Polarisation at HERA - Reanalysis of the HERA II Polarimeter Data -

7.1 MB·English

by  Blanka Sobloher

DESY 11-259
POL2000-2011-002
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Polarisation at HERA
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2 – Reanalysis of the HERA II Polarimeter Data –

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1 B. Soblohera1, R. Fabbria,b2, T. Behnkea3, J. Olssona4, D. Pitzla5, S. Schmitta6,
J. Tomaszewskaa7
]
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d
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s aDeutsches Elektronensynchrotron DESY
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Notkestrasse 85, D-22607 Hamburg, Germany
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c bNow at: Forschungszentrum Ju¨lich FZJ
i Wilhelm-Johnen-Strasse, D-52425 Ju¨lich, Germany
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Abstract
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InthistechnicalnotewebrieflypresenttheanalysisoftheHERApolarimeters(transver-
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1 sal and longitudinal) as of summer 2011. We present the final reanalysis of the TPOL
0 data, and discuss the systematic uncertainties. A procedure to combine and average
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LPOL and TPOL data is presented.
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1e-mail: [email protected]
2e-mail: [email protected]
3e-mail: [email protected]
4e-mail: [email protected]
5e-mail: [email protected]
6e-mail: [email protected]
7e-mail: [email protected]
1
Contents
1 Introduction 3
2 The LPOL Polarimeter 3
2.1 Offline Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 LPOL Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 The TPOL Polarimeter 10
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 Principle of the Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.3 Analysis Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.4 Pedestal Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.5 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.6 Systematic Errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.7 Polarisation Scale from Rise Time Measurements . . . . . . . . . . . . . . . . 52
4 Comparison of LPOL and TPOL Measurements 54
5 Recommendations for Polarisation Values Treatment 57
5.1 Systematic Error Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.2 Error Scale Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.3 Averaging of Polarimeter Measurements . . . . . . . . . . . . . . . . . . . . . 62
6 Summary 66
2
1 Introduction
After theupgradeof theHERAmachinelongitudinally polarisedlepton beamswereavailable
totheHERMES,theH1andtheZEUSExperiment. Thedegreeofpolarisationwasmeasured
for nearly all available data with two independent polarimeters, the transverse polarimeter
TPOL, located close to the HERA-West interaction point, and the longitudinal polarimeter
LPOL, located close to the HERA-East interaction point. Throughout the HERA II running
period from fall 2003 to mid 2007 typically 97.8% of the integrated luminosity used in
∼
polarisation dependent analyses of the experiments is covered by at least one polarimeter [1].
In addition, for some part of data in 2006 and 2007, a new polarimeter was used in
place of the longitudinal polarimeter, the cavity polarimeter. The analysis of data from this
instrument is covered in [2], and is not included in this note.
In this report the analyses of the transverse and the longitudinal polarimeters are pre-
sented. Forthetransversepolarimeter,acompletely newanalysismethodhasbeendeveloped
andispresented, whilefortheLPOLan in-depthevaluation of thesystematic errorshasbeen
performed. This is followed by a recommendation on how to treat the errors of the polarime-
ters and how to combine the data from the two devices to obtain one HERA II polarisation
measurement.
2 The LPOL Polarimeter
The main method of the analysis of the LPOL has been unchanged for a number of years.
The main focus of the work presented in this note has been a careful re-evaluation of the
systematic errors as published in [3]. Studies were undertaken to understand the behaviour
of key parameters in more detail. Extensive searches have been conducted to look for corre-
lations between variables in the LPOL and the LPOL/ TPOL ratio, to understand potential
sources of discrepancy between the two devices. To this end the data of the LPOL have been
restructuredfor easier access, andadditional variables havebeenincludedinthedatabase[4].
The values of systematic uncertainties are given in Tab. 1.
2.1 Offline Analysis
The LPOL operates with a pulsed laser, which is triggered externally. The trigger is syn-
chronised with the HERA clock. The 3ns pulse has a non uniform time profile, and the laser
firing has a sizable jitter of 1.5ns relative to the HERA clock. These two effects generate
±
false asymmetries on the collected Compton photon energy in the LPOL calorimeter, and are
corrected for. This potentially large source of systematic uncertainty has been discussed in
detail in [5], where no significant dependence of the LPOL/TPOL ratio on the value of this
correction has been found. The currently released TPOL data were used in that analysis and
in the study here reported.
