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

[Safinaz]

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 theoritical model ..

Bests.

 

[Orodruin]

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.