A preliminary study of the correlation of halo hits was performed
to determine the background from halo. This study used the Run II
lattice and quadrupole pots with a displacement of 8
.
Since we will have
accurate timing from the trigger scintillators, we can reject
in-time halo particles which leave early time hits in the diagonally
opposite quadrupole spectrometer. Halo background is very
sharply peaked at 
as shown below, and is thus not a
concern for the dipole spectrometer.
About 25% of the tracks
gave hits in both pots in a spectrometer (correlated hits), while
75% gave hits in only one pot (uncorrelated hits). To
calculate the acceptance for halo hits faking a track
which we cannot reject from timing, we use
the following equation
where 
is the total halo acceptance,
is the acceptance for correlated halo, 
is the
acceptance for uncorrelated halo, and H is the fraction of
events with at least one halo hit.
We pessimistically assume that a halo hit or track must pass
through both opposite side pots to be rejected.
For the correlated tracks, 
since >98% of tracks
had early time hits in both pots of the diagonally opposite
spectrometer. For the uncorrelated hits (which pass through only one
pot in-time), 
, but uncorrelated hits can only fake
a track if there is one accepted hit in each pot for the same event.
Assuming a 100 kHZ halo rate with a 1.7 MHz crossing rate, we
find that about 6% of all interactions have a halo hit (H=0.06).
Substituting these values gives 
, which means that for
pessimistic assumptions
about 0.0008 of all interactions will have an accepted halo track.
Halo can only fake diffractive jet events when superimposed with
a dijet event, so only 0.08% of dijet events will have
a halo track. As shown in Fig. 30
the halo tracks are sharply peaked near the beam momentum
of 1000 GeV/c ()
and will largely be removed by the demand of a track with
. The uncorrelated hits will also
be effectively rejected by demanding a valid track, since they dominantly
form unphysical combinations.
With a resolution 
the chance of fluctuating
to >0.004 is less than 0.1%, but we assume only a factor of 50 rejection.
The L1 halo rate of 
of the dijet cross section
will thus be smaller than the signal rate, which is about
of the dijet cross section (assuming a track acceptance of 1%
and a signal of 0.3%).
Figure 30: The momentum distribution of halo particles
that hit the Roman pots.
Although the silicon vertex information will not be useful for rejecting
halo, the other components of the L3 single interaction tool
will be. The rejection factor from scintillator timing which was
three in the multiple interaction case will be at least four
due to the broader z distribution from halo interactions.
The longitudinal momentum cut
will clearly be very effective as a proton with 
carries 996 GeV/c. We estimate greater than a factor of 10 rejection
from this cut. Halo background will clearly not be a problem for
hard diffractive processes.