Another effect which can have a potentially significant impact on the energy measured
in the LPOL calorimeter is the background and pedestal subtraction. Each photomultiplier
(PMT) channel (see Fig. 1) has a pedestal, which can, potentially, vary from channel to
channel. Each signal from PMTs is split into two signal lines, and the second line is installed
to an additional ADC module channel. Each of these extra channels is delayed by 96ns, so
onlytheactualpedestalinsteadofthesignalpluspedestalisgatedtotheADCmodule. Since
3
Source of Uncertainty δP/P (%) Class
Analysing Power 1.2 IIu
- Response Function (0.9)
- Single to multi Photon Extrapolation (0.8)
Long term Stability 0.5 I
Gain Mismatch 0.3 I
Laser Light Polarisation 0.2 I
Pockels Cell Misalignment 0.4 IId
Electron Beam / Laser Beam Interaction Region 0.8 IIId
Total HERA I uncertainty 1.6
Extra Uncertainty for new Calorimeter 1.2 IIu
≤
Total HERA II uncertainty 2.0
Table1: Systematic(relative)uncertaintiesoftheLPOLmeasurements. Theso-calledHERA
I contributions are described in [3]. The extra contribution to the error is estimated from
nd
the studies in [8], and should be applied to the LPOL values measured from July 2 2004
onwards, after thereplacement of thecracked calorimeter crystals. Thetableis adapted from
[9]. The third column indicates the estimated class of systematic error and possible period
dependence, see Sect. 5.1 for details.
Figure1: Schematic drawingof theLPOL
calorimeter. Visible are the four crys-
tals, used to measure the energy, and the
four photomultipliers. The number codes
of the photomultipliers and their location
with respect to the HERA beam pipe are
denoted.
the pedestals are measured with separate ADC channels, a calibration between the pedestals
in the delayed and the non-delayed lines is needed.
Thecalibration is performedconsidering laser Off events (includingboth filled and empty
HERA bunches). Between the two channels a linear dependence is expected, whose offset
and slope will give the calibration. An unbinned maximum likelihood fit with a linear model
is done to the ADC values for the delayed versus the undelayed line. An example of a fit
(taken from [6]) is presented in Fig. 2. The fit is performed every minute, and the resulting
offset and slope values are then used to subtract the pedestal event by event, separately for
each channel:
SCompton = Sraw P
undelayedline undelayedline− undelayed line (1)
P = P Offset /Slope .
undelayed line delayedline− fit fit
(cid:0) 4 (cid:1)
Several factors can affect the pedestal subtraction. The pedestal calibration is performed
usinglaserOffeventsonbothemptyandfilledbunches. Eventsfromfilledbunchesmaysuffer
from additional background sources like synchrotron radiation or Bremsstrahlung. Events
from empty bunches will not be subject to these background sources. Comparing the results
for the pedestal determination for the two classes of events, no significant differences are
observed, indicating that backgrounds from synchrotron radiation and Bremsstrahlung do
not play a significant role in the pedestal calibration.
In Fig. 3 the ratio of the mean values for background energy plus pedestal over only
pedestal is presented for all four PMTs. The distributions do not show significant devia-
tions from unity. They have a width typically below 1%, indicating a negligible amount of
synchrotron and of other background photons. Also shown in Fig. 3 is the dependence of
the LPOL/TPOL ratio on this quantity, with no obvious dependence found. This is also
consistent with results obtained during running, from counting the number of high energy
photons seen by the calorimeter, but independent from the laser trigger. No significantly
enhanced rate is observed, indicating that the dominant source of high energy photons in the
calorimeter is from Compton photons.
A noisy line would result in broader ADC distributions and could affect the calibration
parameters extracted from the linear fit, thus biasing the pedestal subtraction. The spread
of the signal for all four PMTs is presented in terms of ADC values in Fig. 4, for both
undelayed and delayed channels, and for laser Off events. The PMT channels 2 and 3 appear
to bereasonably stable, whilechannel 1(close to the beam pipe)shows significant variations.
A similar behaviour (although less significant) is observed in channel 4. The latter is located
far from the beam pipe, thus suggesting the source of noise variation to bepossibly unrelated
to the HERA beam line.
The observed increase of noise might affect the calibration parameters extracted from
the fit. To investigate whether any correlation exist between the increase of the noise, and
the calibration constants obtained in the fit, the quality of the calibration fit is studied as a
function of time.
For unbinned maximum likelihood fits no direct goodness of fit quantity is available.
Howeveritispossibletocalculateacorrelationcoefficient, whichteststhecorrelationbetween
the values used in the fit, and the assumed model used in the fit. The correlation coefficient
Figure 2: Example of the relative calibration of
thedelayedandthenon-delayedchannelsforthe
same PMT. A linear unbinned maximum likeli-
hood fit is performed to the ADC values of the
delayed versus the undelayed line. The calibra-
tion is performed using laser Off events, with
filled and empty HERA bunches.
