 ...particles.

The vectors in Fig.2.1 are defined by
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 ...
 The terms containing the second derivatives
of 's are proportional to and are hence small and
usually negligible near the minimum.
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 ...space

This assumption is valid for a thin material.
If it is not, we can always slice the material into thin enough sublayers and
apply the method explained here repeatedly.
For a high momentum track, a different treatment is possible as
described later.
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 ...material

We assume that the fluctuation of the energy loss
is negligible in what follows.
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 ...process
 Notice that the helix parameter
vector so obtained is the one for the original track before energy loss and
multiple scattering, which can then be used for vertexing.
It should be also noted that the track segments combined here may
belong to detector regions with different magnetic fields, as long
as the fields can be regarded as constant in each region.
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 ...linking
 Since any straight line can be
regarded as the zero field limit of some helix,
the results shown below is a special case of the results in the
last subsection
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 ...follows
 The *'s in
Eq.2.5.34 represent matrices.
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 ...HREF="node11.html#EQtrackav">2.5.31
 It is easy to generalize the results to
the cases in which two or more regions of no magnetic field are present.
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 ...by

In Subection 2.4.c, we have Taylorexpand
Eq.2.1.1 to the lowest order to get a straight line track.
The track model here, on the other hand, corresponds to
the next order approximation.
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 ...0

This does not spoil the generality of our treatment, since
a nonzero can always recovered as a simple
shift in .
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 ...

We will ignore the small effects on due to the change in the dip angle :
which approximation is justifiable when .
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 ...equation

In practice K is usually regiondependent.
We should, therefore, integrate this equation segment by segment.
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 ...HREF="node21.html#EQdematerial">3.2.12

is now a finite shift of the y
coordinate of the pivot.
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 ...(K=0)

In fact, we have
while we know
from Eq.3.2.8.
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 ...sum

If the new pivot is within the sensitive volume of the tracker which
measured the track in question, we should drop the E_{S} term,
since the multiple scattering effects
in the tracker must presumably be included
in the original error matrix.
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 ...equation

The functional form of is unknown so that it must be
integrated out eventually.
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 ...shown

Notice that,
in the high momentum limit where the track can be approximated
by a parabola, E_{M} is determined solely by the configuration
of the tracking detector in question:
the ylocations of sampling points
and the spatial resolutions thereat.
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 ...here
 Exact formulae for
E_{M} which are valid for any n are given in Appendix B.
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 ...instead
 This method is applicable also to
thinlayer multiple scattering.
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 ...

As a matter of fact, whether the
particle track is measured before or after the multiple scattering
does not make any difference in the result.
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 ...scattering

The multiple scattering only changes ,, and, through the change in ,:
 
(2) 
Notice that the independent variables here are thus and
, E'_{MS} in the above expression is diagonal
when we use which is with its component
set equal to that of .
This implies that the components of E'_{MS}^{1} corresponding to
all but and are infinity or in other words
those of E'_{MS} are zero.
Although E'_{MS}^{1} is illdefined in this sense, we can treat
the infinite components as if they are
finite no matter how large and at the end of
calculations let them go to infinity.
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 ...ylocations

In our coordinate system, y corresponds to r.
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