[Hps-analysis] [EXTERNAL] quick z0 vs. tanL tutorial

[Nelson, Timothy Knight]

I meant to add… the same cos(d_theta) shift you get in this technique also occurs in if using the code that PF wrote to do the top/bottom only multi-track vertexing: it’s simply from the misalignment of the two coordinate frames. Also, if the tracker opening angle is wrong, there is a bigger effect from changing the z-position of the sensors because of where the pivot is...

> On Mar 14, 2023, at 9:52 PM, Nelson, Timothy Knight via Hps-analysis <hps-analysis at jlab.org> wrote:
> 
> Hi All,
> 
> Today became busy so this is rather rushed, but I think describes things well enough.  Basically, the relationship between vertical track slope (which is what tan_lambda is to close approximation) and z0 (vertical position at z=0 of the tracking frame) is sensitive to misalignment between the SVT frame and the tracking frame through a factor of cos(d_theta), the (surely small) misalignment angle between the SVT and tracking frames in the (y,z) plane.  So, unless the misalignment of the SVT is very large, the *slope* of z0 vs. (track slope) - the estimate of target position - stays approximately the same.  I think it’s been so long since this was invented that folks forgot how it worked, but after suggesting it, Sho used it and it’s described pretty well in his thesis, although I’m not sure he covers the fact that it’s insensitive to misalignments in things like the measurement coordinates of the sensors.  Those types of misalignments change the slope of all tracks by a constant, so don’t change the relationship between z0 and (track slope) either to first order. Instead they will change the intercept, y_beam.
> 
> What this estimate of target position *is* sensitive to is *z positions* of sensors, where if one expands the tracker by 10% in z, one changes the estimate of the target position relative to the first layer by 10% also.  However… that’s also going to be a negligible effect, because the relative error on the scale of the tracker in z is very small - hundreds of microns over a meter.
> 
> Finally, what we still haven’t seen, and I thought Norman was going to show, is what the slope of z0 vs. tanL is for the data taken with the SVT wires.
> 
> Best,
> Tim
> 
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> <z0_v_tanL.pdf>