Also vailable as arXiv:1112.1591.

Here is a link to the public note.

A talk presented at the Fermilab Joint Experimental/Theoretical Seminar.

Over more than a decade, the description of heavy quarkonia production at hadron colliders has proved to be challenging. Models that were constructed to accommodate the surprisingly large production cross section of J/ψ and ϒ mesons also make specific predictions about their production polarization but are generally in poor agreement with experimental measurements[1, 2]. Discrepancies between results obtained by different experiments suggest that quarkonia might be strongly polarized when produced, but that different experimental acceptances limit the ability to formulate a complete picture. In fact, although the angular distribution of muons from ϒ→μ

**Analysis Overview**

We analyze 6.7 fb^{-1} of luminosity and reconstruct a total of 550,000 ϒ(1S),
150,000 ϒ(2S) and 76,000 ϒ(3S) meson decays to μ^{+}μ^{-}.
The angular distributions of those that have invariant mass near the ϒ(nS) resonances is
described using a model that contains two components:
the ϒ(nS) signal itself, and the background. The parameters that describe the angular distribution of
ϒ decays can be determined provided the amount of background and the angular distribution of
muons in the background can be constrained. We find that the background is dominated by muons from
b-decays which can be enhanced by requiring that one muon is displaced, that is, it has an impact parameter
inconsistent with production at the primary vertex. We verify that this sample has the same angular distribution
as the complimentary prompt sample by comparing their angular distributions in mass regions that do not contain
ϒ decays.

Furthermore, we observe that the shape of the background component of the di-muon invariant mass distribution is independent of whether a displaced muon is identified. Therefore, we constrain the amount of background in the prompt component by scaling the level of background observed in the displaced component by a linear function of mass which is constrained by a simultaneous fit to the displaced sample and the mass sidebands of the prompt sample. With the angular distribution of the background constrained by the displaced muon sample and the amount of background under the ϒ(nS) signals constrained by the prompt background scale scale factor, we then fit for the angular distribution of the ϒ(nS) component. This procedure may be preferable to extracting the angular distribution of the background from sidebands because there is evidence that the properties of muons produced in correlated B production evolves rapidly with invariant mass.

The following figure shows the di-muon invariant mass distribution obtained using two triggers, both requiring a
muon with _{T}>4 GeV/c_{T}>3 GeV/c

The following figures show that the fitted angular distribution of the continuum background can be simultaneously described in both the prompt muon and displaced muon samples. These compare projections of the fitted angular distributions to the observed distributions in the prompt and displaced muon samples in two ranges of invariant mass, one below the ϒ(1S) peak and the other above the ϒ(3S) peak.

**Results of the analysis**

The analysis of the ϒ(1S), ϒ(2S) and ϒ(3S) states is carried out independently by
selecting di-muon candidates with invariant mass in the range 9.25-9.65, 9.85-10.15 and 10.15-10.50 GeV/c,
respectively, and in several ranges of di-muon transverse momentum. The parameters λ_{θ},
λ_{φ} and λ_{θφ} are fit in both the Collins-Soper and in the S-channel
helicity frames. The following figure shows the one-sigma confidence intervals for the λ_{θ}
and λ_{φ} parameters for the three ϒ states with 6<p_{T}<8 GeV/c.

As a consistency check, we compare the value of the rotationally invariant quantity,

The residual small difference between λ-tilde measured in the two reference frames is used to
derive a systematic uncertainty on the measured values of λ_{θ},λ_{φ}
and λ_{θφ} which is very small in most cases, and at all times smaller than
the statistical uncertainty. The other sources of systematic uncertainty include the imprecise knowledge of
the parametrization of all trigger and reconstruction efficiencies, which were determined from the analysis of
J/ψ→μ^{+}μ^{-} and ϒ→μ^{+}μ^{-} control samples.
The finite size of the Monte Carlo samples used to calculate the acceptance contributes to the overall
uncertainty in the parameters derived from the fit which was evaluated by analyzing ensembles of toy Monte Carlo
samples that were generated using the same signal and background yields observed in each p_{T} range analyzed.
The following plots show the fitted parameters for the three ϒ(nS) states in both Collins-Soper
and S-channel helicity frames. The error bars show both the statistical and systematic uncertainties.

We have performed the first analysis of the full, three-dimensional angular distribution of ϒ(nS)→μ

**References**

[1] | E. Braaten and J. Lee,
Phys. Rev. D63, 071501(R) (2001) |

[2] | S.P. Baranov and N.P. Zotov, JETP Lett. 86, 435 (2007). |

[3] | P. Faccioli, C. Lourenco and J. Seixas,
Phys. Rev. D81, 111502(R) (2010). |

[4] | D. Acosta, et al. (CDF Collab.),
Phys. Rev. Lett. 88, 161802 (2002). |

[5] | V.M. Abazov, et al. (D∅ Collab.),
Phys. Rev. Lett. 101, 182004 (2008). |

[6] | P. Artoisenet, et al.,
Phys. Rev. Lett. 101, 152001 (2008). |

- Di-muon mass plot
- Un-polarized angular acceptance, Collins-Soper frame
- Un-polarized angular acceptance, S-Channel helicity frame
- Comparison of prompt/displaced background distributions
- Comparison of fits to background angular distribution
- Comparison of fits to ϒ(1S) signal angular distribution
- Examples of one-sigma confidence intervals on λ
_{θ}and λ_{φ} - Comparisons of the rotationally invariant quantity lambda-tilde
- Graphs and tables of λ
_{θ}, λ_{θφ}and λ_{θφ} - Angular distribution of the background
- Comparison with published results