Hi,

There was quite a bit of discussion a little while ago about the
conversion between the laboratory x,y,z frame and the frame in which the
analysis is performed. Unfortunately, none of these messages tells me
the definition of U and V.

Let me give you my definition, and then tell me, whether I am correct.

In the Monte Carlo, a detector plane which is rotated by theta (positive
or negative) has the wires running perpendicular to the x' axis, where

x' = x * cos(theta) + y * sin(theta),

i.e. the wires are parallel to

y' = -x * sin(theta) + y * cos(theta).

Planes thus measure the x' coordinate regardless of rotation.

Moreover, any stagger or shift of the drift cells (wires) is done in the
Monte Carlo with respect to the x' axis, which also defines the
orientation (positive/negative shifts) no matter which rotation.

My question now is, with this definition, are u-planes those rotated by
+45deg? The most upstream drift chamber would thus be a u-chamber, while
the prop. chamber upstream nearest to the target would then be a v-plane
according to $CAL_DB/dt_geo.00018.

Conversion then is:

u = x * cos(theta) + y * sin(theta)

with theta>0

v = - [x * cos(theta) + y * sin(theta)]

with theta<0.

The negative sign for v-planes arises, I suspect, because the analysis v
coordinate is opposite to the MC x' for negative angles, so that u/v
form a right handed coordinate system. A positive v shift would hence be
a negative x' shift. Please see the attached for a u/v plane with both a
positive x' shift of 0.5cm.

Peter

Filename: uplane.ps

Filename: vplane.ps

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