diff --git a/FixedOrderGen/src/PhaseSpacePoint.cc b/FixedOrderGen/src/PhaseSpacePoint.cc
index 1a4a75e..f06431d 100644
--- a/FixedOrderGen/src/PhaseSpacePoint.cc
+++ b/FixedOrderGen/src/PhaseSpacePoint.cc
@@ -1,1072 +1,1077 @@
 /**
  *  \authors   The HEJ collaboration (see AUTHORS for details)
  *  \date      2019-2020
  *  \copyright GPLv2 or later
  */
 #include "PhaseSpacePoint.hh"
 
 #include <algorithm>
 #include <cassert>
 #include <cmath>
 #include <cstdint>
 #include <cstdlib>
 #include <iostream>
 #include <iterator>
 #include <limits>
 #include <tuple>
 #include <type_traits>
 #include <utility>
 
 #include "Subleading.hh"
 #include "Utility.hh"
 #include "fastjet/ClusterSequence.hh"
 
 #include "HEJ/Constants.hh"
 #include "HEJ/EWConstants.hh"
 #include "HEJ/PDF.hh"
 #include "HEJ/PDG_codes.hh"
 #include "HEJ/Particle.hh"
 #include "HEJ/RNG.hh"
 #include "HEJ/exceptions.hh"
 #include "HEJ/kinematics.hh"
 #include "HEJ/utility.hh"
 
 #include "JetParameters.hh"
 #include "Process.hh"
 
 namespace HEJFOG {
   HEJ::Event::EventData to_EventData(PhaseSpacePoint psp){
   //! @TODO Same function already in HEJ
     HEJ::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),
             HEJ::rapidity_less{}
         )
     );
     assert(result.outgoing.size() >= 2);
     result.decays = std::move(psp).decays_; // NOLINT(bugprone-use-after-move)
     static_assert(
         std::numeric_limits<double>::has_quiet_NaN,
         "no quiet NaN for double"
     );
     constexpr double nan = std::numeric_limits<double>::quiet_NaN();
     result.parameters.central = {nan, nan, psp.weight()}; // NOLINT(bugprone-use-after-move)
     return result;
   }
 
   PhaseSpacePoint::ConstPartonIterator PhaseSpacePoint::begin_partons() const {
     return cbegin_partons();
   }
   PhaseSpacePoint::ConstPartonIterator PhaseSpacePoint::cbegin_partons() const {
     return {HEJ::is_parton, cbegin(outgoing()), cend(outgoing())};
   }
 
   PhaseSpacePoint::ConstPartonIterator PhaseSpacePoint::end_partons() const {
     return cend_partons();
   }
   PhaseSpacePoint::ConstPartonIterator PhaseSpacePoint::cend_partons() const {
     return {HEJ::is_parton, cend(outgoing()), cend(outgoing())};
   }
 
   PhaseSpacePoint::ConstReversePartonIterator PhaseSpacePoint::rbegin_partons() const {
     return crbegin_partons();
   }
   PhaseSpacePoint::ConstReversePartonIterator PhaseSpacePoint::crbegin_partons() const {
     return std::reverse_iterator<ConstPartonIterator>( cend_partons() );
   }
 
   PhaseSpacePoint::ConstReversePartonIterator PhaseSpacePoint::rend_partons() const {
     return crend_partons();
   }
   PhaseSpacePoint::ConstReversePartonIterator PhaseSpacePoint::crend_partons() const {
     return std::reverse_iterator<ConstPartonIterator>( cbegin_partons() );
   }
 
   PhaseSpacePoint::PartonIterator PhaseSpacePoint::begin_partons() {
     return {HEJ::is_parton, begin(outgoing_), end(outgoing_)};
   }
 
   PhaseSpacePoint::PartonIterator PhaseSpacePoint::end_partons() {
     return {HEJ::is_parton, end(outgoing_), end(outgoing_)};
   }
 
   PhaseSpacePoint::ReversePartonIterator PhaseSpacePoint::rbegin_partons() {
     return std::reverse_iterator<PartonIterator>( end_partons() );
   }
 
   PhaseSpacePoint::ReversePartonIterator PhaseSpacePoint::rend_partons() {
     return std::reverse_iterator<PartonIterator>( begin_partons() );
   }
 
   namespace {
     bool can_swap_to_uno(
         HEJ::Particle const & p1, HEJ::Particle const & p2
     ){
       assert(is_parton(p1) && is_parton(p2));
       return p1.type != HEJ::pid::gluon
           && p2.type == HEJ::pid::gluon;
     }
 
     template<class PartonIt, class OutIt>
     bool uno_possible(
       PartonIt first_parton, OutIt first_out
     ){
       using namespace HEJ;
       // Special case: Higgs can not be outside of uno
       if(first_out->type == pid::Higgs
           || std::next(first_out)->type==pid::Higgs){
         return false;
       }
       // decide what kind of subleading process is allowed
       return can_swap_to_uno( *first_parton, *std::next(first_parton) );
     }
 
