-- 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 $m_t$ slopes in the Ni+Ni 2003 (S261) data and their deviation from our previous (Ni+Ni 1995) results.

FOPI History

Inverse slopes of $\pi^-,p,d$ were extracted from $m_t$ spectra for our Ni+Ni 1994/95 data by B.Hong and are published (Phys.Rev.C57 or Pre-Print). The (NOT efficiency-corrected!) mid-rapidity slopes of those particles are given in the following picture (Click here for a larger image):
B. Hong: pi-, proton and deuteron slopes in Ni+Ni, 1.93 AGeV (1994/5 data)

The centrality dependence of the slopes at mid-rapidity is very weak as it is shown in the next picture (Click here for a larger image) from the publication:
B. Hong: Centrality dependence of proton slopes in Ni+Ni, 1.93 AGeV (1994/5 data)

So the status of the slopes at that point was the following:
  • $T(\pi^-)$ : 115 $\pm$ 6 MeV (high-$m_t$ component)
  • $T(p)$ : 125 $\pm$ 6 MeV
  • $T(d)$ : 139 $\pm$ 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).
Proton slope comparison of Ni+Ni from 1995 and 2003 data

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 mid-rapidity (-1.4 < $y^0$ < -0.2) while the 2003 data range from target rapidity to beyond mid-rapidity (-1.0 < $y^0$ < 0.2).
  • For the slopes, it does not matter whether one uses the refitted or the free-fitted CTRK banks.
  • The Ni+Ni 2003 proton slopes at mid-rapidity 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 foot-point resistor was used for the CDC which results in distortions of the drift field.
  • The sense plane geometry was investigated by A. Chantelauze (LPC, Clermont-Ferrand) 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 $(x,y)$ sense wire positions for different geometries is shown in the next picture (Click here for a larger image).
Sense wire positions in the x-y plane for different geometries

The wire positions of 1995 (green circles), taken from an old rz-File (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 $y=0$. 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 ($p,d$ slopes and $\Lambda,K^0_S$ 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).
Comparison of proton and deuteron slopes for different geometries used in the calibration of the 2003 data

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 5-10 MeV, the deuteron slopes by 15-30 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).
Comparison of proton and deuteron slopes for different calibration methods

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 10-20 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 $\Lambda$ and $K^0_S$), the proton and deuteron slopes roughly go back to the 1995 values.

To summarize these findings:
  • The difference of the $m_t$ 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 $\Lambda$ and $K^0_S$ properties.

Second Round of Test Calibrations

After the Split collaboration meeting, it was clear that it was necessary to disentangle certain effects influencing the $m_t$ slopes. Test Calibrations were generated for different target positions, different (standard) matrix correction methods for the drift field and for different non-linearity corrections due to the distorions imduced by the wrong foot-point resistor. In addition, the properties of $\Lambda$ (and $K^0_S$) 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] : non-linearity 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 non-linearity corrections

The comparison of similar calibrations is shown below (Click here for a larger image).
Slope test: Reproducibility for similar calibrations
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)
Slope test: Reproducibility for different target positions
also is very good. When going from the shifted target position (runs 1899-1919) to the nominal target position (runs 2948-2967), 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).
Slope test: Reproducibility for different sense wire geometries
At a rapidity $y^0$=-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).
Slope test: Reproducibility for matrix correction method
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 5-10 MeV. This effects seems to be a little more pronounced around mid-rapidity.

The influence of the non-linearity correction is extracted from the picture below (Click here for a larger image).
Slope test: Reproducibility for drift field non-linearity correction
The red symbols denote the data from the calibration without matrix and non-linearity correction, the blue symbols represent the calibration using the matrix correction and the black symbols are the data from the calibration with matrix and non-linearity correction. It is obvious that (at least for particles of positive charge) the effects of matrix and non-linearity correction cancel to some extent. Thus, using the present non-linearity correction the $m_t$ slopes are reduced by 5-10 MeV again.

The influence of the various calibration schemes on the $\Lambda$ 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 $\Lambda$ yield by a factor 2
  • the sense wire geometry does not seem to strongly affect the $\Lambda$ 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).
Influence on Lambda invariant mass spectra by matrix and non-linearity corrections
Without any matrix correction the background clearly dominates the invariant mass spectrum (left). Switching on that correction significantly improves the spectrum (middle). The additional non-linearity correction does not seem to do much: Some more candidates are found, but apart from that the $\Lambda$ 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): $T(p)$~135$\pm$5 MeV, $T(d)$~150$\pm$10 MeV
  • Even with all this corrections we do not have the same $\Lambda$, $K^0_S$ quality like in v03e or y03e !

