Measurement of the ${\rm Y}(1S)$, ${\rm Y}(2S)$, and ${\rm Y}(3S)$ Polarizations in $pp$ Collisions at $\sqrt{s}=7\mathrm{TeV}$

The polarizations of the ${\rm Y}(1S)$, ${\rm Y}(2S)$, and ${\rm Y}(3S)$ mesons are measured in proton-proton collisions at $\sqrt{s}=7\mathrm{TeV}$, using a data sample of ${\rm Y}(nS)\to {\mu }^{+}{\mu }^{-}$ decays collected by the CMS experiment, corresponding to an integrated luminosity of $4.9{\mathrm{fb}}^{-1}$. The dimuon decay angular distributions are analyzed in three different polarization frames. The polarization parameters ${\lambda }_{\vartheta }$, ${\lambda }_{\phi }$, and ${\lambda }_{\vartheta \phi }$, as well as the frame-invariant quantity $\tilde{\lambda }$, are presented as a function of the ${\rm Y}(nS)$ transverse momentum between 10 and 50 GeV, in the rapidity ranges $|y|<0.6$ and $0.6<|y|<1.2$. No evidence of large transverse or longitudinal polarizations is seen in the explored kinematic region.

Figure 1

Dimuon mass distributions in the ${\rm Y}$ region for $|y|<0.6$ (open squares) and $0.6<|y|<1.2$ (closed circles).

Figure 2

Two-dimensional projections of the PPD in the ${\lambda }_{\phi }$ vs ${\lambda }_{\vartheta }$ (a) and ${\lambda }_{\vartheta \phi }$ vs ${\lambda }_{\phi }$ (b) planes, for ${\rm Y}(1S)$ with $|y|<0.6$ and $30<p_{\mathrm{T}}<50\mathrm{GeV}$. The 68.3% and 99.7% CL contours are shown for the CS and HX frames. The shaded areas represent physically forbidden regions of parameter space [18].

Figure 3

Values of the ${\lambda }_{\vartheta }$ (top), ${\lambda }_{\phi }$ (middle), and ${\lambda }_{\vartheta \phi }$ (bottom) parameters for the ${\rm Y}(1S)$ (left), ${\rm Y}(2S)$ (middle), and ${\rm Y}(3S)$ (right), in the HX frame, as a function of the ${\rm Y}$ $p_{\mathrm{T}}$ for $|y|<0.6$. The error bars indicate the 68.3% CL interval when neglecting the systematic uncertainties. The three bands represent the 68.3%, 95.5%, and 99.7% CL intervals of the total uncertainties. The points are placed at the average $p_{\mathrm{T}}$ of each bin.

Figure 4

Values of $\tilde{\lambda }$ for the ${\rm Y}(1S)$, ${\rm Y}(2S)$, and ${\rm Y}(3S)$ states (left to right), in the HX, CS, and PX frames, for the $|y|<0.6$ (top) and $0.6<|y|<1.2$ (bottom) ranges. The bands and error bars have the same meaning as in the previous figure.