Physics Requirements. The driving argument for the detector specifications naturally comes from the requirements of the physics programme. Clearly, this is largely uncharted territory. As time goes by, our view of the role of the ILC, and the best way to achieve its goals, will evolve. Results from the Large Hadron Collider experiments will appear that may change the scope of the ILC as a whole. Ongoing Monte Carlo simulation studies lead to an improved understanding of instrumental aspects. And new detector technologies will appear. Nevertheless, meaningful statements can be - and indeed have been - made on the required performance of the various detector subsystems. In this article, the relation between physics programme and the requirements for the forward tracker is briefly discussed. Momentum resolution One of the principal constraints to the tracker design in the literature derives the required momentum resolution from the analysis of the Higgs-strahlung process with subsequent invisible Higgs decay. The mass of the Higgs boson can be precisely determined by a reconstruction of the recoiling Z-boson. For leptonic decays of the Z (and especially for decay to a muon pair), a very narrow mass peak can thus be obtained for the Higgs boson. The width of the mass peak is limited by the tracker momentum measurement down to unprecedented level of Delta (1/pT) = 10-5 (GeV-1) (see for instance hep-ph/0511038 ). The exact form of the requirements on the forward region that can be derived from the recoil mass analysis depend quite strongly on the assumptions as to how the machine will be operated. For default operation at sqrt(s) = 500 GeV and a light Higgs boson (mH=115 GeV/c) the argument reads as follows. Only 5 % (15 %) of muons in the ZH channel has a polar angle below 20 (35) degrees. Therefore, the importance of the very forward tracker for this analysis is limited. Central muons from Z decay - on average - have a average transverse momentum of 93 GeV/c. Thus, the recoil mass analysis leads to a requirement on the asymptotic high-momentum resolution. In this case, the argument constrains design parameters like the space point resolution and lever arm of the tracker, while the material budget is of minor importance. An alternative scenario is the ILC operation only slightly above the Higgs-strahlung threshold. As the center-of-mass energy of the machine is reduced, the forward tracking region gains in importance. The fraction of tracks with polar angle below 20 (35) degrees increases up to 9.4 % (19 %) for sqrt(s)=250 GeV. For 17.9 % (35%) of Higgs-strahlung events at least one muon is reconstructed in the far forward (forward) tracker. In this case the Z-boson is produced essentially at rest and the muons have momenta in the range of mZ/2. For sqrt(s) = 250 GeV, the average transverse momentum of the muons is ~42 GeV/c. For very forward muons - with polar angle less than 20 degrees- the average transverse momentum is reduced to a mere 13 GeV/c. For these tracks multiple scattering may well play an important role for the momentum resolution, even with the very challenging material budget proposed in the literature (Tesla, DODs). In this situation, the relative weight of the material budget increases with respect to the other tracker parameters (space point precision, BR2). Naturally, there are several other physics processes that may give rise to high pT electrons and muon in the final state. For example, excellent momentum resolution is required also for SUSY end-point analyses. In the forward (20 < &theta < 35) and very forward (6 < &theta < 20) region the transverse momentum resolution performance is particularly difficult to maintain. The less favourable magnetic field orientation significantly degrades the performance, even if the tight constraints on spatial resolution and material budget are met equally well as in the barrel region. Also, the error on 1/pT is only constant if the contribution due to multiple scattering is ignored. In practice, this is a valid approximation only for high-momentum tracks (with momenta greater than 10 to several 10s of GeV depending on the material budget). For tracks with momentum below this limit the performance rapidly degrades. It is understood that the aim of &Delta (1/pT) = 10-5 (GeV-1) and similar tracker specifications in the literature are intended for high-momentum tracks in the barrel region of the detector. In the section on momentum resolution, the performance of the forward tracker will be evaluated as a function of the principal parameters of the tracker design. Vertexing Jets orginating in b- or c-quarks and hadronic decays of &tau -leptons can be identified through the lifetime signature of B- and D-hadrons. All ILC detector concepts envisage a high-precision multi-layer vertex detector to precisely reconstruct the decay vertices and reach an unprecedented flavour tagging performance. The role of the tracker in vertexing and the identification of heavy flavour is generally limited to that of providing sufficient lever arm to reduce the uncertainty in the momentum (that is highly correlated with the impact parameters). In the "long barrel" vertex detector layout, however, for very shallow polar angles the innermost measured point is provided by the forward tracker. While this affects only a small angular region, the flavour tagging performance may well turn out to be quite relevant. For 500 GeV collisions in which a tt-pair is produced, the probability to produce a b-quark at a polar angle smaller than 20 (12.5) degrees is 16% (6%). The impact parameter resolution for these tracks is discussed in a separate section . Pattern recognition The term pattern recognition refers to the process by which all hits left by a particular charged particle are identified and accumulated to form a track. Typically, the pattern recognition performance is expressed in terms of the efficiency with which tracks can be found and the purity of the track sample (or, inversely, the fake rate). For most charged particles, pattern recognition depends on a combination of detectors. For a central particle with pT > 1 GeV in the LDC or GLD concept 5 or 6 very precise space points in the vertex detector