     template<class Iterator>
     bool allow_strange(
       Iterator first_parton, Iterator last_parton,
       Process const & proc
     ) {
       const auto boson = proc.boson;
       return !(
         boson
         && std::abs(*boson)== HEJ::pid::Wp
         && std::none_of(
           first_parton, last_parton,
           [boson](HEJ::Particle const & p){
             return vector_boson_can_couple_to(*boson, p.type);
           })
       );
     }
   }
 
   void PhaseSpacePoint::turn_to_subl(
       subleading::Channels const channel,
       Process const & proc,
       HEJ::RNG & ran
   ) {
     using namespace HEJ;
     assert(proc.njets > 2);
 
     switch(channel) {
     case subleading::unordered: {
       bool const can_be_uno_backward = uno_possible(cbegin_partons(),
                                                   outgoing_.cbegin());
       bool const can_be_uno_forward  = uno_possible(crbegin_partons(),
                                                   outgoing_.crbegin());
       return turn_to_uno(can_be_uno_backward, can_be_uno_forward, ran);
     }
     case subleading::central_qqbar: {
       bool const strange_allowed = allow_strange(
         begin_partons(),
         end_partons(),
         proc
       );
       return turn_to_cqqbar(strange_allowed, ran);
     }
     case subleading::extremal_qqbar: {
       bool const strange_allowed = allow_strange(
         begin_partons(),
         end_partons(),
         proc
       );
       return turn_to_eqqbar(strange_allowed, ran);
     }
     default:;
     }
     throw std::logic_error{"enum value not covered"};
   }
 
   void PhaseSpacePoint::turn_to_uno(
       const bool can_be_uno_backward, const bool can_be_uno_forward,
       HEJ::RNG & ran
   ){
     if(can_be_uno_backward && can_be_uno_forward){
       weight_ *= 2.;
       if(ran.flat() < 0.5){
         return std::swap(begin_partons()->type, std::next(begin_partons())->type);
       }
       return std::swap(rbegin_partons()->type, std::next(rbegin_partons())->type);
     }
     if(can_be_uno_backward){
       return std::swap(begin_partons()->type, std::next(begin_partons())->type);
     }
     assert(can_be_uno_forward);
     std::swap(rbegin_partons()->type, std::next(rbegin_partons())->type);
   }
 
   //! select flavour of quark
   HEJ::ParticleID PhaseSpacePoint::select_qqbar_flavour(
       const bool allow_strange, HEJ::RNG & ran
   ){
     const double r1 = 2.*ran.flat()-1.;
     const double max_flavour = allow_strange?HEJ::N_F:HEJ::N_F-1;
     weight_ *= max_flavour*2;
     double const flavour = HEJ::pid::down + std::floor(std::abs(r1)*max_flavour);
     return static_cast<HEJ::ParticleID>(flavour*(r1<0.?-1:1));
   }
 
   void PhaseSpacePoint::turn_to_cqqbar(const bool allow_strange, HEJ::RNG & ran){
     // we assume all FKL partons to be gluons
     auto first = std::next(begin_partons());
     auto last  = std::next(rbegin_partons());
     auto const ng = std::distance(first, last.base());
     if(ng < 2)
       throw std::logic_error("not enough gluons to create qqbar");
     auto flavour = select_qqbar_flavour(allow_strange, ran);
     // select gluon for switch
     if(ng!=2){
       const double steps = 1./(ng-1.);
       weight_ /= steps;
       for(auto rnd = ran.flat(); rnd>steps; ++first){
         rnd-=steps;
       }
     }
     first->type = flavour;
     std::next(first)->type = anti(flavour);
   }
 
   void PhaseSpacePoint::turn_to_eqqbar(const bool allow_strange, HEJ::RNG & ran){
     /// find first and last gluon in FKL chain
     auto first  = begin_partons();
     const bool can_forward = !is_anyquark(*first);
     auto last = rbegin_partons();
     const bool can_backward = !is_anyquark(*last);
     if(std::distance(first, last.base()) < 2)
       throw std::logic_error("not enough gluons to create qqbar");
     auto flavour = select_qqbar_flavour(allow_strange, ran);
     // select gluon for switch
     if(can_forward && !can_backward){
       first->type = flavour;
       std::next(first)->type = anti(flavour);
       return;
     }
     if(!can_forward && can_backward){
       last->type = flavour;
       std::next(last)->type = anti(flavour);
       return;
     }
     assert(can_forward && can_backward);
     weight_*=2.;
     if(ran.flat()>0.5){
       first->type = flavour;
       std::next(first)->type = anti(flavour);
       return;
     }
     last->type = flavour;
     std::next(last)->type = anti(flavour);
   }
 
   template<class ParticleMomenta>
   fastjet::PseudoJet PhaseSpacePoint::gen_last_momentum(
       ParticleMomenta const & other_momenta,
       const double mass_square, const double y
   ) const {
     std::array<double,2> pt{0.,0.};
     for (auto const & p: other_momenta) {
       pt[0]-= p.px();
       pt[1]-= p.py();
     }
 
