Measurements of the Angular Distributions of Muons from ${\rm Y}$ Decays in $p\overline{p}$ Collisions at $\sqrt{s}=1.96\mathrm{TeV}$

The angular distributions of muons from ${\rm Y}(1S,2S,3S)\to {\mu }^{+}{\mu }^{-}$ decays are measured using data from $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ corresponding to an integrated luminosity of $6.7{\mathrm{fb}}^{-1}$ and collected with the CDF II detector at the Fermilab Tevatron. This analysis is the first to report the full angular distributions as functions of transverse momentum $p_T$ for ${\rm Y}$ mesons in both the Collins-Soper and $s$-channel helicity frames. This is also the first measurement of the spin alignment of ${\rm Y}(3S)$ mesons. Within the kinematic range of ${\rm Y}$ rapidity $|y|<0.6$ and $p_T$ up to $40\mathrm{GeV}/c$, the angular distributions are found to be nearly isotropic.

Figure 1

Mass distribution of ${\mu }^{+}{\mu }^{-}$ candidates in the prompt (solid line) and displaced (dashed line) samples, with the ranges of invariant mass used to select the signal and sideband events indicated. Hatched regions indicate the three mass ranges containing the ${\rm Y}(nS)$ signals.

Figure 2

Comparisons of projected angular distributions measured in the Collins-Soper frame for prompt (histograms) and displaced (error bars) dimuon samples in the low-mass (a), (c) and high-mass (b), (d) sidebands for events recorded with the central-central trigger. Displaced samples are normalized to the number of events in the corresponding prompt samples. The $p$ value of the Kolmogorov-Smirnov statistic comparing each distribution is shown.

Figure 3

Examples of projections of angular variables measured in the Collins-Soper (a), (b) and the $s$-channel helicity (c), (d) frames for the range of invariant mass containing the ${\rm Y}(1S)$ signal with $4<p_T<6\mathrm{GeV}/c$ and recorded with the central-central trigger. The prompt sample is shown in black while the displaced sample is shown in grey. The distributions from collision data are shown with error bars and the results of the fits are indicated by the histograms.

Figure 4

Rotational invariant $\tilde{\lambda }$ as a function of $p_T({\rm Y})$ for the ${\rm Y}(1S)$, ${\rm Y}(2S)$, and ${\rm Y}(3S)$ states. Values of $\tilde{\lambda }$ calculated in the Collins-Soper frame are indicated by dark lines, while those calculated in the $s$-channel helicity frame are indicated by grey lines and are horizontally offset to slightly larger $p_T$ values for clarity.

Figure 5

Comparison of the ${\lambda }_{\theta }$ parameter measured for ${\rm Y}(1S)$ decays in the $s$-channel helicity frame (solid symbols) with previous measurements from the CDF [4] (open circles) and the D0 [18] (open triangles) experiments.