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$\gamma$$\gamma$-Trigger

The primary $\gamma$$\gamma$-trigger is made on the DELPHI particle system, which is referred to as a no-tag event if there are no signals in the VSAT detector. In this analysis leptonic $\gamma$$\gamma$-events are of no interest, so the following cuts were imposed on the DELPHI particle system:

• At least three charged tracks should be recorded in the DELPHI detector in order to have a hadronic event. A charged track is required to have a P_T of at least 0.4 GeV and to be in a theta range between 10-90 degrees.

• The invariant mass of the hadronic system should be larger than 3 GeV.

• The total energy and transverse momentum of all particles in the hadronic system should be less than 24.0 and 5.0 GeV respectively. The maximum number of allowed tracks (charged and neutral) should be less than 17. Similar cuts are also made on charged and neutral particles separately, in order to contain the hadronic system as much as possible.

• No other particle with an energy greater than 30 GeV should be seen in the DELPHI detector unless it is in STIC (which is then a STIC+VSAT double tag). This is normally called an anti-tag, and assures that the second electron ends up in the beampipe with a Q² around zero.

Decays from tau pairs created in $\gamma$$\gamma$ collisions can produce more than two charged tracks and give some background. This is however very small in the VSAT Q² region and can be neglected. If there is a single or double hit in the VSAT in coincidence with the DELPHI hadronic system, we get a so called single or double tagged $\gamma$$\gamma$ event. The tagged electron must be well reconstructed in the VSAT so there are some restrictions on the recorded hits:

• An electron is not allowed to hit any of the edges of the detector, as an accurate energy reconstruction then is impossible.

• If an electron is further out than 8 cm, it is likely to interact with the flange of the beampipe in front of VSAT and loose energy. All such triggers are thus removed due to uncertainty in the energy measurement.

• The energy of the measured electron should be greater than 30 GeV, due to the high background rates and low energy resolution at lower energies.

• The joint energy of the hadronic and VSAT system should not be larger than the double beam-energy plus the VSAT energy resolution.

If both of the electrons is tagged the full kinematics of the $\gamma$$\gamma$-system can be obtained. The interesting quantities to measure is the momentum transfer in the lepton-photon vertex (Q_i²) and the invariant mass of the $\gamma$$\gamma$-system ( W_{$\gamma$$\gamma$}). In the VSAT region, where the $\theta$-angles of the scattered leptons are small, the expression for these quantities can be simplified [23]:

Q_i² $$\approx$$ 4E_beamE_isin²$${\frac{\theta_i}{2}}$$        W_{$\gamma$$\gamma$}² $$\approx$$ 4E₁^$\gamma$E₂^$\gamma$

Here E_i^$\gamma$ = E_beam - E_i is the energy of the radiated photon. With the VSAT detector it is possible to achieve and accuracy of 5 GeV in W_{$\gamma$$\gamma$} and 0.02 GeV²/c² in Q² [19].