     const double mperp = std::sqrt(pt[0]*pt[0]+pt[1]*pt[1]+mass_square);
     const double pz=mperp*std::sinh(y);
     const double E=mperp*std::cosh(y);
 
     return {pt[0], pt[1], pz, E};
   }
 
   Decay PhaseSpacePoint::select_decay_channel(
       std::vector<Decay> const & decays,
       HEJ::RNG & ran
   ){
     double br_total = 0.;
     for(auto const & decay: decays) br_total += decay.branching_ratio;
     // adjust weight
     // this is given by (channel branching ratio)/(chance to pick channel)
     // where (chance to pick channel) =
     //       (channel branching ratio)/(total branching ratio)
     weight_ *= br_total;
     if(decays.size()==1) return decays.front();
     const double r1 = br_total*ran.flat();
     double br_sum = 0.;
     for(auto const & decay: decays){
       br_sum += decay.branching_ratio;
       if(r1 < br_sum) return decay;
     }
     throw std::logic_error{"unreachable"};
   }
   namespace {
     //! generate decay products of a boson
     std::vector<HEJ::Particle> decay_boson(
         HEJ::Particle const & parent,
         std::vector<HEJ::ParticleID> const & decays,
         HEJ::RNG & ran
     ){
       if(decays.size() != 2){
         throw HEJ::not_implemented{
           "only decays into two particles are implemented"
         };
       }
       std::vector<HEJ::Particle> decay_products(decays.size());
       for(size_t i = 0; i < decays.size(); ++i){
         decay_products[i].type = decays[i];
       }
       // choose polar and azimuth angle in parent rest frame
       const double E = parent.m()/2;
       const double theta = 2.*M_PI*ran.flat();
       const double cos_phi = 2.*ran.flat()-1.;   // Jacobian Factors for W in line 418
       const double sin_phi = std::sqrt(1. - cos_phi*cos_phi);  // Know 0 < phi < pi
       const double px = E*std::cos(theta)*sin_phi;
       const double py = E*std::sin(theta)*sin_phi;
       const double pz = E*cos_phi;
       decay_products[0].p.reset(px, py, pz, E);
       decay_products[1].p.reset(-px, -py, -pz, E);
       for(auto & particle: decay_products) particle.p.boost(parent.p);
       return decay_products;
     }
   } // namespace
 
   std::vector<HEJ::Particle> PhaseSpacePoint::decay_channel(
       HEJ::Particle const & parent,
       std::vector<Decay> const & decays,
       HEJ::RNG & ran
   ){
     const auto channel = select_decay_channel(decays, ran);
     return decay_boson(parent, channel.products, ran);
   }
 
   namespace {
     //! adds a particle to target (in correct rapidity ordering)
     //! @returns    positon of insertion
     auto insert_particle(std::vector<HEJ::Particle> & target,
       HEJ::Particle && particle
     ){
       const auto pos = std::upper_bound(
           begin(target),end(target),particle,HEJ::rapidity_less{}
       );
       target.insert(pos, std::move(particle));
       return pos;
     }
   } // namespace
 
   PhaseSpacePoint::PhaseSpacePoint(
     Process const & proc,
     JetParameters const & jet_param,
     HEJ::PDF & pdf, double E_beam,
     double const subl_chance,
     Subleading const subl_channels,
     ParticlesDecayMap const & particle_decays,
     HEJ::EWConstants const & ew_parameters,
     HEJ::RNG & ran
   ){
     assert(proc.njets >= 2);
     status_ = Status::good;
     weight_ = 1;
 
     // ensure that all setting are consistent
     // a more thorough check is in EventGenerator
     assert(subl_chance > 0. || subl_channels.none());
 
     const std::size_t nout = proc.njets + (proc.boson?1:0)
                               + proc.boson_decay.size();
     outgoing_.reserve(nout);
 
     // generate parton momenta
     const bool is_pure_jets = (nout == proc.njets);
     auto partons = gen_LO_partons(
         proc.njets, is_pure_jets, jet_param, E_beam, ran
     );
     if(status_ != Status::good) return;
     // pre fill flavour with gluons
     for(auto && parton: std::move(partons)){
       outgoing_.emplace_back(HEJ::Particle{HEJ::pid::gluon, std::move(parton), {}});
     }
 
     const std::optional<subleading::Channels> channel = select_channel(
       subl_channels,
       subl_chance,
       ran
     );
 
     // normalisation of momentum-conserving delta function
     weight_ *= std::pow(2*M_PI, 4);
 
