References - Bogoliubov Laboratory of Theoretical Physics - JINR

(and polarization) along axis X:
〈Pmax−X〉pC =
� P (y)I(y)dy
� I(y)dy =
Pmax
� , (4)
(1 + RY )
and by experiments in two beam collision, for I1,2 relating to intensity profiles for two
beams respectively:
��
P (x, y)I1(x, y)I2(x, y)dxdy
Pmax
〈P 〉Exp = �� = �
I1(x, y)I2(x, y)dxdy
(1 + 1
2RX) · (1 + 1
2RY , (5)
)
with Pmax the polarization at beam maximum intensity and polarization in transverse
plane, RX and RY the squared ratio of the intensity profile width and polarization profile
width (σI/σP ) 2 , for transverse X and Y projections, respectively.
These relations between average polarizations are taken into account when normalizing
pC measurements to H-Jet absolute polarization measurements and when providing
polarization values for RHIC experiments. For example for the typical at RHIC values
of R ∼ 0.1 − 0.2, beam polarization seen by H-Jet is lower than polarization seen by
experiments in beam collisions by ∼ 5 − 10%.
Profile parameter R can be extracted either directly from the measurements of intensity
and polarization profile widths σI and σP , as shown in Fig. 3a, or from the correlation
between polarization and intensity at each target position (for gaussian intensity and polarization
profiles), for example for the measurements with vertical target:
� �RX P I
=
, (6)
Pmax−X
Imax−X
which doesn’t require knowledge on target position. Imax−X and Pmax−X are beam intensity
and polarization 1 (averaged along vertical direction Y ), respectively, when target is
positioned in the beam center along axis X. A typical measurement for 100 GeV beam
is shown in Fig. 3b. In this approach the average over beam transverse cross section
polarization for the measurements with vertical target is
〈P 〉pC = Pmax−X
√ , (7)
1+RX
and similarly if horizontal target is used. The value 〈P 〉pC is compared to H-Jet polarization
measurements, when the normalization for pC polarization measurements is
derived.
The main sources of systematic uncertainties in polarization measurements by pC
polarimeter comes from the drift of the recoil carbon energy correction (2.5% in Run6),
and from corrections due to polarization profile, particularly in runs when one or both
transverse projections of the profile are not measured regularly (2% in Run6).
Combining these uncertainties with uncertainties from polarization normalization using
H-Jet, the final systematic uncertainties for the proton beam polarization measurements
were 4.7% and 4.8% for two RHIC beams and 8.3% for a product of two beam
polarizations in 2006 for 100 GeV beam running.
1 Compared to notation in Eq. (4) we here omitted angle brackets for brevity.
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