1. Introduction

The Material Balance is an important characteristic of the detector and it is important to have a handle on it, as well as to have an accurate description of the detector geometry, which allows the user to study teh effect of the material distribution on the physics observables. Below we consider the following STAR subsystems, from the standpoint of the material balance:

• Silicon Vertex Tracker (the SVT)
• Time Projection Chamber (the TPC)
• TPC and SVT Contributions to the Material Balance

2. The SVT Geometry Description Updates

2a. History

During the updates of the STAR geometry description in 2003 and 2004, it became clear that a significant amount of material was not included in the original (dating back to 1995) version of the geometry code. In particular, this is true for the cabling and support structures of the SVT.

In addition, the first simulation run of 2004 (geo tag Y2004) featured an incomplete description of the SSD (still in development at this point in time), which however was then corrected by the SSD group.

2b. Extra material in the central part and the rim of the SVT barrel

The experimental data on photon conversions in the STAR detector, when compared to the Monte Carlo results, indicated the presence of "extra material" in the real detector, unaccounted for in the then current GEANT model.

The direct deconvolution of the "extra material" map from such studies, although tempting, is not feasible due to large systematic errors which become obvious when one takes a closer look at the problem. It was decided that instead we use these data as indicators of where to look in the physical detector (complete with all sort od technical documentations, pictured etc), in order to add the rigth materials in the right locations. The following elements were identified, that were previously omitted from the model:

• G10 printed circuit boards on each end of each ladder
• Copper cables (high and low voltage) feeding the ladders
• Plastic tubes feeding the coolant from the manifold to the SVT structure, and water contained therein
• The outer shielding which features the support "cage" made of carbon composite tubes
• The main carbon support struts which were originally described as made of Beryllium and had incorrect cross section

All of this has been added or corrected in the new version of the SVT geometry description file, svttgeo2.g. This was activated in the version Y2003B of the STAR geometry. As a reminder, Y2003A is a version which contains mainly bug corrections, whereas Y2003B has the aforementioned SVT improvements, plus additions in endcap calorimeter (to be done), Photon Multiplicity Detector, the FPD and other changes as well.

There is a newer version of the svttgeo2.g code, named svttgeo3.g in which the Silicon Strip Detector part has been factored out in a separate piece of code, "pams/geometry/sisdgeo".

In order to verify the effect of the aforementioned changes, there have been simluations run with Y2003A ("old" SVT) and Y2003B ("new" SVT) geometries. As a rough metrics, plots were produced of the radiation length accrued by geantinos propagating in the detector, as a function of rapidity. It should be noted that this is more of a demonstration of principle and the physics implications may or may not be significant depending on the nature of study in question (the effects might be felt outside the apparent rapidity range covered by the added material)

2c. Extra material in the support cones of the SVT structure

Due to increased interest in the precision of the new tracking algorithm, more attention has been paid to the distribution of material in other elements of the detector. In particular, it has come to light that the actual mass of the SVT detector as reported by the engineers, differs significantly from our calcualtions based on the GEANT model. It was suspected that in fact the peripheral elements such as cables and other structures mounted on the carbon fiber support cones, can provide a substantial contribution to the detector mass,

The model of the feedout cables in the model of the SVT prior to the year 2005 assumed that copper is wrapped around the shape of the carbon cone, as a thin layer. This approximation in itself is probably sufficient to model the scattering and photon conversion effects, however the exact knowledge of the mass involved is important.

As a note, the volume of a cone with radii "R₁" and "R₂", and height "h", is given by a formula: 1/3*Pi*h*(R₁²+R₁R₂+R₂²). In case of a thin conical shell, its volume can also be written as Pi*d*h*(R₁+R₂), where "d" is the thickness of the shell.

The pre-2005 model of the detector featured a total volume of approximately 900 cm**3 of copper on each of the support cones. The total mass of copper in that part of the SVT structure (both sides) is then approximately 17kg. This is way below what the engineers have estimated and the precise weight needs to be determined.

