Douglas W. Higinbotham (Jefferson Lab) What do you get for the proton radius using 1963 data? a.k.a. Horrible Higinbotham’s HUGS Homework Douglas W. Higinbotham (Jefferson Lab) EXAMPLE CODES POSTED ON GITHUB: https://jeffersonlab.github.io/Example-Regression-Codes/

Let’s Make A Deal Behind Two of the Doors Are Goats … Behind One of the Doors Is The Prize!

Monty Hall Problem Door #1 Door #2 Door #3

Monty Hall Problem Door #1 Door #2 Door #3 Wrong Right Wrong

Monty Hall Problem Door #1 Door #2 Door #3 Wrong Right Wrong

Monty Hall Problem Door #1 Door #2 Door #3 Right! Wrong Wrong

Probability Says Switch Your human reaction is to stay with your original choice. I setup the problem before I even arrived today (i.e. you have 1/3 chance to pick correctly at the start) I systematically open one of the two remaining doors to show you a goat, so the remaining door has a 2/3 chance to be the winner! If you are still not convinced: https://en.wikipedia.org/wiki/Monty_Hall_problem

Proton Radius Puzzle There are currently only a few ways to determine the radius of the proton: Atomic Hydrogen Lamb Shift ( ~ 0.88 fm ) Muonic Hydrogen Lamb Shift ( ~ 0.84 fm) And of course elastic electron scattering! New measurements & checks coming PRad: electron scattering MUSE: electron and muon scattering NIST & other labs: Atomic Hydrogen Lamb Shift

Particle Data Group: 2017 Update All I know for sure is that the proton only has one radius . . .

Determining the Charge Radius of Carbon Stanford high Q2 data from I. Sick and J.S. McCarthy, Nucl. Phys. A150 (1970) 631. National Bureau of Standards (NBS) low Q2 data from L. Cardman et. al., Phys. Lett. B91 (1980) 203. See the L. Cardman’s paper for details of the carbon radius ( 2.46 fm ) analysis.

Electron Scattering Charge Radii from Nuclei Fourier Transformation of Ideal Charge Distributions. Example Plots Made By R. Evan McClellan (Jefferson Lab Postdoc) e.g. for Carbon: Stanford high Q2 data from I. Sick and J.S. McCarthy, Nucl. Phys. A150 (1970) 631. National Bureau of Standards low Q2 data from L. Cardman et. al., Phys. Lett. B91 (1980) 203.

Charge Radius of the Proton Proton GE has no measured minima and it is too light for the Fourier transformation to work in a model independent way. Thus for the proton we make use of the ideal that as Q2 goes to zero the charge radius is equal to the slope of GE We don’t measure to Q2 of zero, so this is going to be an extrapolation problem.

GE and GM Contributions To The Cross Section Plots by Ethan Buck (Jefferson Lab SULI Student and W&M undergraduate) Experiments like PRad (Hall B) go to small angle to maximize GE and minimize GM contribution.. Global fits, like typically done with the Mainz 2010 data, need several normalization, GE and GM

Don’t Blindly Fit! “An ever increasing amount of computational work is being relegated to computers, and often we almost blindly assume that the obtained results are correct.” - Simon Širca & Martin Horvat

Warning: Danger of Confirmation Bias In psychology and cognitive science, confirmation bias is a tendency to search for or interpret information in a way that confirms one's preconceptions, leading to statistical errors. i.e. if you start playing with enough data, long enough you can find whatever you radius you want

What did you get from the Hand data?! <0.82 fm (2 people) 0.82 – 0.86 fm (3 people) 0.86 – 0.90 fm (0) >0.90 fm (0) VARIOUS (3 people)

Frequentist or Bayesian Did you fix the intercept?! Frequentist – The experimental data only goes to one within errors so I let the end-point float. Bayesian – I know GE(Q2=0)=1 so I fixed the end-point.

Least Squares Fitting with EXCEL Let’s make sure we understand what exactly our fancy fitting codes are doing, by first doing something very simple by calculating sum of square residuals in a spread sheet.

Fitting with GNUPLOT Simon Sirca makes all the plots in the textbooks with GNUPLOT. A simple tool for making nice looking plots and can very easily fit the Hand data.

Multivariate Errors As per the particle data handbook, one should be using a co-variance matrix and calculating the probably content of the hyper-contour of the fit. Default setting of Minuit of “up”(often call Δχ2 is one. Also note standard Errors often underestimate true uncertainties. (manual of gnuplot fitting has an explicate warning about this) The Interpretation of Errors in Minuit (2004 by James) seal.cern.ch/documents/minuit/mnerror.pdf In ROOT: SetDefaultErrorDef(real #) Default is 1 and doesn’t change unless you change it!

Example plots from: http://data.library.virginia.edu/diagnostic-plots/ R Fits of the Hand Data Goto R example fits. Residual Normal Q-Q Leverage Scale-Location Example plots from: http://data.library.virginia.edu/diagnostic-plots/

Example plots from: http://data.library.virginia.edu/diagnostic-plots/ Example Residual Plot Example plots from: http://data.library.virginia.edu/diagnostic-plots/

Normally Distributed Data Normal Q-Q plots that is not linear usually mean your data have more or less extreme values than would be expected if they truly came from a Normal distribution. Example plots from: http://data.library.virginia.edu/diagnostic-plots/

Example plots from: http://data.library.virginia.edu/diagnostic-plots/ Leverage Plots ( are a few points driving the entire fit?! ) Data points with large residuals (outliners) may distort the outcome and accuracy of a regression. Cook's distance measures the effect of deleting a given observation. Example plots from: http://data.library.virginia.edu/diagnostic-plots/

Fitting Is Fun EXCEL GNUPLUT Python R Please at check the residuals of your fits and don’t just assume that because reduced chi2 is good you have a good fit. EXAMPLE CODES POSTED ON GITHUB: https://jeffersonlab.github.io/Example-Regression-Codes/