publication . Article . Preprint . 2017

Modeling theoretical uncertainties in phenomenological analyses for particle physics

Valentin Niess; Sébastien Descotes-Genon; Jérôme Charles; Luiz Vale Silva;
Open Access
  • Published: 01 Apr 2017 Journal: The European Physical Journal C, volume 77 (issn: 1434-6044, eissn: 1434-6052, Copyright policy)
  • Publisher: Springer Science and Business Media LLC
  • Country: France
Abstract
International audience; The determination of the fundamental parameters of the Standard Model (and its extensions) is often limited by the presence of statistical and theoretical uncertainties. We present several models for the latter uncertainties (random, nuisance, external) in the frequentist framework, and we derive the corresponding p-values. In the case of the nuisance approach where theoretical uncertainties are modeled as biases, we highlight the important, but arbitrary, issue of the range of variation chosen for the bias parameters. We introduce the concept of adaptive p-value, which is obtained by adjusting the range of variation for the bias accordin...
Subjects
free text keywords: Physics and Astronomy (miscellaneous), Engineering (miscellaneous), [PHYS.HPHE]Physics [physics]/High Energy Physics - Phenomenology [hep-ph], Astrophysics, QB460-466, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798, High Energy Physics - Phenomenology, High Energy Physics - Experiment, Physics - Data Analysis, Statistics and Probability, Metrology, Frequentist inference, Flavour, Probability and statistics, Physics, Statistical physics, Standard Model, Quark
Funded by
EC| InvisiblesPlus
Project
InvisiblesPlus
InvisiblesPlus
  • Funder: European Commission (EC)
  • Project Code: 690575
  • Funding stream: H2020 | MSCA-RISE
,
EC| RBI-T-WINNING
Project
RBI-T-WINNING
Ruđer Bošković Institute: Twinning for a step forward of the Theoretical Physics Division
  • Funder: European Commission (EC)
  • Project Code: 692194
  • Funding stream: H2020 | CSA
,
EC| ELUSIVES
Project
ELUSIVES
The Elusives Enterprise: Asymmetries of the Invisible Universe
  • Funder: European Commission (EC)
  • Project Code: 674896
  • Funding stream: H2020 | MSCA-ITN-ETN
37 references, page 1 of 3

1 Statistics concepts for particle physics 3 1.1 p-values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.1 Data tting and data reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.2 Model tting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Likelihood-ratio test statistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Illustration of the approaches in the one-dimensional case 11 3.1 Situation of the problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 The random- approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.3 The nuisance- approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.4 The external- approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4 Comparison of the methods in the one-dimensional case 15 4.1 p-values and con dence intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.2 Signi cance thresholds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.3 Coverage properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.4 Conclusions of the uni-dimensional case . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5 Generalization to multi-dimensional cases 22 5.1 General formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.2 Averaging measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 5.2.1 Averaging two measurements and the choice of a hypervolume . . . . . . . . . 23 5.2.2 Averaging n measurements with biases in a hyperball . . . . . . . . . . . . . . 24 5.2.3 Averages with other approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.2.4 Other approaches in the literature . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.3 Global t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.3.1 Estimators and errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.4 Goodness-of- t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 5.5 Pull parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 5.6 Conclusions of the multi-dimensional case . . . . . . . . . . . . . . . . . . . . . . . . . 30

6 CKM-related examples 31 6.1 Averaging theory-dominated measurements . . . . . . . . . . . . . . . . . . . . . . . . 32 6.2 Averaging incompatible or barely compatible measurements . . . . . . . . . . . . . . . 36 6.3 Averaging quantities dominated by di erent types of uncertainties . . . . . . . . . . . 37 6.4 Global ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 A Singular covariance matrices 43 A.1 Inversion of the covariance matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 A.2 Choice of a generalised inverse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 A.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 A.3.1 Two measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 A.3.2 n fully correlated measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 47 A.3.3 Two fully correlated measurements with an uncorrelated measurement . . . . 48 A.4 Choice of the inverse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Significance (Gaussian units) 6 5 4 3 2 1 Significance (Gaussian units) 6 5 4 3 2 1 1 n

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