Constraints on the ${\chi }_{c1}$ versus ${\chi }_{c2}$ Polarizations in Proton-Proton Collisions at $\sqrt{s}=8\mathrm{TeV}$

The polarizations of promptly produced ${\chi }_{c1}$ and ${\chi }_{c2}$ mesons are studied using data collected by the CMS experiment at the LHC, in proton-proton collisions at $\sqrt{s}=8\mathrm{TeV}$. The ${\chi }_c$ states are reconstructed via their radiative decays ${\chi }_c\to J/\psi \gamma$, with the photons being measured through conversions to $e^{+}{e}^{-}$, which allows the two states to be well resolved. The polarizations are measured in the helicity frame, through the analysis of the ${\chi }_{c2}$ to ${\chi }_{c1}$ yield ratio as a function of the polar or azimuthal angle of the positive muon emitted in the $J/\psi \to {\mu }^{+}{\mu }^{-}$ decay, in three bins of $J/\psi$ transverse momentum. While no differences are seen between the two states in terms of azimuthal decay angle distributions, they are observed to have significantly different polar anisotropies. The measurement favors a scenario where at least one of the two states is strongly polarized along the helicity quantization axis, in agreement with nonrelativistic quantum chromodynamics predictions. This is the first measurement of significantly polarized quarkonia produced at high transverse momentum.

Figure 1

Example of a fitted $J/\psi \gamma$ invariant mass distribution, for the $0.15<|\cos \vartheta |<0.225$ bin, in the 12–18 GeV $p_T$ bin. The vertical bars on the points indicate the statistical uncertainties. The lines show the various fit contributions.

Figure 2

The ${\chi }_{c2}/{\chi }_{c1}$ yield ratio vs $\phi$ (left) and $|\cos \vartheta |$ (right), for the three $J/\psi$ $p_T$ bins. The gray markers (slightly shifted horizontally) show the values before acceptance and efficiency corrections, scaled vertically for an easier shape comparison. The vertical bars represent the statistical uncertainties and the horizontal bars the bin widths. The solid and dashed curves show, respectively, the NRQCD [43] and unpolarized scenarios. The dotted and dash-dotted curves illustrate maximally different natural polarizations in the Collins-Soper frame, leading to large differences in azimuthal anisotropy.

Figure 3

Two-dimensional ${\lambda }_{\vartheta }^{{\chi }_{c2}}$ vs ${\lambda }_{\vartheta }^{{\chi }_{c1}}$ contours, at 68.3%, 95.5%, and 99.7% confidence levels (C.L.), measured combining the three $J/\psi$ $p_T$ bins. The physically allowed region (red rectangle) and six pure angular momentum configurations (markers) are also shown. The crossing of the two dashed lines represents the unpolarized case.

Figure 4

The ${\lambda }_{\vartheta }^{{\chi }_{c2}}$ values (circles) measured when the ${\lambda }_{\vartheta }^{{\chi }_{c1}}$ values (squares) are fixed to the unpolarized (left) or the NRQCD (right) scenarios (green curves), as a function of $p_T/M$ of the $J/\psi$. The purple band on the right is the NRQCD prediction for ${\lambda }_{\vartheta }^{{\chi }_{c2}}$ [43], while in the unpolarized scenario ${\lambda }_{\vartheta }^{{\chi }_{c2}}={\lambda }_{\vartheta }^{{\chi }_{c1}}=0$. The markers are shown at the average $p_T/M$ values in each bin, the vertical bars represent the total uncertainties, and the horizontal bars the bin widths. The dashed lines indicate the physically allowed range of ${\lambda }_{\vartheta }^{{\chi }_{c2}}$.