are available, 2 to 4 intermediate measurements in the Silicion Intermediate Tracker, and a large number (order 100) of measurements in the TPC. The coverage of the vertex detector and TPC extends to relatively small polar angles. Down to &theta ~ 15-20 degrees, several of the innermost vertex detector measurements are available (the density of background hits towards the edge of the innermost vertex detector layers may well render them of limited use in reducing the ambiguities that arise in pattern recognition). The TPC coverage - with a gradually reducing number of read-outs - extends down to 10-15 degrees. The combined performance of all sub-detectors is discussed briefly in this section. For very forward tracks (&theta < 20 degrees) in the same detector concepts the pattern recognition relies heavily on the 7 space points measured in forward tracking disks. Below approximately 15 degrees the Forward Tracking Disks are essentially on their own. Therefore, in a second section the stand-alone performance of the FTD is evaluated in some detail. Several classes of particles present a special challenge to the pattern recognition. Some of them are listed here: Low momentum particles Below approximately 1 GeV the particles curl up to form "loopers" in the intense magnetic field (3-5 T) envisaged for the ILC inner detectors. Such loopers leave numerous hits in the central tracker and finally leave the tracking volume through the forward tracker. The reconstruction of low-momentum particles challenges the pattern recognition capabilities of the detector. The track finding algorithm cannot benefit from the relatively relaxed hit densities in the outer central tracker layers. Another obstacle is the large multiple-scattering contribution to the extrapolation uncertainty of such tracks. Thus, efficient reconstruction of low-momentum tracks leads to a stringent requirement on the pattern performance of the intermediate and forward tracker. Non-prompt particles A second class of particles that lead to specific requirements is formed by non-prompt charged particles. The long life-time of K0s and lambdas leads to charged tracks originating at any point in the tracking volume. Photons may convert at any layer in the tracker. Efficient reconstruction of the resulting tracks - that present a limited number of measurements and particularly have no hits in the highly granular vertex detector - requires that all tracker sub-systems have an inherent capacity to resolve the ambiguities that arise during pattern recognition. Kinks One of the issues that has revealed to be very challenging in the LHC tracker is the reconstruction of charged hadrons that suffer nuclear interactions in the tracker volume. The trajectory model does not foresee large angle "kinks" in the track. Silicon trackers like those of the LHC experiments - with relatively few measurements and strong concentrations of material in thin layers - are especially sensitive to this problem. Therefore, the reconstruction efficiency for hadrons (pions) can be quite reduced with respect to that of muons of similar characteristics. Examples from CMS can be found in . Jets The tracker plays an important role for hadronic final states. The core of energetic jets form the most dense environment that the tracker should cope with. The precise reconstruction of energetic jets and hadronically decaying tau-leptons requires an extremely good two-track separation. Photons The reconstruction, identification and momentum measurement of electrons photons depends primarily on the electromagnetic calorimeter. The tracker design, however, plays a very important role. The material in the tracking volume determines the probability for the photons to convert. For photons that convert, a tracker with sufficient pattern recognition performance, the outgoing tracks and the conversion vertex may be reconstructed. While the performance of photon reconstruction is an important benchmark for the whole detector, in a number of recent studies (A. Birkedal, K. Matchev, M. Perelstein, Dark Matter at Colliders: a Model-Independent Approach, hep-ph/0403004 and C. Bartels, J. List, Model-independent WIMP Searches at the ILC, arXiv:0709.2629 ) into the possibility of a model-independent WIMP search using the channel e + e - &rarrow &gamma + E T miss the role of the forward detector stands out clearly. Cosmological constraints are used to provide a robust and nearly model-indendent prediction (a small number of parameters remains) of the production rate of WIMP pairss in e + e - collissions is derived. Of course, the WIMP pair signal is not observable at colliders. However, for collinear photons the rate of the process e + e - &rarrow &xi &xi &gamma is related to that of e + e - &rarrow &xi &xi in a model-independent way. Therefore, an observation of an excess of single forward photons over the e + e - &rarrow &nu &nu &gamma background provides a direct connection between cosmology and the physics that can be explored at the ILC. The recoil mass analysis of the photons yields a precise determination of the WIMP mass. The signal in this case is peaked in the forward direction d &sigma / d cos &theta &aprop sin -2 &theta. Therefore, the material in the forward tracker is an important parameter. Particle Flow The particle flow paradigm plays a central role in the design of several of the detector concepts. While much remains to be understood, it is clear that particle flow as a means to achieve unprecedented jet resolution leads to a stringent set of requirements on the tracker performance. To benefit fully from the superior momentum resolution of the tracker track reconstruction should be hermetic. This implies the reconstruction should be fully efficient for all azimuthal angles. This performance should be maintained down to a transverse momentum of ~ 100 MeV. Similarly, the coverage should extend into the very forward region down to a very small polar angle (i.e. match the angular coverage of the calorimeters as far as possible). Moreover, track reconstruction is required to be very pure: to minimize the confusion term that limits the particle flow performance, the fake track rate should be tightly controlled. Home Next Article