Polarization of Upsilon(nS) at the Tevatron

Abstract

The polarization of inclusive Upsilon(nS) at the Fermilab Tevatron is calculated within the nonrelativistic QCD factorization framework. We use a recent determination of the NRQCD matrix elements from fitting the CDF data on bottomonium production from Run IB of the Tevatron. The result for the polarization of Upsilon(1S) integrated over the transverse momentum bin 8 < p_T < 20 GeV is consistent with a recent measurement by the CDF Collaboration. The transverse polarization of Upsilon(1S) is predicted to increase steadily for p_T greater than about 10 GeV. The Upsilon(2S) and Upsilon(3S) are predicted to have significantly larger transverse polarizations than Upsilon(1S).

Figures (3)

• Figure 1: Polarization variable $\alpha$ vs. $p_T$ at $\sqrt{s}=2.0$ TeV for inclusive $\Upsilon(1S)$ (shaded band). The curves are the central values for direct $\Upsilon(1S)$, $\Upsilon(1S)$ from $\Upsilon(2S)+\pi \pi$, and $\Upsilon(1S)$ from $\chi_b(1P)+\gamma$ or $\chi_b(2P)+\gamma$.
• Figure 2: Polarization variable $\alpha$ vs. $p_T$ at $\sqrt{s}=2.0$ TeV for inclusive $\Upsilon(2S)$ (shaded band). The curves are the central values for direct $\Upsilon(2S)$, $\Upsilon(2S)$ from $\Upsilon(3S)+\pi \pi$, and $\Upsilon(2S)$ from $\chi_b(2P)+\gamma$.
• Figure 3: Polarization variable $\alpha$ vs. $p_T$ at $\sqrt{s}=2.0$ TeV for $\Upsilon(3S)$ (shaded band). The curve is the central value.