     /** @TODO
      *  uf (jet_param.min_pt) doesn't correspond to our final scale choice.
      *  The HEJ scale generators currently expect a full event as input,
      *  so fixing this is not completely trivial
      */
     reconstruct_incoming(proc, channel, pdf, E_beam, jet_param.min_pt, ran);
     if(status_ != Status::good) return;
     // set outgoing states
     begin_partons()->type = incoming_[0].type;
     rbegin_partons()->type = incoming_[1].type;
 
     if(channel) turn_to_subl(*channel, proc, ran);
 
     if(proc.boson) {
       add_boson(proc, particle_decays, ew_parameters, ran);
       // total momentum has changed, update & check incoming momenta
       std::tie(incoming_[0].p, incoming_[1].p) = incoming_momenta(outgoing_);
       const auto [xa, xb] = xa_xb(E_beam);
       if (xa>1. || xb>1.){
         weight_=0;
         status_ = Status::too_much_energy;
         return;
       }
     }
     assert(weight_ != 0 || status() == Status::good);
     assert(momentum_conserved(1e-7));
   }
 
   void PhaseSpacePoint::add_boson(
     Process const & proc,
     ParticlesDecayMap const & particle_decays,
     HEJ::EWConstants const & ew_parameters,
     HEJ::RNG & ran
   ) {
     auto const & boson_prop = (*proc.boson == HEJ::pid::Z_photon_mix
                                ? ew_parameters.prop(HEJ::pid::Z)
                                : ew_parameters.prop(*proc.boson));
     auto boson = gen_boson(
       *proc.boson, boson_prop.mass, boson_prop.width,
       ran
     );
     const auto pos{insert_particle(outgoing_, std::move(boson))};
     const size_t boson_idx = std::distance(begin(outgoing_), pos);
     auto const & boson_decay = particle_decays.find(*proc.boson);
     if( !proc.boson_decay.empty() ){ // decay given in proc
       decays_.emplace(
         boson_idx,
         decay_boson(outgoing_[boson_idx], proc.boson_decay, ran)
       );
     } else if( boson_decay != particle_decays.end()
                && !boson_decay->second.empty() ){ // decay given explicitly
       decays_.emplace(
         boson_idx,
         decay_channel(outgoing_[boson_idx], boson_decay->second, ran)
       );
     }
   }
 
   // pt generation, see eq:pt_sampling in developer manual
   double PhaseSpacePoint::gen_hard_pt(
     const int np , const double ptmin, const double ptmax, const double /* y */,
     HEJ::RNG & ran
   ){
     // heuristic parameter for pt sampling, see eq:pt_par in developer manual
     const double ptpar = ptmin + np/5.;
 
     const double arctan = std::atan((ptmax - ptmin)/ptpar);
     const double xpt = ran.flat();
     const double pt = ptmin + ptpar*std::tan(xpt*arctan);
     const double cosine = std::cos(xpt*arctan);
     weight_ *= pt*ptpar*arctan/(cosine*cosine);
     return pt;
   }
 
   double PhaseSpacePoint::gen_soft_pt(int np, double max_pt, HEJ::RNG & ran) {
     constexpr double ptpar = 4.;
 
     const double r = ran.flat();
     const double pt = max_pt + ptpar/np*std::log(r);
     weight_ *= pt*ptpar/(np*r);
     return pt;
   }
 
   double PhaseSpacePoint::gen_parton_pt(
       int count, JetParameters const & jet_param, double max_pt, double y,
       HEJ::RNG & ran
   ) {
     constexpr double p_small_pt = 0.02;
 
     if(! jet_param.peak_pt) {
        return gen_hard_pt(count, jet_param.min_pt, max_pt, y, ran);
     }
     const double r = ran.flat();
     if(r > p_small_pt) {
       weight_ /= 1. - p_small_pt;
       return gen_hard_pt(count, *jet_param.peak_pt, max_pt, y, ran);
     }
     weight_ /= p_small_pt;
     const double pt =  gen_soft_pt(count, *jet_param.peak_pt, ran);
     if(pt < jet_param.min_pt) {
       weight_=0.0;
       status_ = Status::not_enough_jets;
       return jet_param.min_pt;
     }
     return pt;
   }
 
   std::vector<fastjet::PseudoJet> PhaseSpacePoint::gen_LO_partons(
       int np, bool is_pure_jets,
       JetParameters const & jet_param,
       double max_pt,
       HEJ::RNG & ran
   ){
     if (np<2) throw std::invalid_argument{"Not enough partons in gen_LO_partons"};
 
     weight_ /= std::pow(16.*std::pow(M_PI,3),np);
     weight_ /= std::tgamma(np+1); //remove rapidity ordering
     std::vector<fastjet::PseudoJet> partons;
     partons.reserve(np);
     for(int i = 0; i < np; ++i){
       const double y = -jet_param.max_y + 2*jet_param.max_y*ran.flat();
       weight_ *= 2*jet_param.max_y;
 
       const bool is_last_parton = i+1 == np;
       if(is_pure_jets && is_last_parton) {
         constexpr double parton_mass_sq = 0.;
         partons.emplace_back(gen_last_momentum(partons, parton_mass_sq, y));
         break;
       }
 
       const double phi = 2*M_PI*ran.flat();
       weight_ *= 2.0*M_PI;
 
       const double pt = gen_parton_pt(np, jet_param, max_pt, y, ran);
       if(weight_ == 0.0) return {};
 
       partons.emplace_back(fastjet::PtYPhiM(pt, y, phi));
       assert(jet_param.min_pt <= partons[i].pt());
       assert(partons[i].pt() <= max_pt+1e-5);
     }
     // Need to check that at LO, the number of jets = number of partons;
     fastjet::ClusterSequence cs(partons, jet_param.def);
     auto cluster_jets=cs.inclusive_jets(jet_param.min_pt);
     if (cluster_jets.size()!=unsigned(np)){
       weight_=0.0;
       status_ = Status::not_enough_jets;
       return {};
     }
 
     std::sort(begin(partons), end(partons), HEJ::rapidity_less{});
 
     return partons;
   }
 
   HEJ::Particle PhaseSpacePoint::gen_boson(
       HEJ::ParticleID bosonid, double mass, double width,
       HEJ::RNG & ran
   ){
     // Usual phase space measure for single particle,
     // see eq:single_particle_phase_space in developer manual
     weight_ /= 16.*std::pow(M_PI, 3);
 
     const double y = (bosonid == HEJ::pid::Higgs)?
       gen_Higgs_rapidity(ran):
       gen_V_boson_rapidity(bosonid, ran);
 
     // off-shell sampling, see eq:breit-wigner-sampling in developer manual
     const double r1 = ran.flat();
     const double s_boson = mass*(
         mass + width*std::tan(M_PI/2.*r1 + (r1-1.)*std::atan(mass/width))
     );
     if(bosonid != HEJ::pid::Higgs){
       // two-particle phase space,
       // compare eq:two_particle_phase_space and eq:one_particle_phase_space
       // in developer manual
       weight_/=M_PI*M_PI*16.;
       // Jacobian, see eq:breit-wigner-sampling_jacobian in developer manual
       weight_*= mass*width*( M_PI+2.*std::atan(mass/width) )
               / ( 1. + std::cos( M_PI*r1 + 2.*(r1-1.)*std::atan(mass/width) ) );
     }
 
     return {
       bosonid,
       gen_last_momentum(outgoing_, s_boson, y),
       {}
     };
   }
 
   namespace {
     bool is_uno_forward(
       std::array<HEJ::Particle, 2> const & incoming,
       std::vector<HEJ::Particle> const & partons
     ) {
       if(partons.size() < 3) return false;
       assert(
         std::is_sorted(
           begin(incoming), end(incoming),
           HEJ::rapidity_less{}
         )
       );
       assert(
         std::is_sorted(
           begin(partons), end(partons),
           HEJ::rapidity_less{}
         )
       );
       assert(is_parton(*partons.rbegin()));
       assert(is_parton(*std::next(partons.rbegin())));
       return
         HEJ::is_anyquark(incoming.back())
         && partons.rbegin()->type == HEJ::pid::gluon
         && HEJ::is_anyquark(*std::next(partons.rbegin()));
     }
 
     bool is_uno_backward(
       std::array<HEJ::Particle, 2> const & incoming,
       std::vector<HEJ::Particle> const & partons
     ) {
       if(partons.size() < 3) return false;
       assert(
         std::is_sorted(
           begin(incoming), end(incoming),
           HEJ::rapidity_less{}
         )
       );
       assert(
         std::is_sorted(
           begin(partons), end(partons),
           HEJ::rapidity_less{}
         )
       );
       assert(is_parton(*partons.begin()));
       assert(is_parton(*std::next(partons.begin())));
       return
         HEJ::is_anyquark(incoming.front())
         && partons.begin()->type == HEJ::pid::gluon
         && HEJ::is_anyquark(*std::next(partons.begin()));
     }
   }
 
   double PhaseSpacePoint::gen_Higgs_rapidity(HEJ::RNG & ran) {
     constexpr double STDDEV_Y_H = 1.6;
+    constexpr double Y_H_UNO_OFFSET = 1.9;
     if(is_uno_forward(incoming(), outgoing())) {
-        return random_normal_trunc(
-          STDDEV_Y_H,
-          ran,
-          std::numeric_limits<double>::lowest(),
-          outgoing_[outgoing().size() - 2].rapidity()
-        );
+        return outgoing_[outgoing().size() - 2].rapidity()
+          - Y_H_UNO_OFFSET
+          - random_normal_trunc(
+            STDDEV_Y_H,
+            ran,
+            -Y_H_UNO_OFFSET,
+            std::numeric_limits<double>::max()
+          );
     } else if(is_uno_backward(incoming(), outgoing())) {
-        return random_normal_trunc(
-          STDDEV_Y_H,
-          ran,
-          outgoing_[1].rapidity(),
-          std::numeric_limits<double>::max()
-        );
+        return outgoing_[1].rapidity()
+          + Y_H_UNO_OFFSET
+          + random_normal_trunc(
+            STDDEV_Y_H,
+            ran,
+            -Y_H_UNO_OFFSET,
+            std::numeric_limits<double>::max()
+          );
     }
     return random_normal(STDDEV_Y_H, ran);
   }
 
   namespace {
     template<class Iterator, class Predicate>
     Iterator find_if_nth(
       Iterator begin, Iterator end, Predicate p, std::size_t n
     ) {
       return std::find_if(
         begin, end,
         [p,n](auto const & i) mutable {
           if(!p(i)) return false;
           if(n > 0) {
             --n;
             return false;
           } else {
             return true;
           }
         }
       );
     }
   }
 
   double PhaseSpacePoint::gen_V_boson_rapidity(
     HEJ::ParticleID const V_boson,
     HEJ::RNG & ran
   ){
     constexpr double STDDEV_Y_V = 1.2;
     const auto can_couple = [V_boson](HEJ::Particle const & p) {
       return vector_boson_can_couple_to(V_boson, p.type);
     };
 
     const std::size_t n_pot_emitters = std::count_if(
       outgoing().begin(), outgoing().end(),
       can_couple
     );
     assert(n_pot_emitters > 0);
     const std::size_t emitter_idx = ran.flat() * n_pot_emitters;
     auto emitter = find_if_nth(
       outgoing_.begin(), outgoing_.end(),
       can_couple,
       emitter_idx
     );
     assert(emitter != outgoing_.end());
     // For a W we get a flavour change in the emitter,
     // so we have to _sum_ over all possible emitters
     // and have to adjust the weight
     // since we only pick a single term in that sum here.
     // For a Z/photon we do not get distinct configurations,
     // so there is no sum and no weight adjustment.
     if(std::abs(V_boson) == HEJ::pid::Wp) {
       emitter->type = static_cast<HEJ::ParticleID>(
         emitter->type - HEJ::charge(V_boson).numerator()
       );
       weight_ *= n_pot_emitters;
     }
 
     const double dy = random_normal(STDDEV_Y_V, ran);
     return emitter->rapidity() + dy;
   }
 
   namespace {
     /// partons are ordered: even = anti, 0 = gluon
     constexpr HEJ::ParticleID index_to_pid(size_t i){
       if(!i) return HEJ::pid::gluon;
       return static_cast<HEJ::ParticleID>( i%2 ? (i+1)/2 : -i/2 );
     }
 
     /// partons are ordered: even = anti, 0 = gluon
     constexpr size_t pid_to_index(HEJ::ParticleID id){
       if(id==HEJ::pid::gluon) return 0;
       return id>0 ? id*2-1 : std::abs(id)*2;
     }
 
     constexpr PhaseSpacePoint::part_mask GLUON = 1u << pid_to_index(HEJ::pid::gluon);
     constexpr PhaseSpacePoint::part_mask ALL = ~0;
 
     PhaseSpacePoint::part_mask init_allowed(HEJ::ParticleID const id){
       if(std::abs(id) == HEJ::pid::proton)
         return ALL;
       PhaseSpacePoint::part_mask out{0};
       if(HEJ::is_parton(id))
         out[pid_to_index(id)] = true;
       return out;
     }
 
     /// decides which "index" (see index_to_pid) are allowed for process
     PhaseSpacePoint::part_mask allowed_quarks(HEJ::ParticleID const boson){
       if(std::abs(boson) != HEJ::pid::Wp){
         return ~GLUON;
       }
       // special case W:
       // Wp: anti-down or up-type quark, no b/t
       // Wm: down or anti-up-type quark, no b/t
       return boson>0?0b00011001100  // NOLINT(readability-magic-numbers)
                     :0b00100110010; // NOLINT(readability-magic-numbers)
     }
   } // namespace
 
   std::array<PhaseSpacePoint::part_mask,2> PhaseSpacePoint::incoming_AWZ(
       Process const & proc,
       std::array<part_mask,2> allowed_partons,
       HEJ::RNG & ran
   ){
     assert(proc.boson);
     auto couple_parton = allowed_quarks(*proc.boson);
     if( // coupling possible through input
            allowed_partons[0] == (couple_parton&allowed_partons[0])
         || allowed_partons[1] == (couple_parton&allowed_partons[1])
     ){
       return allowed_partons;
     }
     // only first can couple
     if( (allowed_partons[0]&couple_parton).any()
       &&(allowed_partons[1]&couple_parton).none()
     ){
       return {allowed_partons[0]&couple_parton, allowed_partons[1]};
     }
     // only second can couple
     if(  (allowed_partons[0]&couple_parton).none()
       && (allowed_partons[1]&couple_parton).any()
     ){
       return {allowed_partons[0], allowed_partons[1]&couple_parton};
     }
     // both can couple
     if(  (allowed_partons[0]&couple_parton).any()
       && (allowed_partons[1]&couple_parton).any()
     ){
       double rnd = ran.flat();
       weight_*=3.;
       if(rnd<1./3.){
         return {
           allowed_partons[0] & couple_parton,
           allowed_partons[1] & ~couple_parton
         };
       }
       if(rnd<2./3.){
         return {
           allowed_partons[0] & ~couple_parton,
           allowed_partons[1] & couple_parton
         };
       }
       return {
         allowed_partons[0] & couple_parton,
         allowed_partons[1] & couple_parton
       };
     }
     throw std::invalid_argument{"Incoming state not allowed."};
   }
 
