Primary Vertex Reconstruction for Heterogeneous Architecture at CMS

• This poster reports on vertex reconstruction at CMS in HL-LHC conditions.
• Based on DPS note DPSNOTENUMBER
• The CMS vertex reconstruction is a two-step procedure consisting of vertex finding and fitting. The vertex is found producing clusters of tracks coming from the same interaction vertex using the Deterministic Annealing (DA) algorithm [1], and then an Adaptive Vertex Fit [2] computes the best estimate of the vertex position and the parameters of the associated tracks.
• Given the high impact on reconstruction time of this procedure (up to 10% of the whole time with HL-LHC conditions), new algorithms have been developed for the two steps mentioned above
• Both the new algorithms have been designed to be runnable in parallel on a GPU. Both versions (CPU and GPU) have been developed. All the results shown here are obtained running on CPU.

New Clustering

• the new clustering procedure sorts the tracks in the z coordinate, splits them in blocks of same size (set by default to 512) with a fixed overlap fraction between blocks (set by default to 0.5) and performs independently the DA along all the blocks;
• All the results shown have been obtained with a block size of 512 and and overlap fraction of 0.5

New Estimator

• the new estimator, which replaces the Adaptive Vertex Fitter, iteratively estimates the vertex 3D coordinates and errors using the weighted mean of tracks impact point at the beamspot position and uncertainty. The iterations include an outlier rejection to improve the performance.

• Reconstructed offline vertices are considered matched to a simulated vertex if the following conditions are satisfied:
  • \(|\Delta z| < 1\; \textrm{mm}\);
  • \(|\Delta z|/\sigma_z < 3\) where \(\sigma_z\) is the uncertainty in the reconstructed vertex z position.
• Reconstructed vertices that are not matched to a simulated vertex are counted as misidentified (fakes).
• Reconstructed vertices that are matched to the same simulated vertex are counted as duplicates.
• If more than one simulated vertices is matched to the same reconstructed vertex, the latter is counted as multimatched (merged).
• \( \textrm{Efficiency} = \frac{n_{\textrm{matched sim}}}{n_{\textrm{sim}}} \)
• \( \textrm{Fake rate} = \frac{1-n_{\textrm{matched reco}}}{n_{\textrm{reco}}} \)
• Resolution for matched reco vertices: \(\textrm{Resolution of x} = \sigma (x_{\textrm{sim}} - x_{\textrm{reco}}) \)
• Pull for matched reco vertices: \(\textrm{Pull of x} = \sigma (\frac{x_{\textrm{sim}} - x_{\textrm{reco}}}{\sigma_{\textrm{reco}}}) \)

• The vertexing performance has been measured in a simulated \(t \bar{t}\) sample with superimposed pileup (PU) events:
• the number of PU events generated follows a poissonian distribution with <PU>=200;
• Measurements run with a single process with 10 concurrent threads on Intel Skylake Gold processor, with no other processes running on the machine.
• Run4 CMS detector conditions and geometry are used in the simulations.

• the current vertexing algorithm (black);
• the new DA clustering in blocks and the current adaptive vertex fit (red);
• the current DA clustering and the new weighted mean vertex estimator (green);
• the new DA clustering in blocks and weighted mean vertex estimator (pink).

• The plot shows the time spent on the Primary Vertex Producer for different configurations
• Parts of the old algorithm have impact on the timing:
  • New Clustering + Old Fitter performance benefits the substitution of the clustering
  • Old Clustering + New Estimator performance is still affected by the Old Clustering

• The two separated algorithms (clustering and fitter) and the combination of the two have been tested for physics performances as well as computational performances
• Considering they are a work in progress running on CPU with no optimization (no parallel execution), the results obtained for efficiency, resolution and timings are really promising
Future plans:
• The GPU implementation is currently being tested and will take advantage of the architecture as well as the algorithm parallelization
• The two algorithms are thought mainly to solve the time consuming RECO in high PU scenarios, but an effort is being made to test them in a Run 3 scenario given it’s better efficiency and resolution than the previous algorithms used in CMS

1. Chabanat, E; Estre, N; Deterministic Annealing for Vertex Finding at CMS, 2005, 10.5170/CERN-2005-002.287
2. Frühwirth, R; Waltenberger, W; Vanlaer, P; Adaptive Vertex Fitting, 2007, CMS-NOTE-2007-008