the active neutrino interaction rate Γ, as shown in fig. 6(right). (Results for lower temperatures can be found here.) The columns are

1: T / GeV (146 values)
2: k / T (120 values)
3: Γ / T (full result)

The lepton number washout rate, normalized to the Hubble rate, is shown in fig. 11(right). The neutrino Yukawa couplings have been fixed to reproduce the solar neutrino mass difference (further details can be found in the paper). The energy density determining the Hubble rate was taken from here. The columns are

1: T / GeV (203 values)
2: γaa / H (full result)

Finally we list the lepton number susceptibility matrix and its inverse, determined in appendix A and illustrated in fig. 12. The coefficients parametrizing these quantities are defined in eqs. (A.1) and (A.2). The columns are

1: T / GeV (203 values)
2: a / T2
3: b / T2
4: c × T2
5: d × T2