Experimental High Energy Physics Group, Department of Physics, University of Rajasthan, Jaipur-302004

- The events are cleaned and hot_cells are removed.
- The cells with no hits in immediate neighbours are considered as isolated hits and are stored in a Ttree
- The data for each cell, whenever it is found as a isolated cell, is collected and the adc distribution forms the mip for that cell.
- The mip statistics is then used for relative gain normalization.

The steps (1) , (2.) and (3.) have been discussed in detail in past. This writeup concentrates only on (4.) i.e the Gain Normalization Procedure. The writeup here attepts to understand the varations in the factors affecting the gains. It also attempts to determine how frequently should the gain_factors be determined.

We studied gain normalization factors of different datasets of CuCu 200AGeV data . We observed that the gain normalization factors within the SMChain do not vary from one days dataset to another. But the gain normalization of one SMChain wrt another does. So we have represented the total gain normalization factor into two factors

Total_GNF = Cell_GNF * SMChain_GNF

- We have to use large statistics to determine Cell_GNF. Here 330K events of day22 data were used because we needed to collect enough statistics for each cell. <
- The gain_NF of one SM_chain wrt other SM_chains, SMChain_GNF, is determined as follows.
- Collect isolated cells for a small number of events.
- Using an pre-determined set of cell_GNF normalize the adc value of these isolated cells.
- Since these are now relatively normalized, the isolated cell adc distribution of all cells within an smchain are expected to fit to a single landau Even in the cases where a clearly developed mip was not seen in uncorrected data, mip was observed in corected data
- The SMChain_GNF can then be determined by two methods:
- using the MPV values of the landau fit to SMChain mips : mpv_SMChain_GNF
- using mean values of SMChain mips within the range 0-500 ADC: mean_SMChain_GNF

- The values of mean and mpv SMChain_GNF differ from each other. These factors are found to vary within short time span and as a result these are different from one day to another ( discussed later). SMChain_GNF used here are determined using 3-4% ( here 13K events for day22 data ) of the statistics required for determining cell_GNF.

To prove that the cell_GNF determined for one set of data ( here day25) can be used for normalizing another day's data( here day22) we have made comparison of SMChain_GNF for day22 data determined using gain factors for day22 and day25 data of CuCu200AGeV.

- The cell_GNFs were determined for data from both these days independently.
- For a small subset of day22 data, we determined SMChain_GNF using cell_GNF for whole day22 data and hence calculated the total gain factors(total_GNF).
- For the same data of day22 but using day25 cell_GNF we have again calculated the the total gain factors.
- The difference in the cell_GNF for a smchain for two datasets , were found to be small and were of the order of 5-10%. see figure for difference between Cell_GNF of day22 and day25. Here the fractional difference between cell_GNF values for all cells of sm19 and chain 40 are plotted.
- The mean and RMS of the distbn. of fractional difference for all the smchain combinations (a total of 49 combinations) is plotted in the plot 1 of this figure. That all the mean values are close to zero shows the stability of these factors over a certain time span.
- The other plots of this figure give the difference in the total_GNF which includes the difference in cell_GNF as well as SMChain_GNF. Plot 2 gives the fractional difference when using mpv_SMChain_GNF and Plot 3 gives the fractional difference when using mean_SMChain_GNF.
- After applying only Cell_GNF and no SMChain_GNF the mean and mpv values were very scattered as expected. See the blue lines in plot 1 and plot2 of this figure
- If we apply mean_SMChain_GNF along with Cell_GNF the mean and MPV values are more clustered around a mean value. See green curves in the plot 1 and plot 2 of this figure
- If we apply mpv_SMChain_GNF along with CELL_GNF the MPV values show a sharp peak while distribution of means is also better than that observed than in (ii). See Red curves in plot 1 and plot2 of this figure
- The plots 3 and 4 of this figure show the resultant PMD mip for 13K events after applying the total_GNF using mean_SMChain_GNF and mpv_SMChain_GNF respectively
- The above study was repeated using day25 cell_GNF instead of day22 cell_GNF and the results are given in figure: See this figure
- Cell_GNF are stable and can be used for a longish span of data ( till the difference is <20%). These require a larger statistics and can be stored once for say every 5 days of data taking.
- mpv_SMChain_GNF are more effective than mean_SMChain_GNF, these 50 numbers(one for each SMChain combination) should also be stored in the DB. The numbers used in the present example are 13K event which is a very small amount of data. SMChain_GNF are fast varying but within the day they vary by ~6%. See this figure . So we need to determine these quantities more frequently than cell_GNF I would propose that they are determined twice a day.

In order to determine which of the two SMChain_GNF gives a better correction, we applied these to a small dataset of unnormalized isolated cell adc values. After applying total_GNF, the mean and the mpv of the resulting SMChainMIP was collected. We observed: