$\gamma p\to a_2 p$ and $\gamma p\to f_2 p$

We present the model published in [Mat19a] concerning tensor meson photoproduction \begin{align} \vec \gamma (p_\gamma, \lambda_\gamma) p(p_N, \lambda_p) \to T(p_T, \lambda_T) p(p'_N, \lambda_p'), \end{align} with a linearly polarized beam. The code can be downloaded in Resources section and simulated in the Simulation section.

Models

For each exchange $E = \rho, \omega, b_1, h_1$ the amplitudes takes the form \begin{align} {\cal M}_{\lambda_\gamma \lambda_T ; \lambda_p \lambda'_p} &= -\sum_E T^{E}_{\lambda_\gamma \lambda_T}(t) R^E(s,t) B^E_{\lambda_p \lambda'_p}(t), \end{align} The Regge propagator is given by: \begin{equation}\label{eq:ReggePropa} R(s,t) = \frac{\tau + e^{-i\pi\alpha(t)}}{2} \, (-)^{\ell} \Gamma\left[\ell-\alpha(t)\right] (\alpha' s)^{\alpha(t)} . \end{equation} The Regge trajectories for the vector $V = \rho, \omega$ and the axial-vector $A = h_1,b_1$ are \begin{align*} \alpha_V(t) & = \alpha'_V t + 0.5 & \alpha_A(t) & = \alpha'_A (t-m_\pi^2) \end{align*} The bottom vertex depends on two helicity couplings for the vector exchange and one coupling for the axial-vector exchange. The top vertex depends on five couplings \begin{align} B^{V}_{\lambda_p \lambda'_p}(t) &= \left( \frac{-t'}{4m_p^2} \right)^{\frac{1}{2}|\lambda_p - \lambda'_p|} \left[ G^V_1 \delta_{\lambda_p, \lambda'_p} + 2 \lambda_p G^V_2 \delta_{\lambda_p, -\lambda'_p} \right] \\ B^A_{\lambda_p \lambda_p}(t) &= \left( \frac{-t'}{4m_p^2} \right) G_2^A \delta_{\lambda_p, -\lambda'_p} \\ T^{E}_{\lambda_\gamma \lambda_T}(t) & = \beta^{\gamma T}_E \left(\frac{-t'}{m_T^2}\right)^{\frac{1}{2}|\lambda_\gamma-\lambda_T|} \beta_{\lambda_\gamma \lambda_T}(t). \end{align} The nucleon couplings are \begin{align} G_1^\rho & = 1.63 & G_2^\rho &= 13.01& G_1^\omega &= 8.13& G_2^\omega & = 1.86 \end{align} The fitted overall photon couplings are \begin{align} \text{minimal: }&& \beta^V & = 0.251 \pm 0.053 & \beta^A & = 0.821 \pm 0.023 \\ \text{TMD: }&& \beta^V & = 1.060 \pm 0.073 & \beta^A & = 0.581 \pm 0.053 \\ \end{align} The model includes only isoscalar axial-vector exchanges $\beta^{\gamma T}_{b_1} = 0$. The $a_2$ and $f_2$ couplings are related by isospin relations \begin{align} \beta^V & = \beta^{\gamma a_2}_\omega = 3\beta^{\gamma a_2}_\rho = \beta^{\gamma f_2}_\rho = 3\beta^{\gamma f_2}_\omega , & \beta^A & = \beta^{\gamma a_2}_{h_1} = 3\beta^{\gamma f_2}_{h_1} \end{align} The helicity structures $\beta_{\lambda,\lambda_T}$ for the two models are

References

[Mat20a] V. Mathieu, et al (JPAC), ``Exclusive tensor meson photoptoduction,'' arXiv:2005.01617 [hep-ph]

Resources

• C/C++: C/C++ file (main.cpp)
• Input file: par_simu.txt .
• Output files: obs.txt , sdme0.txt , sdme1.txt , sdme2.txt , sdme_nat.txt , sdme_unnat.txt .
• gnuplot file: gnuplotObs.txt , gnuplotSDME.txt
• Contact person: Vincent Mathieu
• Last update: May 2020

Simulation

Results