   std::array<PhaseSpacePoint::part_mask,2> PhaseSpacePoint::incoming_eqqbar(
       std::array<part_mask,2> allowed_partons, HEJ::RNG & ran
   ){
     auto const gluon_idx = pid_to_index(HEJ::pid::gluon);
     auto & first_beam = allowed_partons[0];
     auto & second_beam = allowed_partons[1];
     if(first_beam[gluon_idx] && !second_beam[gluon_idx]){
       first_beam.reset();
       first_beam.set(gluon_idx);
       return allowed_partons;
     }
     if(!first_beam[gluon_idx] && second_beam[gluon_idx]) {
       second_beam.reset();
       second_beam.set(gluon_idx);
       return allowed_partons;
     }
     if(first_beam[gluon_idx] && second_beam[gluon_idx]) {
       // both beams can be gluons
       // if one can't be a quark everything is good
       auto first_quarks = first_beam;
       first_quarks.reset(gluon_idx);
       auto second_quarks = second_beam;
       second_quarks.reset(gluon_idx);
       if(first_quarks.none() || second_quarks.none()){
         return allowed_partons;
       }
       // else choose one to be a gluon
       double rnd = ran.flat();
       weight_*=3.;
       if(rnd<1./3.){
         allowed_partons[0].reset();
         allowed_partons[0].set(gluon_idx);
         allowed_partons[1].reset(gluon_idx);
       } else if(rnd<2./3.){
         allowed_partons[1].reset();
         allowed_partons[1].set(gluon_idx);
         allowed_partons[0].reset(gluon_idx);
       } else {
         allowed_partons[0].reset();
         allowed_partons[0].set(gluon_idx);
         allowed_partons[1].reset();
         allowed_partons[1].set(gluon_idx);
       }
       return allowed_partons;
     }
     throw std::invalid_argument{
       "Incoming state not allowed for pure extremal qqbar."};
   }
 
   std::array<PhaseSpacePoint::part_mask,2> PhaseSpacePoint::incoming_uno(
       std::array<part_mask,2> allowed_partons, HEJ::RNG & ran
   ){
     auto const gluon_idx = pid_to_index(HEJ::pid::gluon);
     auto & first_beam = allowed_partons[0];
     auto & second_beam = allowed_partons[1];
     auto first_quarks = first_beam;
     first_quarks.reset(gluon_idx);
     auto second_quarks = second_beam;
     second_quarks.reset(gluon_idx);
     if(first_quarks.any() && second_quarks.none()){
       first_beam.reset(gluon_idx);
       return allowed_partons;
     }
     if(first_quarks.none() && second_quarks.any()) {
       second_beam.reset(gluon_idx);
       return allowed_partons;
     }
      if(first_quarks.any() && second_quarks.any()) {
       // both beams can be quarks
       // if one can't be gluon everything is good
       if(!first_beam[gluon_idx] || !second_beam[gluon_idx]){
         return allowed_partons;
       }
       // else choose one to be a quark
       double rnd = ran.flat();
       weight_*=3.;
       if(rnd<1./3.){
         allowed_partons[0].reset(gluon_idx);
         allowed_partons[1].reset();
         allowed_partons[1].set(gluon_idx);
       } else if(rnd<2./3.){
         allowed_partons[1].reset(gluon_idx);
         allowed_partons[0].reset();
         allowed_partons[0].set(gluon_idx);
       } else {
         allowed_partons[0].reset(gluon_idx);
         allowed_partons[1].reset(gluon_idx);
       }
       return allowed_partons;
     }
     throw std::invalid_argument{
       "Incoming state not allowed for pure unordered."};
   }
 
   /**
    * @brief Returns list of all allowed initial states partons
    *
    * checks which partons are allowed as initial state:
    * 1. only allow what is given in the Runcard (p -> all)
    * 2. A/W/Z require something to couple to
    *  a) no qqbar => no incoming gluon
    *  b) 2j     => no incoming gluon
    *  c) >3j    => can couple OR is gluon => 2 gluons become qqbar later
    * 3. pure eqqbar requires at least one gluon
    * 4. pure uno requires at least one quark
    */
   std::array<PhaseSpacePoint::part_mask,2> PhaseSpacePoint::allowed_incoming(
       Process const & proc,
       std::optional<subleading::Channels> channel,
       HEJ::RNG & ran
   ){
     // all possible incoming states
     std::array<part_mask,2> allowed_partons{
         init_allowed(proc.incoming[0]),
         init_allowed(proc.incoming[1])
       };
     // special case: A/W/Z without qqbar
     if(
       is_AWZ_process(proc)
       && (!channel || *channel == subleading::unordered)
     ) {
       return incoming_AWZ(proc, allowed_partons, ran);
     }
     if(!channel) return allowed_partons;
     switch(*channel) {
     case subleading::central_qqbar:
       return allowed_partons;
     case subleading::extremal_qqbar:
       return incoming_eqqbar(allowed_partons, ran);
     case subleading::unordered:
       return incoming_uno(allowed_partons, ran);
     default:;
     };
     throw std::logic_error{"enum value not covered"};
   }
 
