QCD Bound States (QCD)

Although being the first of the new charmonium-like states discovered since 2003 \cite{BelleX3872}, the $X(3872)$ is still one of the most puzzling ones concerning the properties. Since the mass is indistinguishably close to the sum $m(D^0) + m(\bar{D}^{\ast 0})$, it is unclear whether it lays above or beneath the $DD^{\ast}$ threshold. Furthermore, the natural width is very small and basically unknown up to a rather rough upper limit of $\Gamma_X < 1.2$ MeV \cite{PDG15}. Due to these extra-ordinary properties, this state is frequently suggested to be an exotic hadron, possibly featuring a different and more complex internal structure than a simple conventional mesonic $q\bar{q}$ state. In particular, several theoretical models (e.g. \cite{BraatenLS,HanhartLS,KalashLS}) relate not only the mass $m_X$ and the Breit-Wigner-like width $\Gamma_X$ to the internal structure, but explicitly also the line-shape of the resonance. This offers another experimental handle to identify the nature of the $X(3872)$.

In this work, we study the expected sensitivity of energy scans of narrow resonances performed with the HESR in combination with the PANDA detector at FAIR. The goal is to access experimentally the aforementioned properties for different hypothetical experimental and physical scenarios of the $X(3872)$. It represents an update and extension of an earlier simulation study of that state carried out in 2011 based on a different software revision \cite{Galuska2012}. Furthermore, this exemplary study serves as a proof of principle for high precision spectroscopy using the energy scan method with the PANDA experiment in general.

This release note is an excerpt of my PhD thesis which was submitted on July 21th this year.

This is the analysis note on the physics chapter of my PhD thesis, which I submitted two weeks ago. As for the current publication rules, the content of the chapter needs to be reviewed internally before I can show any results on conferences (which I intend to do e.g. at EuNPC).

I leave the publication date as the current date, as I don't know anything further.

The treatment of radiative decays in the tensor formalism is subtle.On the example of radiative J/psi decays the procedure is developed,discussing several methods to construct the amplitudes.In the appendices,spin wave functions,different gauges and form factors for radiative dcays are adressed.

Formulae for the differential cross sections for antiproton proton -> omega pi0, with omega decaying into pi+ pi- pi0 and into pi0 gamma, are derived using the tensor formalism(Rarita-Schwinger)

A recipe is given how to construct the decay amplitude for 1 -> 2 + 3 ;2 -> 4 +
5; 3 -> 6 + 7 in tensor formalism(Rarita-Schwinger)for arbitrary integral spins.

Taking the process antiproton proton to omega pi0,omega to pi0 gamma as example the rho matrix of the final state is derived in the helicity formalism taking into account P- and C-conservation.The differential cross section and the gamma polarization observables are calculated using Mathematica.A comparison with similar calculations for the decay omega to pi+ pi+ pi0 is performed.