The Phase-Space-Scale-Factor in Topology γ p -> p π+ (π-)

Data used for this analysis

PERIOD RUN Target Pol. Electron Beam Energy
1 55521 - 55536 L+-(<=) 1.645 GeV
2 55537 - 55555 L+-(<=) 1.645 GeV
3 55556 - 55595 L++(=>) 1.645 GeV
5 55630 - 55678 L--(=>) 2.478 GeV
6 56164 - 56193 L++(=>) 2.478 GeV
7 56196 - 56233 L+-(<=) 2.478 GeV

Step 1 : We have chosen bound nucleon events in the butanol and carbon target

Topology γ p -> p π+ (π-) γ p -> p π- (π+) γ p -> π+ π- ( p ) \ γ p -> p π+ π- ( )
Case B MMCut < -0.1 MMCut < -0.1 MMCut < 0.85 MMCut < -0.1

Step 2 : We have made TH2D histogram with bound nucleon events in butanol and carbon target

The X-axis means PBin (φ is defined as the π+ azimuthal angles in the rest frame of π+ π- system).
The Y-axis means the photon energy and the unit is GeV. The bin size of Y-axis is 100 MeV.

Butanol

Carbon
γ p -> p π+ ( π- )
γ p -> p π- ( π+ )
γ p -> π+ π- ( p )
γ p -> p π+ π- ( )
γ p -> p π+ ( π- )
γ p -> p π- ( π+ )
γ p -> π+ π- ( p )
γ p -> p π+ π- ( )

step 3: Divide bound nucleon events from the butanol target by the carbon target.

γ p -> p π+ ( π- )
γ p -> p π- ( π+ )
γ p -> π+ π- ( p )
γ p -> p π+ π- ( )

step 4: We make the projected histograms in each E(γ) bin

black : Topology γ p -> p π+ ( π- ) , red : mean of Topologies
black : Topology γ p -> p π- ( π+ ) , red : mean of Topologies
black : Topology γ p -> π+ π- ( p ) , red : mean of Topologies
black : Topology γ p -> p π+ π- ( ) , red : mean of Topologies
black : Topology γ p -> p π+ ( π- ) , red : mean of Topologies
black : Topology γ p -> p π- ( π+ ) , red : mean of Topologies
black : Topology γ p -> π+ π- ( p ) , red : mean of Topologies
black : Topology γ p -> p π+ π- ( ) , red : mean of Topologies

step 5: Fit the projected histograms

red : mean of Topologies

red : mean of Topologies

step 6: Phase Space Scale Factor on the photon energy (using the fitting data)