Strip-to-Strip Calibration

1. Strip Response Normalisation of the MINOS Detectors Philip Symes, University of Sussex Calibration Workshop @ FNAL Sept 2005 Strip-to-Strip Calibration

2. 0 Structure • Strip-to-strip calibration techniques • Description of the current method • Tests with MC • Areas where improvements could be made • Comparison with Data • Towards rolling calibration

3. 1.1 The MINOS Calibration Chain • The MINOS calibration chain has several links • The strip-to-strip correction normalises the response within each detector, taking into account: • Clear fibre + pigtails • Gain • Scintillator response differences • WLS collection + connector efficiencies

4. 1.2 Calibration Techniques • Goal is to characterise the response of a muon through each strip • Complications arise due to path-length, attenuation, clear fibre lengths etc. but most importantly (because of the low light level of many of the strips) “zeros” • There are (at least) three ways that zeros can be accounted for: • Use single-ended hits to reconstruct zeros at the other end • Use the tracker to identify missing strips-ends • Estimate the number of zeros based on the light level of the strip-end • Notes: The first method relies on having double-ended readout The second method relies on an accurate prediction of the missing strip The third method must be iterative since you need the answer first

5. 1.3 Description of the Current Method • The method chosen is the same as that used at CalDet, and is an iterative technique • The calibration requires various stages of systematic corrections to ensure the cosmic muon sample is the same in all strips • The following slides explain the iterative part of the procedure Iteration

6. 1.4 Path-length Corrections • Corrects for effect of path-length through strips due to different muon track incident angles • The method finds the average path-length through the strip for a given angle • The method has to take into account corner clipping • The formula used for the correction is:

7. 1.5 Zero Corrections • The Poisson probability from the photo-electron spectrum of getting 0-p.e. is given by • where lambda is the number of pes produced per cm and ds is the path-length through the strip • If this is integrated over all path-lengths, the formula below can be derived, which predicts the average probability of getting a zero given the strip light level and muon angles

8. 1.6 Sparsification Corrections (1-p.e. correction) • The sparsification thresholds are typically 0.2-0.3 p.e. • Therefore, as well as zeros, around 4% of the single-pe peak effectively becomes a “zero” • Using the same derivation as before, the probability of getting a single pe can be calculated for a particular light level and set of muon angles • This correction is only important for low light level strip-ends

9. 1.7 Using the Probabilities • For each hit, the <P(0)> and <P(1)> probabilities are calculated • The strip-end histogram is then filled as follows: • where • p is the fully corrected ADC-like hit value • t/2 is the mean of the sparsified part of the single-pe peak • f is the fraction of the single-pe peak that is sparsified • The mean of this histogram is therefore corrected for zeros

10. 1.8 Iteration: Stopping conditions • The first pass over the data assumes that the light levels of all the strip-ends are 4 pes (a previous set of calibration constants can also be used as a starting point) • After an iteration, the mean of each strip-end histogram is calculated in pes and divided by the light light level used in the zero reconstruction • If this ratio is ~1 then the light level used was correct and the iteration stops • In fact, the goal of the iteration is to make the ratio for each strip-end tend to 1.29 • The significance of 1.29 is related to the fact that the underlying distribution is Landau

11. 1.9 Iteration: Stopping conditions • 1.29 is an estimate of the ratio of the Landau MPV to the mean • The assumption being that for zero reconstruction it’s better to tune the light levels to the most probable value rather than the mean since P(0;l) is not linear with l • The value of 1.29 was measured at CalDet by fitting to through-going beam muons:

12. 1.10 Iteration: Predicting the New Light Level • If the calculated ratio is not 1.29, an estimate of the true light level can be made • Since: • And using the approx: • Then: • Thus, during each loop the quantity on the right is calculated • and the next iteration uses the new light level • - • Where: • x - corrected mean in MEU • l - calibration constant in pe. • <P(0)>xy - prob that hit is not seen • Bi - prob that hit i with ni pe is not seen • N - number of entries • Bar => calculated; Hat => true

13. 2.1 Tests with MC: Sample and Cuts • MC • Reconstructed using R1.14 – thanks to Batch Group • Have ~280 muons/strip-end after cuts • Detector muon response = 357.9 ADC • Cuts • Track length: minimum of 8 planes with 6 track-like planes • Track quality: only use strips that are part of the first track in any snarl • Showers: no showers along track • Track angle: max average path-length through strips of 2.5 cm from a given du/dz and dv/dz angle • Minimum light level set to photo-electron sparsification value: hits below this level are reconstructed differently • Maximum light level set to 30 photo-electrons or 8 times the strip-end light level in pe • Cut of 15 cm around ends of strips and coil hole

