This web page provides a summary of the measurement of polarization of Upsilon(1S) mesons. This measurement provides a test for NRQCD, which predicts a transverse polarization at high pT.

This measurement was performed using 2.9 fb^{-1} of data. We utilize a template method wherein fully transverse and fully longitudinal Monte Carlo samples are generated and subjected to detector acceptance and efficiency effects to form templates. Monte Carlo is iteratively re-weighted to match data pT distributions. Based on the shapes of the polar angle distributions of the positive muon in the s-channel helicity frame, we determine a polarization parameter by matching a polarization-weighted combination of templates to data in each of eight Upsilon pT bins. Events are selected using a mass fit, and backgrounds are evaluated using mass sidebands.

We find that the Upsilons are unpolarized at low pT before developing strongly-longitudinal characteristics at high-pT, in contrast with the NRQCD prediction. The results are shown below, represented by the parameter alpha which has possible values ranging from -1 (fully longitudinal) to 1 (fully transverse). The parameter eta in the table is the fraction of longitudinally-polarized events.

The analysis is discussed in detail in CDF public note 9966.

Figure 1: Mass histogram showing all three Upsilon peaks and their separation. (eps), (jpg)

Figure 2: Mass histograms for Y(1S) in pT bins including fits from which the exponential background shapes were determined. (eps), (jpg)

Figure 3: Cos(theta*) histogram including data (green), T (red) and L (blue) templates, and the best fit (black) for the first Y(1S) pT bin (2-3 GeV/c). (eps), (jpg)

Figure 4: Cos(theta*) histogram including data (green), T (red) and L (blue) templates, and the best fit (black) for the second Y(1S) pT bin (3-4 GeV/c). (eps), (jpg)

Figure 5: Cos(theta*) histogram including data (green), T (red) and L (blue) templates, and the best fit (black) for the third Y(1S) pT bin (4-6 GeV/c). (eps), (jpg)

Figure 6: Cos(theta*) histogram including data (green), T (red) and L (blue) templates, and the best fit (black) for the fourth Y(1S) pT bin (6-8 GeV/c). (eps), (jpg)

Figure 7: Cos(theta*) histogram including data (green), T (red) and L (blue) templates, and the best fit (black) for the fifth Y(1S) pT bin (8-12 GeV/c). (eps), (jpg)

Figure 8: Cos(theta*) histogram including data (green), T (red) and L (blue) templates, and the best fit (black) for the sixth Y(1S) pT bin (12-17 GeV/c). (eps), (jpg)

Figure 9: Cos(theta*) histogram including data (green), T (red) and L (blue) templates, and the best fit (black) for the seventh Y(1S) pT bin (17-23 GeV/c). (eps), (jpg)

Figure 10: Cos(theta*) histogram including data (green), T (red) and L (blue) templates, and the best fit (black) for the eighth Y(1S) pT bin (23-40 GeV/c). (eps), (jpg)

Figure 11: Measured polarizations (alpha) compared with D0 results (from PRL 101 182004). (eps), (jpg)

Figure 12: Measured polarizations (alpha) compared with CDF Run I results (from PRL 88 161802). (eps), (jpg)

Figure 13: Measured polarizations (alpha) compared with NRQCD predictions (from Braaten & Lee, PRD 63 071501).(eps), (jpg)

Figure 14: Table of results. (ps), (jpg)

Figure 15: Y(1S) background cos(theta*) distributions in each pT bin. (eps), (jpg)

Figure 16: Y(1S) cos(theta*) distributions (red) compared to unpolarized MC (black) in the four lowest-pT bins, where ~zero polarization is measured. (eps), (jpg)