Precision measurement of the mass difference between light nuclei and anti-nuclei with the ALICE experiment at the LHC

We report on a measurement of the difference $\Delta \mu = \Delta (m / |z|)$ between the mass-over-charge ratio of deuteron (d) and anti-deuteron ($\overline{\rm d}$), and $^3{\rm He}$ and $^3{\overline{\rm He}}$ nuclei, carried out with ALICE (A Large Ion Collider Experiment) in Pb-Pb collisions at a centre-of-mass energy per nucleon pair $\sqrt{s_{\rm NN}}=~2.76~\rm{TeV}$. Our measurement yields ${\Delta \mu}_{\rm{d\bar{d}}}/{\mu}_{\rm{d}} = [0.9 \pm 0.5 (\rm{stat.}) \pm 1.4 (\rm{syst.})] \times 10^{-4}$ and ${\Delta \mu}_{\rm{^{3}He ^{3}\overline{He}}}/{\mu}_{\rm{^{3}He}} = [-1.2 \pm 0.9 (\rm{stat.}) \pm 1.0 (\rm{syst.})] \times 10^{-3}$. Combining these results with existing measurements of the masses of the (anti-)nucleons, the relative binding energy differences are extracted, ${\Delta \varepsilon}_{\rm{d\bar{d}}}/{\varepsilon}_{\rm{d}} = -0.04 \pm 0.05(\rm{stat.}) \pm 0.12(\rm{syst.})$ and ${\Delta \varepsilon}_{\rm{^{3}He ^{3}\overline{He}}}/{\varepsilon}_{\rm{^{3}He}} = 0.24 \pm 0.16(\rm{stat.}) \pm 0.18(\rm{syst.})$. These results test, to an unprecedented precision, the CPT invariance in the sector of light nuclei.