Last Round of Test Calibrations

With the bad run problem solved and the slopes of $p$ and $d$ converging towards acceptable values, nearly the complete statistics of Ni 2003 was re-calibrated (4100 runs, generation h05cp0). Looking at the total yield of $\Lambda$ it was found that it increased by about 15%. However, their $dN/dy$ distribution showed a double-peak structure around mid-rapidity. 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 mid-rapidity $m_t$ spectra of $\pi^-$, $p$ and $d$ of the v03e and h06cp0 generations are presented in the following figure (Click here for a larger image).
Slopes of pi-, protons and deuterons in the 'v03e' and 'h06cp0' calibrations

Rapidity distributions of the corresponding $\Lambda$ slopes in 'v03e' and 'h06cp0' are displyed here (Click here for a larger image):
Slopes of Lambdas in the 'v03e' and 'h06cp0' calibrations

The slopes found for $\pi^-$, $p$, $d$ and $\Lambda$ in v03e and h06cp0 are listed in the next table:
  T [MeV]
  v03e h06cp0
$\pi^-$ 95 105
$p$ 150 130
$d$ 195 165
$\Lambda$ 129 125
Unlike the primary particles which exhibit substantial variations of the slopes between the two generations, the $\Lambda$ slopes seem to only weakly depend on the calibration method, probably also due to some cancellation effects between $\pi^-$ and $p$ (slope) properties.

The yield distribution of $\Lambda$ in h06cp0 worsened with respect to v03e and is shown in the picture below (Click here for a larger image).
Lambda yield distributions in the 'v03e' and 'h06cp0' calibrations
The total $\Lambda$ 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 $z$ coordinates, ... This has to be investigated in more detail.

A comparison of normalized $\theta_{lab}$, $p_{lab}$ and $y_{lab}$ distributions for $p$ and $\pi^-$ is plotted in the next figure (Click here for a larger image).
Spectra of protons and pi- from Lambda decay
The black histograms contain the v03e spectra, the others ( red for $p$, blue for $\pi^-$) the respective h06cp0 spectra. The polar angle ($\theta_{lab}$) spectra indicate that the minimum angle is shifted by +2-3$^\circ$ in h06cp0. The total momenta of the $p$ are now peaked at lower values (probably due to the different sense wire geometry) while the effect is nearly absent for the $\pi^-$. Finally, the rapidity distributions show that, mainly as a result of the angular shift, the primary particles get shifted towards target rapidities (For a $p$ with a total momentum of 0.6 GeV and a $\Delta\theta$ of 3$^\circ$ the shift is as high as -0.08). Possible causes for this can be the calibration of $z_0$ 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).
Comparison of the CPAR Banks in 'v03e' and 'h06cp0'

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)
Comparison of Generations H06 to N06: Rapidity and Polar Angle of Protons

shows that by using the new Resist value, the new generations beyond H06 again agree with v03e. Looking at the mid-rapidity $m_t$ spectra (next figure (Click here for a larger image)) one clearly sees that the slopes of the protons from the free-fit CTRK bank agree very well while those from the refit CTRK bank are different between v03e (y03e) and I06 to N06.
Comparison of Generations H06 to N06: Slopes of refit and freefit CTRK Protons

The difference is about 10 MeV (cf. Test Calibrations April/May 2006) and the reason for this is unknown. In addition, the $d_0$ 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).
Comparison of Generations H06 to N06: d0 of Protons

The poroperties of $\Lambda$ and $K^0_S$ 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 $(x,y)$ 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 $(x,y)$ 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 $\Lambda$ and $K^0_S$ 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 footpoint-resistor 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 $z_0$ distribution of the protons is much more narrow for 503l than for 203l shown in the picture below (Click here for a larger image).
Comparison of the matrix correction methods: 503l versus 203l

Yes because the properties of $\Lambda$ and $K^0_S$ 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 $\alpha_L$ was studied for the generations O06 to T06 and compared to L06. The Lorentz angles used are listed in the following table:
Generation $\alpha_L$ [$^\circ$]
L06cp0cl2rf503l 42.0
L95cp0cl2rf503l 42.6
L03cp0cl2rf503l 42.0
O06cp0cl2rf503l 41.0
P06cp0cl2rf503l 41.5
Q06cp0cl2rf503l 42.5
R06cp0cl2rf503l 41.3
S06cp0cl2rf503l 41.7
T06cp0cl2rf503l 41.8

The optimum Lorentz angle seems to be around 41.5$^\circ$, perhaps in the range from 41.3$^\circ$ to 41.7$^\circ$. 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 30-35 MeV!). $\Lambda$ and $K^0_S$ 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 $m_t$ inverse slopes extracted from the refit of freefit CTRK data. Furthermore, the quality of the reconstructed $\Lambda$ and $K^0_S$ 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 free-fit 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):
Final slopes in Ni+Ni and Al+Al

The $\pi^-, p, d$ from Ni+Ni are from the P06cp0cl2rf503l generation, $\Lambda$ and $K^0_S$ are from v03e. In Al+Al everything was analysed for the M03l generation. The systematic errors for $\Lambda$ and $K^0_S$ from Al+Al have not been analysed yet but it is expected that they are of the same magnitude those in Ni+Ni.
Topic revision: r15 - 2006-07-18, MarkusMerschmeyer
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