Rivet analyses

Decay parameters in Λb0 → Λc+(π, K) with Λc+ → Λ0(π+, K+) or Λc+ → pKS0

Experiment: LHCB (LHC)

Inspire ID: 2824757

Status: VALIDATED NOHEPDATA

Authors: - Peter Richardson

References: - arXiv: 2409.02759

Beams: * *

Beam energies: ANY

Run details: - Any source of unpolarized Lambda_b0 baryons, originally pp

Measurement of the decay parameters in in Λb0 → Λc+(π, K) with Λc+ → Λ0(π+, K+) or Λc+ → pKS0, with Λ0 → pπ. The data was read from Tables 1 and 2 in the paper.

Source code:LHCB_2024_I2824757.cc

// -*- C++ -*-
#include "Rivet/Analysis.hh"
#include "Rivet/Projections/UnstableParticles.hh"

namespace Rivet {


  /// @brief Lambda_b0 -> Lambda_c+ pi-,K-
  class LHCB_2024_I2824757 : public Analysis {
  public:

    /// Constructor
    RIVET_DEFAULT_ANALYSIS_CTOR(LHCB_2024_I2824757);


    /// @name Analysis methods
    /// @{

    /// Book histograms and initialise projections before the run
    void init() {
      // Initialise and register projections
      declare(UnstableParticles(Cuts::abspid == 5122), "UFS");
      for (unsigned int ip = 0; ip < 2; ++ip) {
        for (unsigned int ix = 0; ix < 2; ++ix) {
          for (unsigned int iy = 0; iy < 3; ++iy) {
            string base = toString(ip) + "_" + toString(ix) + "_" + toString(iy);
            book(_h_cos1[ip][ix][iy], "h_cos_1_" + base, 20, -1, 1);
            if (iy == 2) continue;
            book(_h_cos2[ip][ix][iy], "h_cos_2_" + base, 20, -1, 1);
            book(_p_cos12[ip][ix][iy], "p_cos_12_" + base, 1, -1, 1);
            book(_h_phi2[ip][ix][iy], "h_phi_2_" + base, 20, -M_PI, M_PI);
          }
        }
      }
    }


