Proposal for a Table of Evaluated Λ Binding Energies Patrick Achenbach U Mainz Nov. 2o19
Collecting Data from Nature A medieval European vision of The Review of Particle Physics God measuring the Universe detailing more than by an unknown painter ca. 1250 38,000 measurements ca. 2016 Proposal for a Table of Evaluated Λ Binding Energies Nov. 2o19 P Achenbach, U Mainz
Status Quo in Hypernuclear Physics • Different, not fully compatible, compilations of Λ binding energies exist • Masses, spins, excited states, and lifetimes even more scattered • Individual authors and experiments do averages, reviews and selections • Theoreticians sometimes work with only one set of experimental data • Is the community satisfied with the current data situation? • Is this community not interested in an evaluated table as a reference? • What is this community recommending in case of disputed values? The three wise monkeys at the Tōshō - gū shrine in Nikkō, Japan: Problem, "see no evil, which problem? hear no evil, speak no evil" Proposal for a Table of Evaluated Λ Binding Energies Nov. 2o19 P Achenbach, U Mainz
“I have a dream that one day… we hold these truths to be self-evident ”: • A Review provides averages, fits and best limits • It is regularly updated and published, and easily online available • The data are compiled data critically by groups of evaluators • Experiment contacts have verified the data entries • Ideograms show the contributions of measurements to averages • Scale factors are introduced in cases of likely underestimations of errors • For data in substantial conflict, error bars that range across the whole span of results are set, or no average at all is provided • Recommendations on inconsistent and unresolvable discrepant data are provided Proposal for a Table of Evaluated Λ Binding Energies Nov. 2o19 P Achenbach, U Mainz
Canonical Table(s) of Λ Binding Energies 170 keV [M. Jurič et al., Nucl. Phys. B 52 (1973) 1] Emulsion data available for different decay channels Combination of channels might be affected by different systematics Proposal for a Table of Evaluated Λ Binding Energies Nov. 2o19 P Achenbach, U Mainz
Hypertriton as an Example About 200 analyzed events from emulsion in total decay → π - + 3 He: B Λ = 70 ± 60 keV 3 H Λ 50 keV difference decay → π - + 1 H+ 2 H: B Λ = 120 ± 80 keV 3 H Λ Total: B Λ = 130 ± 50 keV [M. Juric et al. NP B52 (1973)] Proposal for a Table of Evaluated Λ Binding Energies Nov. 2o19 P Achenbach, U Mainz
Hypertriton as an Example Energy resolution about 1 – 2 MeV - - Events apparently Gaussian distributed What are the (quantitative and qualitative) limitations of the data? Proposal for a Table of Evaluated Λ Binding Energies Nov. 2o19 P Achenbach, U Mainz
Systematic Effects on Data Treatment [M. Jurič et al., Nucl. Phys. B 52 (1973) 1] Proposal for a Table of Evaluated Λ Binding Energies Nov. 2o19 P Achenbach, U Mainz
Canonical Table(s) of Λ Binding Energies [D. H. Davis, Nucl. Phys. A 754 (2005) 3c] A common systematic error has been estimated externally Cancelling of Λ mass dependence explicitly stated Proposal for a Table of Evaluated Λ Binding Energies Nov. 2o19 P Achenbach, U Mainz
Lesson from Frank Anscombe Calculations such as averages rest on assumptions about the behaviour of the data. Those assumptions may be false, and then the calculations may be misleading. We ought always to try to check whether the assumptions are reasonably correct; and if they are wrong we ought to be able to perceive in what ways they are wrong. [Frank Anscombe] It means one should ask, e.g., the following: • Are the statistical and systematic errors complete? • Are all errors symmetric? • Are all measurements normally distributed? • Were all used estimators unbiased and consistent? • Were outliers of values treated (discarded) consistently? Proposal for a Table of Evaluated Λ Binding Energies Nov. 2o19 P Achenbach, U Mainz
Canonical Table(s) of Λ Binding Energies [Nuclear Wallet Card, National Nuclear Data Center, BNL, 8th ed. (2011)] Properties of hypernuclei are presented as an appendix Format was too brief to go into details of the evaluation Not updated or revised since almost 10 years Proposal for a Table of Evaluated Λ Binding Energies Nov. 2o19 P Achenbach, U Mainz
Canonical Table(s) of Λ Binding Energies [E. Botta, T. Bressani, A. Feliciello, Nucl. Phys. A 960 (2017) 165] Tabulated values from different experiments and methods Correction applied for values which were considered biased No averages over values from different experiments Proposal for a Table of Evaluated Λ Binding Energies Nov. 2o19 P Achenbach, U Mainz
