Beam polarization

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Important note: This page has been reviewed by Avetik, but has incorrect or incomplete information! Use the information below with caution.

Intro

The lepton beam in the HERA collider is transversely polarized in the arcs due to the [Sokolov-Ternov effect][1]. To obtain a longitudinal polarization at the location of the HERMES experiment a pair of [spin rotators][2] located before and after the HERMES experiment, at both ends of the East straight section, turns the polarization vector in three steps from the transverse to longitudinal direction. This was the case for so called HERA-I, running period, i.e. till 2000. During HERA-II running period(2002-2007) an additional Spin rotators were installed before and after H1 and ZEUS detectors, allowing collider experiments to test Standard Model with measurements sensitive to Electron(Positron) Polarisation.

Essentials

The polarization P of the lepton beam with respect to a specified vector is defined as an asymmetry:

$P={\frac {N_{+}-N_{-}}{N_{+}+N_{-}}}$ ,

where $N_{+}$ is the number of leptons with spin pointing along the vector, and $N_{-}$ the number of leptons with spin pointing in the opposite direction. A polarization of 0% means that an equal number of leptons have spin pointing in either directions.

Polarimeters

Two polarimeters were installed for the measurement of the polarization. They are both based on asymmetries in the cross section for Compton back-scattering of left and right circularly polarized laser light off the polarized lepton beam.

The transverse polarimeter (TPOL) measures the transverse lepton polarization in the West Hall, where no spin rotators were installed. It uses the spatial up-down asymmetry of the back-scattered Compton photons for left or right circularly polarized laser light off a polarized lepton bunch. Not every interaction between the continuous laser beam and the bunched lepton beam generates a Compton photon (single-photon mode).
- "The HERA Polarimeter and the First Observation of Electron Spin Polarization at HERA" (Nucl. Instr. and Meth. A329 (1993) 79; DESY 92-136)
The longitudinal polarimeter (LPOL) measures the longitudinal lepton polarization in the East Hall, between the two spin rotator. It uses the integrated energy asymmetry between Compton photons when scattering left or right circularly polarized laser light off a polarized lepton bunch. Due to the higher laser intensity, many Compton photons are generated simultaneousely in every interaction between the 100 Hz pulsed laser beam and the bunched lepton beam (multi-photon mode).
- "The Longitudinal Polarimeter at HERA" (Nucl. Instr. and Meth. A479 (2002) 334)

Offline processing

Every minute the LPOL and TPOL polarimeters provide a measurement of the polarization. Before this data is made available for use in a physics analysis, it undergoes several procedures.

TPOL focus correction: After the upgrade of the HERA collider in 2001 a dependence of the TPOL polarization on the size of the Compton photon beam projected on the TPOL calorimeter was noticed. This is now corrected for offline.
LPOL and TPOL smoothing: Because the polarization of the lepton beam usually changes only on time scales that are longer than 20min (the characteristic rise time $\tau$ ), the statistical uncertainty on each 1-minute measurement can be reduced by a smoothing procedure. By fitting the polarization measurements of the complete fill with a spline, the statistical uncertainty becomes negligible. The only uncertainty left on a each data point is systematic.

LPOL / TPOL ratio

The polarization measurements of the LPOL and TPOL can be compared by determining their ratio LPOL / TPOL. To reduce the effect of the statistical uncertainty, the ratio is usually determined for 5-minute intervals. The remaining width in the distribution of the ratio LPOL / TPOL is an indication of the systematic disagreement between the measurements.

Central value

To reduce the effect of the statistical uncertainty the polarization value rPolFit of the table g1Beam should be used. The field rPol should NOT be used, because this field is filled regardless of data quality information and it is afflicted by large statistical fluctuations. The field rPolFit automatically selects the "best" polarimeter for each fill (unfortunately this only works on a fill-by-fill basis), and contains the smoothed polarization values to reduce the statistical uncertainty. The remaining uncertainty is the systematic uncertainty only. Because of a problem in the LPOL optics, only TPOL measurements are used for all electron data collected during the year 2006.

If your analysis is very sensitive to the polarization (for example, you are not just using the polarization for a helicity balancing method), you should consider imposing an upper limit on the time interval between the burst and the last polarization measurement (iPolFitGap of the table g1Beam). If more than 5 minutes (300 seconds) have passed since the last polarization measurement usually the data quality bit 28 is set.

