Comparison between code and data for $\pi$ and $e^+$ cross sections

Different kinematic regions where different fit/parameterization (based on experimental data) are listed as follows:


$\blacklozenge$ epc: photoproduction of pion/nucleons in elastic scattering and resonance regions;
$\blacklozenge$ Wiser: photoproduction of pion/nucleons in DIS (Deep Inelastic Scattering) region;
$\blacklozenge$ qfs: electron scattering in elastic and resonance regions;
$\blacklozenge$ Whitlow: electron scattering in DIS region;
$\blacklozenge$ rosetail: radiation tail from electron elastic scattering;

Kinematics: Beam energy = 5.650 GeV, $\theta_e=45^O$
Target: 4 cm LH2 for electron runs, 15 cm LH2 for positron runs

$p_e$(GeV/c)	1.5	0.9	0.55
$\pi^-$ (epc)(nb/GeV-sr)	0.000	0.000	0.000
$\pi^-$(wiser)(nb/GeV-sr)	2.981	204.446	1607.051
$\pi^-$(data)(nb/GeV-sr)	4.793	250.74	1579.9
$e^-$(qfs) (nb/GeV-sr)	0.4993	1.684	3.8437
$e^-$(Whitlow) (nb/GeV-sr)	0.305	1.324	2.219
$e^-$(rosetail)(nb/GeV-sr)	0.0110	0.2514	1.5205
$e^-$(data) (nb/GeV-sr)	0.2016	1.3317	5.2569
$e^+$(epc) (nb/GeV-sr)	0.00465	0.00568	0.00859
$e^+$(wiser) (nb/GeV-sr)	0.01092	1.00106	11.19969
$e^+$(data) (nb/GeV-sr)	0.00072	0.20570	2.49902
$\pi^-/e^-$(epc/[qfs+rosetail])	0.000	0.000	0.00000
$\pi^-/e^-$(wiser/[qfs+rosetail])	5.843	105.640	299.588
$\pi^-/e^-$(epc/[whitlow+rosetail])	0.000	0.000	0.000
$\pi^-/e^-$(wiser/[whitlow+rosetail])	9.445	129.764	429.775
$\pi^-/e^-$(data)	23.775	188.286	300.538
$e^+/e^-$(epc/[qfs+rosetail])	0.00424	0.00194	0.00138
$e^+/e^-$(wiser/[qfs+rosetail])	0.02140	0.51726	2.08786
$e^+/e^-$(epc/[whitlow+rosetail])	0.00686	0.00239	0.00198
$e^+/e^-$(wiser/[whitlow+rosetail])	0.03459	0.63539	2.99515
$e^+/e^-$(data)	0.036	0.155	0.4754

$\bigstar$ The internal radiation length used in Wiser's fit is: 2.7%
$\bigstar$ The radiation length used in rosetail is:
for 4cm liquid H$_2$ target
before interaction: 2.8 mil Al + 4 cm/2 LH2 = 0.08% + 0.23%= 0.31%
after interaction: 4 cm/2 LH2 + 7 mil Al/$\sin\theta$ + 16mil Al + 20 cm Air + 7 mil Kapton
= 0.23% + 1.01% = 1.24%

From the table above we compare data with wiser OR epc code for pion, and compare data with (whitlow+rosetail) OR (qfs+rosetail) for $e^-$. From the comparison we can see that wiser gives good result for $\pi$ cross section, and whitlow's fit is good for $e^-$ cross section. However, there is an overestimation in wiser's code for $e^+$ cross section. We expect this is because we didn't include the angular distribution of $\pi^0 \rightarrow e^+ + e^-$. We will include this in the future. At present we just take this overestimation into account when estimating positron background for e99117 runplan.