Better method? 06/14/06

It can be seen that the lowest Q2 deuterium and carbon nuclear transparency is obviously wrong. 

It seems that we need a new procedure to correcting for FSI.  Another idea may be to focus on the missmass distribution just below the 2pi threshold.
   carbon, lowest Q2.

One could use this region (where krel is large, and FSI effects are small) and shift SIMC until it matches the data in this region.  Then the FSI parameterization would need to make the low missmass SIMC distribution match the data.

However, I think that there are just too many unknowns with the low missmass data.  A cut should be used to select just the region shown in the plot above.  This is somewhat similar to the tight delta cut method that was used in the past.

I found that the missmass cut could be lowered to 11.25 for carbon at the lowest Q2.  The hsdelta distribution looks good, and there is still a small shift in mmx.  This shift is smaller than without the new missmass cut, and is similar to that seen with the fsi parameterization in the entry below. 



The transparency for carbon at the lowest Q2:

New parameterization 06/14/06

 

Revisit after new Pauli blocking prescription 06/14/06

After talking to Dipangkar, I started to search for an arbitrary parameterization of krel that would make the SIMC mmx, missmass and hsdelta distributions match the data.   I found a function that seemed to make the simc distributions match the data for carbon at the lowest Q2. 

As it says in the title, the black histograms are the data, the green histograms are SIMC without any normalization factor, and the red is SIMC with an arbitrary normalization so that one can compare the SIMC distribution to the data. 

The first thing to notice is that there is a small peak in the data at
missmass approx 11.2 GeV.  This kind of peak can easily be produced with
a Jost function approach.  However, the data peak is not positioned at
the threshold missmass,  which is where the Jost function peak is located.

It was extremely difficult to get the missmass distributions to match at
the same time that the mmx distributions matched.  I thought what is
shown in the plots was a good compromise.

The green histograms indicate the enhancement of the SIMC yield, and so
the carbon transparency at the lowest Q2 will decrease significantly.
While adjusting the parameterization, I tried to minimize this enhancement.

The parameterization for the fsi weight was a combination of two Jost
functions that were only a function of the relative momentum between the
recoiling neutron and the remaining nucleons.  I shifted the position of
the Jost function peaks by subtracting 100-200 MeV from the relative
momentum.  NB

Fitting the Jost function 04/27/06

Jost function using unradiated spectra 04/14/06

Jost function using unradiated spectra 04/13/06

Radiated missing mass 04/12/06

This is equivalent to the method using the "Vertex" variables.

I printed out the "Vertex" missing mass and the New "Orig" missing mass to the screen and ran simc.  The two values were the same for many screens of events.  I also checked plots of the two versions of the missmass.  When I superimposed these plots, they overlap.

My conlcusion is that there is no difference between the two approaches in calculating krel.  Either the vertex missmass or the New Orig missmass can be used.

Threshold events 04/11/06

The problem with events near threshold (missing mass of the two-neutron system close to 2*M_n) was described in 04/10/06, below.  This is a problem for the lowest Q^2 setting for deuterium.

The reason why events near threshold are being reconstructed at larger missing mass is due to the tail from radiation.  All of the plots below come from SIMC ntuples.

The first plot has acceptance cuts, includes the ntuple Weight variable, and a cut on the vertex missing mass abs([vertexmm]-1.89)<0.011.

So, these events have the vertex missing mass very close to threshold.

Using these cuts, I plotted the reconstructed missing mass.  The black hist is with all the physics included.  As you can see, there is the problem of events near threshold being reconstructed at larger missing mass.

The red hist has only the radiation turned off.

The light blue hist has radiation, decay, eloss, resolution turned off.  At this point, the reconstructed missing mass is the same as the vertex missing mass for all events.


The improvement across all missing mass with the radiation turned off can be seen in the panel below.  The first plot has all the physics, while the secon plot has only radiation turned off.

Investigation of the increased SIMC yield 04/10/06

As noted in the entry below (04/08/06), the SIMC yield for deuterium is very sensitive to the value of del, and the yield increased by a very large amount at the best value of del=1.4.  This will have a large impact on the transparency.

The panel below contains four plots from the SIMC ntuple for deuterium at Q2=1.1 GeV2.  There are no plots of experimental data.