Note: The recommendation of the POL2000 group is to use the mean of both polarimeters weighted by their systematic uncertainties, because it is unknown which polarimeter was responsible for the disagreement from 2005 until 2007. Unfortunately this is currently not possible without a substantial change to the uDST production chain. The polarimeter used for each fill is stored in the field bProdMethods field of the g1DAQ table.

Systematic uncertainty

The systematic uncertainty can be separated in two categories: the scale uncertainty which affects the overall scale of the measurements but does not result in scattering of the polarization measurements, and the remaining "non-scale uncertainties" which create scattering of the measured values around the central value. In general you should access the systematic uncertainty on the polarization measurement in the fields rPolNormFit for the scale uncertainty and rPolSystFit for the non-scale uncertainties in the table g1Beam of the uDST files.

Systematic uncertainty during HERA I

During the HERA I running period from 1997 until 2000, the systematic uncertainty on the polarization measurement was determined as $\sigma (P)/P=3.26\%$ for the TPOL, and $\sigma (P)/P=1.6\%$ for the LPOL.

Systematic uncertainty during HERA II

After an upgrade of the TPOL system in 2001 the systematic uncertainty of the polarization measurements of the TPOL was reduced to $\sigma (P)/P=2.9\%$ .

After an damaging incident with synchrotron radiation in May 2004, the LPOL was rebuild. The systematic uncertainty on the polarization measurement of the LPOL was increased to $\sigma (P)/P=2.0\%$ for the HERA II running period from 2004 until 2007, to account for the unknown scale uncertainty with the new calorimeter, and for systematic effects that could not be studied during the HERA I running period but might be present in the HERA II running period.

Increased systematic uncertainty between 2005 and 2007

Between the years 2005 and 2007 there were large unexplained deviations in the ratio LPOL / TPOL. It is likely that an unknown systematic effect was influencing either the LPOL or TPOL measurements, but there has been no progress in understanding or correcting this problem. The correct treatment of the systematic uncertainty for this period is explained in internal report POL2000-07-016 "Using the HERA Polarization Measurements - Recommendations for the Summer 2007 Conferences" and summarized in an email from Riccardo Fabbri.

NEW (January 2012): these are obsolete numbers. Section needs to be updated after the POL2000 reanalysis described in arXiv:1201.2894 as the absolute (non-scale) uncertainty is not valid and the scale uncertainties were adjusted

A gaussian fit to the LPOL / TPOL ratio distributions has a standard deviation up to 4%, which is larger than the 2.6% that we expect from the combined non-scale uncertainties of both polarimeters (the scale uncertainties are determined by the deviation of the average from unity). The unknown non-scale uncertainty component is therefore approximately 3%.

The systematic uncertainty between the years 2005 and 2007 is therefore increased by 3% as follows:

When only one polarimeter is used the additional uncertainty of 3% has to be added to the individual systematic uncertainty resulting in a systematic uncertainty of $\sigma (P)/P=4.2\%$ for the TPOL, and $\sigma (P)/P=3.6\%$ for the LPOL.
When the LPOL and TPOL measurements are combined using their systematic uncertainties as weighting factors an additional systematic uncertainty of 3% has to be added in quadrature to the combined systematic uncertainty of approximately 1.6% ( ${\sqrt {1/\sigma (LPOL)^{2}+1/\sigma (TPOL)^{2}}}$ ), resulting in a total systematic uncertainty of $\sigma (P)/P=3.4\%$ .
See also below (latest re-analysis of January 2012)

More info

NEW (January 2012): Polarisation at HERA - Reanalysis of the HERA II Polarimeter Data, arXiv:1201.2894

Example how the uncertainty was calculated for draft 93 (DVCS with Recoil)

Recommendation of systematic uncertainties for HERA-II (2003-2007) by the polarimeter group:

The following list of references is considered the bible for the LPOL experts:

Dissertation thesis of Felix Menden

The LPOL group maintains a comprehensive list of internal polarimetry reports (IPR). This includes the following IPR with information about the systematic uncertainty:

Other beam related pages