# Determination of BSMD Relative Gains

**BSMD relative gains from VPDMB events from fill 10471 of the 2009 pp500 run.**

BSMD relative gains are calculated for each strip by dividing the average slope for the eta bin of that strip by the strip's slope (previously obtained). However, it is important to note that the method by which the average slope is obtained is not particularly important. When the actual calibration is performed, we will use the data to determine what the actual gain of a strip with relative gain 1 (i.e., average slope) is, and then we will be able to use the relative gains to determine the absolute gains of all strips. Therefore, we choose a relatively simple method of calculating the average slope by parameterizing the slope vs. eta distribution by one or more lines.

**Figure 1**: BSMDE+P strip slopes vs eta, with average slope parameterizations.

The linear parameterization we choose for the eta plane is given below. Note that for negative eta, we simply reflect the positive eta distribution about eta=0. For the ph plane, we simply choose an average slope of -.032.

The strip relative gain is calculated from relGain(strip)=y(eta)/slope(strip), where y(eta) is determined using the above equations and slope(strip) is the slope for that strip. Note that if the strip has bad status the relative gain is set to 0. Each strip's relative gain is also assigned an error, propagated from the error in the fit to a falling exponential that determined the slope: relGainErr(strip)=relGain(strip)*slopeErr(strip)/slope(strip). The results are below. Figures 2 and 3 show eta and phi strip relative gains vs. eta and phi; figures 4 and 5 show eta and phi strip relative gain errors vs eta and phi; figure 6 shows log base 10 of the relative gain vs softId for each plane; and figure 7 shows the distribution of the log base 10 values of the relative gains for each plane. All figures are also in the pdf relGainsAll.pdf, attached.

**Figure 2+3**: BSMDE relative gains (left) and relative gain errors ((relGainErr(strip)=slopeErr(strip)/y(eta)) (right) vs eta and phi

**Figure 4+5**: BSMDP relative gains (left) and relative gain errors (relGainErr(strip)=slopeErr(strip)/y(eta)) (right) vs eta and phi

**Figure 6**: log10 of relative gain vs. softID for BSMDE+P

**Figure 7**: Distribution of log10 of relative gains for each plane

As a final step, we generate a table containing the relative gain and the gain status for each strip and upload it to the database with some special flavor. The gain status is determined by combining the status bits from all three of the status checks -- the overall level, the fill level, and the gain level -- in the following order.

bit 0: 1=nonfatal, 0=fatal (if status is 1, strip has no problems)

overall statuses:

bit 1: bad mpv, fabs(mpv)>50 (fatal)

bit 2: bad rms, rms<1 || rms>15 (fatal)

bit 3: bad nzs ratio, nzsr<.95 (fatal)

bit 4: bad rms, rms>11.5 (nonfatal)

bit 5: bad zspar1, zspar1<.00003 || zspar1>.02 (nonfatal)

bit 6: bad zspar2, zspar2<.00003 || zspar2>.02 (nonfatal)

bit 7: bad zspar3, zspar3<.00003 || zspar3>.02 (nonfatal)

5 && 6 && 7 is fatal

fill-specific statuses:

bit 8: bad mpv, mpv<-100 || mpv>400 (fatal)

bit 9: bad rms, rms<1 || rms>15 (fatal)

bit 10: bad nzs ratio, nzsr<.95 (fatal)

bit 12: some overall stat was fatal (fatal)

gain-determined statuses:

bit 13: dead strip (fatal)

bit 14: bad integral ratio 1, ir1<.07 (fatal)

bit 15: bad integral ratio 2, ir2<1 (fatal)

bit 16: bad integral ratio 3, ir3>.1 (fatal)

bit 18: bad module (fatal) (note that there was once a cut for bit 17: it was found superfluous and removed, but for the sake of consistency this was left as bit 18)

If a bit is fatal, no bit after it is checked: therefore, there are only 37 combinations of statuses that actually occur. These are assigned to numbers between 1-512 by the following table, which gives the status codes, the bits from the above list, the gain status that each code corresponds to, and the number of strips with each status. Green means good status, which everyone can use; yellow means caution, strips with this status may be usable but not everyone will want to use them; black means bad status, no one should use these strips.

**Table 1: **Gain status codes

status code from gain determination | status bits from gain determination (see list above) | gain status in db | # of strips with this status |

1 |
0 | 1 | 30412 |

17 | 4 | 10 | 45 |

33 | 5 | 11 | 53 |

65 | 6 | 12 | 205 |

97 | 5;6 | 13 | 8 |

129 | 7 | 14 | 1447 |

145 | 4;7 | 15 | 1 |

161 | 5;7 | 16 | 9 |

193 | 6;7 | 17 | 146 |

512 | 9 | 20 | 56 |

1024 | 10 | 30 | 1 |

4098 | 1;12 | 40 | 2 |

4100 | 2;12 | 50 | 36 |

4104 | 3;12 | 60 | 266 |

4320 | 5;6;7;12 | 70 | 1783 |

4336 | 4;5;6;7;12 | 71 | 3 |

8192 | 13 | 80 | 155 |

8224 | 5;13 | 81 | 1 |

8256 | 6;13 | 82 | 12 |

8288 | 5;6;13 | 83 | 2 |

8320 | 7;13 | 84 | 42 |

8352 | 5;7;13 | 85 | 8 |

8384 | 6;7;13 | 86 | 72 |

16384 | 14 | 90 | 39 |

16400 | 4;14 | 91 | 116 |

16448 | 6;14 | 92 | 1 |

16464 | 4;6;14 | 93 | 4 |

16512 | 7;14 | 94 | 2 |

16528 | 4;7;14 | 95 | 7 |

16578 | 6;7;14 | 96 | 1 |

32784 | 4;15 | 100 | 12 |

65536 | 16 | 110 | 1 |

262144 | 18 | 120 | 921 |

262160 | 4;18 | 121 | 92 |

262208 | 6;18 | 122 | 7 |

262272 | 7;18 | 123 | 25 |

262336 | 6;7;18 | 124 | 1 |

Linear parameterization for the eta plane: y is the average slope used in the calculation of the relative gain. Note that y is determined for each eta bin (covering .1 in eta=15 strips because that is what will be used for the determination of the absolute gains) from the value of eta at the center of the bin.

Eta Plane:

0<eta<.5: y=eta*2/125-.036.

.5<eta<.7: y=-.024.

.7<eta<.9: y=.04*eta-.052.

.9<eta<1: y=-3*eta/25+.092.

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