I am fitting a model (very simple, just exponential + Gaussian) to data, in this model there is one nuisanceParameter included. This nuisanceParameter is constrained with N(0,1) Gaussian.
The funny thing is, no matter how I change the data yields, or how I change the initial error of the nuisanceParameter, the fitted error is always 7.04752e-01 (which is just sqrt(0.5) ). And I see “COVARIANCE MATRIX CALCULATED SUCCESSFULLY”
would anyone have some ideas? please look the attached log and workspace.

This is caused by the fact that the dependency of your model on your nuisance parameter is very weak.
If you compute the derivatives of your model at the minimum is what you get.
Looking at the model I see that the nuisance parameter (“lumi_2012”) enters in the model (apart from the constraints) in nsig_BSM_jj_jj. Now at the minimum this function has a value very close to zero, so there is no more dependency on the nuisance parameter.
Then you have two gaussian constraints on the nuisance parameters with sigma = 1 (I think you should have only one). For this reasons the error is sort(0.5).