    /// Perform the per-event analysis
    void analyze(const Event& event) {
      // loop over Lambda_b0 baryons
      for (const Particle& Lamb : apply<UnstableParticles>(event, "UFS").particles()) {
        int sign = Lamb.pid() / 5122;
        if (Lamb.children().size() != 2) continue;
        Particle baryon1, meson1;
        if (Lamb.children()[0].pid() == sign * 4122
            && (Lamb.children()[1].pid() == -sign * 211 || Lamb.children()[1].pid() == -sign * 321)) {
          baryon1 = Lamb.children()[0];
          meson1 = Lamb.children()[1];
        }
        else if (Lamb.children()[1].pid() == sign * 4122
                 && (Lamb.children()[0].pid() == -sign * 211 || Lamb.children()[0].pid() == -sign * 321)) {
          baryon1 = Lamb.children()[1];
          meson1 = Lamb.children()[0];
        }
        else
          continue;
        if (baryon1.children().size() != 2) continue;
        unsigned int ib = meson1.abspid() == 211 ? 0 : 1;
        Particle baryon2, meson2;
        unsigned int ic = 0;
        if (baryon1.children()[0].pid() == sign * 3122 && baryon1.children()[1].pid() == sign * 211) {
          baryon2 = baryon1.children()[0];
          meson2 = baryon1.children()[1];
          ic = 0;
        }
        else if (baryon1.children()[1].pid() == sign * 3122 && baryon1.children()[0].pid() == sign * 211) {
          baryon2 = baryon1.children()[1];
          meson2 = baryon1.children()[0];
          ic = 0;
        }
        else if (baryon1.children()[0].pid() == sign * 3122 && baryon1.children()[1].pid() == sign * 321) {
          baryon2 = baryon1.children()[0];
          meson2 = baryon1.children()[1];
          ic = 1;
        }
        else if (baryon1.children()[1].pid() == sign * 3122 && baryon1.children()[0].pid() == sign * 321) {
          baryon2 = baryon1.children()[1];
          meson2 = baryon1.children()[0];
          ic = 1;
        }
        else if (baryon1.children()[0].pid() == sign * 2212
                 && (baryon1.children()[1].pid() == -sign * 311 || baryon1.children()[1].pid() == 310)) {
          baryon2 = baryon1.children()[0];
          meson2 = baryon1.children()[1];
          ic = 2;
        }
        else if (baryon1.children()[1].pid() == sign * 2212
                 && (baryon1.children()[1].pid() == -sign * 311 || baryon1.children()[1].pid() == 310)) {
          baryon2 = baryon1.children()[1];
          meson2 = baryon1.children()[0];
          ic = 2;
        }
        else
          continue;
        // deal with Kbar0 in Lambda_c+ -> Kbar0 p
        if (ic == 2 && meson2.pid() != 310) {
          if (meson2.children().size() == 1) {
            meson2 = meson2.children()[0];
          }
          if (meson2.pid() != 310) continue;
        }
        // first boost to the Lambdab0 rest frame
        LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Lamb.mom().betaVec());
        FourMomentum pbaryon1 = boost1.transform(baryon1.mom());
        FourMomentum pbaryon2 = boost1.transform(baryon2.mom());
        FourMomentum pmeson2 = boost1.transform(meson2.mom());
        // boost to lambda_c rest frame
        LorentzTransform boost2 = LorentzTransform::mkFrameTransformFromBeta(pbaryon1.betaVec());
        Vector3 axis1 = pbaryon1.p3().unit();
        FourMomentum pp = boost2.transform(pbaryon2);
        double cTheta1 = pp.p3().unit().dot(axis1);
        _h_cos1[(1 - sign) / 2][ib][ic]->fill(cTheta1);
        // that's it for Lambda_c+ -> p+ K_S0
        if (ic == 2) continue;
        if (baryon2.children().size() != 2) continue;
        Particle baryon3, meson3;
        if (baryon2.children()[0].pid() == sign * 2212 && baryon2.children()[1].pid() == -sign * 211) {
          baryon3 = baryon2.children()[0];
          meson3 = baryon2.children()[1];
        }
        else if (baryon2.children()[1].pid() == sign * 2212 && baryon2.children()[0].pid() == -sign * 211) {
          baryon3 = baryon2.children()[1];
          meson3 = baryon2.children()[0];
        }
        else
          continue;
        Vector3 axis2 = pp.p3().unit();
        LorentzTransform boost3 = LorentzTransform::mkFrameTransformFromBeta(pp.betaVec());
        FourMomentum pbaryon3 = boost3.transform(boost2.transform(boost1.transform(baryon3.mom())));
        double cTheta2 = pbaryon3.p3().unit().dot(axis2);
        _h_cos2[(1 - sign) / 2][ib][ic]->fill(cTheta2);
        _p_cos12[(1 - sign) / 2][ib][ic]->fill(cTheta1 * cTheta2, cTheta1 * cTheta2);
        Vector3 trans1 = axis1 - axis1.dot(axis2) * axis2;
        Vector3 trans2 = pbaryon3.p3() - pbaryon3.p3().dot(axis2) * pbaryon3.p3();
        double phi2 = atan2(trans1.cross(trans2).dot(axis2), trans1.dot(trans2));
        _h_phi2[(1 - sign) / 2][ib][ic]->fill(phi2);
      }
    }

