Add documentation for vertex time reconstruction

Follow up to !69290 (merged) and !69404 (merged) to document information regarding vertex time.

/cc @aleopold @dshope

HighGranularityTimingDetector/HGTD_Reconstruction/HGTD_RecAlgs/README.md

+# HGTD Reconstruction Algorithms
+
+## Vertex Time Reconstruction
+
+Reconstruction of vertex time is implemented in the algorithm `VertexTimeAlg`
+(defined in
+[`src/VertexTimeAlg.h`](https://gitlab.cern.ch/atlas/athena/-/blob/main/HighGranularityTimingDetector/HGTD_Reconstruction/HGTD_RecAlgs/src/VertexTimeAlg.h)).
+Its configuration is located in the
+[`HGTD_Config`](https://gitlab.cern.ch/atlas/athena/-/tree/main/HighGranularityTimingDetector/HGTD_Config)
+package in
+[`HGTD_VertexTimeConfig.py`](https://gitlab.cern.ch/atlas/athena/-/blob/main/HighGranularityTimingDetector/HGTD_Config/python/HGTD_VertexTimeConfig.py).
+The algorithm runs during reconstruction with `Reco_tf.py` during the RDO-to-AOD
+stage, which is configured in
+[`HGTD_RecoConfig.py`](https://gitlab.cern.ch/atlas/athena/-/blob/main/HighGranularityTimingDetector/HGTD_Config/python/HGTD_RecoConfig.py).
+
+For details on the reconstruction algorithm and its implementation, see the
+[TWiki
+page](https://twiki.cern.ch/twiki/bin/viewauth/Atlas/VertexTimeReconstruction).
+
+### How to retrieve vertex time information from AOD
+
+Vertex time information is saved in AODs as decorations on `xAOD::Vertex`. Since
+only a subset of all vertices have a time reconstructed, a `hasValidTime`
+decoration is available to check if the vertex has a valid precision time.
+`hasValidTime` (type `uint8_t`) is set to `1` if a valid precision time is
+available, and is set to `0` otherwise. Vertex time and its resolution are
+available via the corresponding `time` and `timeResolution` decorations (type
+`float`) - the values are stored and returned in nanoseconds (`ns`). If a valid
+precision time is not available for the vertex, these two values are set to the
+default values of `time` $=0$ and `timeResolution` $=50/\sqrt{12}$.
+
+The algorithm reconstructs a time for the hard scatter interaction only.
+Consequently, all vertices for which
+```c++
+// Assuming we have a variable `const xAOD::Vertex* vertex`
+vertex->vertexType() == xAOD::VxType::VertexType::PriVtx
+```
+returns `false` (i.e. all vertices that are not primary) have `hasValidTime` set
+to `0`.
+
+The code below shows an example of obtaining timing information of a vertex
+```c++
+// Assuming we have a variable `const xAOD::Vertex* vertex`
+
+// Always first check if a vertex has a time available
+if (vertex->hasValidTime()) {
+  float vertex_time { vertex->time() };
+  float vertex_timeResolution { vertex->timeResolution() };
+}
+```
+
+### How to run vertex time reconstruction
+
+To run vertex time reconstruction and have vertex timing information available
+in AODs, full reconstruction from either HITS or RDO can be run with
+`Reco_tf.py` with Athena version 25.0.1 or later. For example, to run locally do
+```bash
+asetup Athena,25.0.1  # or any later version
+
+Reco_tf.py --AMIConfig r15365 \
+           --inputHITSFile <path-to-sample>/mc21_14TeV.601237.PhPy8EG_A14_ttbar_hdamp258p75_allhad.simul.HITS.e8481_s4272/* \
+           --outputAODFile <outputFileName>
+```
+The suggested sample is a $t\bar{t}$ allhad $\mu=0$ sample from the
+[ATLMCPROD-10908](https://its.cern.ch/jira/browse/ATLMCPROD-10908) production
+intended for HGTD studies.
+
+Alternatively, the algorithm can also be run standalone on AODs (e.g. if vertex
+time information is not saved in the AOD, or some changes in the algorithm are
+needed). In this case, the algorithm needs to be configured in a JO file. An
+example JO showing how to run the algorithm is available
+[here](https://gitlab.cern.ch/jedebevc/athena/-/blob/189deb26a551c7aabdd00017c1972cfed7d20c95/Control/Local/VertexTimePerformance/share/VertexTimePerf_JO.py)
+(the suggested input file is the same $t\bar{t}$ allhad $\mu=0$ sample mentioned
+previously). An algorithm that uses vertex time information should then be
+merged after `VertexTimeAlgCfg`, so that it has the vertex time decorations
+available.