5
/ DC> <ADC>Synchr+PedPed110011011.........00990090044682682611230 PPMMTT24120 250 260 270 280 LUansdeerl2 a9o0yffe dev leinnets300 Yield 111224680200000 PMT1 EMRχCEMRχCMM22nnMoMoeeee //ttnnaaaa SSrrnnssnnnnii eedd t t aas s ff nn tt 11..00 22 00 991100225577.. 00±±.... 3388 00 116600 7777±±.. ..330000//00 333300003300..222277990088
A
< 0.96 120
1.06230 240 250 260 270 280 290 300 SSiiggmmaa 00..000066228822 ±± 00..000000111177
1.04 PMT3 100
1.02
1 80
0.98
0.96 60
1.06230 240 250 260 270 280 290 300
1.04 PMT4 40
1.02
1 20
0.98
0.96 00.95 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05
230 240 250 260 270 280 Days fro2m9 0Jan 1st 200360 0 <ADC>Synchr+Ped / <ADC>Ped
ol 1.5 ol 1.05
Lpol/Tp 1.4 Lpol/Tp11..0034 PMT1
1.3
1.02
1.2
1.01 EEnnttrriieess 55332211
1.1 MMeeaann 11..000022
1
MMeeaann yy 11..002244
1
0.99 RRMMSS 00..000077007755
0.9 0.98 RRMMSS yy 00..0055338822
0.8 0.97 χχ22 // nnddff 88..551122 // 66
pp00 11..001188 ±± 00..110000
0.7 0.96 pp11 00..0000552299 ±± 00..1100001100
0.6 0.95
230 240 250 260 270 280 290 300 0.98 0.99 1 1.01 1.02 1.03
Days from Jan 1st 2006 <ADC>Synchr+Ped / <ADC>Ped
Figure 3: Top left panel: Ratio A of the mean values for background radiation plus pedestal
over pedestal energies for a subset of data taken in the second half of 2006, as a function of
time. Top right panel: Distribution of the ratio A for the same data sample. The spread
of the data is below 1%. Bottom left panel: The LPOL/TPOL ratio for the same period.
Superimposed to the one minute data (black points) are shown the 8 hour average values
(red filled circles). Bottom right panel: Dependence of the LPOL/TPOL ratio on the ratio
A. No statistically significant dependence is found.
between two measurable quantities x and y in a sample of size N is defined as [7]:
N
1 x x y y
i i
r = −h i −h i , (2)
xy
N 1 s s
x y
− Xi=1(cid:16) (cid:17)(cid:16) (cid:17)
with x and s ( y and s ) are the mean value and the estimated variance of the variable
x y
h i h i
x (y). If one assumes a functional dependence between x and y of y = f(x), the deviation
between the data point i and the function can be written as
y y = f y + y f , (3)
i i i i
−h i −h i −
(cid:16) (cid:17) (cid:16) (cid:17)
which is decomposed into a component explained by the proposed linear model f = a+b x,
·
and a deviation not justified by the model. After some algebra [7], one obtains that the
6
Figure4: Widthof thepedestaldistributionforlaser Offevents intheundelayed (top panels)
and in the 96ns delayed ADC channels, as a function of the time.
sample correlation coefficient provides a measurement of the ratio of the sum of deviations
given by the model over the sum of the total data deviations,
2
N f y
r = r2 = v i=1 i−h i . (4)
xy u (cid:16) (cid:17)2
uPN y y
q u k=1 k −h i
u
tP (cid:16) (cid:17)
The calculated values of the linear fit correlation coefficient is presented in Fig. 5 for all
four PMT lines. As observed for the noise, the coefficients are stable for PMT channels 2 and
7
Figure 5: The behaviour of the correlation coefficient (as defined in the text) for the pedestal
calibration is shown for the analysed period in 2006, separately for the four PMTs.
3, while for channels 1 and 4 more significant variations are found. Typically the values are
largerforthelessnoisychannels. Beyondthesequalitative observations, noclearquantitative
correspondence between the noise variation and the correlation coefficients can be found.
The LPOL/TPOL ratio is investigated versus the correlation coefficients in Fig. 6, for
two data taking periods of similar size, and independently for all four PMTs. No sizable
correlation is found for channels 2 and 3, while for channels 1 and 4 the results are less
stable.
To investigate whether a net effect is present in the data, events from all four PMTs and
for different data periods are combined. To avoid biasing the data, data are grouped into
periods of similar LPOL/TPOL ratio. Each group then is re-normalised to a LPOL/TPOL
ratio of one at a correlation coefficient values in the bin from 0.87 and 0.88. The resulting
distributions are then averaged in bins of the correlation coefficient. The results are shown
in Fig. 7. The upper panel shows the measured LPOL/TPOL ratio as a function of the
correlation coefficient separately for all four PMT channels, and for the investigated data
periods. Onedatasample(withlightbluemarkers)hascoefficient valuesoutsidethecommon
normalisation region, and has been normalised to the only data sample overlapping its values
(in red markers) in the region 0.90 0.91, after prior common normalisation of the latter.