At first I found out what is causing events with large Jost function weight.  This is shown in the first plot in the panel below.  The black points are the Jost function fsi weight vs. the reconstructed (nuclear) missing mass.  The red line is the Jost function fsi weight vs. the vertex missing mass.  The fsi weight becomes very large near the single pion threshold at 2*M_n because the Jost function weight approaches alpha**2/beta**2, which is greater than 400!  At the single pion threshold, krel=0, and the struck nucleon and spectator neutron has no relative momentum.

We can now see that the almost doubled simc yield across all the reconstructed missing mass is due to events that were near threshold at the vertex were reconstructed at larger missing mass (due to eloss and/or resolution).  I then attempted to find where these events were coming from, and this is shown in the remaining three plots in the panel. 

I made a cut to select a small reconstructed missing mass region (green area in the first plot).  These can be called the problematic events.  The good + problematic events were selected by extending the thin green area all the way down to the x axis.  In the remaining three plots, the red histograms are the problematic events, while the black is the good + problematic events.  "E missing" is E_beam - E_SOS - E_HMS.

The variables in these remaining three plots (E missing, t, and E missing vs. t) were the best variables I could find that showed a different distribution between the red and black histograms.  This does not really help explain where these problematic events come from, nor does it help us with a cut that we can apply to both the data and simc to remove these problematic events.



One more thing, below are plots of the reconstructed missing mass minus the vertex missing mass. The first plot shows the good+problematic events using the same cut, while the red histogram is just the problematic events.  This shows that events in this narrow region of the reconstructed missing mass has a positive slope after the peak.  The bottom plot is

Missing mass shifts using the Jost function 04/08/06

The weight applied event-by-event was (see Dave's thesis pg 155)
fsiweight=1.0 + del * ((A-1.0)**2) * (1.0/J**2 - 1.0)

The variable "del" was adjusted by hand until the missing mass peak in SIMC had the same shape as the data.  SIMC was given an arbitrary normalization when matching the peaks.  For deuterium, it was found that a value of del=1.4 provided a reasonable match at all kinematic settings.

In the panel below, the fitting for deuterium at Q^2 = 1.1 GeV^2 is shown.  Pauli blocking with the Fantoni occupation number was used for all SIMC plots.  In the top plot, the experimental data is shown in black and SIMC without the Jost function FSI, normalization or missing mass shifts is shown in green.  The same SIMC data except with an arbitrary normalization is shown in red.  The normalization is chosen to make the data and SIMC peaks around the same height, although its value is set by hand. 

In the bottom plot of the same panel, the Jost function FSI was turned on, and delta was adjusted until the red histogram matched the data.  For this fit, del = 1.4.  The green histogram, which is the SIMC data without the arbitrary normalization increased significantly.  This means that Yield_SIMC for deuterium at Q^2=1.1 GeV^2 is going to increase, and the transparency will go down.



The panels for all the

Corrected krel 04/06/06

	  krelx = vertex.Pmx + 1.5*pferx*pfer
	  krely = vertex.Pmy + 1.5*pfery*pfer
	  krelz = vertex.Pmz + 1.5*pferz*pfer

	  krelx = vertex.Pmx - 1.5*pferx*pfer
	  krely = vertex.Pmy - 1.5*pfery*pfer
	  krelz = vertex.Pmz - 1.5*pferz*pfer

krel 04/02/06

	if (doing_deutpi ) then
	  MM = sqrt(max(0.d0,vertex.Emiss**2-vertex.Pmiss**2))
	  krel = sqrt( max(0.d0,MM**2-4.*targ.Mrec_struck**2) )
	else if (doing_hepi ) then
	  MM = sqrt(max(0.d0,vertex.Emiss**2-vertex.Pmiss**2))
	  krelx = vertex.Pmx + 1.5*pferx*pfer
	  krely = vertex.Pmy + 1.5*pfery*pfer
	  krelz = vertex.Pmz + 1.5*pferz*pfer
	  krel = sqrt(krelx**2+krely**2+krelz**2)
	  if(vertex.Em.lt.6.0) krel = -krel
	endif
	ntup.krel = krel

krel = sqrt( max(0.d0,MM**2-4.*targ.Mrec_struck**2) )

when the target is deuterium.

However, when I plot ben_krel vs. krel for he-3 (top plot) and carbon (bottom plot), there is almost no correlation.  NB kreli is actually ntup.krel.

Jost function 04/01/06 (rev. 04/09/06)