diff --git a/include/HEJ/utility.hh b/include/HEJ/utility.hh
index b57d7df..6bbf2bf 100644
--- a/include/HEJ/utility.hh
+++ b/include/HEJ/utility.hh
@@ -1,104 +1,114 @@
 /**
  * \file
  * \brief Contains various utilities
  *
  *  \authors   The HEJ collaboration (see AUTHORS for details)
  *  \date      2019-2020
  *  \copyright GPLv2 or later
  */
 #pragma once
 
 #include <array>
 #include <memory>
 #include <string>
 
 #include "boost/core/demangle.hpp"
 
 #include "fastjet/PseudoJet.hh"
 
 namespace HEJ {
 
   inline
   std::string join(
       std::string const & /* delim */
   ){
     return "";
   }
 
   inline
   std::string join(
       std::string const & /* delim */, std::string const & str
   ){
     return str;
   }
 
   //! Join strings with a delimiter
   /**
    *   @param delim      Delimiter to be put between consecutive strings
    *   @param first      First string
    *   @param second     Second string
    *   @param rest       Remaining strings
    */
   template<typename... Strings>
   std::string join(
       std::string const & delim,
       std::string const & first, std::string const & second,
       Strings&&... rest
   ){
     return join(delim, first + delim + second, std::forward<Strings>(rest)...);
   }
 
   //! Return the name of the argument's type
   template<typename T>
   std::string type_string(T&& /*unused*/){
     return boost::core::demangle(typeid(T).name());
   }
 
   //! Eliminate compiler warnings for unused variables
   template<typename... T>
   constexpr void ignore(T&&... /*unused*/) {}
 
   //! Check whether two doubles are closer than ep >= 0 to each other
   inline
   constexpr bool nearby_ep(double a, double b, double ep){
     assert(ep >= 0);
     return std::abs(a-b) < ep;
   }
 
   //! Check whether all components of two PseudoJets are closer than ep to each other
   inline
   bool nearby_ep(
       fastjet::PseudoJet const & pa, fastjet::PseudoJet const & pb,
       double ep
   ){
     assert(ep >= 0);
     for(size_t i = 0; i < 4; ++i){
       if(!nearby_ep(pa[i], pb[i], ep)) return false;
     }
     return true;
   }
 
   inline
   bool nearby(
       fastjet::PseudoJet const & pa, fastjet::PseudoJet const & pb,
       double const norm = 1.
   ){
     return nearby_ep(pa, pb, 1e-7*norm);
   }
 
   namespace detail {
     template<typename T, std::size_t N, std::size_t... Ns>
     struct ArrayTag{
       using type = typename ArrayTag<std::array<T, N>, Ns...>::type;
     };
     template<typename T, std::size_t N>
     struct ArrayTag<T, N> {
       using type = std::array<T, N>;
     };
   }
   // helper for multidimensional std::array, for example
   // MultiArray<T, N1, N2> = std::array<std::array<T, N1>, N2>
   template<typename T, std::size_t N, std::size_t... Ns>
   using MultiArray = typename detail::ArrayTag<T, N, Ns...>::type;
 
+  //! Check momentum conservation
+  template <class Event>
+  bool momentum_conserved(Event const &ev, const double tolerance = 1e-7) {
+    fastjet::PseudoJet diff;
+    for (auto const &in : ev.incoming()) diff += in.p;
+    const double norm = diff.E();
+    for (auto const &out : ev.outgoing()) diff -= out.p;
+    return nearby_ep(diff, fastjet::PseudoJet{}, tolerance*norm);
+  }
+
 } // namespace HEJ
diff --git a/src/PhaseSpacePoint.cc b/src/PhaseSpacePoint.cc
index 450be43..8e1b0a5 100644
--- a/src/PhaseSpacePoint.cc
+++ b/src/PhaseSpacePoint.cc
@@ -1,987 +1,983 @@
 /**
  *  \authors   The HEJ collaboration (see AUTHORS for details)
  *  \date      2019-2020
  *  \copyright GPLv2 or later
  */
 #include "HEJ/PhaseSpacePoint.hh"
 
 #include <algorithm>
 #include <cassert>
 #include <cmath>
 #include <cstdlib>
 #include <functional>
 #include <iterator>
 #include <limits>
 #include <numeric>
 #include <random>
 #include <tuple>
 
 #include "fastjet/ClusterSequence.hh"
 #include "fastjet/JetDefinition.hh"
 
 #include "HEJ/Constants.hh"
 #include "HEJ/Event.hh"
 #include "HEJ/JetSplitter.hh"
 #include "HEJ/PDG_codes.hh"
 #include "HEJ/RNG.hh"
 #include "HEJ/event_types.hh"
 #include "HEJ/kinematics.hh"
 #include "HEJ/resummation_jet.hh"
 #include "HEJ/utility.hh"
 
 namespace HEJ {
   namespace {
     constexpr int MAX_JET_USER_IDX = 1000;
 
     bool is_nonjet_parton(fastjet::PseudoJet const & parton){
       assert(parton.user_index() != -1);
       return parton.user_index() > MAX_JET_USER_IDX;
     }
 
     bool is_jet_parton(fastjet::PseudoJet const & parton){
       assert(parton.user_index() != -1);
       return parton.user_index() <= MAX_JET_USER_IDX;
     }
 
     namespace user_idx {
       //! user indices for partons with extremal rapidity
       enum ID: int {
         qqbar_mid1 = -9,
         qqbar_mid2 = -8,
         qqbarb = -7,
         qqbarf = -6,
         unob = -5,
         unof = -4,
         backward_fkl = -3,
         forward_fkl = -2,
       };
     } // namespace user_idx
     using UID = user_idx::ID;
 
     double phase_space_normalisation(
         int num_Born_jets, int num_out_partons
     ){
       return std::pow(16.*std::pow(M_PI,3), num_Born_jets - num_out_partons);
     }
 
