Observation of the ${\chi }_{b1}(3P)$ and ${\chi }_{b2}(3P)$ and Measurement of their Masses

The ${\chi }_{b1}(3P)$ and ${\chi }_{b2}(3P)$ states are observed through their $\mathrm{\Upsilon }(3S)\gamma$ decays, using an event sample of proton-proton collisions collected by the CMS experiment at the CERN LHC. The data were collected at a center-of-mass energy of 13 TeV and correspond to an integrated luminosity of $80.0{\mathrm{fb}}^{-1}$. The $\mathrm{\Upsilon }(3S)$ mesons are identified through their dimuon decay channel, while the low-energy photons are detected after converting to $e^{+}{e}^{-}$ pairs in the silicon tracker, leading to a ${\chi }_b(3P)$ mass resolution of 2.2 MeV. This is the first time that the $J=1$ and 2 states are well resolved and their masses individually measured: $10513.42\pm 0.41(\text{stat})\pm 0.18(\text{syst})\mathrm{MeV}$ and $10524.02\pm 0.57(\text{stat})\pm 0.18(\text{syst})\mathrm{MeV}$; they are determined with respect to the world-average value of the $\mathrm{\Upsilon }(3S)$ mass, which has an uncertainty of 0.5 MeV. The mass splitting is measured to be $10.60\pm 0.64(\text{stat})\pm 0.17(\text{syst})\mathrm{MeV}$.

Figure 1

The dimuon invariant mass distribution, in two equidistant $|y|$ ranges. The midrapidity dimuons have a significantly better mass resolution.

Figure 2

The PES as a function of the measured photon energy, obtained using ${\chi }_{c1}\to J/\psi \gamma$ decays from the 2015–2016 (open circles) and 2017 (filled circles) data samples. The points are drawn at the average $E_{\gamma }$ in each bin. The curve represents the parametrization mentioned in the text.

Figure 3

The invariant mass distributions of the ${\chi }_{bJ}\to \mathrm{\Upsilon }(nS)\gamma$ candidates ($n=1$, 2, 3), after the PES correction. The inset shows the ${\chi }_{b1}(1P)$ and ${\chi }_{b1}(2P)$ masses fitted before (open squares) and after (filled circles) the PES correction, with vertical bars representing the statistical uncertainties. The world-average values [33] are shown by the horizontal bands, with dashed lines representing their total uncertainties.

Figure 4

The invariant mass distribution of the ${\chi }_{bJ}(3P)\to \mathrm{\Upsilon }(3S)\gamma$ candidates. The vertical bars are the statistical uncertainties. The curves represent the fitted contributions of the two signal peaks, the background, and their sum.