Large fit uncertainty from TFractionFitter

[LongHoa]

Dear Experts,

Recently I used TFractionFitter to do template fit.
The fit looks good by eyes. The status of the fit is “CONVERGED” but the uncertainty is ways larger than I expected.
What could possibly the reasons?
This is the fit plot:

And the fit log:

[Log_CrossSection/ExtractSignal/Bias/ZMASS_Binning/2016/Center/Fit/ele_barrel_00_postvfp.log]
target 298.693268
signal 285.265533
bkgrd 157.740311
 **********
 **   49 **SET PRINT           0
 **********
 **********
 **   50 **SET NOGRAD
 **********
 PARAMETER DEFINITIONS:
    NO.   NAME         VALUE      STEP SIZE      LIMITS
     1 frac0        5.00000e-01  1.00000e-02    0.00000e+00  9.90000e-01
     2 frac1        5.00000e-01  1.00000e-02    0.00000e+00  9.50000e-01
 **********
 **   51 **SET ERR         0.5
 **********
 **********
 **   52 **SET PRINT           0
 **********
 **********
 **   53 **SET STR           1
 **********
 **********
 **   54 **MIGRAD        1220        0.01
 **********
 MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
 FCN=-2020.91 FROM MIGRAD    STATUS=CONVERGED     115 CALLS         116 TOTAL
                     EDM=3.3694e-07    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  frac0        9.83530e-01   6.48374e-01   3.15513e-02  -1.74467e-05
   2  frac1        1.64668e-02   1.60617e-02   3.99552e-03  -4.48499e-03
                               ERR DEF= 0.5

Thank you very much,
Hoa.

[LongHoa]

I did investigate a bit more careful and I found that the statistics of the background in the observed spectrum is too low, thus it cause very large uncertainty in the background fraction.
But I still don’t know why it can lead to large uncertainty in signal fraction and how to fix it.

[moneta]

Hello,
The overestimation of errors is a known pitfall of TFractionFitter. See this note, https://arxiv.org/pdf/0803.2711.pdf, especially paragraph 4.

Best,

Lorenzo

[LongHoa]

Hello Lorenzo,

Thank you for your answer. I will read the paper you send.

Best,
Hoa.