   } // namespace
 
   Event::EventData to_EventData(PhaseSpacePoint psp){
     Event::EventData result;
     result.incoming = std::move(psp).incoming_; // NOLINT(bugprone-use-after-move)
     result.outgoing = std::move(psp).outgoing_; // NOLINT(bugprone-use-after-move)
     // technically Event::EventData doesn't have to be sorted,
     // but PhaseSpacePoint should be anyway
     assert(
         std::is_sorted(
             begin(result.outgoing), end(result.outgoing),
             rapidity_less{}
         )
     );
     assert(result.outgoing.size() >= 2);
     static_assert(
         std::numeric_limits<double>::has_quiet_NaN,
         "no quiet NaN for double"
     );
     constexpr double nan = std::numeric_limits<double>::quiet_NaN();
     result.decays = std::move(psp).decays_; // NOLINT(bugprone-use-after-move)
     result.parameters.central = {nan, nan, psp.weight()}; // NOLINT(bugprone-use-after-move)
     return result;
   }
 
   std::vector<fastjet::PseudoJet> PhaseSpacePoint::cluster_jets(
       std::vector<fastjet::PseudoJet> const & partons
   ) const{
     fastjet::ClusterSequence cs(partons, param_.jet_param.def);
     return sorted_by_rapidity(cs.inclusive_jets(param_.jet_param.min_pt));
   }
 
   bool PhaseSpacePoint::pass_resummation_cuts(
       std::vector<fastjet::PseudoJet> const & jets
   ) const{
     return cluster_jets(jets).size() == jets.size();
   }
 
   namespace {
     // find iterators to central qqbar emission
     auto get_central_qqbar(Event const & ev) {
       // find born quarks (ignore extremal partons)
       auto const firstquark = std::find_if(
           std::next(ev.begin_partons()), std::prev(ev.end_partons(), 2),
           [](Particle const & s){ return (is_anyquark(s)); }
       );
       // assert that it is a q-q_bar pair.
       assert(std::distance(firstquark, ev.end_partons()) != 2);
       assert(
           ( is_quark(*firstquark) && is_antiquark(*std::next(firstquark)) )
           || ( is_antiquark(*firstquark) && is_quark(*std::next(firstquark)) )
       );
       return std::make_pair(firstquark, std::next(firstquark));
     }
 
     //! returns index of most backward q-qbar jet
     template<class Iterator>
     int get_back_quark_jet(Event const & ev, Iterator firstquark){
       // find jets at FO corresponding to the quarks
       // technically this isn't necessary for LO
       std::vector<int> const born_indices{ ev.particle_jet_indices() };
       const auto firstquark_idx = std::distance(ev.begin_partons(), firstquark);
       int const firstjet_idx = born_indices[firstquark_idx];
       assert(firstjet_idx>0);
       assert( born_indices[firstquark_idx+1] == firstjet_idx+1 );
 
       return firstjet_idx;
     }
 
     //! returns index of most backward q-qbar jet
     int getBackQuarkJet(Event const & ev){
       const auto firstquark = get_central_qqbar(ev).first;
       return get_back_quark_jet(ev, firstquark);
     }
   } // namespace
 
   double PhaseSpacePoint::estimate_emission_rapidity_range(
     Event const & ev
   ) const {
     assert(std::is_sorted(begin(ev.jets()), end(ev.jets()), rapidity_less{}));
 
     const double ymin = is_backward_g_to_h(ev)?
       ev.outgoing().front().rapidity():
       most_backward_FKL(ev.jets()).rapidity();
     const double ymax = is_forward_g_to_h(ev)?
       ev.outgoing().back().rapidity():
       most_forward_FKL(ev.jets()).rapidity();
     double delta_y = ymax - ymin;
     // neglect tiny probability for emission between central qqbar pair
     if(ev.type() == event_type::central_qqbar) {
       const int qjet = getBackQuarkJet(ev);
       delta_y -= ev.jets()[qjet+1].rapidity() - ev.jets()[qjet].rapidity();
     }
     assert(delta_y >= 0);
     return delta_y;
   }
 
   double PhaseSpacePoint::estimate_ng_mean(Event const & ev) const {
     // Formula derived from fit in arXiv:1805.04446 (see Fig. 2)
     constexpr double GLUONS_PER_RAPIDITY = 0.975052;
     return GLUONS_PER_RAPIDITY*estimate_emission_rapidity_range(ev);
   }
 
   int PhaseSpacePoint::sample_ng(Event const & event, RNG & ran){
     if (param_.nlo.enabled == true){
         std::uniform_int_distribution<> dist(0, 1);
         const int ng = dist(ran);
         weight_ *= 2;
         assert(ng < 2);
         assert(ng >= 0);
         return ng;
     }
     else{
         const double ng_mean = estimate_ng_mean(event);
         std::poisson_distribution<int> dist(ng_mean);
         const int ng = dist(ran);
         assert(ng >= 0);
         assert(ng < MAX_JET_USER_IDX);
         weight_ *= std::tgamma(ng + 1)*std::exp(ng_mean)*std::pow(ng_mean, -ng);
         return ng;
     }
   }
 