   std::pair<double, double> PhaseSpacePoint::xa_xb(
     double const E_beam
   ) const {
     const double sqrts=2*E_beam;
     const double xa=(incoming_[0].E()-incoming_[0].pz())/sqrts;
     const double xb=(incoming_[1].E()+incoming_[1].pz())/sqrts;
     return std::make_pair(xa, xb);
   }
 
   void PhaseSpacePoint::reconstruct_incoming(
       Process const & proc,
       std::optional<subleading::Channels> const channel,
       HEJ::PDF & pdf, double E_beam,
       double uf,
       HEJ::RNG & ran
   ){
     std::tie(incoming_[0].p, incoming_[1].p) = incoming_momenta(outgoing_);
     const auto [xa, xb] = xa_xb(E_beam);
     // abort if phase space point is outside of collider energy reach
     if(xa > 1. || xb > 1.) {
       weight_=0;
       status_ = Status::too_much_energy;
       return;
     }
     auto const & ids = proc.incoming;
     std::array<part_mask,2> allowed_partons
       = allowed_incoming(proc, channel, ran);
     for(size_t i = 0; i < 2; ++i){
       if(ids[i] == HEJ::pid::proton || ids[i] == HEJ::pid::p_bar){
       // pick ids according to pdfs
         incoming_[i].type =
           generate_incoming_id(i, i?xb:xa, uf, pdf, allowed_partons[i], ran);
       } else {
         assert(allowed_partons[i][pid_to_index(ids[i])]);
         incoming_[i].type = ids[i];
       }
     }
   }
 
   HEJ::ParticleID PhaseSpacePoint::generate_incoming_id(
       size_t const beam_idx, double const x, double const uf,
       HEJ::PDF & pdf, part_mask allowed_partons, HEJ::RNG & ran
   ){
     std::array<double,NUM_PARTONS> pdf_wt{};
     pdf_wt[0] = allowed_partons[0]?
       std::fabs(pdf.pdfpt(beam_idx,x,uf,HEJ::pid::gluon)):0.;
     double pdftot = pdf_wt[0];
     for(size_t i = 1; i < pdf_wt.size(); ++i){
       pdf_wt[i] = allowed_partons[i]?
         4./9.*std::fabs(pdf.pdfpt(beam_idx,x,uf,index_to_pid(i))):0;
       pdftot += pdf_wt[i];
     }
     const double r1 = pdftot * ran.flat();
     double sum = 0;
     for(size_t i=0; i < pdf_wt.size(); ++i){
       if (r1 < (sum+=pdf_wt[i])){
         weight_*= pdftot/pdf_wt[i];
         return index_to_pid(i);
       }
     }
     std::cerr << "Error in choosing incoming parton: "<<x<<" "<<uf<<" "
       <<sum<<" "<<pdftot<<" "<<r1<<std::endl;
     throw std::logic_error{"Failed to choose parton flavour"};
   }
 
   double PhaseSpacePoint::random_normal( double stddev, HEJ::RNG & ran ){
     const double r1 = ran.flat();
     const double r2 = ran.flat();
     const double lninvr1 = -std::log(r1);
     const double result = stddev*std::sqrt(2.*lninvr1)*std::cos(2.*M_PI*r2);
     weight_ *= exp(result*result/(2*stddev*stddev))*std::sqrt(2.*M_PI)*stddev;
     return result;
   }
 
   double PhaseSpacePoint::random_normal_trunc(
     const double stddev,
     HEJ::RNG & ran,
     const double min,
     const double max
   ) {
     assert(min <= max);
     double result;
     std::uint64_t trials = 0;
     do {
       ++trials;
       const double r1 = ran.flat();
       const double r2 = ran.flat();
       const double lninvr1 = -std::log(r1);
       result = stddev*std::sqrt(2.*lninvr1)*std::cos(2.*M_PI*r2);
     } while(result < min || result > max);
     weight_ *= exp(result*result/(2*stddev*stddev))*std::sqrt(2.*M_PI)*stddev / trials;
     return result;
   }
 
   bool PhaseSpacePoint::momentum_conserved(double ep) const{
     fastjet::PseudoJet diff;
     for(auto const & in: incoming()) diff += in.p;
     for(auto const & out: outgoing()) diff -= out.p;
     return HEJ::nearby_ep(diff, fastjet::PseudoJet{}, ep);
   }
 
   std::optional<subleading::Channels> PhaseSpacePoint::select_channel(
     Subleading const subl_channels,
     double const chance,
     HEJ::RNG & ran
   ) {
     const double r = ran.flat();
     if(r > chance) {
       weight_ /= 1 - chance;
       return {};
     }
     // pick a random subleading channel (flat)
     const std::size_t num_channels = subl_channels.count();
     weight_ *= num_channels / chance;
     std::size_t channel_idx = r / chance * num_channels;
     for(
       unsigned channel = subleading::first;
       channel <= subleading::last;
       ++channel
     ) {
       if(subl_channels.test(channel)) {
         if(channel_idx == 0) {
           return {static_cast<subleading::Channels>(channel)};
         } else {
           --channel_idx;
         }
       }
     }
     throw std::logic_error{"unreachable"};
   }
 
 } // namespace HEJFOG