Matthew Jones Purdue University

Measurement of the ϒ(nS)μ+μ- Decay Angular DistributionQuestions from pre-blessing(part 3) http://www-cdf.fnal.gov/~mjones/internal/Upsilon.html Matthew Jones Purdue University B Production and Decay Meeting

http://www-cdf.fnal.gov/~mjones/internal/Upsilon.html B Production and Decay Meeting

Question #17 • This analysis uses |y|<0.6… • Other analyses used |y|<0.4 (Run I) or CMUP only. • Can differences in angular distributions be blamed on different rapidity coverage? • Repeat the |y|<0.6 analysis for |y|<0.4 • Look for significant differences in angular distributions and cross section. • Detailed comparison of angular distribution done only for ϒ(1S) state since this is what most other analyses have looked at. B Production and Decay Meeting

Question #17 • No evidence for significant variation of cross section with rapidity: |y(ϒ)|< 0.6 |y(ϒ)|< 0.4 B Production and Decay Meeting

Question #17 • No evidence for large systematic changes in angular distribution with smaller rapidity coverage. |y(ϒ)|< 0.4 |y(ϒ)|< 0.6 B Production and Decay Meeting

Question #18 • Remove constraints on physical parameters • Important because there are well documented errors in the Hessian matrix with bounded parameters. • Example: Dotted ellipses: one-sigma confidence intervals from covariance matrix. Solid curves: one-sigma confidence intervals from MINOS. Physical limits for λθ and λφ B Production and Decay Meeting

Question #18 • This improves the parabolic error estimate in most cases, but the low pT bins for the ϒ(3S) behave badly in the Collins-Soper frame: Some parameter values lead to negative weights which can’t be handled cleanly in the likelihood fit. This introduces “hard” limits in the parameter space. Why do these pT ranges behave worse than the others? B Production and Decay Meeting

Question #18 The background function (exponential or gamma function) does not describe the mass distribution near the ϒ(3S) peak. Related issue: when the prompt scale factor is a quadratic function, why does it peak in the middle of the invariant mass distribution? B Production and Decay Meeting

Question #18 • The prompt scale factor function shouldn’t know anything about the ϒ(nS) signals… it must be biased by inadequacies of the signal function (single Gaussian). • An important observation (from way back in June): ratio of prompt/displaced background is approximately constant. • A better procedure: • Simultaneous fit to prompt + displaced mass distribution • Displaced background function is exponential or gamma distribution • Prompt background is scaled by a linear function of mass • Only fit to the prompt sidebands, below the ϒ(1S) and above the ϒ(3S) B Production and Decay Meeting

Question #18 The prompt scale factor really should be a linear function... A quadratic is not required, nor is it justified. Candidates with 9<m(μ+μ-)<10.5 GeV/c2 in the prompt sample are excluded from the fit. Any peculiar features of the ϒ(nS) peaks cannot bias the fit. This strengthens the arguments for using the displaced sample as a proxy for the prompt background. B Production and Decay Meeting

Question #18 • How big is this effect? The worst case looks like this: Bias to the ϒ(1S) state is relatively small. Bias to the ϒ(2S) state is small, but significant in some pT bins. Bias to the ϒ(3S) state is large enough to push parameters to the boundary of the physical region in some pT bins. B Production and Decay Meeting

Question #19 • Resulting fits for the ϒ(3S) state: No special treatment needed to ensure that the parameters remain in the physical region. Some disagreement between CS and SH frames included in systematic uncertainties. B Production and Decay Meeting

Question #20 • Calculate uncertainties using MINOS • Asymmetric uncertainties now used in all tables and figures. λθ λφ λθφ B Production and Decay Meeting

Question #21 • Compare uncertainties from toy MC with fits to data. • Agreement is not perfect but that is not entirely surprising for a toy Monte Carlo. λθ λφ λθφ CS frame λθ λφ λθφ SH frame B Production and Decay Meeting

Question #11 B Production and Decay Meeting

Question #11 Previous comparison from September 20th Combination of MINOS uncertainties and linear prompt scale factor yields slightly better agreement with Note 10154. B Production and Decay Meeting

Question #11 • Is this really a problem? • Jim finds that this is not modeled well and it does induce an acceptance bias. • Difficult to quantify the effect without repeating the whole analysis. No σLxy cut With σLxy<0.25 mm Obvious structure from the silicon detector, asymmetric in Z. Efficiency does depend on cosθ B Production and Decay Meeting

Summary • This time I really think all questions have been addressed • Main conclusion from the analysis: • No strong polarization even at high pT even for the 3S state. • The polarization was not “hiding” in the CS frame. • Polarization does not seem to evolve rapidly with |y|. • Public web page almost ready: • http://www-cdf.fnal.gov/~mjones/internal/blessed/ • PRL draft given to godparents. B Production and Decay Meeting

Matthew Jones Purdue University