# GlueX Physics Photoproduction

## Photoproduction

### Linear Polarization

In GlueX, the linearly polarized photons will be produced by coherent bremstrahlung. In this process, the photons in the coherent scattering peak from the crystal radiator are polarized. The direction of the polarization vector (in the lab) depends on the orientation of the crystal, but is fixed (in the lab). The degree of polarization of the coherent peak depends on the ratio of the photon energy to the end-point energy.

In the photo-production of mesons (via t-channel processes), the relevant

#### Reference Frames

The lab frame is typically taken with the z-axis along the incoming photon direction and the y-axis normal to the surface of the Earth. The x-axis is then taken ${\hat x}={\hat y}\times {\hat z}$. Related to the lab frame is the center of mass frame. The coordinate directions are the same, but the two frames are connected by a boost along the z-axis with $\beta =E_{{\gamma }}/(E_{{\gamma }}+m_{{p}})$ and the total energy in the center of mass is ${\sqrt {s}}={\sqrt {m_{{p}}^{{2}}+2m_{{p}}E_{{\gamma }}}}$.

In t-channel photo production, a particle X is produced recoiling against an out-going proton. The Mandelstam t is given as $t=(p_{{X}}^{{\mu }}-k^{{\mu }})(p_{{\mu X}}-k_{{\mu }})$ where k is the photon momentum and $p_{{X}}$ is the 4-momentum of the produced particle $X$.