The beam and target polarization direction

Step 1. The equation for polarization observable, Pz

The following is the equation for the target asymmetry, Pz

Step 2. Target Polarization for FROST

To get the exact target asymmetry, we need to know the exact target polarization direction.
I have used values in the following table as the target polarization.

period	Target Polarization	Electron beam energy (E(e)) [GeV]
1	<=	1.645
2	<=	1.645
3	=>	1.645
4	=>	2.478
5	<=	2.478
6	=>	2.478
7	<=	2.478

Step 3. Target asymmetry, Pz (E(γ) : 700 - 800 MeV)

The target asymmetries made in several combinations have very nice agreement.

Step 4. The η(547) resonance in γ p -> p ( η )

The asymmetry E has 1
The resonance of the spin 3/2 is not existed
We can check the reasonable combination of the beam and target polarization direction

The following histograms are made as the example. These are data of period 2. Its target polarization is L+- (<=)
The following histograms are made with the events, which have the photon energy between 700 GeV and 800 GeV.

Tar-Pol: <=, Beam-Pol:-> ( spin : 1/2)	Tar-Pol: <=, Beam-Pol:<- ( spin : 3/2)

Step 5. The reasonable beam and target polarization direction

period	Target Polarization			TGBI Bank	Beam Polarization (BPol)	Λ/2
	From table	From Jo	From FSU (TPol)
1	L+- ( <= )	L++ ( => )	<= (1)	0	-> (2)	IN
				1	<- (1)
2	L+- ( <= )	L++ ( => )	<= (1)	0	<- (1)	OUT
				1	-> (2)
3	L++ ( => )	L+- ( <= )	=> (2)	0	-> (2)	IN
				1	<- (1)
4	L-+ ( <= )	L-+ ( <= )	=> (2)	0	-> (2)	IN
				1	<- (1)
5	L-- ( => )	L+- ( <= )	<= (1)	0	-> (2)	IN
				1	<- (1)
6	L++ ( => )	L++ ( => )	=> (2)	0	<- (1)	OUT
				1	-> (2)
7	L+- ( <= )	L+- ( <= )	<= (1)	0	<- (1)	OUT
				1	-> (2)

Target Polarization, =>(<=) mean the target polarization is parallel(anti-parallel) to the beam
Beam Polarization, ->(<-) mean the beam polarization is parallel(anti-parallel) to the beam
There are different target polarization from table and Jo in the yellow part of the upper table