14. 2.2 Tests with MC: Corrections • Standard gain and attenuation corrections were applied to the sample of hits • The path-length corrections and zero reconstruction were carried out with 10 iterations • A histogram of the ratio mean/light level after convergence peaks at 1.29 as expected, with a handful of strip-ends not converging correctly • Strip-ends that do not converge are fixed using other channels (see later)

15. 2a Comparison of MC Constants with Truth (1) • Left plot has gradient of 1 (red): calibration constants fully correct for strip-to-strip differences • Right plot shows narrow distribution of residual differences (in black) compared to the distribution of strip-to-strip variations (red)

16. 2b Comparison of MC Constants with Truth (2) • Residual shows variations in accuracy with light level (left), caused by variation in convergence value • This is caused by a small change in shape of the underlying PMT response with light level (right)

17. 2b Cosmic Muon Samples:Track Angle Spectra

18. 2c Cosmic Muon Samples:Track Distributions • Track lengths • Raw hit distrubutions

19. 2c Cosmic Muon Samples:Track Distributions • Track lengths • Raw hit distrubutions

20. 2c Cosmic Muon Samples:Hits Locations in MC • Number of hits in each strip crossing location, averaged over each super-module

21. 2d Cosmic Muon Samples:Hits Locations in Data • Number of hits in each strip crossing location, averaged over each super-module in data

22. 2e Cosmic Muon Samples:Hit Cross-section Profiles • Dependence of number of hits on radial distance from centre of detector is a function of detector shape • Raw hit response is dominated by position of fibres within modules

23. 2f Cosmic Muon Samples:Hit Cross-section Profiles • Vertical position of hits in MC (4 left) and data (4 right) shows little vertical dependence on the no. of hits used in the sample

24. 3a Gain Correction • In order for photo-electron—based corrections: zero and 1-pe corrections, to work correctly, we need p.e.-like light levels • Calibration constants are multiplied back to ADC-like hits by the same phototube at the end • The distribution of gains is shown on top • The gain-corrected light levels in ADC for the data sample is shown below

25. 3a Attenuation Corrections 1 • The attenuation corrected response is provided by the sigmap branch • Attenuation corrections therefore have to be added to the inputted data to take account of different strip lengths, etc., to perform an unbiased strip-to-strip calibration • The variation of attenuations along the longest strips are corrected from up-to 600% to within 5% • The residual difference has a negligible effect on strip-end light levels

26. 3a Attenuation Corrections 2 • Attenuation corrections applied to the cosmic ray sample (data and MC look similar) in 4 different views (left) • The distribution of attenuation corrections applied is 0.3-1.9 (right).

27. 3a Attenuation Corrections 3 • Even after zero correction, there is a 5% residual under-correction in both data and MC in 8m long strips (shown left) and all strips (right)

28. 3a Path-length Corrections 1 • The energy calculated path-length through the strip as a function of incident angle through the strip is shown (right) • The energy deposited as a function of average path-length through the strip is shown in U and V-views (left)

29. 3a Pathlength Corrections 2 • The energy deposited as a function of average path-length is shown with and without the correction. • There is a 10% under-correction due to path-length between 1-2.5 cm (the range used).

30. 3a Pathlength Corrections 3 • The average path-length is shown as a function of track angle (ds/dz) and a fit is made in the 1.0-2.5 cm region (left). • The distribution of number of tracks at each angle shows few path-lengths above 2.5 cm.

31. 3a Zero Corrections 2 • On the left is the weighting of the zero correction applied to hits in MC – this is fractional height of the 0-bin in this histogram • On the right is the same distribution in data – the two are similar MC Data

32. 3a Zero Corrections 3 • Left: re-weighting with the zero reconstruction reduces the mean strip-end light levels (data) • Right: the difference in the number of hits seen by different ends of the same strip is reduced once this zero reconstruction is applied

33. 3a Sparsification Corrections 2 (1-p.e. correction) • The size of this correction is very small (average 0.2%) in MC (left) and data (right), so will have a small effect on the constants • The size assumed amount of the 1-p.e. peak below dynode threshold / sparsification (3.5%) may not be ideal at low light levels MC Data

