systematic uncertainties in double ratio
Download
Skip this Video
Download Presentation
Systematic Uncertainties in Double Ratio

Loading in 2 Seconds...

play fullscreen
1 / 20

Systematic Uncertainties in Double Ratio - PowerPoint PPT Presentation


  • 76 Views
  • Uploaded on

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Systematic Uncertainties in Double Ratio' - jubal


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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
systematic uncertainties in double ratio

Systematic Uncertainties in Double Ratio

Manuel Calderon de la Barca Sanchez

current systematic uncertainties
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
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.
background pdf current procedure
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.
resolution current procedure
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.
current results
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
crystal ball parameter variation
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.
s variation
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.
systematic uncertainty issues
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.
do single ratios depend on a fixed s
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.
resolution indeed should not affect ratio
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.
variation of resolution with mass
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.
proposal use s m for systematic uncertainty estimate
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.
single ratios in pp with default s m
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)
systematic uncertainty on single ratio pp case
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%
single ratios in pbpb with default s m
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
systematic uncertainty on single ratio pbpb case
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%
systematic uncertainty on double r atio
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%
advantages of this methd
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
slide20
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%
ad