Measurement of the Polarization of the ${\rm Y}(1S)$ and ${\rm Y}(2S)$ States in $p\overline{p}$ Collisions at $\sqrt{s}=1.96\mathrm{TeV}$

We present a study of the polarization of the ${\rm Y}(1S)$ and ${\rm Y}(2S)$ states using a $1.3{\mathrm{fb}}^{-1}$ data sample collected by the D0 experiment in 2002–2006 during run II of the Fermilab Tevatron Collider. We measure the polarization parameter $\alpha =({\sigma }_T-2{\sigma }_L)/({\sigma }_T+2{\sigma }_L)$, where ${\sigma }_T$ and ${\sigma }_L$ are the transversely and longitudinally polarized components of the production cross section, as a function of the transverse momentum ($p_T^{{\rm Y}}$) for the ${\rm Y}(1S)$ and ${\rm Y}(2S)$. Significant $p_T^{{\rm Y}}$-dependent longitudinal polarization is observed for the ${\rm Y}(1S)$. A comparison with theoretical models is presented.

Figure 1

Signal extraction from the dimuon invariant mass distribution for events in the $0.4<|\cos {\theta }^{*}|<0.5$ region. (a), (c) $2<p_T^{{\rm Y}}<4\mathrm{GeV}/c$; (b), (d) $10<p_T^{{\rm Y}}<15\mathrm{GeV}/c$. Dashed curves are the combinatoric background.

Figure 2

Monte Carlo $|\cos {\theta }^{*}|$ distributions after all selection requirements for different $\alpha$ values: $-1$ (dashed histogram), 0 (solid histogram), and $+1$ (dotted histogram). (a) $0<p_T^{{\rm Y}}<1\mathrm{GeV}/c$, (b) $p_T^{{\rm Y}}>15\mathrm{GeV}/c$.

Figure 3

Comparison of data (points) and Monte Carlo (solid histogram) for ${\rm Y}(1S)$ with $2<p_T^{{\rm Y}}<4\mathrm{GeV}/c$: (a) momentum of ${\rm Y}(1S)$, (b) polar angle of ${\rm Y}(1S)$, (c) angle between muons, (d) $|\cos {\theta }^{*}|$.

Figure 4

Dependence of $\alpha$ on $p_T^{{\rm Y}}$ for inclusive ${\rm Y}(1S)$ candidates. Black circles are data. The band is the NRQCD prediction [15]. Curves are two limiting cases (see text) of the $k_t$-factorization model [11].

Figure 5

Dependence of $\alpha$ on $p_T^{{\rm Y}}$ for inclusive ${\rm Y}(2S)$ production. Circles are our data. The band is the NRQCD prediction [8].