NC background

Neutral current Background

On this page I will describe my study of the Neutral current background for the FNAL setup.
The goal is to explain discrepancies that I see when trying to reproduce the results of the FNAL group.

Test 1:
All my plots are normalize for 300Kton, 1MW beam, 5*1.7E7 sec/year, 1290km
My flux files are http://nwg.phy.bnl.gov/%7Ediwan/nwg/hst/ numuv14.hbk for test 1

Test 2:
For the test 2 , the flux file is http://www.phy.bnl.gov/~bishai/nwg/fluxes and the files is
wble120e250i002dr380dz1300km_12oa_flux.txt
Normalized for 300Kton, 1MW beam, 30E+20 POT and 1300km

Index:

My two method to compute background
Cross-checking using the two methods
Comparing with FNAL group (test 1) hbook file from October 2006
Comparing with FNAL group (test 2) hbook file from Mars 2007

I have two ways of building the NC background:

MC method:
I use the atmospheric superk MC and I reweight each events by (BNL flux/ SK flux).
That way I can apply our usual precuts to the MC and apply different likelihood efficiencies for different source of background.
You can see details of the normalization issues there.

Spectrum method:
In this case:

Multiply the numu flux by the numu NC cross-section (cross-section comes from Globes),
Multiply by precuts efficiency as a function of true energy
GO see note about precuts efficiency
Apply energy smearing (matrix of erec/vs etrue created with atm MC after precuts were applied)
Multiply by likelihood efficiency as a function of the reconstructed energy

And the normalization is the same as for the signal and is explained there.

Note about the precuts efficiency in the case of the spectrum method:
The precuts are: fully contained fiducial volume (FCFV) , e-like, 1 ring, no decay electron
The efficiency of the precuts was computed using the atmospheric SK Monte Carlo (FCMC sample). But the FCMC sample doesn't not contain NC elastic events which are not visible in a water Cherenkov detector. Therefore I need to know how many of those event there are, and change the precuts efficiency accordingly.
Using the Neut vectors(ALLMC sample), before reconstruction I can know the total number of NC events.

FCMC and ALLMC neutral current events inside fiducial volume
FCMC/ALLMC
And I need to multiply the precuts efficiency by the FCMC/ALLMC file.

Cross-checking using the two methods:
In order to check that those two methods are equivalent, I take the ratio of the two outputs in two different cases:

Case 1:
Is to check the normalization, so I try to go down to the simplest case.
MC method: use true energy, did not apply precuts (except FV cut), did not apply likelihood efficiency
Spec method: just look at flux*xsc, but nothing else.
And here are the plots:
outputs (Spectrum as a function of Etrue)
ratio

As you can see the plots agree fairly well.

Case 2:
This is to check that the overall methods are roughly equivalent so I apply everything as described above.
And here are the plots:
outputs (Spectrum as a function of Erec)
ratio

As you can see the plots agree very well, and show that the two methods are equivalent.

Note: If I do not correct by the ratio ALLMC/FCMC, here is what I got
outputs
ratio

Comparision with FNAL group results: Test 1

Now I want to compare my results with the one obtained by the FNAL group.
The spectrum that I am trying to reproduce is the total BG of the bottom plot of Fig.6 p.13 of hep-ph/0608023
They have: total number of BG events =566 evts
total number of beam nue BG =272 evts.

so number of NC events= 294 (I ignore numu CC at the moment)

I already showed (see there) that I can roughly reproduce the number of beam nue events, and I know that the other main cause of background is NC.

In order to make sure that my problem doesn't come from a normalization of the flux, I made sure that I can reproduce the numbers presented in (version14, which is the flux file that I used):
http://nwg.phy.bnl.gov/%7Ediwan/nwg/hst/evrates.txt
Note that those numbers are given at a distance of 2450km and mine are computed at 1290km, therefore you have to multiply those number by (2450^2/1290^2)=3.60 to compare them.
Here are the main one I will use: numuNC = 16908.83*3.6=60871

Note the numbers on the webpage are slightly different than the one shown in table3 of the more recent draft of the FNAL group, and I don't know why. For example
numu CC webpage = 51800*3.6=186'482 (corrected for distance)
numu CC draft = (300*5*1.7*5.2*120/28) *2.41 = 136'956 (using the normalization given in the draft but for 300kton)

Using the spectrum method, I will look at the plots for the NC background. There are 4 plots in each file and the total number of events is written on each plot.

1	2
3	4

plot 1 =numu flux* NC cross-section
plot2=plot1*precuts efficiency as a function of the true energy

(note the precuts efficiency must be multiply by ALLMC/FCMC to be correct)

plot3=plot2*energy smearing matrix
plot4=plot3* likelihood efficiency as a function a the reconstructed energy.

Here are the plot when I apply everything.
Here are the plots without the energy smearing applied.

Comments:

As you can see on plot1 of each file my total number of events is 63177, which is pretty close to the 60871 which was given above.
The effect of the energy smearing is extremely important.
My total number on plot 4 (with smearing) is very different (a factor of ~5 bigger) from the N=294 stated in hep-ph/0608023 even if my number of events on plot 1 agree pretty well.
When I use the MC method my total number of event in plot 4 is 1713.13 and the spectrum look like that. This is consistent with the 1411 I get on plot 4 this plot (with smearing case). (Note in that case I cannot produce the same 4 plots than with the spectrum method).

Finally when I use my NC BG to create the usual Event spectrum plots, here is what I get:

Spectrum method
MC method

Comparision with FNAL group results: Test 2

This is exactly the same work that the one done in test1, but for the more updated flux file.

The flux file is http://www.phy.bnl.gov/~bishai/nwg/fluxes and the files is
wble120e250i002dr380dz1300km_12oa_flux.txt
Normalized for 300Kton, 1MW beam, 30E+20 POT and 1300km

First here is my final event spectrum and here (local copy) is the FNAL group final event spectrum.
This is given for sin^2(2t13)=0.04 and 3 different delta phase.

Everything agrees reasonably well, except the NC background. I get 3 times more NC background.

Note: Here also I get very similar event spectrum whether I use the MC method to compute the background or the spectrum method.

Next I compared the efficiency tables:

FNAL	Fanny
Precuts (E true) chiaki_superk_eff.eps	Precuts (E true) (only for NC) and ALLMC/FCMC as explained before
Energy smearing ??	Energy smearing matrix
Likelihood (E rec) chiaki_dlh_eff.eps	Likelihood (E rec) (Only for NC)

And here are their effect in my case:

1	2
3	4

plot 1 =numu flux* NC cross-section
plot2=plot1*precuts efficiency as a function of the true energy

(note the precuts efficiency must be multiply by ALLMC/FCMC to be correct)

plot3=plot2*energy smearing matrix
plot4=plot3* likelihood efficiency as a function a the reconstructed energy.

Here are the plots: linear and log

Conclusions:

The precuts efficiencies agree fairly well.
I don't have the necessary file to compare the energy smearing
The likelihood efficiencies are different by a factor of 4
--> could that be the explanation??
In the talk given at Fermilab in September 2006, on p.31 Chiaki's efficiency was much consistent with mine.. what changed?