Helicity balancing

Page maintainer: Stan Belostotski

This page is considered done. It been reviewed by Aram. There may be missing elements, but they are all flagged and the text has no errors.

Intro

'Preamble' During the polarized data taking period, the target polarization is flipped at 60s (hydrogen) or 90s(deuterium) interval. The beam polarization is reversed only on (about) a monthly basis. The possibility to reverse both target and beam polarization is an important advantage of the HERMES experiment. This allows one to combine two data sets with opposite target (beam) polarization, and thus, practically exclude effect of the spectrometer acceptance on the measured polarization observables. The extraction of a polarization observable is especially convenient if the analyzed data sample is beam or/and target helicity balanced (luminosity weighted beam/target polarization is equal to zero). For such a data sample polarization observables can be extracted on event basis using simple formalism based on either moment method or maximum likelihood method.

Essentials

• At first, helicity balancing formalism was applied for extraction of longitudinal spin transfer to the Fehler beim Parsen (Konvertierungsfehler. Der Server („https://wikimedia.org/api/rest_“) hat berichtet: „Cannot get mml. Server problem.“): {\displaystyle \left.\Lambda \right.} hyperon.
  S.Belostotski "Extraction of Lambda polarization from unpolarized Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle (P_{T}=0)} runs" Int.Report 98-091
• Recently, a formalism has been developed without requirement of exact helicity balancing such that low beam polarization cut is no longer required.
  S.Belostotski, Yu.Naryshkin, D.Veretennikov, DLL release report 2008

• Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left. A_{UT} \right.} : Helicity balancing is applied for extraction of DSA and azimuthal asymmetry both for target and beam.
  S.Belostotski "Extraction of polarization observables from helicity balanced data sample" Int.Report 09-009

Figure made by Z.Ye.

• DVCS: It is well known that the DVCS cross section depends on both beam and target polarizations. The measurement of azimuthal asymmetries with respect to target or beam polarization provides an access to corresponding term of the cross section. To be sure that experimentally observed modulations in the azimuthal angle are attributed only to pure beam or target polarization dependent parts of the cross section, it is essential to have 'effectively balanced' data sets.
  For example, in DVCS analysis of Transverse Target Spin Asymmetry [1] using the data taken in the years 2002-2005 the beam was longitudinally polarized, with resulting non-zero luminosity-averaged polarization. An upper cut was applied on polarization in order to reduce the average net-polarization (so called 'beam-balancing').
  In the recent analysis of Longitudinal Target Spin Asymmetry [2] the beam balancing cuts were not applied. Instead, the maximum likelihood fitting technique was used for simultaneous extraction of single beam-spin and target-spin asymmetries together with the double-spin asymmetry. In this case the possible imbalances of the data sets in beam polarization were taken into account by introducing an appropriate weights in the fitting function [3] .
  
  [1]. "TTSA", A. Airapetian et al, JHEP 06 (2008) 066
  [2]. "Exclusive leptoproduction of real photons on a longitudinally polarized hydrogen target", Release Report 2009
  [3]. "DVCS from nuclear targets", Release Report 2008 (Appendix B,C)