Canonical Table(s) of Λ Binding Energies [A. Gal, E. V. Hungerford, D. J. Millener, Rev. Mod. Phys. 88 (2016) 035004] Most recent and most complete review of experimental values Is it including all necessary information for the data? Proposal for a Table of Evaluated Λ Binding Energies Nov. 2o19 P Achenbach, U Mainz
Combination of Experimental Results Inclusion of correlations according to PDG procedure: Modified systematic errors for each measurement Treated as independent and averaged in standard way with other data p -value permits to infer mutual consistency Proposal for a Table of Evaluated Λ Binding Energies Nov. 2o19 P Achenbach, U Mainz
12 Λ C Emulsion Data Visualization can point to unidentified problems in the data: Sometimes data points lie apart from main body, other times data split into groups – Assuming statistical errors average of 10.76 ± 0.19 MeV from Davis and Pniewski and 10.80 ± 0.18 MeV from Dłuzewski et al. seem to be correct – Asymmetry with a longer tail and lower p -value of 0.39 for a summed χ2 = 5.2 and ndf = 5 are indications that average value is not very robust – Evidence of unreported systematic problems (Don Davis, John Millener) Proposal for a Table of Evaluated Λ Binding Energies Nov. 2o19 P Achenbach, U Mainz
Correction of ( π +,K+) data • Normalization of ( π +,K+) data to 12 Λ C emulsion value • Observed offset of ( π +,K+) data 7 L Li, 9 L Be, 10 L B, 13 L C to emulsion 7 L Li, 9 L Be, 12 L C , 13 L C, 16 L O to FINUDA [E. Botta, T. Bressani, A. Feliciello, NPA 960 (2017)] [T. Gogami et al., PRC 93 (2016)] Proposal for a Table of Evaluated Λ Binding Energies Nov. 2o19 P Achenbach, U Mainz
Recalibration of Emulsion Data [P. Liu, J. Chen, D. Keane, Z. Xu, Y Ma, arXiv:1908.03134] Authors claim that changes over the last decades of the assumed particle and nuclear masses, entering into the definition of the hypernuclear binding energies, are a plausible source of systematic errors in emulsion data Proposal for a Table of Evaluated Λ Binding Energies Nov. 2o19 P Achenbach, U Mainz
B Λ Independence on Λ Mass – In case that Λ mass is measured in emulsion a compensation of the dependence on its actual value is achieved by range-energy calibration – Other masses changed only marginally Proposal for a Table of Evaluated Λ Binding Energies Nov. 2o19 P Achenbach, U Mainz
Unanswered Questions in Hypernuclear Physics • Do we have a complete set of statistical and systematic errors? • Are all of the known errors symmetric? • Are all of the known measurements normally distributed? • Were all used estimators unbiased and consistent? • Were outliers of values treated (and discarded) consistently? • Which data have been superseded or excluded by later experiments? • Were cross-correlated errors considered for combined results? • Were likelihood functions used for combined results? • Which algorithms were used for treating inconsistent or discrepant data? Comprehensive, regularly updated, and systematic compilation needed PDG will not include hypernuclear data in the Review (to my knowledge) Proposal for a Table of Evaluated Λ Binding Energies Nov. 2o19 P Achenbach, U Mainz
Proposal to Achieve this Goal 1) Form an expert group of several evaluators from Germany, Italy, Japan, and the U.S. (and possibly other countries), 2) Prepare a commonly accepted table of re-evaluated hypernuclear data with a full assessment of input values, procedures, and uncertainties, especially systematic ones, 3) Publish in a special issue of Nuclear Physics A where all relevant issues can be listed and discussed in detail, 4) Make the published data online available with the National Nuclear Data Center at Brookhaven National Laboratory, 5) Repeat the process regularly after a few years or when new data are available. Proposal for a Table of Evaluated Λ Binding Energies Nov. 2o19 P Achenbach, U Mainz
Appendix: A Lesson on Data Visualisation from Frank Anscombe
Examples for Problems in Fitting Data Data sets which could be e.g. binding energies for different mass numbers: 1: 2: 3: 4: All 4 averages identical and all 4 variances nearly identical: All 4 data sets can be fitted with a linear dependence for B Λ on A : 1: 2: 3: 4: All 4 data sets were fitted well, considering the reduced χ 2 of exactly 1.0: Proposal for a Table of Evaluated Λ Binding Energies Nov. 2o19 P Achenbach, U Mainz
Frank Anscombe‘s Quartet All four sets are identical when examined using simple summary statistics Proposal for a Table of Evaluated Λ Binding Energies Nov. 2o19 P Achenbach, U Mainz
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