TH-PHD-2018-006

The investigation of the properties of the proton is one of the major topics in modern hadron physics. The inner structure of the proton can be accessed via electromagnetic form factors. Of great interest is the time-like region ($q^2$ > 0), which can be investigated in reactions of $\bar{p}p \rightarrow {\ell}^+{\ell}^-$ (${\ell}$ = $e$, $\mu$, $\tau$).

This work reports on feasibility studies for the measurement of time-like electromagnetic form factors of the proton, $|G_E|$ and $|G_M|$, in reactions of $\bar{p}p \rightarrow {\mu}^+{\mu}^-$ at the future \PANDA experiment (FAIR, Darmstadt). The studies are performed at four different beam momenta between 1.5 and 3.3 GeV/$c$. The high luminosity, which will be available at \PANDA/FAIR, will allow for the collection of data with high statistics, which is a prerequisite for the separate extraction of the electromagnetic proton form factors from the signal angular distribution of the reconstructed ${\mu}^-$ (${\mu}^+$).

At first, the studies were performed for the conditions of the latest data taking phase at \PANDA (\PANDA Phase-3). The achievable accuracy of the form factors is determined by means of Monte-Carlo simulation and the subsequent data analysis for the signal reaction, assuming $R = |G_E|/|G_M|$ to be equal unity. Data samples for both the signal and for all relevant background channels have been generated and simulated using the PandaRoot software framework together with dedicated event generators.

For the most challenging background channel $\bar{p}p \rightarrow \pi^+\pi^-$, data sets of 10$^8$ events were generated and used for the determination of the suppression factor. The simulated data samples also allow for the calculation of the expected pion contamination statistics, which will remain in the signal data after the application of all selection criteria. The signal-to-background separation has been optimized through the use of multivariate classification methods (Boosted Decision Trees). A background subtraction will be necessary to remove the pion contamination from the reconstructed data at \PANDA. This effect has been taken into account in these feasibility studies. For this purpose, a method was developed in order to construct angular distributions for the pion contamination with both the expected statistics and a mostly realistic shape. The influence of this shape on the extracted precision of the form factors was investigated in a separate study. Systematic uncertainties were estimated as well.

It will be shown, that a sufficient suppression of all other relevant background channels (as for example $\bar{p}p \rightarrow \pi^+\pi^- \pi^0$, $\bar{p}p \rightarrow \pi^0\pi^0$, $\bar{p}p \rightarrow K^+K^-$, etc.) will be achieved at \PANDA.

Due to the high rest mass of the muon, QED radiative corrections in the signal $\bar{p}p \rightarrow \mu^+\mu^-$ are expected to be small compared to $\bar{p}p \rightarrow e^+e^-$, mainly caused by final state radiation. The influence of final state radiation on the signal statistics is studied using the PHOTOS software package.

Since \PANDA will be able to investigate both channels of $\bar{p}p \rightarrow {\ell}^+{\ell}^-$ (${\ell}$ =$e$, $\mu$), it is possible to determine the ratio of the effective form factor obtained with both channels. This allows to perform a sensitive test of lepton universality ($e$-$\mu$) at \PANDA.

A separate study was performed for the conditions of the first data acquisition time period of \PANDA (\PANDA Phase-1).