   void PhaseSpacePoint::boost_AWZH_bosons_from(
       std::vector<fastjet::PseudoJet> const & boosted_bosons, Event const & event
   ){
     auto const & from = event.outgoing();
 
     auto find_AWZH = [](Particle const & p){ return is_AWZH_boson(p); };
     size_t boosted_idx = 0;
     for(
       auto original_boson = std::find_if(begin(from), end(from), find_AWZH);
       original_boson != end(from);
       original_boson = std::find_if(++original_boson, end(from), find_AWZH),
       ++boosted_idx
     ){
       auto insertion_point = std::lower_bound(
           begin(outgoing_), end(outgoing_), *original_boson, rapidity_less{}
       );
 
       // copy AWZH particle
       const int new_idx = std::distance(begin(outgoing_), insertion_point);
       assert(new_idx >= 0);  // insert invalidates distance
       outgoing_.insert(insertion_point,
           {original_boson->type, boosted_bosons[boosted_idx], original_boson->colour}
       );
       assert(outgoing_[new_idx].type == original_boson->type);
       assert(std::is_sorted(begin(outgoing_), end(outgoing_), rapidity_less{}));
 
       // copy & boost decay products
       const int idx = std::distance(begin(from), original_boson);
       assert(idx >= 0);
       const auto decay_it = event.decays().find(idx);
       if(decay_it != end(event.decays())){
         auto decayparticles = decay_it->second;
         // change the momenta of the decay products.
         fastjet::PseudoJet sum;
         for(auto & particle: decayparticles){
           auto & p = particle.p;
           // boost _to_ rest frame of input boson
           p.unboost(original_boson->p);
           // then boost _from_ rest frame of shuffled boson
           p.boost(boosted_bosons[boosted_idx]);
           if(p.E() < std::abs(p.pz())){
             throw std::underflow_error("Reshuffled decay with E<|pz|");
           }
           sum += p;
         }
         if(!nearby(boosted_bosons[boosted_idx], sum, boosted_bosons[boosted_idx].E())){
           throw std::underflow_error("Boson and decays momenta do not match after reshuffling");
         }
         decays_.emplace(new_idx, decayparticles);
       }
     }
   }
 
   namespace {
 
     template<class ConstIterator, class Iterator>
     void label_extremal_qqbar(
       ConstIterator born_begin, ConstIterator born_end,
       Iterator first_out
     ){
       // find born quarks
       const auto firstquark = std::find_if(
         born_begin, born_end-1,
           [](Particle const & s){ return (is_anyquark(s)); }
       );
       assert(firstquark != born_end-1);
       const auto secondquark = std::find_if(
         firstquark+1, born_end,
           [](Particle const & s){ return (is_anyquark(s)); }
       );
       assert(secondquark != born_end);
       assert( ( is_quark(*firstquark) && is_antiquark(*secondquark) )
             || ( is_antiquark(*firstquark) && is_quark(*secondquark) ));
       assert(first_out->type     == ParticleID::gluon);
       assert((first_out+1)->type == ParticleID::gluon);
 
       // copy type from born
       first_out->type     = firstquark->type;
       (first_out+1)->type = secondquark->type;
     }
   } // namespace
 
   void PhaseSpacePoint::label_qqbar(Event const & event){
     assert(std::is_sorted(begin(outgoing_), end(outgoing_), rapidity_less{}));
     assert(filter_partons(outgoing_).size() == outgoing_.size());
     if(qqbarb_){
       label_extremal_qqbar(event.outgoing().cbegin(), event.outgoing().cend(),
                            outgoing_.begin() );
       return;
     }
     if(qqbarf_){ // same as qqbarb with reversed order
       label_extremal_qqbar( event.outgoing().crbegin(), event.outgoing().crend(),
                             outgoing_.rbegin() );
       return;
     }
     // central qqbar
     const auto firstquark = get_central_qqbar(event).first;
 
     // find jets at FO corresponding to the quarks
     // technically this isn't necessary for LO
     const auto firstjet_idx = get_back_quark_jet(event, firstquark);
 
     // find corresponding jets after resummation
     fastjet::ClusterSequence cs{to_PseudoJet(outgoing_), param_.jet_param.def};
     auto const jets = fastjet::sorted_by_rapidity(
                         cs.inclusive_jets( param_.jet_param.min_pt ));
     std::vector<int> const resum_indices{ cs.particle_jet_indices({jets}) };
 
     // assert that jets didn't move
     assert(nearby_ep( ( event.jets().cbegin()+firstjet_idx )->rapidity(),
                       jets[ firstjet_idx ].rapidity(),   1e-2) );
     assert(nearby_ep( ( event.jets().cbegin()+firstjet_idx+1 )->rapidity(),
                       jets[ firstjet_idx+1 ].rapidity(), 1e-2) );
 
     // find last partons in first (central) jet
     size_t idx_out = 0;
     for(size_t i=resum_indices.size()-2; i>0; --i)
       if(resum_indices[i] == firstjet_idx){
         idx_out = i;
         break;
       }
     assert(idx_out != 0);
 
