Υ Suppression in Hot and Cold Nuclear Matter at STAR or: Yield Extraction with Low Statistics

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Υ Suppression in Hot and Cold Nuclear Matter at STAR or: Yield Extraction with Low Statistics Anthony Kesich University of California, Davis

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Υ Suppression in Hot and Cold Nuclear Matter at STAR or: Yield Extraction with Low Statistics. Anthony Kesich University of California, Davis. Outline. Current Status Chi 2 Fitting Bias Correction Likelihood Fitting Composite Signals Mismatched line shapes The Future. - PowerPoint PPT Presentation

Transcript of Υ Suppression in Hot and Cold Nuclear Matter at STAR or: Yield Extraction with Low Statistics

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Υ Suppression in Hot and Cold Nuclear Matter at STARor:Yield Extraction with Low Statistics

Anthony KesichUniversity of California, Davis

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Outline

• Current Status• Chi2 Fitting• Bias Correction• Likelihood Fitting• Composite Signals• Mismatched line shapes• The Future

April 9, 2014

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Current status of Upsilon results

• Our paper was submitted in December• Now in referee stage• While responding, we found a critical

error• Now corrected. Back on publication

track• Let’s discuss fitting methods– Others can learn from my

mistake

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FITTING!So without further ado…

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Example : Yield from a Gaussian pdf• Suppose we are performing a counting experiment– Measuring a particle’s mass in the absence of

background• e.g. time of flight of anti-alpha particle in the STAR

detector– Distribution is Gaussian, with some mean mass

and width given by the detector resolution• For simplicity, assume we can make this into a Normal

Standard distribution– e.g. if the resolution is known, and if the mass of the alpha particle

is equal to the mass of the anti-alpha particle.– Suppose you want to obtain yield using a fit to the

data• How would you do it?

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Example : Continued

• One possibility– Construct a Gaussian pdf (2 parameters: m,

s)– Add one parameter as normalization

(counts)

• Is this a good way?

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Simple Extraction

• Signal only; no background• Signal is a simple Gaussian• Throw a known number, extract result from chi2 fit

– 0.1% errorApril 9, 2014

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Simple Extraction (lower statistics)

• Only 2% of previous sample• 5.6% error

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Simple Extraction (even lower statistics)

• 20% of previous sample• 10.5% error

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Least squares with binned data• Least squares: minimize c2 with

– assumes Poisson statistics, i.e.: mean = variance– here, l is PDF which we assume (hope?) is parent

distribution.• Modified least-squares method: minimize c2 with

– Easier computationally: use data, instead of assumed PDF– Can lead to problems if a bin contains no entries

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Adjustable normalization: careful!• If we add an arbitrary normalization:

– Here, n is the arbitrary normalization constant.• Suitably normalized, it can be used to estimate the yield.

– Minimizing c2 leads to an estimator of the normalization:• For least squares:

• For modified least squares:

– In our example of 1,000 events: N =944.2 +/- 30.9• What method do you think ROOT is using by default?

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…and this isn’t a fluctuation

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But it can be corrected (somewhat)

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• 1000 thrown per event• Yield corrected by adding chi2• 0.71% bias vs -5.8%

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Until you go back to low statistics

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• 200 thrown per event• Yield corrected by adding chi2• 8.6% bias vs -12.7% Not a huge improvement

– Empty-bin effect

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But really, just use Likelihood

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BUT THE WORLD ISN’T THAT SIMPLE

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Extracting yields from composite signals

• Signal is a Gaussian• Background is an exponentialApril 9, 2014

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Extracting yields from composite signals

• 1) Extraction via fit parameters• 2) Integrate data and subtract

background (green dashed curve)April 9, 2014

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Extracting yields from composite signals

• Extraction from fit outperforms subtraction

• But we know the lineshape here….April 9, 2014

300 thrown

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The Crystal Ball function

• Gaussian paired with power law• Models “lossy” functionsApril 9, 2014

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Chi2 vs Likelihood with incorrect line shapes

• Threw 300 events with a Crystal Ball function and fit it to a Gaussian

• Chi2 gets the shape right (somewhat)• Likelihood gets the yield rightApril 9, 2014

Chi2 Likelihood

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Still holds at high statistics

• Threw 50,000 events with a Crystal Ball function and fit it to a Gaussian

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Chi2 Likelihood

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Composite signals with incorrect line shapes

• Signal is Crystal Ball with exponential bkg

• Fit to Gaussian with exponential bkg April 9, 2014

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Composite signals with incorrect line shapes

• Signal is Crystal Ball with exponential bkg

• Fit to Gaussian with exponential bkg April 9, 2014

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Results of many “incorrect” fits

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Results of many “incorrect” fits

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</talk>

• STAR Upsilon results are in the publication process

• Chi2 fitting is biased at low statistics–Use likelihood.

• Be wary of line shape assumptions– Integrating data help remove biases

• Keep learning• Keep sharing

April 9, 2014