    pair<double, double> calcAlpha(Histo1DPtr hist) const {
      if (hist->numEntries() == 0.) return make_pair(0., 0.);
      double sum1(0.), sum2(0.);
      for (const auto& bin : hist->bins()) {
        double Oi = bin.sumW();
        if (Oi == 0.) continue;
        double ai = 0.5 * (bin.xMax() - bin.xMin());
        double bi = 0.5 * ai * (bin.xMax() + bin.xMin());
        double Ei = bin.errW();
        sum1 += sqr(bi / Ei);
        sum2 += bi / sqr(Ei) * (Oi - ai);
      }
      return make_pair(sum2 / sum1, sqrt(1. / sum1));
    }

    vector<pair<double, double>> calcBetaGamma(Histo1DPtr hist) const {
      if (hist->numEntries() == 0.) return vector<pair<double, double>>(2, make_pair(0., 0.));
      ;
      double sum[7] = {
          0., 0., 0., 0., 0., 0., 0.,
      };
      for (const auto& bin : hist->bins()) {
        double Oi = bin.sumW();
        if (Oi == 0.) continue;
        double ai = (bin.xMax() - bin.xMin()) / 2. / M_PI;
        double bi = M_PI / 32. * (cos(bin.xMin()) - cos(bin.xMax()));
        double ci = -M_PI / 32. * (sin(bin.xMin()) - sin(bin.xMax()));
        double Ei = bin.errW();
        sum[0] += bi * Oi / sqr(Ei);
        sum[1] += ci * Oi / sqr(Ei);
        sum[2] += ai * bi / sqr(Ei);
        sum[3] += ai * ci / sqr(Ei);
        sum[4] += sqr(bi) / sqr(Ei);
        sum[5] += sqr(ci) / sqr(Ei);
        sum[6] += bi * ci / sqr(Ei);
      }
      double gamma = (sum[0] / sum[4] - sum[2] / sum[4] - sum[1] / sum[6] + sum[3] / sum[6])
          / (sum[6] / sum[4] - sum[5] / sum[6]);
      double beta = (sum[0] / sum[6] - sum[2] / sum[6] - sum[1] / sum[5] + sum[3] / sum[5])
          / (sum[4] / sum[6] - sum[6] / sum[5]);
      return {make_pair(beta, 1. / sqrt(sum[4])), make_pair(gamma, 1. / sqrt(sum[5]))};
    }