     // check that there is sufficient pt in jets from the quarks
     const double minpartonjetpt = 1. - param_.soft_pt_regulator;
     if (outgoing_[idx_out].p.pt()<minpartonjetpt*( event.jets().cbegin()+firstjet_idx )->pt()){
       weight_=0.;
       status_ = StatusCode::wrong_jets;
       return;
     }
 
     if (outgoing_[idx_out+1].p.pt()<minpartonjetpt*( event.jets().cbegin()+firstjet_idx+1 )->pt()){
       weight_=0.;
       status_ = StatusCode::wrong_jets;
       return;
     }
     // check that no additional emission between jets
     // such configurations are possible if we have an gluon gets generated
     // inside the rapidities of the qqbar chain, but clusted to a
     // differnet/outside jet. Changing this is non trivial
     if(resum_indices[idx_out+1] != resum_indices[idx_out]+1){
       weight_=0.;
       status_ = StatusCode::gluon_in_qqbar;
       return;
     }
     outgoing_[idx_out].type   = firstquark->type;
     outgoing_[idx_out+1].type = std::next(firstquark)->type;
   }
 
   void PhaseSpacePoint::label_quarks(Event const & ev){
     const auto WZEmit = std::find_if(
       begin(ev.outgoing()), end(ev.outgoing()),
       [](Particle const & s){ return (std::abs(s.type) == pid::Wp || s.type == pid::Z_photon_mix); }
     );
 
     if (WZEmit != end(ev.outgoing())){
       if(!qqbarb_) {
         const size_t backward_FKL_idx = unob_?1:0;
         const auto backward_FKL = std::next(ev.begin_partons(), backward_FKL_idx);
         outgoing_[backward_FKL_idx].type = backward_FKL->type;
       }
       if(!qqbarf_) {
         const size_t forward_FKL_idx = unof_?1:0;
         const auto forward_FKL = std::prev(ev.end_partons(), 1+forward_FKL_idx);
         outgoing_.rbegin()[unof_].type = forward_FKL->type; // NOLINT
       }
     } else {
       if(!is_backward_g_to_h(ev)) {
         most_backward_FKL(outgoing_).type = ev.incoming().front().type;
       }
       if(!is_forward_g_to_h(ev)) {
         most_forward_FKL(outgoing_).type = ev.incoming().back().type;
       }
     }
 
     if(qqbar_mid_||qqbarb_||qqbarf_){
       label_qqbar(ev);
     }
   }
 
   PhaseSpacePoint::PhaseSpacePoint(
       Event const & ev, PhaseSpacePointConfig conf, RNG & ran
   ):
     unob_{ev.type() == event_type::unob},
     unof_{ev.type() == event_type::unof},
     qqbarb_{ev.type() == event_type::qqbar_exb},
     qqbarf_{ev.type() == event_type::qqbar_exf},
     qqbar_mid_{ev.type() == event_type::qqbar_mid},
     param_{std::move(conf)},
     status_{unspecified}
   {
     // legacy code: override new variable with old
     if(param_.max_ext_soft_pt_fraction){
       param_.soft_pt_regulator = *param_.max_ext_soft_pt_fraction;
       param_.max_ext_soft_pt_fraction = {};
     }
 
     weight_ = 1;
     auto const & Born_jets = ev.jets();
     const int ng = sample_ng(ev, ran);
     weight_ /= std::tgamma(ng + 1);
     const int ng_jets = sample_ng_jets(ev, ng, ran);
     std::vector<fastjet::PseudoJet> out_partons = gen_non_jet(
        ng - ng_jets, CMINPT, param_.jet_param.min_pt, ran
     );
 
     const auto qperp = std::accumulate(
       begin(out_partons), end(out_partons),
       fastjet::PseudoJet{}
     );
 
     std::vector<fastjet::PseudoJet> jets;
     std::vector<fastjet::PseudoJet> bosons;
     std::tie(jets, bosons) = reshuffle(ev, qperp);
     if(weight_ == 0.) {
       status_ = failed_reshuffle;
       return;
     }
     if(! pass_resummation_cuts(jets)){
       status_ = failed_resummation_cuts;
       weight_ = 0.;
       return;
     }
 
     // split jets in multiple partons
     std::vector<fastjet::PseudoJet> jet_partons = split(
       ev, jets, ng_jets, ran
     );
     if(weight_ == 0.) {
       status_ = StatusCode::failed_split;
       return;
     }
 
     const double ymin = is_backward_g_to_h(ev)?
       ev.outgoing().front().rapidity():
       most_backward_FKL(jet_partons).rapidity()
       ;
     const double ymax = is_forward_g_to_h(ev)?
       ev.outgoing().back().rapidity():
       most_forward_FKL(jet_partons).rapidity()
       ;
     if(qqbar_mid_){
       const int qqbar_backjet = getBackQuarkJet(ev);
       rescale_qqbar_rapidities(
         out_partons, jets,
         ymin, ymax,
         qqbar_backjet
       );
     }
     else{
       rescale_rapidities(out_partons, ymin, ymax);
     }
     if(! cluster_jets(out_partons).empty()){
       weight_ = 0.;
       status_ = StatusCode::empty_jets;
       return;
     }
     std::sort(begin(out_partons), end(out_partons), rapidity_less{});
     assert(
       std::is_sorted(begin(jet_partons), end(jet_partons), rapidity_less{})
     );
     const auto first_jet_parton = out_partons.insert(
       end(out_partons), begin(jet_partons), end(jet_partons)
     );
     std::inplace_merge(
       begin(out_partons), first_jet_parton, end(out_partons), rapidity_less{}
     );
 
     if(! jets_ok(ev, out_partons)){
       weight_ = 0.;
       status_ = StatusCode::wrong_jets;
       return;
     }
 
     weight_ *= phase_space_normalisation(Born_jets.size(), out_partons.size());
 
     outgoing_.reserve(out_partons.size() + 2); // two slots for possible A, W, Z, H
     for( auto it = std::make_move_iterator(out_partons.begin());
               it != std::make_move_iterator(out_partons.end());
             ++it
     ){
       outgoing_.emplace_back( Particle{pid::gluon, *it, {}});
     }
     assert(!outgoing_.empty());
 
     label_quarks(ev);
     if(weight_ == 0.) {
       //! @TODO optimise s.t. this is not possible
       // status is handled internally
       return;
     }
 
     // reattach bosons & decays
     if(!bosons.empty()){
       try {
         boost_AWZH_bosons_from(bosons, ev);
       } catch (std::underflow_error const & e){
         weight_ = 0.;
         status_ = StatusCode::failed_reshuffle;
         return;
       }
     }
 
     reconstruct_incoming(ev.incoming());
     status_ = StatusCode::good;
   }
 
   std::vector<fastjet::PseudoJet> PhaseSpacePoint::gen_non_jet(
       int const ng_non_jet, double const ptmin, double const ptmax, RNG & ran
   ){
     // heuristic parameters for pt sampling
     const double ptpar = 1.3 + ng_non_jet/5.;
     const double temp1 = std::atan((ptmax - ptmin)/ptpar);
 
     std::vector<fastjet::PseudoJet> partons(ng_non_jet);
     for(int i = 0; i < ng_non_jet; ++i){
       const double r1 = ran.flat();
       const double pt = ptmin + ptpar*std::tan(r1*temp1);
       const double temp2 = std::cos(r1*temp1);
       const double phi = 2*M_PI*ran.flat();
       weight_ *= 2.0*M_PI*pt*ptpar*temp1/(temp2*temp2);
       // we don't know the allowed rapidity span yet,
       // set a random value to be rescaled later on
       const double y = ran.flat();
       partons[i].reset_PtYPhiM(pt, y, phi);
       // Set user index higher than any jet-parton index
       // in order to assert that these are not inside jets
       partons[i].set_user_index(i + 1 + MAX_JET_USER_IDX);
 
       assert(ptmin-1e-5 <= partons[i].pt() && partons[i].pt() <= ptmax+1e-5);
     }
     assert(std::all_of(partons.cbegin(), partons.cend(), is_nonjet_parton));
     return sorted_by_rapidity(partons);
   }
 
   void PhaseSpacePoint::rescale_qqbar_rapidities(
       std::vector<fastjet::PseudoJet> & out_partons,
       std::vector<fastjet::PseudoJet> const & jets,
       const double ymin1, const double ymax2,
       const int qqbar_backjet
   ){
     const double ymax1 = jets[qqbar_backjet].rapidity();
     const double ymin2 = jets[qqbar_backjet+1].rapidity();
     constexpr double ep = 1e-7;
     const double tot_y = ymax1 - ymin1 + ymax2 - ymin2;
 
     std::vector<std::reference_wrapper<fastjet::PseudoJet>> refpart(
       out_partons.begin(), out_partons.end());
 
     double ratio = (ymax1 - ymin1)/tot_y;
 
     const auto gap{ std::find_if(refpart.begin(), refpart.end(),
                             [ratio](fastjet::PseudoJet const & p){
                               return (p.rapidity()>=ratio);} ) };
 
     double ymin = ymin1;
     double ymax = ymax1;
     double dy = ymax - ymin - 2*ep;
     double offset = 0.;
     for(auto it_part=refpart.begin(); it_part<refpart.end(); ++it_part){
       if(it_part == gap){
         ymin = ymin2;
         ymax = ymax2;
         dy = ymax - ymin - 2*ep;
         offset = ratio;
         ratio = 1-ratio;
       }
       fastjet::PseudoJet & part = *it_part;
       assert(offset <= part.rapidity() && part.rapidity() < ratio+offset);
       const double y = ymin + ep + dy*((part.rapidity()-offset)/ratio);
       part.reset_momentum_PtYPhiM(part.pt(), y, part.phi());
       weight_ *= tot_y-4.*ep;
       assert(ymin <= part.rapidity() && part.rapidity() <= ymax);
     }
     assert(is_sorted(begin(out_partons), end(out_partons), rapidity_less{}));
   }
 
   void PhaseSpacePoint::rescale_rapidities(
       std::vector<fastjet::PseudoJet> & partons,
       double ymin, double ymax
   ){
     constexpr double ep = 1e-7;
     for(auto & parton: partons){
       assert(0 <= parton.rapidity() && parton.rapidity() <= 1);
       const double dy = ymax - ymin - 2*ep;
       const double y = ymin + ep + dy*parton.rapidity();
       parton.reset_momentum_PtYPhiM(parton.pt(), y, parton.phi());
       weight_ *= dy;
       assert(ymin <= parton.rapidity() && parton.rapidity() <= ymax);
     }
   }
 
   namespace {
     template<typename T, typename... Rest>
     auto min(T const & a, T const & b, Rest&&... r) {
       using std::min;
       return min(a, min(b, std::forward<Rest>(r)...));
     }
   }
 
   double PhaseSpacePoint::probability_in_jet(Event const & ev) const{
     const double dy = estimate_emission_rapidity_range(ev);
     const double R = param_.jet_param.def.R();
     // jets into which we predominantly emit
     const int njets = ev.jets().size() - unof_ - unob_ - qqbarb_ - qqbarf_; //NOLINT
     assert(njets >= 1);
     const size_t nextremal_jets = std::min(njets, 2);
     const double p_J_y_large = (njets - nextremal_jets/2.)*R*R/(2.*dy);
     const double p_J_y0 = njets*R/M_PI;
     return min(p_J_y_large, p_J_y0, 1.);
   }
 
   int PhaseSpacePoint::sample_ng_jets(Event const & event, int ng, RNG & ran){
     const double p_J = probability_in_jet(event);
     std::binomial_distribution<> bin_dist(ng, p_J);
     const int ng_J = bin_dist(ran);
     weight_ *= std::pow(p_J, -ng_J)*std::pow(1 - p_J, ng_J - ng);
     return ng_J;
   }
 
   std::pair< std::vector<fastjet::PseudoJet>,
              std::vector<fastjet::PseudoJet> >
   PhaseSpacePoint::reshuffle(
       Event const & ev,
       fastjet::PseudoJet const & q
   ){
     // Create a copy of the outgoing momenta not containing decay products
     std::vector<fastjet::PseudoJet const *> born_momenta;
     born_momenta.reserve(ev.jets().size());
     std::transform(ev.jets().cbegin(), ev.jets().cend(),
                    back_inserter(born_momenta),
                    [](fastjet::PseudoJet const & t) { return &t; });
 
     auto bosons = filter_AWZH_bosons(ev.outgoing());
 
     std::vector<fastjet::PseudoJet const *> p_boson_momenta;
     std::transform(bosons.cbegin(), bosons.cend(),
                    back_inserter(p_boson_momenta),
                    [](Particle const & t) { return &(t.p); });
 
     std::vector<fastjet::PseudoJet> boson_momenta;
     std::transform(bosons.cbegin(), bosons.cend(),
                    back_inserter(boson_momenta),
                    [](Particle const & t) { return t.p; });
 
     // reshuffle all momenta
     if(q == fastjet::PseudoJet{0, 0, 0, 0}) return {ev.jets(), boson_momenta};
     // add bosons to reshuffling
     if(!bosons.empty()) {
       born_momenta.insert( born_momenta.end(), p_boson_momenta.begin(), p_boson_momenta.end() );
     }
     auto shuffle_momenta = resummation_jet_momenta(born_momenta, q);
     if(shuffle_momenta.empty()){
       weight_ = 0;
       return {};
     }
     // additional Jacobian to ensure Born integration over delta gives 1
     weight_ *= resummation_jet_weight(born_momenta, q);
 
     // take out bosons again
     if(!bosons.empty()) {
       std::vector<fastjet::PseudoJet> shuffle_bosons;
       for(size_t i = 0; i < bosons.size(); ++i) {
         shuffle_bosons.push_back(shuffle_momenta.back());
         shuffle_momenta.pop_back();
       }
       std::reverse(shuffle_bosons.begin(), shuffle_bosons.end());
 
       return {shuffle_momenta, shuffle_bosons};
     }
 
     return {shuffle_momenta, {}};
   }
 
   std::vector<int> PhaseSpacePoint::distribute_jet_partons(
       int ng_jets, std::vector<fastjet::PseudoJet> const & jets, RNG & ran
   ){
     size_t first_valid_jet = 0;
     size_t num_valid_jets = jets.size();
     const double R_eff = 5./3.*param_.jet_param.def.R();
     // if there is an unordered jet too far away from the FKL jets
     // then extra gluon constituents of the unordered jet would
     // violate the FKL rapidity ordering
     if((unob_||qqbarb_) && jets[0].delta_R(jets[1]) > R_eff){
       ++first_valid_jet;
       --num_valid_jets;
     }
     else if((unof_||qqbarf_) && jets[jets.size()-1].delta_R(jets[jets.size()-2]) > R_eff){
       --num_valid_jets;
     }
     std::vector<int> np(jets.size(), 1);
     for(int i = 0; i < ng_jets; ++i){
       ++np[first_valid_jet + ran.flat() * num_valid_jets];
     }
     weight_ *= std::pow(num_valid_jets, ng_jets);
     return np;
   }
 
 #ifndef NDEBUG
   namespace {
     bool tagged_FKL_backward(
         std::vector<fastjet::PseudoJet> const & jet_partons
     ){
       return std::find_if(
           begin(jet_partons), end(jet_partons),
           [](fastjet::PseudoJet const & p){
             return p.user_index() == UID::backward_fkl;
           }
       ) != end(jet_partons);
     }
 
     bool tagged_FKL_forward(
         std::vector<fastjet::PseudoJet> const & jet_partons
     ){
       // the most forward FKL parton is most likely near the end of jet_partons;
       // start search from there
       return std::find_if(
           jet_partons.rbegin(), jet_partons.rend(),
           [](fastjet::PseudoJet const & p){
             return p.user_index() == UID::forward_fkl;
           }
       ) != jet_partons.rend();
     }
 
   } // namespace
 #endif
 
   std::vector<fastjet::PseudoJet> PhaseSpacePoint::split(
     Event const & Born_event,
     std::vector<fastjet::PseudoJet> const & jets,
     int ng_jets
     , RNG & ran
   ){
     return split(
       Born_event,
       jets,
       distribute_jet_partons(ng_jets, jets, ran),
       ran
     );
   }
 
   bool PhaseSpacePoint::pass_extremal_cuts(
       fastjet::PseudoJet const & ext_parton,
       fastjet::PseudoJet const & jet
   ) const{
     if(ext_parton.pt() < param_.min_extparton_pt) return false;
     return (ext_parton - jet).pt()/jet.pt() < param_.soft_pt_regulator;
   }
 
   std::vector<fastjet::PseudoJet> PhaseSpacePoint::split(
     Event const & Born_event,
     std::vector<fastjet::PseudoJet> const & jets,
     std::vector<int> const & np,
     RNG & ran
   ){
     assert(! jets.empty());
     assert(jets.size() == np.size());
     assert(pass_resummation_cuts(jets));
     constexpr auto no_such_jet_idx = std::numeric_limits<std::size_t>::max();
 
     const size_t most_backward_FKL_idx = is_backward_g_to_h(Born_event)?
       no_such_jet_idx: // we have backward Higgs instead of FKL jet
       (0 + unob_ + qqbarb_); // NOLINT
     const size_t most_forward_FKL_idx = is_forward_g_to_h(Born_event)?
       no_such_jet_idx: // we have forward Higgs instead of FKL jet
       (jets.size() - 1 - unof_ - qqbarf_); // NOLINT
     const size_t qqbar_jet_idx = qqbar_mid_?
       getBackQuarkJet(Born_event):
       no_such_jet_idx;
     auto const & jet = param_.jet_param;
     const JetSplitter jet_splitter{jet.def, jet.min_pt};
 
     std::vector<fastjet::PseudoJet> jet_partons;
     // randomly distribute jet gluons among jets
     for(size_t i = 0; i < jets.size(); ++i){
       auto split_res = jet_splitter.split(jets[i], np[i], ran);
       weight_ *= split_res.weight;
       if(weight_ == 0) return {};
       assert(
           std::all_of(
               begin(split_res.constituents), end(split_res.constituents),
               is_jet_parton
           )
       );
       const auto first_new_parton = jet_partons.insert(
           end(jet_partons),
           begin(split_res.constituents), end(split_res.constituents)
       );
       // mark uno and extremal FKL emissions here so we can check
       // their position once all emissions are generated
       // also mark qqbar_mid partons, and apply appropriate pt cut.
       auto extremal = end(jet_partons);
       if (i == most_backward_FKL_idx){ //FKL backward emission
         extremal = std::min_element(
             first_new_parton, end(jet_partons), rapidity_less{}
         );
         extremal->set_user_index(UID::backward_fkl);
       }
       else if(((unob_ || qqbarb_) && i == 0)){
         // unordered/qqbarb
         extremal = std::min_element(
             first_new_parton, end(jet_partons), rapidity_less{}
         );
         extremal->set_user_index((unob_)?UID::unob:UID::qqbarb);
       }
 
       else if (i == most_forward_FKL_idx){
         extremal = std::max_element(
             first_new_parton, end(jet_partons), rapidity_less{}
         );
         extremal->set_user_index(UID::forward_fkl);
       }
       else if(((unof_ || qqbarf_) && i == jets.size() - 1)){
         // unordered/qqbarf
         extremal = std::max_element(
             first_new_parton, end(jet_partons), rapidity_less{}
         );
         extremal->set_user_index((unof_)?UID::unof:UID::qqbarf);
       }
       else if((qqbar_mid_ && i == qqbar_jet_idx)){
         extremal = std::max_element(
             first_new_parton, end(jet_partons), rapidity_less{}
         );
         extremal->set_user_index(UID::qqbar_mid1);
       }
       else if((qqbar_mid_ && i == qqbar_jet_idx+1)){
         extremal = std::min_element(
             first_new_parton, end(jet_partons), rapidity_less{}
         );
         extremal->set_user_index(UID::qqbar_mid2);
       }
       if(
           extremal != end(jet_partons)
           && !pass_extremal_cuts(*extremal, jets[i])
       ){
         weight_ = 0;
         return {};
       }
     }
     assert(is_backward_g_to_h(Born_event) || tagged_FKL_backward(jet_partons));
     assert(is_forward_g_to_h(Born_event) || tagged_FKL_forward(jet_partons));
     std::sort(begin(jet_partons), end(jet_partons), rapidity_less{});
     if(
       !extremal_ok(Born_event, jet_partons)
         || !split_preserved_jets(jets, jet_partons)
     ){
       weight_ = 0.;
       return {};
     }
     return jet_partons;
   }
 
   bool PhaseSpacePoint::extremal_ok(
     Event const & Born_event,
     std::vector<fastjet::PseudoJet> const & partons
   ) const{
     assert(std::is_sorted(begin(partons), end(partons), rapidity_less{}));
     if(unob_ && partons.front().user_index() != UID::unob) return false;
     if(unof_ && partons.back().user_index()  != UID::unof) return false;
     if(qqbarb_ && partons.front().user_index() != UID::qqbarb) return false;
     if(qqbarf_ && partons.back().user_index()  != UID::qqbarf) return false;
     if(is_backward_g_to_h(Born_event)) {
       if(partons.front().rapidity() < Born_event.outgoing().front().rapidity()){
         return false;
       }
     } else if(most_backward_FKL(partons).user_index() != UID::backward_fkl) {
       return false;
     }
     if(is_forward_g_to_h(Born_event)) {
       return partons.back().rapidity() <= Born_event.outgoing().back().rapidity();
     }
     return most_forward_FKL(partons).user_index() == UID::forward_fkl;
   }
 
   bool PhaseSpacePoint::split_preserved_jets(
         std::vector<fastjet::PseudoJet> const & jets,
         std::vector<fastjet::PseudoJet> const & jet_partons
   ) const{
     assert(std::is_sorted(begin(jets), end(jets), rapidity_less{}));
 
     const auto split_jets = cluster_jets(jet_partons);
     // this can happen if two overlapping jets
     // are both split into more than one parton
     if(split_jets.size() != jets.size()) return false;
     for(size_t i = 0; i < split_jets.size(); ++i){
       // this can happen if there are two overlapping jets
       // and a parton is assigned to the "wrong" jet
       if(!nearby_ep(jets[i].rapidity(), split_jets[i].rapidity(), 1e-2)){
         return false;
       }
     }
     return true;
   }
 
   template<class Particle>
   Particle const & PhaseSpacePoint::most_backward_FKL(
       std::vector<Particle> const & partons
   ) const{
     return partons[0 + unob_ + qqbarb_];
   }
 
   template<class Particle>
   Particle const & PhaseSpacePoint::most_forward_FKL(
       std::vector<Particle> const & partons
   ) const{
     const size_t idx = partons.size() - 1 - unof_ - qqbarf_;
     assert(idx < partons.size());
     return partons[idx];
   }
 
   template<class Particle>
   Particle & PhaseSpacePoint::most_backward_FKL(
       std::vector<Particle> & partons
   ) const{
     return partons[0 + unob_ + qqbarb_];
   }
 
   template<class Particle>
   Particle & PhaseSpacePoint::most_forward_FKL(
       std::vector<Particle> & partons
   ) const{
     const size_t idx = partons.size() - 1 - unof_ - qqbarf_;
     assert(idx < partons.size());
     return partons[idx];
   }
 
   bool PhaseSpacePoint::contains_idx(
       fastjet::PseudoJet const & jet, fastjet::PseudoJet const & parton
   ) const {
     auto const & constituents = jet.constituents();
     const int idx = parton.user_index();
     const bool injet = std::find_if(
         begin(constituents), end(constituents),
         [idx](fastjet::PseudoJet const & con){return con.user_index() == idx;}
     ) != end(constituents);
     const double minpartonjetpt = 1. - param_.soft_pt_regulator;
     return ((parton.pt()>minpartonjetpt*jet.pt())&&injet);
   }
 
   bool PhaseSpacePoint::jets_ok(
     Event const & Born_event,
     std::vector<fastjet::PseudoJet> const & partons
   ) const{
     fastjet::ClusterSequence cs(partons, param_.jet_param.def);
     const auto jets = sorted_by_rapidity(cs.inclusive_jets(param_.jet_param.min_pt));
     if(jets.size() != Born_event.jets().size()) return false;
     int in_jet = 0;
     for(auto const & jet : jets){
       assert(jet.has_constituents());
       for(auto && parton: jet.constituents()){
         if(is_nonjet_parton(parton)) return false;
       }
       in_jet += jet.constituents().size();
     }
     const int expect_in_jet = std::count_if(
         partons.cbegin(), partons.cend(), is_jet_parton
     );
     if(in_jet != expect_in_jet) return false;
     // note that PseudoJet::contains does not work here
     if(
       !is_backward_g_to_h(Born_event) &&
       !contains_idx(most_backward_FKL(jets), most_backward_FKL(partons))
     ) return false;
     if(
       !is_forward_g_to_h(Born_event)
       &&  !contains_idx(most_forward_FKL(jets), most_forward_FKL(partons))
     ) return false;
     if(unob_ && !contains_idx(jets.front(), partons.front())) return false;
     if(qqbarb_ && !contains_idx(jets.front(), partons.front())) return false;
     if(unof_ && !contains_idx(jets.back(), partons.back())) return false;
     if(qqbarf_ && !contains_idx(jets.back(), partons.back())) return false;
 #ifndef NDEBUG
     for(size_t i = 0; i < jets.size(); ++i){
       assert(nearby_ep(jets[i].rapidity(), Born_event.jets()[i].rapidity(), 1e-2));
     }
 #endif
     return true;
   }
 
   void PhaseSpacePoint::reconstruct_incoming(
       std::array<Particle, 2> const & Born_incoming
   ){
     std::tie(incoming_[0].p, incoming_[1].p) = incoming_momenta(outgoing_);
     for(size_t i = 0; i < incoming_.size(); ++i){
       incoming_[i].type = Born_incoming[i].type;
     }
     assert(momentum_conserved());
   }
 
   bool PhaseSpacePoint::momentum_conserved() const{
-    fastjet::PseudoJet diff;
-    for(auto const & in: incoming()) diff += in.p;
-    const double norm = diff.E();
-    for(auto const & out: outgoing()) diff -= out.p;
-    return nearby(diff, fastjet::PseudoJet{}, norm);
+    return HEJ::momentum_conserved(*this);
   }
 
 } //namespace HEJ