
MarkusMerschmeyer  08 May 2006
Inverse Slopes in Ni+Ni, 1.93 AGeV
This Wiki page is meant to give an overview over the calibration and analysis efforts undertaken in order to understand the particle
slopes in the Ni+Ni 2003 (S261) data and their deviation from our previous (Ni+Ni 1995) results.
FOPI History
Inverse slopes of
were extracted from
spectra for our Ni+Ni 1994/95 data by B.Hong and are published (
Phys.Rev.C57 or
PrePrint). The (NOT efficiencycorrected!) midrapidity slopes of those particles are given in the following picture (Click
here for a larger image):
The centrality dependence of the slopes at midrapidity is very weak as it is shown in the next picture (Click
here for a larger image) from the publication:
So the status of the slopes at that point was the following:
 : 115 6 MeV (high component)
 : 125 6 MeV
 : 139 7 MeV
The Problem
The whole problem started with a simple comparison of the proton slopes from the 1995 and 2003 Ni+Ni data (Click
here for a larger image).
Some things are easily visible from this plot:
 The acceptance range in rapidity is different for the two experiments: The 1995 data are valid from around target rapidity roughly up to midrapidity (1.4 < < 0.2) while the 2003 data range from target rapidity to beyond midrapidity (1.0 < < 0.2).
 For the slopes, it does not matter whether one uses the refitted or the freefitted CTRK banks.
 The Ni+Ni 2003 proton slopes at midrapidity are 30 MeV 'hotter' than in the Ni+Ni 1995 data.
Two possible causes for this difference in slopes were identified:
 The fact that in Ni+Ni 2003 a wrong footpoint resistor was used for the CDC which results in distortions of the drift field.
 The sense plane geometry was investigated by A. Chantelauze (LPC, ClermontFerrand) while modeling a CDC sector using Garfield; it was found that the sense wire positions used in 1995 AND 2003 did not correspond to the ones in the original blueprints of the CDC.
A certain range of
sense wire positions for different geometries is shown in the next picture (Click
here for a larger image).
The wire positions of 1995 (green circles), taken from an old rzFile (x119cdc.rz), and those of 2003 (black squares), calculated directly by our GEANT framework, are shifted by 2.5 mm with respect to each other. The new (and most probably correct) positions found by A. Chantelauze are given by the blue triangles. The wire positions represented by the red triangles were obtained by omitting a fudge factor called 'cdc_displace' in the subroutine 'wirpos' in our GEANT. This factor gives the magnitude of a displacement of the sense plane (orthogonal to the plane and relative to its anchor) in order to have the first potential wire at
. Without this displacement the red and blue triangles nearly coincide.
Finally, the new geometry using the wire positions given by the blue triangles was implemented into the simulation and into the calibration framework. The results of the work of A. Chantelauze can be found
here.
First Round of Test Calibrations
In order to investigate the effect of the change in wire geometry and to test the matrix correction method for the distorted drift field, a number of test calibrations was done by N. Herrmann in the first half of 2005. The results of that investigation (
slopes and
properties) are summarized under
TestCalibrationsS261 and some examples were presented during our collaboration meeting in Split in May 2005 (
CM Split Talk).
The following figure shows a comparison of proton and deuteron slopes for different geometries used in the calibration of the 2003 data (Click
here for a larger image).
For all sets of data, the refit CTRK tracks were used. The red squares denote the reference data (
y03e generation of 2003 data, 2003 geometry, shifted target position). The blue triangle, black circle and green triangle correspond to three calibrations of the
y03e type for the old (unshifted) target position applying the 2003 (blue,
y03e), the 1995 (black,
yo03e) and the new geomtery (green,
yn03e), respectively. It is clearly visible that the target position has no influence on the slopes. Going from the 2003 geometry to the one of 1995 or to the new one, decreases the proton slopes by 510 MeV, the deuteron slopes by 1530 MeV.
The comparison of proton and deuteron slopes for different calibration methods can be seen in the next figure (Click
here for a larger image).