34. 3a Resultsphoto-electron response • The results in p.e. show the differences in strip response de-convolved from phototube gain differences • The distributions are different in data (right) and MC (left) due to the different “truth” values in MC and real data • The average strip-end Landau MPV is is about 4 p.e. MC Data

35. 3a Resultsphoto-electron response • The statistical uncertainty in p.e. is the only error in the calibration dependent on the number of entries • The uncertainties shown in MC (left) and data (right) are absolute uncertainties, in units of p.e. • These correspond to 4.3% from 280 entries in MC and 2.1% from 1200 entries in data Data MC

36. 3a Resultsphoto-electron response • Photo-electron response in MC as a function of position in the detector (plane and strip) • Strip-ends in the newer planes of the detector tend to have a higher response • Scale is normalised to 1 for the average p.e. response

37. 3a Resultsphoto-electron response • Photo-electron response in data shows more patterns, e.g. in terms of strip no, bad electronics and read-out module

38. 3a ResultsADC response • When normalised, the response in ADC is the constant put into the database • This constant includes the gain differences between strip-ends, which themselves have a wide spread (see earlier) MC Data

39. 3a ResultsADC response • Comparing “siglin-average” with iteratively calculated constants in MC and data • Damaged strip-ends appear in data (and not MC) are “fixed” • Most strip-ends follow a roughly linear relationship, but this diverges at the high and low ends MC Data Fixed se’s

40. 3a ResultsADC response • Typical strip-ends in the data with ~1200 entries per strip-end • The strip-ends follow the expected shape, but with large uncertainties in bin content

41. 6a Patterns of Mis-calibration at FarDet • This is the difference between calibration constant and truth dependent on position in FarDet (E&W sides) • No systematic patterns can be seen, though some “bad” PMTs are visible (red)

42. 2b Validation of Constants with Datastopping muons • Once attenuation and strip-to-strip corrections have been applied, the detector response is flat in cross-section and between planes • The plot below shows the flat response on the same scale as the variations with no calibration • On the right are the residual systematics, showing variations along the strip Plots by Jeff H

43. 3a Stability of Detector • How often calibration needs to be done

44. 4a Truncation Procedure for Improved Precision (1) • Optimum truncation values at FarDet (left) for different light level strip-ends shows a universal optimum at ~80% • The 80% truncation point (p.e.) has a linear relationship with light level (right)

45. 3 Optimum Convergence Values • Convergence values as a function of light level (untruncated on left, truncated on right) • This value changes from 1.29 as the shape of the underlying Landau distribution is slightly different between high and low light levels

46. 3a Bad Calibration Constant Fixes • Dodgy strip-ends which have too few entries or will not converge to a stable value in the iteration can be fixed: • If both ends had sufficient entries, but neither end converged then fix using other planes • If both had sufficient entries but one one didn't converge then fix using the other end of the strip • If end has insufficient entries but other end is OK then fix using the other end of the strip • and if other end doesn't converge either: fix using adjacent planes. • If the strip-ends are dead, setting the light-level to the average value gives the best estimate if the strip-ends are subsequently fixed

47. 8 New Calibration Constants • During this work, some small bugs/systematics have been found and fixed, and this should propagate to the database • Last round of FarDet constants are using data about 1 year old. • NearDet data used for constants is also old and stability may have improved. • Can Jeff H comment on whether he would be able to test a new set of constants to see whether they improve his calibrations?

48. 5 Towards Rolling Calibration • The procedure used for truncation is very similar to the procedure put forward for rolling calibration • The light level of the strip is known approximately from a previous calibration • Files holding data for each day read-in to strip-end histograms • New data can be made for that day with zero correction applied • Data from that day and previous days added together and truncated to get calibration constant • This value then put into offline database

49. 9 Summary • Strip-to-strip calibration is in a good state at NearDet and FarDet • Response variations seen at NearDet are not due to strip-to-strip mis-calibration • The procedure for a rolling calibration is ready to rumble • Mark Dorman can take the calibration from here • Less talking, more writing

50. 2.2 Cosmic Muon Samples • MC • Reconstructed using R1.14 – thanks to Batch Group • Have ~280 muons/strip-end after cuts • Detector muon response = 357.9 ADC • DATA • 3 months of data from Jul-Sep 2004 • Have ~1200 muons/strip-end • Average detector response = 370 ADC