PLOTS THAT EXPLAIN THE TECHNIQUE FOR NUMU FROM PI
Copied from the other subpage :
Get the (X,Y) position by randomly shooting from the fit of a plane to the (X,Y) distribution of the event rates (flux*xsec).
See the plots at the bottom of the other subpage : that's the plane I used (lower right hand).
make one energy spectrum in a (small) region around the detector center(flux*xsec). Get (X,Y). Compute the off-axis value for (X,Y) (called theta). Draw E according to the center spectrum and correct the energy for the correct off axis angle value : E_final_ = E * theta_center / theta . The point is to avoid the binning in the top down plot... : we have 4 bins along the X axis, (2m each), the top down plot could not be done with smaller bins.
Energy profile obtained with this method (left, with 10,000,000 numus) and from JNUBEAM*NEUT(~500,000 numus) :
Difference of these 2 plots in sigmas ( left-right/sqrt(sigma_left2 + sigma_right_2)) : The X axis corresponds to the true X axis.
The differences do not exceed 3 sigma (fortunately). In some bins they are rather large, what does this mean ? I think it comes from the fact that we use a fit plane for the vertex etc. so we completely smoothe away the statistical fluctutations present in the standard plot (the variation is not always what it should be probably due to fluctuations ??). Is this a problem ?
Ratios : event rates obtained with this method / event rates directly obtained from JNUBEAM*NEUT Each plot correspond to 1 of the 16 bins in (x,y) along the (-400,+400) 2D square at 2KM. top right hand corner is bin (1,1) (centered on -300,-300). top left hand corner is bin (4,1) (centered on 300,-300) and bottom left hand corner is (4,4) (centered on 300,300).
there are differences especially around +400,+400 . Note that at the Water Cherenkov detector we will not use the 4 corner bins.
BINNED METHOD : (x,y) are shot according to the same pdf as above, but then the correct bin is chosen (among the 16 (x,y) bins) and the energy is shot according to the event rate spectrum in that bin.
Obviously this leads to excellent agreement provided we have enough stats otherwise the technique also breaks down (at low energy). The HE tail is reproduced almost exactly, but since we have low stats in the JNUBEAM output that means we perfectly reproduce those fluctuations... This is a drawback in all the methods.