The red squares and the blue triangles show the 1995 and 2003 data sets, respectivley. Using the new geometry already brings down the slopes by 1020 MeV (black circles). If, in addition, a matrix correction method (green triangles) is applied in order to account for the distorted drift field (which was also tested to deliver good properties for
and
), the proton and deuteron slopes roughly go back to the 1995 values.
To summarize these findings:
 The difference of the slopes between the 1995 data (drift field OK, old geometry) and the 2003 data (distorted drift field, 2003 geometry) is about 20 MeV for protons and about 30 MeV for deuterons.
 Investigating the effects of sense wire geometry shows that when going from the 2003 geometry to the new geometry, the protons slopes decrease by about 10 MeV, the deuteron slopes by about 15 MeV. Although the wire positions of the 1995 geometry and the new geometry are somewhat different, the slope difference between those geometries is less severe than between the 2003 and 1995 geometries.
 The influence of the distorted drift field in the CDC on the slopes is at least as high as the influence of the wire geometry. The matrix correction method can remedy the differences of the slopes. However, one has to be careful using it because of the influence on the and properties.
Second Round of Test Calibrations
After the Split collaboration meeting, it was clear that it was necessary to disentangle certain effects influencing the
slopes. Test Calibrations were generated for different target positions, different (standard) matrix correction methods for the drift field and for different nonlinearity corrections due to the distorions imduced by the wrong footpoint resistor. In addition, the properties of
(and
) in these calibrations were studied.
The results of this effort were presented during the December 2005 collaboration meeting (
Dec. 2005 Talk).
Calibration nomeclature (The name of the calibraton e.g. is
G05cp0cl203l; for a more detailed description, please ask N. Herrmann):
 G05 : calibration generation
 cp[x] : nonlinearity correction method (x=0 : none, x>0 : correction applied)
 cl[y] : matrix correction method (y=0 : none, y>0 : correction applied)
The slopes of protons and deuterons were compared for five criteria:
 Reproducibility for similar calibrations
 Reproducibility for different target positions
 Reproducibility for different sense wire geometries
 Reproducibility for different matrix correction methods
 Reproducibility for different drift field nonlinearity corrections
The comparison of similar calibrations is shown below (Click
here for a larger image).
The calibrations
v03e and
y03e (shifted target position) do not show a significant deviation concerning the slopes; it is less than 5 MeV.
The reproducibility of the slopes for different target positions (Click
here for a larger image)
also is very good. When going from the shifted target position (runs 18991919) to the nominal target position (runs 29482967), the slopes change by at maximum 5 MeV.
Using different sense wire geometries (
1994/95 ,
NEW and
2003 ) with the nominal target position gives quite different slopes as shown in the next figure (Click
here for a larger image).
At a rapidity
=0.2, the proton slopes are
130, 135 and
145 MeV, the deuteron slopes are
150, 165 and
185 MeV, respectively. This means that compared to 1994/95 the slopes for the new geometry slightly increase while compared to the 2003 geometry they decrease.
The effects of the target position and the matrix correction method are presented below (Click
here for a larger image).
Proton and deuteron slopes are shown
with and
without using the matrix correction (
with and
without for the nominal target position,
with and
without for the shifted target). Applying the matrix correction for the drift field increases the slopes by 510 MeV. This effects seems to be a little more pronounced around midrapidity.
The influence of the nonlinearity correction is extracted from the picture below (Click
here for a larger image).
The
red symbols denote the data from the calibration
without matrix and nonlinearity correction, the
blue symbols represent the calibration using the matrix correction and the
black symbols are the data from the calibration
with matrix and nonlinearity correction. It is obvious that (at least for particles of positive charge) the effects of matrix and nonlinearity correction cancel to some extent. Thus, using the present nonlinearity correction the
slopes are reduced by 510 MeV again.
The influence of the various calibration schemes on the
properties can be summarized as follows:
 similar calibrations (v03e, y03e) essentially give the same results; at this level of statistics no stronger statement is possible
 going from the nominal target position to the shifted position increases the raw yield by a factor 2
 the sense wire geometry does not seem to strongly affect the properties; at most there could be a very slight improvent when going to the new geometry
The effect of the matrix correction on the other hand is quite strong and shown below (Click
here for a larger image).
