References - Bogoliubov Laboratory of Theoretical Physics - JINR

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R = −Pt/Pl τ(1 + ε)/2ε; hence only a single measurement is necessary, strongly decreasing
the systematic uncertainties.
In a polarimeter one can only measure polarization components normal to the analyzer,
however use is made of the fact that the longitudinal component, Pℓ, of the
proton spin precesses in the dipole magnet of the HMS, and transforms into a longi-
tudinal, P fpp
ℓ
as well as a normal component, P fpp
n , In first approximation Pℓ precesses
by χθ = γκp(Θdipole + θtar − θfp), resulting in P fpp
n
≈ Pℓ × sin χθ at the polarimeter. In
addition, due to the presence of quadrupoles in the HMS, the longitudinal component
also produces an additional transverse polarization component, due to the non-dispersive
precession angle χφ. The effect of this precession, by χφ = γκp(φfp − φtar), cancels only
if the event distribution is symmetric in the angle difference (φfp − φtar).
The azimuthal asymmetry measured in the polarimeters is a function of the scattering
angle in the analyzer, ϑ; for a given bin of the incident proton momentum this distribution
has the form:
f ± (ϑ, ϕ) =
η(ϑ, ϕ)
2π
� 1 ± Pbeam(a1 + AyP fpp
y )cosϕ− Pbeam(b1 + AyP fpp
x
sin ϕ +0(nϕ) � ,
(9)
Here a1 and b1 are helicity independent asymmetries, η(ϑ, ϕ) is the polarimeter response
efficiency, and ± stands for the two beam helicities; Pbeam is the longitudinal beam polarization
and Ay is the analyzing power averaged over the incident proton momentum and
ϑ bin. To obtain the physical asymmetry we form the difference of helicity asymmetry,
divided by the sum, f + −f −
f + +f − ; the systematic asymmetries are canceled in first order with
this procedure.
3 AnalysisofGEp-IIIandGEp-2γ Experiments
For a given beam energy Ee, the scattering
angle θp and momentum pp of the recoiling
proton in elastic scattering are related by
equation:
pp = 2MpEe(Ee + Mp)cosθp
M 2 p +2MpEe + E2 e sin 2 (10)
θp
The difference between the measured momentum
and the momentum predicted by
10 at the measured angle, Δp = p−pel(θp),
therefore defines the degree of “inelasticity”
of a given event. Fig 2 shows distribution
of events p − pel(θp); elastic events
are located at Δp = 0, with a width determined
by the HMS momentum and angular
Figure 2: Δp spectrum for Q 2 =8.5GeV 2 with no
cuts.
resolution, the beam energy, and the HMS central angle. As seen from Fig. 2, although
it is possible to identify elastic and inelastic events based on the reconstructed proton
momentum pp and scattering angle θp, the resolution of the HMS is insufficient to achieve
a clean separation.
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