−
The dependence of the LPOL/TPOL ratio on the correlation parameter is presented in the
bottom panel of the picture, after merging together all the normalised data samples. No
significant dependence on the correlations coefficient r is found.
8
ol 1.06 ol 1.06
p1.05 Laser off events p1.05
T T
ol/1.04 PMT1 ol/1.04
p p
L1.03 L1.03
1.02 1.02
1.01 1.01
1 1
Laser off events
0.99 0.99 PMT1
0.98 Days: 236 - 260 0.98 Days: 260 - 296
0.97 0.97
0.845 0.85 0.855 0.86 0.865 0.87 0.875 0.88 0.885 0.89 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0 .9
1.06 1.06
1.05 1.05
1.04 PMT2 1.04
1.03 1.03
1.02 1.02
1.01 1.01
1 1
0.99 0.99
PMT2
0.98 0.98
0.907.908 0.91 0.912 0.914 0.916 0.918 0.92 0.922 0.924 0.907.908 0.91 0.912 0.914 0.916 0.918 0.92 0.922 0.924
Fit: Correlation Coefficient Fit: Correlation Coefficient
ol 1.06 ol 1.06
p1.05 Laser off events p1.05
T T
ol/1.04 PMT3 ol/1.04
p p
L1.03 L1.03
1.02 1.02
1.01 1.01
1 1
Laser off events
0.99 0.99 PMT3
0.98 Days: 236 - 260 0.98 Days: 260 - 296
0.97 0.97
0.908 0.91 0.912 0.914 0.916 0.918 0.92 0.922 0.924 0.912 0.914 0.916 0.918 0.92 0.922 0.924 0.926 0.928
1.06 1.06
1.05 1.05
1.04 PMT4 1.04
1.03 1.03
1.02 1.02
1.01 1.01
1 1
0.99 0.99
PMT4
0.98 0.98
0.97 0.81 0.82 0.83 0.84 0.85 0.86 0.970.8 0.81 0.82 0.83 0.84 0.85
Fit: Correlation Coefficient Fit: Correlation Coefficient
Figure 6: The LPOL/TPOL ratio is plotted versus the correlation coefficient (as defined in
the text) separately for the four PMTs and for two different periods of data taking.
2.2 LPOL Conclusions and Outlook
A comprehensive re-analysis of systematic errors for the LPOL has been conducted. Care
has been taken to minimise the dependence on simulation in this, the emphasis has been
on understanding the data and comparisons with the other polarimeters at HERA. Within
the precision possible, the background subtraction method has no impact on the polarisation
measurement.
Even though the noise in the signal lines was found to vary significantly in the channels
1 and 4, no significant effect on the pedestal calibration procedure was found, and no clear
evidence for an impact of this variation on the LPOL/TPOL ratio was found.
A number of other effects have been studied, including the effect of the timing of the
laser pulse, the effect of empty HERA bunches etc., but no clear systematic impact on the
polarisation determination was found.
9
ol 1.15
p
T
ol/ 1.1
p
L
1.05
1
0.95
0.9
0.85
1.05
0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91
1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0.96
0.95
0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91
Fit: Correlation Coefficient
Figure 7: Upper panel: The LPOL/TPOL ratio versus the fit correlation coefficient is shown
for the PMT channel 1 and for different contiguous periods (each colour and marker code
correspondingtoadifferentperiod)fulfillingtherequirementsmentioned inthetext. Bottom
panel: Theratioispresentedforallmergeddatasamplesafternormalisation. Alinearbinned
fit is superimposed to the data, showing no clear trend of the data within the data precision.
Theextractedfitparametersoffsetandslopeare1.021 0.047 and 0.026 0.054respectively,
± − ±
for a χ2/NDF value of 71.84/38.
3 The TPOL Polarimeter
3.1 Introduction
ThetransversepolarimeterTPOLislocated inthestraightsectionWestoftheHERAtunnel.
Circularly polarised laser photons are Compton scattered off the lepton beam and are trans-
ported 66m downstream through a beam line to a sampling calorimeter. The calorimeter has
been designed to measure precisely the average position of an electromagnetic shower created
by a single photon. To this end the calorimeter is split horizontally into two halves, which
are read out independently. The energy asymmetry η defined as
E E
U D
η = − (5)
E +E
U D
is related to the vertical position of the photon hitting the face of the calorimeter through a
non-linear transformation, the η(y) transformation. The energies used in the definition of η
are pedestal subtracted.
The interaction rate between laser and lepton beam is such that on average less than
1% of all photons are scattered back into the calorimeter, thus ensuring that to a very good
approximation only single photons hit the calorimeter.
The information on the polarisation of the lepton beam is contained in the vertical dis-
tribution of the photons, where vertical has been defined relative to the plane formed by the
10