The Hadronic Final State

The HERWIG [4] generator¹ has been used for this generator level study to produce tagged $\gamma$$\gamma$ events corresponding to LEP1 and LC beam energies (45.6 and 175 GeV respectively). For each tagging region considered, every final state particle (other than the tag) has been entered into a histogram corresponding to its pseudorapidity ( $\eta$ = - lntan($\theta$/2)), where $\theta$ is the polar angle of the particle measured from the direction of the beam that has produced the target photon) using the particle energy as a weight. The resulting `energy flow' distributions are shown in Figure , and are true energy distributions without the loss of energy due to acceptance effects.

 

The histograms are energy flows per event corresponding to x < 0.1 events (solid line) and x > 0.1 events (dashed line). The following cuts were made: W_generated > 5 GeV (above charm threshold); E_tag > 0.75  E_beam (N.B. changes with beam energy); $\theta_{tag}^{}$ > 30 mrad. The cross-sections after the cuts are shown in Table .

 

Table: Cross-sections for each beam energy and tagging region after the cuts described in the text. Note that requiring a minimum invariant mass reduces the cross section in the $\theta_{tag}^{}$ = 30 - 60 mrad range at E_beam = 45.6 GeV.

	$\sigma_{cuts}^{}$ (pb)
	Ebeam = 45.6 GeV		Ebeam = 175 GeV
$\theta_{tag}^{}$ (mrad)	x < 0.1	x > 0.1	x < 0.1	x > 0.1
30-60	75.29	9.99	23.92	10.85
60-120	13.87	18.39	3.67	3.71
120-200	1.15	6.10	0.43	0.77
> 200	0.11	2.48	0.08	0.26

 

The shapes of the energy flow distributions are quite similar for the different beam energies considered. This is an important observation as it means that the progress and conclusions of the LEP studies of F₂^$\gamma$, especially at low-x, are almost directly applicable to the LC analysis. It is already known that HERWIG generates the final state particles more forwardly than the LEP data [2,5], but nevertheless the distributions are a reasonably good approximation to those those expected at the LC (assuming Beamsstrahlung does not alter these energy flow distributions too much).

If the shapes are so similar under a change of beam energy, then those seen at beam energies of 45.6 GeV and 175 GeV indicate what those at higher beam energies might be like.

There are two vital components to a low-x F₂^$\gamma$ measurement at the LC. The first is having the small angle tagger (LCAL) to measure the low angle tags, and hence the low-x events. This also maintains tagging continuity in Q² from LEP to the LC [6]. The second is to constrain the final state models of the $\gamma$$\gamma$ Monte Carlos with the data. To do this, one must understand the hadronic response of the whole detector very well, especially the mask (if it is to be instrumented) and the LCAL. This would provide vital sampling of the energy flow in the forward region opposite to the tag (approximately 3 < $\eta$ < 4). One need only look at the lower $\theta_{tag}^{}$ ( 30 < $\theta_{tag}^{}$ < 120) regions, where the low-x cross-section is higher, to see the importance of at least sampling the final state at small angles, because this is where the largest differences are seen between low-x (x < 0.1) and high-x (x > 0.1) events. Looking at the photon structure problem at low-x another way, one is likely to see in the final state the signature of a low-x rise, due to the process that would be responsible for it, before ever unfolding to extract F₂^$\gamma$ - once again it is the knowledge of the hadronic response of the detector that is important.

As the tagging angle increases the situation becomes easier because the final state is more well contained in the central detector (the p_T of the final state is higher in order to balance the higher p_T of the tag). This is reflected by the energy flow distributions moving more towards the central detector (CD) as $\theta_{tag}^{}$ increases. In this tag region the measurement of F₂^$\gamma$ is therefore less model dependent, so the study of the evolution of F₂^$\gamma$ at high Q² is still an achievable goal.