News: On Jan.28,2005 Dave Lynn weighed the cables, which yielded the following data:
LV Cable 1.24 pounds, HV Cable 0.78 pounds, Signal Cable 0.36 pounds

There are 36 each, on either end of the cones. This in fact means a total weight of 74 kilos, which is significantly larger than the pre-2005GEANT model describes and more in line with previous numbers reported by the SVT crew during installation of the detector.

3. Geometry variations in 2004

3.1 Rad Length vs eta

Let's take a look at the radiation length vs eta plots, for the tags Y2004 and Y2004C and thei ratio:

Ratio of Y2004C and Y2004

The "problem area", whereby we trace the lines corresponding to eta=1.2 and eta=1.6, is depicted below. Please note that the scale is drawn in units equal to 2 cm.

It is obvious from the above plot that due to the finite size of the diamond, which is rather comparable to the size of the structures we are looking at, the excess material can appear in the rapidity bins much more central than 1.2 or 1.6, for the events further away from Z=0.

3.2 Binning in Z

To quantify that, we have repeated the above study, using the 5 cm bins in Z. As a result, we have 4 bins at Z=(15..20),( 20..25),(25..30) and (30..35) cm. Here are plots for the both the absolute rad length (upper plot for the 4 bins) and the ratio of Y2004C/Y2004 (lower plot for same 4 Z-bins). The sequence of plots is 15 and 20 in the first row and 25 and 30 in the second.

3.3 A new study by Wei MIng Zhang

Wei Ming took a new look at the radiation length distributions. It is largely compatible with the above results, but coveres a different range of parameters:

• a wider range of the vertex Z
• exclusion from the fiducial of the parts of the TPC endcap wheel where large amounts of material (ribs) are present (a realistic cut for any EEMC analysis).
• the rapidity interval covered by the EEMC, i.e. the medium-forward region

Here are the plots for the regions covered by the inner and outer sectors of the EEMC:

4. SVT vs no-SVT

Consider two geometries - the most current y2005c, and same geometry, but without the central SVT barrel and with water drained from the manifolds. The SSD and all the cabling attached to the support cones, and the cones themselves are still in place.

To quantify the effect of the SVT material in the conditions described above, we have conducted a similar study, using 5 cm bins: Z=(0..5),(5..10),(10..15),(15..20),( 20..25),(25..30) and (30..35) cm. Here are plots for the both the absolute rad length -- both with and without the SVT -- and the ratio of same:

Rad Length

Ratio

5. The TPC Geometry Description Updates

5a. The TPC Endcap

The TPC geometry model is one of the oldest pieces of the STAR software, and dates back to 1995. In 2005, David Underwood updated the code with the inclusion of readout boards and related elements of the construction on the endcap (the endcap area is of importance mainly for analyses involving the Endcap ECAL). The additional code was pretty invloved and contained an obscure syntax error, which led to positioning of some of the parts (PCBs) being incorrect. Below is a sketch of the detector part in question:

We can now proceed to compare the Underwood version with the old one. Here's a plot of the rad. length as a function of eta, and the ratio of such histogram produced with new and old code:

The effect of the extra material is clearly visible but at the same time it's not too large, adding a fractional amount of roughly 20% to the base value.

5b. Effects of the positioning error

Here is the graphic of the ratio of the same rad.length plots, produced respectively after the errors were rectified, and before:

While this ratio appears to fluctuate, the plot deomstrates that on average, the material amount doesn' change much between these two versions.

5c. Gerrit's Radiation Length Plot

In the recent STAR Upgrade Meeting, Gerrit presented the following plot of the material balance, using same approach and figure of merit as in the plots above:

While the plot matches the data above in the region 0<eta<1.4, there is a discrepance above that range, with rad. length numbers in excess of 2.5 units. This is currently being investigated. According to Gerrit, the error most likely is in his code.

6. TPC and SVT contributions to the Material Balance

Here's another picture of the STAR cross-section, with line segments depicting the eta range betwen 1.0 and 2.4 units, in intervals of 0.2.

We can now plot the accrued radiaton length as a function of eta, for the TPC, SVT and their combination. The result is shown below: