diff --git a/RecoVertex/PrimaryVertexProducer/interface/SequentialPrimaryVertexFitterAdapter.h b/RecoVertex/PrimaryVertexProducer/interface/SequentialPrimaryVertexFitterAdapter.h
index 436957fcf729d..bd5f866e2f21f 100644
--- a/RecoVertex/PrimaryVertexProducer/interface/SequentialPrimaryVertexFitterAdapter.h
+++ b/RecoVertex/PrimaryVertexProducer/interface/SequentialPrimaryVertexFitterAdapter.h
@@ -15,7 +15,7 @@
 class SequentialPrimaryVertexFitterAdapter : public PrimaryVertexFitterBase {
 public:
   SequentialPrimaryVertexFitterAdapter() : fitter(nullptr){};
-  SequentialPrimaryVertexFitterAdapter(VertexFitter<5>* vertex_fitter) : fitter(vertex_fitter){};
+  SequentialPrimaryVertexFitterAdapter(const VertexFitter<5>* vertex_fitter) : fitter(vertex_fitter){};
   ~SequentialPrimaryVertexFitterAdapter() override = default;
 
   std::vector<TransientVertex> fit(const std::vector<reco::TransientTrack>& dummy,
@@ -41,6 +41,6 @@ class SequentialPrimaryVertexFitterAdapter : public PrimaryVertexFitterBase {
 
 protected:
   // configuration
-  VertexFitter<5>* fitter;  // Kalman or Adaptive
+  const VertexFitter<5>* fitter;  // Kalman or Adaptive
 };
 #endif
diff --git a/RecoVertex/PrimaryVertexProducer/interface/WeightedMeanFitter.h b/RecoVertex/PrimaryVertexProducer/interface/WeightedMeanFitter.h
index 810902c4a42ea..881bf2014187c 100644
--- a/RecoVertex/PrimaryVertexProducer/interface/WeightedMeanFitter.h
+++ b/RecoVertex/PrimaryVertexProducer/interface/WeightedMeanFitter.h
@@ -460,7 +460,7 @@ namespace WeightedMeanFitter {
 
 // adapter for the multiprimaryvertexfitter scheme
 // this code was originally introduced as part of PrimaryVertexProducer.cc
-// by Adriano Dee et.al., then moved here with minor modifications
+// by Adriano Di Florio <AdrianoDee>, Giorgio Pizzati <giorgiopizz> et.al. in #39995, then moved here with minor modifications
 class WeightedMeanPrimaryVertexEstimator : public PrimaryVertexFitterBase {
 public:
   WeightedMeanPrimaryVertexEstimator() = default;
diff --git a/RecoVertex/PrimaryVertexProducer/plugins/PrimaryVertexProducer.cc b/RecoVertex/PrimaryVertexProducer/plugins/PrimaryVertexProducer.cc
index 0b6e6f7cda4e8..b8536fe59d749 100644
--- a/RecoVertex/PrimaryVertexProducer/plugins/PrimaryVertexProducer.cc
+++ b/RecoVertex/PrimaryVertexProducer/plugins/PrimaryVertexProducer.cc
@@ -205,13 +205,12 @@ void PrimaryVertexProducer::produce(edm::Event& iEvent, const edm::EventSetup& i
   std::vector<reco::TransientTrack> t_tks;
 
   if (useTransientTrackTime_) {
-    edm::Handle<edm::ValueMap<float> > trackTimeResosH;
-    iEvent.getByToken(trkTimeResosToken, trackTimeResosH);
+    auto const& trackTimeResos_ = iEvent.get(trkTimeResosToken);
+    auto trackTimes_ = iEvent.get(trkTimesToken);
 
     if (useMVASelection_) {
       trackMTDTimeQualities_ = iEvent.get(trackMTDTimeQualityToken);
 
-      trackTimes_ = iEvent.get(trkTimesToken);
       for (unsigned int i = 0; i < (*tks).size(); i++) {
         const reco::TrackRef ref(tks, i);
         auto const trkTimeQuality = trackMTDTimeQualities_[ref];
@@ -219,9 +218,9 @@ void PrimaryVertexProducer::produce(edm::Event& iEvent, const edm::EventSetup& i
           trackTimes_[ref] = std::numeric_limits<double>::max();
         }
       }
-      t_tks = (*theB).build(tks, beamSpot, trackTimes_, *(trackTimeResosH.product()));
+      t_tks = (*theB).build(tks, beamSpot, trackTimes_, trackTimeResos_);
     } else {
-      t_tks = (*theB).build(tks, beamSpot, iEvent.get(trkTimesToken), *(trackTimeResosH.product()));
+      t_tks = (*theB).build(tks, beamSpot, trackTimes_, trackTimeResos_);
     }
   } else {
     t_tks = (*theB).build(tks, beamSpot);
diff --git a/RecoVertex/PrimaryVertexProducer/src/AdaptiveChisquarePrimaryVertexFitter.cc b/RecoVertex/PrimaryVertexProducer/src/AdaptiveChisquarePrimaryVertexFitter.cc
index 4b5bb01c270ca..199e0918e6380 100644
--- a/RecoVertex/PrimaryVertexProducer/src/AdaptiveChisquarePrimaryVertexFitter.cc
+++ b/RecoVertex/PrimaryVertexProducer/src/AdaptiveChisquarePrimaryVertexFitter.cc
@@ -258,19 +258,19 @@ double AdaptiveChisquarePrimaryVertexFitter::update(const reco::BeamSpot &beamsp
 
   // initial value for S, 0 or inverse of the beamspot covariance matrix
   Error3 S0;
-  double c0 = 0, c1 = 0, c2 = 0;
+  double c_beam[3] = {0, 0, 0};
   if (beam_weight > 0) {
     S0 = get_inverse_beam_covariance(beamspot);
-    c0 = -(S0(0, 0) * beamspot.x0() + S0(0, 1) * beamspot.y0() + S0(0, 2) * beamspot.z0());
-    c1 = -(S0(1, 0) * beamspot.x0() + S0(1, 1) * beamspot.y0() + S0(1, 2) * beamspot.z0());
-    c2 = -(S0(2, 0) * beamspot.x0() + S0(2, 1) * beamspot.y0() + S0(2, 2) * beamspot.z0());
+    for (unsigned int j = 0; j < 3; j++) {
+      c_beam[j] = -(S0(j, 0) * beamspot.x0() + S0(j, 1) * beamspot.y0() + S0(j, 2) * beamspot.z0());
+    }
   }
 
   for (unsigned int k = 0; k < nv; k++) {
     rho_vtx = 0;
     Error3 S(S0);
     // sum track contributions
-    double c[3] = {c0, c1, c2};
+    double c[3] = {c_beam[0], c_beam[1], c_beam[2]};
     for (unsigned int j = tkfirstv_[k]; j < tkfirstv_[k + 1]; j++) {
       const unsigned int i = tkmap_[j];
       const auto w = tkweight_[j];
diff --git a/RecoVertex/PrimaryVertexProducer/src/VertexTimeAlgorithmFromTracksPID.cc b/RecoVertex/PrimaryVertexProducer/src/VertexTimeAlgorithmFromTracksPID.cc
index a777fbab6cddb..db1fd074b4621 100644
--- a/RecoVertex/PrimaryVertexProducer/src/VertexTimeAlgorithmFromTracksPID.cc
+++ b/RecoVertex/PrimaryVertexProducer/src/VertexTimeAlgorithmFromTracksPID.cc
@@ -35,27 +35,27 @@ void VertexTimeAlgorithmFromTracksPID::fillPSetDescription(edm::ParameterSetDesc
   VertexTimeAlgorithmBase::fillPSetDescription(iDesc);
 
   iDesc.add<edm::InputTag>("trackMTDTimeVMapTag", edm::InputTag("trackExtenderWithMTD:generalTracktmtd"))
-      ->setComment("");
+      ->setComment("Input ValueMap for track time at MTD");
   iDesc.add<edm::InputTag>("trackMTDTimeErrorVMapTag", edm::InputTag("trackExtenderWithMTD:generalTracksigmatmtd"))
-      ->setComment("");
+      ->setComment("Input ValueMap for track time uncertainty at MTD");
   iDesc.add<edm::InputTag>("trackMTDTimeQualityVMapTag", edm::InputTag("mtdTrackQualityMVA:mtdQualMVA"))
-      ->setComment("");
+      ->setComment("Input ValueMap for track MVA quality value");
   iDesc.add<edm::InputTag>("trackMTDTofPiVMapTag", edm::InputTag("trackExtenderWithMTD:generalTrackTofPi"))
-      ->setComment("");
+      ->setComment("Input ValueMap for track tof as pion");
   iDesc.add<edm::InputTag>("trackMTDTofKVMapTag", edm::InputTag("trackExtenderWithMTD:generalTrackTofK"))
-      ->setComment("");
+      ->setComment("Input ValueMap for track tof as kaon");
   iDesc.add<edm::InputTag>("trackMTDTofPVMapTag", edm::InputTag("trackExtenderWithMTD:generalTrackTofP"))
-      ->setComment("");
+      ->setComment("Input ValueMap for track tof as proton");
 
-  iDesc.add<double>("minTrackVtxWeight", 0.5)->setComment("");
-  iDesc.add<double>("minTrackTimeQuality", 0.8)->setComment("");
+  iDesc.add<double>("minTrackVtxWeight", 0.5)->setComment("Minimum track weight");
+  iDesc.add<double>("minTrackTimeQuality", 0.8)->setComment("Minimum MVA Quality selection on tracks");
 
-  iDesc.add<double>("probPion", 0.7)->setComment("");
-  iDesc.add<double>("probKaon", 0.2)->setComment("");
-  iDesc.add<double>("probProton", 0.1)->setComment("");
+  iDesc.add<double>("probPion", 0.7)->setComment("A priori probability pions");
+  iDesc.add<double>("probKaon", 0.2)->setComment("A priori probability kaons");
+  iDesc.add<double>("probProton", 0.1)->setComment("A priori probability protons");
 
-  iDesc.add<double>("Tstart", 256.)->setComment("");
-  iDesc.add<double>("coolingFactor", 0.5)->setComment("");
+  iDesc.add<double>("Tstart", 256.)->setComment("DA initial temperature T");
+  iDesc.add<double>("coolingFactor", 0.5)->setComment("DA cooling factor");
 }
 
 void VertexTimeAlgorithmFromTracksPID::setEvent(edm::Event& iEvent, edm::EventSetup const&) {