    /// Normalise histograms etc., after the run
    void finalize() {
      normalize(_h_cos1);
      normalize(_h_cos2);
      normalize(_h_phi2);
      // compute values for specific modes
      pair<double, double> a_b[2][2][2], a_c[2][2][2], a_s[2][2][2], beta[2][2][2], gamma[2][2][2];
      for (unsigned int ip = 0; ip < 2; ++ip) {
        for (unsigned int ib = 0; ib < 2; ++ib) {
          for (unsigned int ic = 0; ic < 2; ++ic) {
            pair<double, double> p1 = calcAlpha(_h_cos1[ip][ib][ic]);
            pair<double, double> p2 = calcAlpha(_h_cos2[ip][ib][ic]);
            pair<double, double> p3 = make_pair(9. * _p_cos12[ip][ib][ic]->bin(1).mean(2),
                                                9. * _p_cos12[ip][ib][ic]->bin(1).stdErr(2));
            double ferr = sqrt(sqr(p1.second / p1.first) + sqr(p2.second / p2.first)
                               + sqr(p3.second / p3.first));
            // lamda decay first as sign well known
            double l3 = p2.first * p3.first / p1.first;
            double e3 = l3 * ferr;
            l3 = sqrt(max(l3, 0.));
            e3 = 0.5 * e3;
            // sign ambiguity so fix alpha for lambda0 -> p pi to known sign
            if (ip == 1) l3 *= -1.;
            a_s[ip][ib][ic] = make_pair(l3, e3);
            // lambda_b decay
            double l1 = p1.first * p3.first / p2.first;
            double e1 = l1 * ferr;
            l1 = sqrt(max(l1, 0.));
            e1 = 0.5 * e1;
            if (p3.first * l3 < 0.) l1 *= -1.;
            a_b[ip][ib][ic] = make_pair(l1, e1);
            // lambda_c decay
            double l2 = p1.first * p2.first / p3.first;
            double e2 = l2 * ferr;
            l2 = sqrt(max(l2, 0.));
            e2 = 0.5 * e2;
            if (p2.first * l3 < 0.) l2 *= -1.;
            a_c[ip][ib][ic] = make_pair(l2, e2);
            vector<pair<double, double>> temp = calcBetaGamma(_h_phi2[ip][ib][ic]);
            for (auto& val : temp) {
              double error = sqrt(sqr(val.second / val.first) + sqr(p3.second / p3.first));
              val.first /= p3.first;
              val.second = val.first * error;
            }
            beta[ip][ib][ic] = temp[0];
            gamma[ip][ib][ic] = temp[1];
          }
        }
      }
      // perform averages
      // Lambda^0 -> p pi
      pair<double, double> alam[2];
      for (unsigned int ip = 0; ip < 2; ++ip) {
        double sum1(0.), sum2(0.);
        for (unsigned int ib = 0; ib < 2; ++ib) {
          for (unsigned int ic = 0; ic < 2; ++ic) {
            sum1 += a_s[ip][ib][ic].first / sqr(a_s[ip][ib][ic].second);
            sum2 += 1. / sqr(a_s[ip][ib][ic].second);
          }
        }
        alam[ip] = make_pair(sum1 / sum2, sqrt(1. / sum2));
        Estimate0DPtr tmp;
        book(tmp, 1, 6, 1 + ip);
        tmp->set(alam[ip].first, alam[ip].second);
      }
      Estimate0DPtr tmp;
      book(tmp, 1, 6, 3);
      tmp->set(0.5 * (alam[0].first - alam[1].first), 0.5 * sqrt(sqr(alam[0].second) + sqr(alam[1].second)));
      book(tmp, 1, 6, 4);
      tmp->set((alam[0].first + alam[1].first) / (alam[0].first - alam[1].first),
               4. * (sqr(alam[0].first * alam[1].second) + sqr(alam[1].first * alam[0].second))
                   / pow(alam[0].first - alam[1].first, 4));
      // Lambda_b decays
      pair<double, double> ab[2][2];
      for (unsigned int ib = 0; ib < 2; ++ib) {
        for (unsigned int ip = 0; ip < 2; ++ip) {
          double sum1(0.), sum2(0.);
          for (unsigned int ic = 0; ic < 2; ++ic) {
            sum1 += a_b[ip][ib][ic].first / sqr(a_b[ip][ib][ic].second);
            sum2 += 1. / sqr(a_b[ip][ib][ic].second);
          }
