1 / 20

Systematic Uncertainties in Double Ratio

Systematic Uncertainties in Double Ratio . Manuel Calderon de la Barca Sanchez. Signal PDF Background PDF Resolution. Current Systematic Uncertainties. Analysis Note, Section 9.5 http ://cms.cern.ch/iCMS/jsp/openfile.jsp?tp=draft&files=AN2011_062_v4.pdf. Signal PDF : Current Procedure.

jubal
Download Presentation

Systematic Uncertainties in Double Ratio

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Systematic Uncertainties in Double Ratio Manuel Calderon de la Barca Sanchez

  2. Signal PDF • Background PDF • Resolution Current Systematic Uncertainties Analysis Note, Section 9.5 http://cms.cern.ch/iCMS/jsp/openfile.jsp?tp=draft&files=AN2011_062_v4.pdf

  3. Signal PDF : Current Procedure • The mass resolution and CB-tail parameters are fixed in the nominal fit to their MC estimated values a= 1.6 and npow = 2.3. • When calculating the systematic, we change the fixed a and n parameters by a random amount using their covariance matrix. • This is repeated 500 times and the systematic error is taken as three times of the rms/mean.

  4. Background PDF : Current Procedure • The nominal background model is a second order polynomoinalthroughout the 8-14 GeVcc mass-fitting range. • As a variation, a linear model is employed in the restricted mass-fitting range 8-12 GeV/c2. • The difference in the fitted parameters is taken as a systematic. • When performing a simultaneous fit to both samples, the background parameters are allowed to float independently for both samples. • As a fit variation, these parameters are constrained to be the same.

  5. Resolution : Current Procedure • When varying input resolution, the fitter is very stable and robust for the ppsample. • But for the PbPb sample, there is a large fluctuation in the fit result. Since there isn’t enough statistics in data, we studied the HI MC to find out the resolution. • In the nominal case, the resolution is fixed to its MC value(0.092 MeV), which is consistent with the 7 TeVppmeasurement(0.096 MeV). • We vary it with 3 times of the error of the MC uncertainty (+/- 0.004 MeV) to study the systematic. (Note, these should probably be GeV) • For the 500 toy experiments, we fixed the resolution to different value with a gaussian function. • The mean is set to 0.092 and sigma equals to 0.004. • Thesystematic error is taken as the rms/mean of the toy experiments.

  6. Current Results • From: espace web page (Zhen’s page) • https://espace.cern.ch/cms-quarkonia/heavyion/new_systematic.aspx • R_2   = Y(2S) / Y(1S)   :   raw yields ratioR_23 = [Y(2S)+Y(1S)] / Y(1S)   :   raw yields ratio • Chi_2 = R_2(PbPb) / R_2(pp)  :  double ratioChi_23 = R_23(PbPb) / R_23(pp)  :double ratio

  7. Crystal Ball parameter variation • Top: • R23PbPb: 0.001185/0.256 = 0.46% • Bottom: • χ23. : 0.00088/0.3139 = 0.25% • Each has a different set of Crystal Ball parameters • Change in a and npow by random amount using their covariance matrix • Problem: • Size of variation is governed by MC statistics • Both a and npowvary independently for the 1S and for the 2S (and 3S). • This scheme says that the tails will be different for the different states! • We do not have any reason to expect that the crystal ball tails will differ amongst the states.

  8. s variation • Top plot: • R23PbPb: 0.009473/0.2435 = 3.9% • Bottom plot: • χ23. : 0.009698/0.3143 = 3.1% • Vary s = 92 MeV with 3 times of the error of the MC uncertainty (+/- 4MeV) to study the systematic • Problem: • Size of variation is governed by MC statistics • If s varies independently for the 1S, 2S, 3S states, we are saying that resolution is different. • Can the resolution of the 3S be better than the resolution of the 1S? No. But procedure allows it. • Variation of resolution should not be independent for the different states.

  9. Systematic Uncertainty issues • Signal PDF (CB parameters) and Resolution systematic uncertainties • rely on size of MC statistics • allow parameters to vary independently between states (?) • Note: not sure about this, but from looking at Zhen’s procedure, it seems like it does. • Can we do an improved estimate? • Should not depend on the MC statistics • Parameters (either of CB or the s of the mass resolution) should vary according to known physics • Example presented here: • Systematic Uncertainty in Resolution, s. • Variation in Signal PDF (CB parameters) is already a small effect, so will focus only on resolution here.

  10. Do single ratios depend on a fixed s? • Resolution governed by s • Gaussian std. deviation. • Choosing a different (fixed) s will • change yields. • will not change ratio, to first order • R2 = • s cancels in single ratio. • Only if s is different between states will this play a role for single ratios. • There is a variation, but it is not random: • Resolution parameter s increases linearly with pT. Hence it increases with mass. • We need a function s(m) to embody this dependence.