Without any matrix correction the background clearly dominates the invariant mass spectrum (left). Switching on that correction significantly improves the spectrum (middle). The additional nonlinearity correction does not seem to do much: Some more candidates are found, but apart from that the
properties degrade.
Summary of this part:
 It is in principle not possible to know the slopes with an accuracy of better than 5 MeV
 Current Slopes (for calibration G05cp0cl203l): ~1355 MeV, ~15010 MeV
 Even with all this corrections we do not have the same , quality like in v03e or y03e !
Last Round of Test Calibrations
With the bad run problem solved and the slopes of
and
converging towards acceptable values, nearly the complete statistics of Ni 2003 was recalibrated (4100 runs, generation
h05cp0). Looking at the total yield of
it was found that it increased by about 15%. However, their
distribution showed a doublepeak structure around midrapidity. In order to cure this, the first 400 runs of the Ni 2003 data were again calibrated with a slightly different procedure (generation
h06cp0). These results were presented during our collaboration meeting in April 2006 (
Apr. 2006 Talk).
Rapidity Shift  Charge Division Calibration
The midrapidity
spectra of
,
and
of the
v03e and
h06cp0 generations are presented in the following figure (Click
here for a larger image).
Rapidity distributions of the corresponding
slopes in 'v03e' and 'h06cp0' are displyed here (Click
here for a larger image):
The slopes found for
,
,
and
in
v03e and
h06cp0 are listed in the next table:

T [MeV] 

v03e 
h06cp0 

95 
105 

150 
130 

195 
165 

129 
125 
Unlike the primary particles which exhibit substantial variations of the slopes between the two generations, the
slopes seem to only weakly depend on the calibration method, probably also due to some cancellation effects between
and
(slope) properties.
The yield distribution of
in
h06cp0 worsened with respect to
v03e and is shown in the picture below (Click
here for a larger image).
The total
yield in
h06cp0 is about 20% higher with respect to
v03e. The rapidity distribution for
h06cp0 looks like it is shifted to the left. Thus, something in that calibration can not be correct, e.g. the polar angle, the
coordinates, ... This has to be investigated in more detail.
A comparison of normalized
,
and
distributions for
and
is plotted in the next figure (Click
here for a larger image).
The
black histograms contain the
v03e spectra, the others (
red for
,
blue for
) the respective
h06cp0 spectra. The polar angle (
) spectra indicate that the minimum angle is shifted by +23
in
h06cp0. The total momenta of the
are now peaked at lower values (probably due to the different sense wire geometry) while the effect is nearly absent for the
. Finally, the rapidity distributions show that, mainly as a result of the angular shift, the primary particles get shifted towards target rapidities (For a
with a total momentum of 0.6 GeV and a
of 3
the shift is as high as 0.08). Possible causes for this can be the calibration of
or the charge division. A look into the CPAR banks of the two generations reveals that the charge division (
Resist ) indeed is calibrated quite differently (Click
here for a larger image).
New Test Calibrations  Characterization of Particle Properties
As a result of the problems mentioned above, a series of test calibrations (generations
H06cp0cl2rf503l to
N06cp0cl2rf503l) were done having a
Resist value of 310 which is much closer to the
v03e value. All information concerning the particle properties of those calibrations can be found under the following link:
Test Calibrations April/May 2006.
The comparison of the rapidity and polar angle distributions of protons in the figure below (Click
here for a larger image)
shows that by using the new
Resist value, the new generations beyond
H06 again agree with
v03e. Looking at the midrapidity
spectra (next figure (Click
here for a larger image)) one clearly sees that the slopes of the protons from the freefit CTRK bank agree very well while those from the refit CTRK bank are different between
v03e (
y03e) and
I06 to
N06.
The difference is about 10 MeV (cf.
Test Calibrations April/May 2006) and the reason for this is unknown. In addition, the
distributions of the new generations are less narrow than those of
v03e or
y03e illustrated in the next figure (Click
here for a larger image).
