Draft: Faraway (viz. T-Track) vertex reconstruction & Lambda selection line
Introduction
This MR introduces a faraway tracks (viz. t-tracks) vertexing algorithm and dedicated HLT1 line for long-lived particles. The algorithm uses Faraway tracks (viz. t-tracks) reconstructed by HybridSeeding as an input.
1. Faraway Tracks (viz. T-tracks) Extrapolation Model
The new vertexing algorithm for faraway tracks (viz. T-Tracks) considers the non-linear extrapolation of tracks from SciFi in the upstream direction. This algorithm will substantially improve the mass resolution of composite particles and provide a fit chi2, which is highly discriminant for background rejection in selection lines.
The non-linear extrapolation is described as follows:
x(z) = x_0 + tx (z-z_0) + \frac{q}{p} (z-z_0) f(z,\frac{q}{p})
y(z) = y0 + ty (z-z0)
where
f(z,\frac{q}{p}) = a0 \frac{e^{a1(\frac{q}{p}-a2)} + e^{-a1(\frac{q}{p}+a2)}}{1+e^{a3(z-a4)}}
a0, a1, a2, a3, a4 - constants, determined from MC;
2. Faraway (viz. T-track) vertex reconstruction algorithm
Vertex reconstruction is done in three steps:
- POCA
zestimation using neural network. - Estimating vertex position with a given POCA
zas a mean point between track coordinates. - Clarification of Faraway track (viz. T-Track) and vertex parameters using vertex position hypothesis.
2.1. POCA z estimation using neural network
A two-layer neural network is used for POCA z estimation.
The size of the layers is 14 and 5. Both layers utilize the tanh activation function.
The six inputs are calculated using SciFi track variables: y^A - y^B, ty^A - ty^B, x^A - x^B, tx^A - tx^B, qop^A, qop^B.
2.2. Estimation of vertex position
The track extrapolation model, described in this section is used for initial vertex position estimation. Given two tracks are extrapolated to a found POCA z. The x and y vertex positions are calculated as a mean of the corresponding track coordinates.
2.3. Clarification of Faraway track/vertex (viz. T-Track) parameters
The unsatisfactory resolution of qop estimation by HybridSeeding leads to the need for clarification to improve the mass resolution of the mother particle. In addition, track slopes tx are another parameters, that are improved. The procedure is performed with a given vertex position hypothesis, which acts as a constraint on tracks.
The clarified values are found as follows:
(\frac{q}{p})^{A,B} = -\frac{tx_{sf}^{A,B} (z_{ov} - z_{sf}) + x_{sf}^{A,B} - x_{ov} }{f^{A,B}(z_{ov} - z_{sf})}
tx^{A,B} = - \frac{x_{sf}^{A,B} - x_{ov}}{z_{ov}-z_{sf}} + (\frac{q}{p})^{A,B} (z_{ov} - z_{sf}) f'^{A,B}
where A,B - denotes either one of tracks, f - function, described in extrapolation model section, f' = df/dz