          ab[ip][ib] = make_pair(sum1 / sum2, sqrt(1. / sum2));
          Estimate0DPtr tmp;
          book(tmp, 1, 1 + ib, 1 + ip);
          tmp->set(ab[ip][ib].first, ab[ip][ib].second);
        }
        Estimate0DPtr tmp;
        book(tmp, 1, 1 + ib, 3);
        tmp->set(0.5 * (ab[0][ib].first - ab[1][ib].first),
                 0.5 * sqrt(sqr(ab[0][ib].second) + sqr(ab[1][ib].second)));
        book(tmp, 1, 1 + ib, 4);
        tmp->set((ab[0][ib].first + ab[1][ib].first) / (ab[0][ib].first - ab[1][ib].first),
                 4. * (sqr(ab[0][ib].first * ab[1][ib].second) + sqr(ab[1][ib].first * ab[0][ib].second))
                     / pow(ab[0][ib].first - ab[1][ib].first, 4));
      }
      // Lambda_c decays
      for (unsigned int ic = 0; ic < 2; ++ic) {
        pair<double, double> ac[2], bc[2], gc[2];
        for (unsigned int ip = 0; ip < 2; ++ip) {
          double sum1(0.), sum2(0.);
          for (unsigned int ib = 0; ib < 2; ++ib) {
            sum1 += a_c[ip][ib][ic].first / sqr(a_c[ip][ib][ic].second);
            sum2 += 1. / sqr(a_c[ip][ib][ic].second);
          }
          ac[ip] = make_pair(sum1 / sum2, sqrt(1. / sum2));
          Estimate0DPtr tmp;
          book(tmp, 1, 3 + ic, 1 + ip);
          tmp->set(ac[ip].first, ac[ip].second);
          sum1 = sum2 = 0.;
          for (unsigned int ib = 0; ib < 2; ++ib) {
            sum1 += beta[ip][ib][ic].first / sqr(beta[ip][ib][ic].second);
            sum2 += 1. / sqr(beta[ip][ib][ic].second);
          }
          bc[ip] = make_pair(sum1 / sum2, sqrt(1. / sum2));
          book(tmp, 2, 1 + ip, 1 + ic);
          tmp->set(bc[ip].first, bc[ip].second);
          sum1 = sum2 = 0.;
          for (unsigned int ib = 0; ib < 2; ++ib) {
            sum1 += gamma[ip][ib][ic].first / sqr(gamma[ip][ib][ic].second);
            sum2 += 1. / sqr(gamma[ip][ib][ic].second);
          }
          gc[ip] = make_pair(sum1 / sum2, sqrt(1. / sum2));
          book(tmp, 2, 3 + ip, 1 + ic);
          tmp->set(gc[ip].first, gc[ip].second);
        }
        Estimate0DPtr tmp;
        book(tmp, 1, 3 + ic, 3);
        tmp->set(0.5 * (ac[0].first - ac[1].first), 0.5 * sqrt(sqr(ac[0].second) + sqr(ac[1].second)));
        book(tmp, 1, 3 + ic, 4);
        tmp->set((ac[0].first + ac[1].first) / (ac[0].first - ac[1].first),
                 4. * (sqr(ac[0].first * ac[1].second) + sqr(ac[1].first * ac[0].second))
                     / pow(ac[0].first - ac[1].first, 4));
      }
      // finally lambda_c -> p KS0
      pair<double, double> ap[2];
      for (unsigned int ip = 0; ip < 2; ++ip) {
        double sum1(0.), sum2(0.);
        for (unsigned int ib = 0; ib < 2; ++ib) {
          pair<double, double> p1 = calcAlpha(_h_cos1[ip][ib][2]);
          double val = p1.first / ab[ip][ib].first;
          double err = sqr(val) * (sqr(p1.second / p1.first) + sqr(ab[ip][ib].second / ab[ip][ib].first));
          sum1 += val / err;
          sum2 += 1. / err;
        }
        ap[ip] = make_pair(sum1 / sum2, sqrt(1. / sum2));
        Estimate0DPtr tmp;
        book(tmp, 1, 5, 1 + ip);
        tmp->set(ap[ip].first, ap[ip].second);
      }
      book(tmp, 1, 5, 3);
      tmp->set(0.5 * (ap[0].first - ap[1].first), 0.5 * sqrt(sqr(ap[0].second) + sqr(ap[1].second)));
      book(tmp, 1, 5, 4);
      tmp->set((ap[0].first + ap[1].first) / (ap[0].first - ap[1].first),
               4. * (sqr(ap[0].first * ap[1].second) + sqr(ap[1].first * ap[0].second))
                   / pow(ap[0].first - ap[1].first, 4));
    }
    /// @}


    /// @name Histograms
    /// @{
    Histo1DPtr _h_cos1[2][2][3], _h_cos2[2][2][2], _h_phi2[2][2][2];
    Profile1DPtr _p_cos12[2][2][2];
    /// @}
  };


  RIVET_DECLARE_PLUGIN(LHCB_2024_I2824757);

}