Upsilon Decay Angular Distribution Analysis

Primary Author: M. Jones

This web page provides a concise summary of the analysis.

Published in Phys. Rev. Letters 108, 151802 (2012).
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+μ- decays are described by the distribution
in the rest ϒ rest frame, previous experiments have only measured λθ as a function of ϒ transverse momentum in one reference frame, and significant polarization could be manifest by significantly non-zero values of λφ or λθφ even when λθ∼0[3]. The analysis described here is a new technique with which to study the angular distribution of muons in ϒ decay and is the first to provide information on all three coefficients, measured in multiple reference frames and to provide new tests that demonstrate a level of self-consistency.

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 pT>4 GeV/c identified in both the CMU and CMP systems (CMUP) in addition to an oppositely charged muon with pT>3 GeV/c found in either the CMU or the CMX muon systems. The figure on the left shows the fit which is used to determine the fraction of ϒ(nS) signal that is present in the displaced sample, while the figure on the right shows the prompt background scale factor function superimposed on the ratio of the prompt and displaced invariant mass distributions.


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.

The angular distribution of the background in both prompt and displaced samples has a common set of fitted parameters that are independent of the parameters that describe the ϒ(nS) decay angular distributions. The following figures show comparisons of the angular distributions for prompt and displaced muons in the range of di-muon invariant mass containing the ϒ(1S) signal.


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 λθ, λφ and λθφ 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 λθ and λφ parameters for the three ϒ states with 6<pT<8 GeV/c.


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

calculated in each reference frame for the three ϒ(nS) states as a function of pT. The following figure shows that there is generally good agreement. In most cases, the size of the discrepancy is found to be consistent with the sizes of deviations expected based purely on statistical fluctuations, which were calculated using a toy Monte Carlo.

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 λθφ and λθφ 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 pT 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+μ- decays at a hadron collider and for the first time have measured the spin alignment of the ϒ(3S) state. We find that angular distributions the ensemble of ϒ(nS) decays observed in proton anti-proton collisions at √1.96 TeV is generally consistent with being isotropic even at high values of transverse momentum. These preliminary results are consistent with the CDF Run I measurement [4] and inconsistent with a measurement using data from Run II by the D∅ collaboration[5]. A comparison of the ϒ(1S) parameter α≡λθ in the S-channel helicity frame with predictions from NRQCD[1], the kT factorization model[2] and with a partial NNLO calculation[6] is shown below.


[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).

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