Erratum to: Electromagnetic dipole moments of charged baryons with bent crystals at the LHC

1 Erratum to: Eur. Phys. J. C (2017) 77:828 https://doi.org/10.1140/epjc/s10052-017-5400-x

In this Erratum, an improved simulation of the channeling efficiency of protons and antiprotons as a function of the particle momentum is shown in Fig. 1 for different configurations of $\mathrm{Si}$ crystals bent along the (110) plane. Multiple scattering with nuclei and inner shell electrons was not properly taken into account and it has been corrected using the simulation code CRYSTAL  [1], which is designed for simulations of trajectories of charged particles interacting with crystalline structures. The code solves the equation of motion for a charged particle interacting with the electric field generated by atomic strings or planes accounting for multiple scattering according to Refs.  [2, 3]. The code accounts for a wide variety of effects, namely multiple and single Coulomb scattering on nuclei and electrons, nuclear scattering, ionization losses, crystal geometry. and, for the case of leptons, emission of radiation. The model used in the code has been validated for electrons at sub-$\mathrm {\,Ge V}$ energy, for electrons and positrons at $20\mathrm {\,Ge V}$, for electrons and positrons at $120\mathrm {\,Ge V}$, as well as for protons at few hundreds of $\mathrm {\,Ge V}$ for crystals at room temperature.

The new distribution of the channeling efficiency for 7$\mathrm { \,cm}$ long and 14$\mathrm { \,mrad}$ bent $\mathrm{Si}$ crystal is significantly different from the previous version, presenting a maximum around 400 $\mathrm {\,Ge V}$ and going to zero at lower energies. This result has no impact on the rest of the paper, since channeling efficiency for ${\varLambda } ^+_{\mathrm {c}}$ baryons is simulated using a parameterisation based on current theoretical description and channeling measurements, following Ref.  [4].

In addition, a wrong plus and a wrong minus sign have been identified in Eqs. (5) and (7), respectively.

The corrected equations are reported below:

$$\begin{aligned} {\varvec{\Omega }}_\mathrm{EDM}= & {} \frac{d \mu _B}{\hslash }\left( \mathbf{E} -\frac{\gamma }{\gamma +1}({\varvec{\beta }}\cdot \mathbf{E}){\varvec{\beta }}+{\varvec{\beta }}\times \mathbf{B}\right) , \\ s_{x}\approx & {} s_0 \dfrac{d}{g-2} (1- \cos {\varPhi }). \\ \end{aligned}$$

It is worth it to note that Eqs. (7) and (8) of the paper apply for up- and down-bending crystals, with the bending angle $\theta _C$ taken negative and positive, respectively. The equations are in agreement with Ref.  [5] where an opposite sign convention is used for the bending angle $\theta _C$. The wrong sign errors have no impact on other results reported in the paper.

Fig. 1

Dependence of the channeling efficiency of protons and antiprotons with the particle momentum for 1 $\mathrm { \,mm}$, 1$\mathrm { \,cm}$ and 7$\mathrm { \,cm}$ long $\mathrm{Si}$ crystals bent along the (110) plane by a 0.1$\mathrm { \,mrad}$, 1$\mathrm { \,mrad}$, and 14$\mathrm { \,mrad}$ bending angle, respectively. The curves for the anti-proton interacting with the 1$\mathrm { \,cm}$ and 7$\mathrm { \,cm}$ long $\mathrm{Si}$ crystals are superimposed