Add white paper for transport jacobian correction

Core/src/Propagator/detail/JacobianEngine.cpp

@@ -138,6 +138,7 @@ BoundMatrix boundToBoundTransportJacobian(
   // Calculate the jacobian from free to bound at the final surface
   FreeToBoundMatrix freeToBoundJacobian =
       surface.freeToBoundJacobian(geoContext, freeParameters);
+  // https://acts.readthedocs.io/en/latest/white_papers/correction-for-transport-jacobian.html
   // Calculate the full jacobian from the local/bound parameters at the start
   // surface to local/bound parameters at the final surface
   return freeToBoundJacobian *

docs/white_papers.toml

@@ -15,4 +15,13 @@ pdf_url = "https://github.com/felix-russo/gaussian-track-densities/releases/down
 [white_papers.metadata]
 authors = [ "Felix Russo",]
 title = "Gaussian Track Densities"
-description = "Given the impact parameters $(d_0, z_0, t_0)$ of a track in Perigee parametrization, one can model the probability of the particle passing exactly through a point $(d, z, t)$ using a multivariate Gaussian distribution. In this white paper, we derive the maximum and the width of such a distribution for $d = 0$. This is useful in vertex seed finding, where we only consider the track density along the beam axis. We use the analytical results from this white paper in the unit test of the ACTS module AdaptiveGridTrackDensity."
+description = "Given the impact parameters $(d_0, z_0, t_0)$ of a track in Perigee parametrization, one can model the probability of the particle passing exactly through a point $(d, z, t)$ using a multivariate Gaussian distribution. In this white paper, we derive the maximum and the width of such a distribution for $d = 0$. This is useful in vertex seed finding, where we only consider the track density along the beam axis. We use the analytical results from this white paper in the unit test of the Acts module AdaptiveGridTrackDensity."
+[[white_papers]]
+repository = "https://github.com/beomki-yeo/path-correction-term-from-momentum-variation"
+slug = "correction-for-transport-jacobian"
+pdf_url = "https://github.com/beomki-yeo/path-correction-term-from-momentum-variation/releases/download/v2.0/main.pdf"
+
+[white_papers.metadata]
+authors = [ "Beomki Yeo",]
+title = "A Correction Term for Transport Jacobian from the Direction Variation"
+description = "In the track extension model of ACTS, the covariance of a track is updated for every surface intersection by applying a jacobian matrix, the composition of the coordinate transformation and free space transport. In the derivation of the transport jacobian, it is necessary to consider the path difference coming from the track displacement, which appears as a direction variation term with respect to the path length. \n\n\nThe motivation of this white paper is that the author failed in finding any reference explaining this clearly. (Please let the author know if anyone finds it) There are bunch of references which calculate this term with an ideal helix model, but it is not very useful with the runge-kutta based track extension model. Therefore, in this note, we are deriving the term thoroughly and demonstrate how it is implemented in the source code."