The poroperties of
and
are best in the
L06 generation, therefore all further investigations were done on the basis of this generation.
Does the (x,y) Geometry of the Sense Wires affect the Proton Slopes?
In order to see whether the
positions of the sense wires do have any effect on the slope difference, the
L06cp0cl2rf503l generation was recalibrated with the Ni 1995 and Ni 2003
geometries. Thus, two new generations were generated:
L95cp0cl2rf503l and
L03cp0cl2rf503l. Indeed, the refit CTRK bank proton slopes of
L03 are back up to the
v03e values while now the freefit slopes do not have the same value but are 5 MeV higher. For
L95 the slope difference is still about 10 MeV plus an overall shift of about 4 MeV towards higher values. The
and
properties have not changed dramatically,
L03 is very similar to
L06,
L95 is somewhat worse (cf.
Test Calibrations April/May 2006).
Influence of the Matrix Correction of the Drift Field
The question whether the matrix correction method (
503l or
203l; ask Norbert about that) of the "normal" (not footpointresistor induced) drift field distortions affects particle properties, is quickly answered:
No and
Yes!
No because the proton (and deuteron) slopes are more or less insensitive to the methos applied. The only striking thing is that the
distribution of the protons is much more narrow for
503l than for
203l shown in the picture below (Click
here for a larger image).
Yes because the properties of
and
strongly depend on the approach (cf.
Test Calibrations April/May 2006). Thus it is clear that one has to use the
503l matrix correction method.
Influence of the Lorentz Angle
Finally, the dependence of particle properties on the Lorentz angle
was studied for the generations
O06 to
T06 and compared to
L06. The Lorentz angles used are listed in the following table:
Generation 
[] 
O06cp0cl2rf503l 
41.0 
R06cp0cl2rf503l 
41.3 
P06cp0cl2rf503l 
41.5 
S06cp0cl2rf503l 
41.7 
T06cp0cl2rf503l 
41.8 
L06cp0cl2rf503l 
42.0 
L03cp0cl2rf503l 
42.0 
Q06cp0cl2rf503l 
42.5 
L95cp0cl2rf503l 
42.6 
The optimum Lorentz angle seems to be around 41.5
, perhaps in the range from 41.3
to 41.7
. For this value, the slopes difference between refit and freefit CTRK particles is only 7 MeV for protons (instead of 10 MeV) and around 24 MeV for deuterons (instead of 3035 MeV!).
and
properties also look very promising for those angles (cf.
Test Calibrations April/May 2006).
As a concluding remark for this part one has to state that despite all efforts to understand the calibration and its effects on particle properties, there remains a difference between particle
inverse slopes extracted from the refit of freefit CTRK data. Furthermore, the quality of the reconstructed
and
which was found in
v03e has not been fully reached in all later calibrations! Unfortunately, the slopes found in that generations (
v03e) do not at all agree with the ones of Byungsik's publication of Ni 1994/1995 data (where the drift field was OK! (the effect of the different geometry is small!)).
Summary and Conclusions
Even the
P06cp0cl2rf503l calibration does not produce consistent slopes between the refit and freefit CTRK banks (which for example are fine in Al+Al 2006). However, it is a fair compromise and the systematic errors of the particle slopes have been studied in detail (see picutre below). Therefore, it was agreed to produce a final calibration of Ni 2003 according to this calibration scheme.
Epilogue: Final Slopes
A long series of systematic checks of the slope behavior under cuts on particle mass or momentum, variations of the fit range and the comparison of the results from the refit and freefit CTRK banks has been done. Now, systematic errors (grey boxes) are assigned to the particle slopes of Ni+Ni and Al+Al which are summarized in the following plot (Click
here for a larger image):
The
from Ni+Ni are from the
P06cp0cl2rf503l generation,
and
are from
v03e. In Al+Al everything was analysed for the
M03l generation. The systematic errors for
and
from Al+Al have not been analysed yet but it is expected that they are of the same magnitude those in Ni+Ni.