What Are Sigma Regions for Observable R(D) in Theoretical Models?

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SUMMARY

The discussion focuses on the concept of sigma regions, specifically the 1σ and 2σ regions for the observable R(D) in theoretical models. It clarifies that standard deviations relate to experimental precision rather than being derived from theoretical models. A parameter set within the 1σ region indicates that the results fall within the 68% least extreme outcomes, while those outside are considered among the 32% most extreme and are thus rejected at the 1σ confidence level. Understanding these regions is crucial for interpreting experimental results in the context of theoretical predictions.

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Safinaz
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Hi all,

I'd like to understand what does it mean by allowed 1 or 2 ## \sigma ## regions for some observable, like R(D) in Fig. 1 left [ 1206.2634v2] ?

And how can I calculate or plot this value or region according to any theoretical model ..

Bests.
 
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Standard deviations have to do with experimental precision. It is not something you derive from the theoretical model.

If a parameter set is within the ##1\sigma## region, it means that if reality is described by the theory and with those particular parameter values, then the result is within the 68% least extreme outcomes you could have found in the experiment. For all parameter sets outside of the allowed ##1\sigma## region, the results are among the 32% most extreme results given those parameters and the parameter set is rejected at ##1\sigma## (or "at the 68% confidence level").

Footnote: This naturally requires you to define what you mean by an outcome being extreme.
 

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