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#include "Angles.h"
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#include <iostream>
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//
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//
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//
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void getAngles_SanityCheck( LabVectors &l, Angles &a ) {
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//
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// define the frames & coordinate systems
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// --------------------------------------------------------------------------------------------------
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TVector3 Xframe = l.vec4l.BoostVector();
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TVector3 Z1frame = l.vecz1.BoostVector();
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TVector3 Z2frame = l.vecz2.BoostVector();
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// "partons" (pg6)
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TLorentzVector kq( 0, 0, (l.vec4l.E()+l.vec4l.Pz())/2, (l.vec4l.E()+l.vec4l.Pz())/2 );
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TLorentzVector kqbar( 0, 0, (l.vec4l.Pz()-l.vec4l.E())/2, (l.vec4l.E()-l.vec4l.Pz())/2 );
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TLorentzVector veckq_in_Xframe(kq);
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TLorentzVector veckqbar_in_Xframe(kqbar);
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veckq_in_Xframe.Boost(-1*Xframe);
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veckqbar_in_Xframe.Boost(-1*Xframe);
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// Zn vectors
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TLorentzVector vecz1_in_Xframe (l.vecz1);
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TLorentzVector vecz2_in_Xframe (l.vecz2);
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TLorentzVector vecz1_in_Z1frame (l.vecz1);
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TLorentzVector vecz2_in_Z2frame (l.vecz2);
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vecz1_in_Xframe.Boost(-1*Xframe);
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vecz2_in_Xframe.Boost(-1*Xframe);
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vecz1_in_Z1frame.Boost(-1*Z1frame);
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vecz2_in_Z2frame.Boost(-1*Z2frame);
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// coord system in the CM frame
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TVector3 uz_in_Xframe = vecz1_in_Xframe.Vect().Unit();
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TVector3 uy_in_Xframe = (veckq_in_Xframe.Vect().Unit().Cross(uz_in_Xframe.Unit())).Unit();
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TVector3 ux_in_Xframe = (uy_in_Xframe.Unit().Cross(uz_in_Xframe.Unit())).Unit();
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TRotation rotation;
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rotation = rotation.RotateAxes( ux_in_Xframe,uy_in_Xframe,uz_in_Xframe ).Inverse();
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// coords for Z2. rotate CM around y by pi
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TVector3 ux_in_Xframe_z2(ux_in_Xframe);
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TVector3 uy_in_Xframe_z2(uy_in_Xframe);
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TVector3 uz_in_Xframe_z2(uz_in_Xframe);
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TRotation aroundy;
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aroundy.Rotate(TMath::Pi(),uy_in_Xframe_z2);
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ux_in_Xframe_z2.Transform(aroundy);
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uz_in_Xframe_z2.Transform(aroundy);
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TRotation rotation2;
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rotation2 = rotation2.RotateAxes( ux_in_Xframe_z2,uy_in_Xframe_z2,uz_in_Xframe_z2 ).Inverse();
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//
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// for going to the Z frames from the CM frame
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//
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TLorentzVector vecz1_in_Xframe_newcoords(vecz1_in_Xframe);
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vecz1_in_Xframe_newcoords.Transform(rotation);
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TVector3 Z1frame_from_Xframe_newcoords = vecz1_in_Xframe_newcoords.BoostVector();
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TLorentzVector vecz2_in_Xframe_newcoords(vecz2_in_Xframe);
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vecz2_in_Xframe_newcoords.Transform(rotation2);
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TVector3 Z2frame_from_Xframe_newcoords = vecz2_in_Xframe_newcoords.BoostVector();
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// check ...
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TLorentzVector vecl1m_in_Z1(l.vecl1m );
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TLorentzVector vecl1p_in_Z1(l.vecl1p );
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vecl1m_in_Z1.Boost(-1*Xframe);
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vecl1p_in_Z1.Boost(-1*Xframe);
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vecl1m_in_Z1.Transform(rotation);
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vecl1p_in_Z1.Transform(rotation);
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vecl1m_in_Z1.Boost(-1*Z1frame_from_Xframe_newcoords);
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vecl1p_in_Z1.Boost(-1*Z1frame_from_Xframe_newcoords);
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std::cerr << "closure: " << vecl1m_in_Z1.Vect().Dot(vecl1p_in_Z1.Vect()) /
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(vecl1m_in_Z1.Vect().Mag()*vecl1p_in_Z1.Vect().Mag())
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<< std::endl;
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// kq.Print();
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// kqbar.Print();
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std::cout << "closure1: " << veckq_in_Xframe.Vect().Unit().Dot(veckqbar_in_Xframe.Vect().Unit())
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<< std::endl;
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//std::cerr << "closure2: " << vecz1_in_Xframe_newcoords.Vect().Unit().Dot(uz_in_Xframe) << std::endl;
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std::cerr << "closure2: " << vecz1_in_Xframe_newcoords.Vect().CosTheta() << std::endl;
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//
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TVector3 tmp = uz_in_Xframe;
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std::cerr << "closure:: cosTheta(uz) wrt nominal z: " << tmp.CosTheta() << std::endl;
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std::cerr << "closure:: cosTheta(uz) [from dot] wrt uz:" << tmp.Unit().Dot(uz_in_Xframe) << std::endl;
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tmp.Print();
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tmp = tmp.Transform(rotation);
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tmp.Print();
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std::cerr << "closure:: cosTheta(uz) wrt nominal z [after rot]: " << tmp.CosTheta() << std::endl;
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std::cerr << "closure:: cosTheta(uz) [for dot] wrt uz [after rot]:" << tmp.Unit().Dot(uz_in_Xframe) << std::endl;
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std::cerr << std::endl;
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// more checks
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TVector3 newx(0,1,0);
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TVector3 newy(0,0,1);
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TVector3 newz(1,0,0);
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TRotation r;
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r.RotateAxes(newx,newy,newz);
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TVector3 test(0,0,1);
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std::cerr << "test0: " << test.CosTheta() << std::endl;
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test.Print();
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test.Transform(r);
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std::cerr << "test1: " << test.CosTheta() << std::endl;
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test.Print();
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}
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