Erratum to: Dark matter direct detection of a fermionic singlet at one loop

1 Erratum to: Eur. Phys. J. C https://doi.org/10.1140/epjc/s10052-018-5935-5

The complex phase of the Yukawa coupling $y_A$ has been erroneously set to zero in the code for Fig. 3a in [1]. The corrected figure is shown in Fig. 1. The Wilson coefficients $c^N_1$ change sign at about $m_\psi \simeq 225$ GeV and $c^N_{4,5,6}$ at $m_\psi \simeq 425$ GeV. In the Majorana dark matter (DM) case, all the Wilson coefficients are in the range $10^{-5}$–$10^{-4}$, except in the region of DM mass when a Wilson coefficient changes sign. No other results have been affected by this error.

Fig. 1

Dirac DM (top) and Majorana DM (bottom) with a vector-like fermion F of mass $m_F=600$ GeV and a scalar S of mass $m_S=500$ GeV. The Yukawa couplings are fixed to $y_V=1$ and $y_A=1.3\, e^{i\,1.4}$ and Higgs portal coupling $\lambda _{HS}=3$. The Wilson coefficients are evaluated for ${}^{132}_{54}\mathrm {Xe}$ at $E_R=8.59$ keV and are displayed in dimensionless units by rescaling with the square of the electroweak VEV $v=246.2$ GeV

We further want to clarify that the large enhancement of the differential rate for Dirac DM with a vector-like fermion in Fig. 4a in [1] is mainly due to the electric dipole moment $d_\psi$. The contribution from the magnetic dipole moment $\mu _\psi$ is large but subdominant, because the relevant non-relativistic operator $\mathcal {O}_5^N$ is suppressed by $\vec {v}_{\perp }$ compared to $\mathcal {O}_{11}^N$. The different spectral shapes in Fig. 4b in [1] are due to the absence of dipole moments for Majorana DM.