Pointing Requirement to the Outer Layer of the Micro Vertex Detector

Wieman
8-June-04

As one is tracking in from the outer pointing detector to the outer layer of the micro vertex detector, one must limit the accidental association of a random hit in the outer layer of the micro vertex detector with the track. Full simulations are required to determine what level of false hits can be tolerated, but we assume the limit is not more than a few percent.

As shown in: http://www-rnc.lbl.gov/~wieman/GhostTracks.htm

The probability of a false association is:

eq. 1

is the track projection resolution

is the random hit density on the outer surface of the micro vertex detector

As shown in: http://www-rnc.lbl.gov/~wieman/HitDensityMeasuredLuminosity2.htm

This depends on luminosity and the micro vertex detector readout rate and it scales as:

Where r is the radius from the beam to the barrel of the micro vertex detector

The projection resolution, s, of two layers of a pointing detector depends on position resolution and multiple coulomb scattering and is as follows:

projected uncertainty due to position error x1 in the inner layer

projected uncertainty due to position error x2 in the outer layer

Combined error

distance from projection point to layer 1

distance from projection point to layer 2

Multiple scattering angle
from particle properties data book

Xf is fraction of radiation length

Two layer projection error, combining position error component with multiple coulomb scattering:

eq. 2

distance from projection point to first layer

distance from projection point to second layer

position resolution of the pointing detector

Fig. 1 Plot of eq. 2 showing the projected tracking error from the SVT to the outer layer of the micro vertex detector at 4.5 cm radius. The one case is for the inner layer of the SVT removed so pointing is done with the SVT layers at radius 10 cm and 14 cm. The second case is for the SVT using the inner layer at 6 cm radius and the mid layer at 10 cm radius. The average SVT radiation length fraction is 1.89%.

Fig. 2 Plot of eq. 1 showing the probability of falsely associating a pileup hit in the outer layer of the micro vertex detector with the track projected from the SVT. This uses the projected tracking errors shown in fig. 1 and a pileup hit density on the micro vertex detector of 17 /cm^2.

Presumably these false hit associations add to the combinatorial background and should be limited to a few percent.

Calculation of two points on fig. 1 using eq. 2 are shown below with input parameters.

Pointing accuracy of outer two layers of the SVT back to the outer layer of the micro vertex detector

Pointing accuracy of the inner two layers of the SVT to the outer layer of the micro vertex detector