docs: Add comment on computation of impact parameter from the doublet #3728
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…acts-project#3728) One of the criterion used in doublet finding relies on computing the minimal distance between the origin and the straight line connecting the two points of the doublet. This distance is compared against a maximum impact parameter (`impactMax`) provided by the user. Let's consider for instance the middle-top doublet search. <img width="479" alt="Geometry" src="https://github.com/user-attachments/assets/bb1c3f87-d687-4f49-9582-02e91773f8ad"> In the attached image: - `A` is the origin - `B` is the middle space point, thus `AB = rM` (radius of middle space point) - `C` is the top space point What the code does is to compute `BD` (`xNewFrame` in the code) and `CD` (`yNewFrame` in the code) and then a simple geometric similarity to compute the impact parameter. The code currently does: `Im / CD = AB / BD`, where `Im` is the impact parameter we are trying to compute. Thus `Im = (AB * CD) / BD <= impactMax`. Unfortunately `Im` is equal to `AF`, while we really want to compute `AE`. The proper computation would be `Im / CD = AB / BC`, which leads to `Im = (AB * CD) / BC <= impactMax`. In this case `Im = AE`. However, `BC` has to be computed from `CD` and `BD`. In order to avoid square roots I'm using square quantities. It is also possible that the code assumes that the `alpha` angle is too small to make a difference and thus uses an approximation... But there are no comments in the code about this
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One of the criterion used in doublet finding relies on computing the minimal distance between the origin and the straight line connecting the two points of the doublet. This distance is compared against a maximum impact parameter (
impactMax) provided by the user.Let's consider for instance the middle-top doublet search.
In the attached image:
Ais the originBis the middle space point, thusAB = rM(radius of middle space point)Cis the top space pointWhat the code does is to compute
BD(xNewFramein the code) andCD(yNewFramein the code) and then a simple geometric similarity to compute the impact parameter.The code currently does:
Im / CD = AB / BD, whereImis the impact parameter we are trying to compute. ThusIm = (AB * CD) / BD <= impactMax. UnfortunatelyImis equal toAF, while we really want to computeAE. The proper computation would beIm / CD = AB / BC, which leads toIm = (AB * CD) / BC <= impactMax. In this caseIm = AE.However,
BChas to be computed fromCDandBD. In order to avoid square roots I'm using square quantities.It is also possible that the code assumes that the
alphaangle is too small to make a difference and thus uses an approximation... But there are no comments in the code about this