   Next: Examples of Applications Up: Track Fitting in r-z Previous: Pivot Transformation

## Track Fitting with Multiple Scattering

Now let us turn our attention to the r-z track fitting under the influence of multiple scattering. The treatment here provides a way to calculate the E0 of the last subsection including multiple scattering effects in track fitting. From now on, we take (y0,z0) = (0,0) and .The multiple scattering modifies the track parameter of the particle as (90)
where (91)
represents the change of the dip angle due to the multiple scattering as a function of y. This results in (92)
where the parmeters with the suffix are those at the initial point before multiple scattering.

Now, let us assume that we are given (n+1) hit points, ,measured at fixed y positions, .Then the minimization of the : (93)
The parameter vector that gives the minimum is (94)
with (95)
Through the above equation, the change in due to the multiple scattering induces a change in : (96)
From this we obtain the full error matrix including multiple scattering: (97)

Again the problem reduces to the evaluation of the correlation matrix in the coordinate measurements: (98)
with (99)
where the last expression is valid for .The full error matrix is then written in the form: (100)
where the first term is from the coordinate measurement errors while the second term from the multiple scattering: (101)

In the case of equal space sampling with the same position resolution, EM and EMS reduce to (102)
with (103)
in the large n limit.   Next: Examples of Applications Up: Track Fitting in r-z Previous: Pivot Transformation
Keisuke Fujii
12/4/1998