  11. Resolution indeed should not affect ratio • https://espace.cern.ch/cms-quarkonia/heavyion/lowEta.aspx • Left: floating sigma, 79 MeV. (2s+3s)/1s = 0.76, 2s/1s = 0.44 • Right: fixed sigma at 95 MeV. (2s+3s)/1s = 0.75, 2s/1s = 0.44 • (From Zhen’s page): we find that the resolution affects the yields but notaffect the yield ratio • Similar arguments will apply for the variation in the CB shape: it should affect yields but not ratio.

  12. Variation of Resolution with mass • Resolution at J/y mass: • 30 MeV, |y|<1.4 • 47 MeV, 1.4 < |y| < 2.4 • Guesstimate average ~ 36 ± 5 MeV • Resolution at ϒ mass: • 92 MeV (from MC) • 79 MeV • fit to pp data • 114 MeV • fit to PbPb data • Numbers from Zhen’s resolution page.

  13. Proposal: Use s(m) for systematic uncertainty estimate • Default case: • s(J/y) = 36, s(ϒ)=92 • s(ϒ) as in MC • Line Fit to blue points • pp Test case • s(J/y) = 41, s(ϒ)=79 • s(ϒ)as in fit to pp data • Line Fit to red points • PbPbTest case • s(J/y) = 31, s(ϒ)=114 • s(ϒ)as in fit to PbPbdata • Line Fit to green points • Compare ratios obtained from above test cases. • Variation in ratios between cases: systematic uncertainty • Here I do a quick estimate using Gaussians, I’m sure it can be improved.

  14. Single ratios in pp, with default s(m). • Default case, pp • Use 3 Gaussians (one for each state) • Amplitudes: 1s: 2s: 3s = 100 : 44 : 31 • Means : masses of each state • Sigmas (in MeV): 1s : 2s : 3s = 92 : 97.0 : 99.9 • Ratios: • 2s/1s = 0.464 • (2s+3s)/1s = 0.800 • Note: if sigmas were held constant (at any value), ratios would be exactly • 44/100 = 0.44 and • (44+31)/100 = 0.75. • Difference from 0.44 and 0.75 due to change in resolution as a function of mass, s(m) • Next, change slope of s(m)

  15. Systematic uncertainty on single ratio, pp case • Use fit to red points. • Sigmas (in MeV): 1s : 2s : 3s = 79 : 82.4 : 84.3 • Ratios for this case: • 2s/1s = 0.458 • (2s+3s)/1s = 0.790 • Single Ratios, pp: • Systematic Uncertainty • 2s/1s : (0.463-0.458)/0.463 • → 1.1% • (2s+3s) : (0.800-0.790)/0.800 • → 1.3%

  16. Single ratios in PbPb, with default s(m). • Default case, pp • Use 3 Gaussians (one for each state) • Amplitudes: 1s: 2s: 3s = 100 : 16.7 : 9.3 • Means : masses of each state • Sigmas (in MeV): 1s : 2s : 3s = 92 : 97.0 : 99.9 • Ratios: • 2s/1s = 0.1760 • (2s+3s)/1s = 0.2770 • Note: if sigmas were held constant (at any value), ratios would be exactly • 16.7/100 = 0.167 and • (16.7+9.3)/100 = 0.26. • Difference from 0.167 and 0.26 is due to change in resolution as a function of mass, s(m) • Next, change slope of s(m), using PbPb data

  17. Systematic uncertainty on single ratio, PbPb case • Use fit to green points. • Sigmas (in MeV): 1s : 2s : 3s = 114 : 121.3 : 125.7 • Ratios for this case: • 2s/1s = 0.1778 • (2s+3s)/1s = 0.2803 • Single Ratios PbPb : • Systematic Uncertainty • 2s/1s : (0.1778-0.176)/0.176 • → 1.0% • (2s+3s) : (0.2803-0.277)/0.277 • → 1.2%

  18. Systematic Uncertainty on Double Ratio • Default case: • Both pp and PbPbsigmas consistent with MC • Both vary as in fit to blue points. • Double ratio 1: 0.2770/0.8003 = 0.3461 • Systematic change: • pp sigma varies as in fit to pp data. • As in fit to red points. • PbPb sigma varies as in fit to PbPb data. • As in fit to green points. • Double ratio 2 : 0.2803/0.7897 = 0.3549 • Systematic Uncertainty: • (0.3549-0.3461)/0.3549 = 2.5%

  19. Advantages of this methd • Uncertainty estimate • Is data driven • Uses measured resolutions at J/y and ϒ mass. • Does not depend on the MC statistics. • Depends on two reasonable models of the variation of the resolution with mass. • One has identical variation in PbPb and pp • One has a different slope between PbPb and pp

  20. Uncertainty estimate • Does not depend on the MC statistics. • Depends on behavior of detector: variation of the resolution with mass. • Uses two reasonable test cases: • One has identical s(m) variation in PbPb and pp • One has a different slope for s(m) between PbPb and pp • One slope is from MC, the others are data-driven • Slopes are from measured resolutions at J/y and ϒ mass. Conclusion:Systematic Uncertainty on Double Ratiodue to Uncertainty in our knowledge of the mass resolution: 2.5%

More Related