An enormous amount of pairs will be created during collisions, for instance a few times pairs per a bunch crossing at JLC-I. Although most of them are inherently scattered in very forward angles, they can be greatly deflected by a strong magnetic field produced by an on-coming beam, so that they can enter the detector region while becoming background. This process has already been studied in details by simulations using ABEL  and GUINEA-PIG. 
Figure 7: Electrons and positrons scattered by beam-beam interaction at JLC-I, where the the vertical and horizontal axes are the scattering angles in vertical and horizontal directions, respectively.
Figure 7 shows the angular distributions after the beam-beam interaction obtained by ABEL for JLC-I. Many particles (electrons or positrons) are scattered at large angles beyond 200mrad. We can also clearly see an asymmetric distribution in the azimuthal direction. More particles are deflected in the vertical direction than in the horizontal one because of a very flat transverse beam profile (). Actually, a method to measure nanometer-beam-size has been proposed using these angular distributions.  Since the energies of the particles are relatively small, a few hundreds MeV, most of them are confined to around the beam axis in a solenoidal magnetic field of 2 Tesla for the case of JLC-I. When they hit the QC1 at the opposite side, many of the photons are back-scattered uniformly into the detector region and become serious background.
A masking system has been proposed to shield the back-scattered photons (Fig.8). A conical mask of heavy metal(tungsten) has been chosen to effectively absorb the photons. The front aperture of the mask was optimized for the core of the particles to pass through the mask.
Figure 9: Particles of pairs at the front face of the mask (44cm from the IP) for JLC-I, where the vertical axis is their energy and the horizontal one is their radial position.
Figure 8: Masking system in a solenoidal magnetic field of 2 Tesla around the IP for JLC-I.
Figure 9 shows the radial distribution of the particles as a function of their energies at the front face of the mask, 0.44m from the IP. As can be clearly seen in the figure, there is the maximum core radius of 5cm, at an energy of 0.1GeV. It is safely smaller than the aperture of 6.7cm. Particles outside the core are inherently scattered by much larger angles than the deflected ones, which represent possible background in the detector to be considered.
Figure 10: Hits per a bunch crossing by the pairs in B=2Tesla as a function of the radius( of a cylinder for two angular regions ((a) and (b)) for JLC-I.
In order to numerically estimate the background due to pairs in a vertex detector, we plot the number of hits for the particles to traverse a surface of a cylinder as a function of its radius, assuming no interaction there(Fig.10). Remembering that a train consists of 72 bunches in this case(JLC-I(c)), the total number of hits is on the order of per a train crossing during nsec at =2cm. In the central tracking region at 30cm, the total number of hits is expected to be less than 100/train.
Very recently D.Schulte proposed a similar masking system (Fig.11) with more detailed simulations for TESLA at LC95.  He found that back-scattered electrons (positrons) contribute to the hits at the vertex detector more than do the primary particles, although they would reach the detector more than 20 nano-seconds later. To reduce their number, additional masks are introduced around a superconducting quadrupole magnet and inside the mask, as shown in Fig.11. A graphite mask was found to effectively absorb back-scattered particles of lower energies.
Figure 12: Hits per a bunch crossing in the inner layer of the vertex detector for TESLA, where the vertex detector covers the angular region 200mrad.
Figure 11: Masking system for TESLA proposed by D.Schulte at LC95, where 66mrad and 33mm. The nearest superconducting quadrupole magnet is located 3m from the IP, and the aperture is 48mm.
With this configuration, he calculated the number of hits in the inner layer of the vertex detector at 1530mm as a function of the half aperture of the inside mask (). In this case, the back-scattered particles were also taken into account by the simulation. As clearly shown in Fig.12, a smaller can significantly reduce the number of hits, even at 15mm. Since the bunch separation of TESLA is 1sec, while it is 1.4-5.8nsec for JLC-I, the resultant hit number can be compared to the number per a train crossing for JLC-I.