Boost.h

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// SPDX-License-Identifier: LGPL-3.0-or-later
// Copyright (C) 2026 Wouter Deconinck, Barak Schmookler, Stephen Maple
 
#pragma once
 
#include <Math/Vector4D.h>
#include <Math/LorentzRotation.h>
#include <Math/LorentzVector.h>
#include <Math/RotationX.h>
#include <Math/RotationY.h>
#include <Math/Boost.h>
 
using ROOT::Math::PxPyPzEVector;
 
namespace eicrecon {
 
using ROOT::Math::LorentzRotation;
 
inline LorentzRotation determine_boost(PxPyPzEVector ei, PxPyPzEVector pi) {
 
  using ROOT::Math::Boost;
  using ROOT::Math::RotationX;
  using ROOT::Math::RotationY;
 
  // Save original input for constructing target "head-on" boost
  PxPyPzEVector eo = ei;
  PxPyPzEVector po = pi;
 
  // Step 1: Boost to CM frame
  const auto cmBoost = (ei + pi).BoostToCM();
  const Boost boost_from_og_to_cm(cmBoost);
 
  ei = boost_from_og_to_cm(ei);
  pi = boost_from_og_to_cm(pi);
 
  // Step 2: Rotate so pi is aligned along +z
  RotationY rotAboutY(-1.0 * atan2(pi.Px(), pi.Pz()));
  RotationX rotAboutX(+1.0 * atan2(pi.Py(), pi.Pz()));
 
  ei = rotAboutX(rotAboutY(ei));
  pi = rotAboutX(rotAboutY(pi));
 
  // Step 3: Construct "ideal" head-on configuration (same energies, back-to-back along z)
  double e_energy = eo.E();
  double p_energy = po.E();
  double e_pz     = -eo.P();
  double p_pz     = +po.P();
 
  PxPyPzEVector eh(0, 0, e_pz, e_energy);
  PxPyPzEVector ph(0, 0, p_pz, p_energy);
 
  // Step 4: Boost to the frame where those particles look like the current ei/pi
  const auto hoBoost = (eh + ph).BoostToCM();    // CM of head-on frame
  const Boost boost_from_cm_to_headon(-hoBoost); // Boost from CM to head-on
 
  // Final transformation = headon boost * rotations * CM boost
  LorentzRotation tf;
  tf *= boost_from_cm_to_headon;
  tf *= rotAboutX;
  tf *= rotAboutY;
  tf *= boost_from_og_to_cm;
 
  return tf;
}
 
inline PxPyPzEVector apply_boost(const LorentzRotation& tf, const PxPyPzEVector& part) {
 
  // Step 5: Apply boosts and rotations to any particle 4-vector
  // (here too, choices will have to be made as to what the 4-vector is for reconstructed particles)
 
  // Boost and rotate particle 4-momenta into the headon frame
  return tf(part);
}
 
} // namespace eicrecon