Estudio del proceso $e^{+}e^{-} \to \tau^{+} \tau\gamma$ en el detector DELPHI del acelerador LEP

This report describes a study of events consisting of a \ttq pair plus a well isolated energetic photon, reconstructed at the DELPHI detector at LEP. Our aim is to look for deviations with respect to first-order QED corrections. The data analyzed comprise the full statistics recorded by DELPHI during 1992 and 1993, corresponding to approximately 1.5 million hadronic $Z^0$ decays. \\ In a first analysis, we study a possible contribution to this process due to anomalously high dipole moments of the $\tau$ lepton, using the energy spectrum of the isolated photon. The main requirements are a reasonable efficiency and a precise energy reconstruction in the high energy range. This last requirement was achieved by cross-checking the electromagnetic calorimeter response with the kinematical reconstruction of \mmg events. Following a good agreement between data and the expectation from the SM for all the photon energy spectrum, we have derived {\bf direct} upper limits on the anomalous magnetic (in Bohr magneton units) and electric dipole moments of the $\tau$ lepton, which read: \begin{gather*} \begin{align*} a_\tau \; &< \; 0.077~(95\%~C.L.) \\ d_\tau \; &< \; 4 \times 10^{-16}~e{\cdot}cm~(95\%~C.L.) \end{align*} \end{gather*} In a second analysis, we perform a search for the process \zhg through the channel $H \rta \tau^+ \tau^-$, where $H$ could be a general scalar, similar to the Higgs boson expected in the SM. The analysis is based on the study of the \ttq pair mass spectrum. It relies on two main features: on one hand, the {\em signal / background} ratio is strongly enhanced by applying a variable isolation angle cut, depending on $M_{\tau^+ \tau^-}$. On the other hand, a kinematical reconstruction of the \ttg event is performed, achieving a good mass resolution for all the mass range. A good agreement is found between data and the SM expectation for all the mass range, with NO1evidence of a peaking structure. Therefore, an upper limit can be extracted for the process \zhg for the mass range $5~GeV \, - \, 70~GeV$, assuming a 100\% branching ratio of the $H$ boson decaying into a \ttq pair. This limit is in the range: \begin{equation*} BR (Z^0 \rta H \gamma) \times BR (H \rta \tau^+ \tau^-) \; < \; 2 \times 10^{-5} \; - \; 1 \times 10^{-5}~(95\%~C.L.) \end{equation*} In a next step, we combine this limit with a similar one coming from an analysis of \bbg events, in order to cover the same Higgs boson mass range as above in a more effective way. Assuming SM Higgs boson decays, this new limit is in the range: \begin{equation*} BR (Z^0 \rta H \gamma) \, < \, 3 \times 10^{-5} \; - \; 5 \times 10^{-6}~(95\%~C.L.) \end{equation*}