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| // -*- C++ -*-
#include "Rivet/Analysis.hh"
#include "Rivet/Projections/Beam.hh"
#include "Rivet/Projections/FinalState.hh"
#include "Rivet/Projections/UnstableParticles.hh"
namespace Rivet {
/// @brief J/Psi, psi(2S) -> Sigma+ Sigmabar-
class BESIII_2020_I1791570 : public Analysis {
public:
/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2020_I1791570);
/// @name Analysis methods
///@{
/// Book histograms and initialise projections before the run
void init() {
// Initialise and register projections
declare(Beam(), "Beams");
declare(UnstableParticles(), "UFS");
declare(FinalState(), "FS");
// Book histograms
book(_h_T1, "/TMP/T1",20,-1.,1.);
book(_h_T2, "/TMP/T2",20,-1.,1.);
book(_h_T3, "/TMP/T3",20,-1.,1.);
book(_h_T4, "/TMP/T4",20,-1.,1.);
book(_h_T5, "/TMP/T5",20,-1.,1.);
book(_h_cThetaL,"/TMP/cThetaL",20,-1.,1.);
if(isCompatibleWithSqrtS(3.1,1e-2))
book(_h_mu,1,1,1);
else if(isCompatibleWithSqrtS(3.686,1e-2))
book(_h_mu,1,1,2);
else
throw Error("Unexpected sqrtS ! Only 3.1 and 3.686 GeV atr supported");
book(_wsum,"/TMP/wsum");
}
void findChildren(const Particle & p,map<long,int> & nRes, int &ncount) {
for( const Particle &child : p.children()) {
if(child.children().empty()) {
nRes[child.pid()]-=1;
--ncount;
}
else
findChildren(child,nRes,ncount);
}
}
/// Perform the per-event analysis
void analyze(const Event& event) {
// get the axis, direction of incoming electron
const ParticlePair& beams = apply<Beam>(event, "Beams").beams();
Vector3 axis;
if(beams.first.pid()>0)
axis = beams.first .momentum().p3().unit();
else
axis = beams.second.momentum().p3().unit();
// types of final state particles
const FinalState& fs = apply<FinalState>(event, "FS");
map<long,int> nCount;
int ntotal(0);
for (const Particle& p : fs.particles()) {
nCount[p.pid()] += 1;
++ntotal;
}
// loop over Sigma+ baryons
const UnstableParticles & ufs = apply<UnstableParticles>(event, "UFS");
Particle Sigma,SigBar;
bool matched(false);
for (const Particle& p : ufs.particles(Cuts::abspid==3222)) {
if(p.children().empty()) continue;
map<long,int> nRes=nCount;
int ncount = ntotal;
findChildren(p,nRes,ncount);
matched=false;
// check for antiparticle
for (const Particle& p2 : ufs.particles(Cuts::pid==-p.pid())) {
if(p2.children().empty()) continue;
map<long,int> nRes2=nRes;
int ncount2 = ncount;
findChildren(p2,nRes2,ncount2);
if(ncount2==0) {
matched = true;
for(auto const & val : nRes2) {
if(val.second!=0) {
matched = false;
break;
}
}
// fond baryon and antibaryon
if(matched) {
if(p.pid()>0) {
Sigma = p;
SigBar = p2;
}
else {
Sigma = p2;
SigBar = p;
}
break;
}
}
}
if(matched) break;
}
if(!matched) vetoEvent;
// find proton
Particle proton;
matched = false;
for (const Particle & p : Sigma.children()) {
if(p.pid()==2212) {
matched=true;
proton=p;
}
else if(p.pid()!=111) {
matched = false;
break;
}
}
if(!matched) vetoEvent;
// find antiproton
Particle pbar;
matched = false;
for (const Particle & p : SigBar.children()) {
if(p.pid()==-2212) {
matched=true;
pbar=p;
}
else if(p.pid()!=111) {
matched = false;
break;
}
}
if(!matched) vetoEvent;
// boost to the Sigma rest frame
LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Sigma.momentum().betaVec());
Vector3 e1z = Sigma.momentum().p3().unit();
Vector3 e1y = e1z.cross(axis).unit();
Vector3 e1x = e1y.cross(e1z).unit();
Vector3 axis1 = boost1.transform(proton.momentum()).p3().unit();
double n1x(e1x.dot(axis1)),n1y(e1y.dot(axis1)),n1z(e1z.dot(axis1));
// boost to the Sigma bar
LorentzTransform boost2 = LorentzTransform::mkFrameTransformFromBeta(SigBar.momentum().betaVec());
Vector3 axis2 = boost2.transform(pbar.momentum()).p3().unit();
double n2x(e1x.dot(axis2)),n2y(e1y.dot(axis2)),n2z(e1z.dot(axis2));
double cosL = axis.dot(Sigma.momentum().p3().unit());
double sinL = sqrt(1.-sqr(cosL));
double T1 = sqr(sinL)*n1x*n2x+sqr(cosL)*n1z*n2z;
double T2 = -sinL*cosL*(n1x*n2z+n1z*n2x);
double T3 = -sinL*cosL*n1y;
double T4 = -sinL*cosL*n2y;
double T5 = n1z*n2z-sqr(sinL)*n1y*n2y;
double mu = -(n1y-n2y);
_h_T1->fill(cosL,T1);
_h_T2->fill(cosL,T2);
_h_T3->fill(cosL,T3);
_h_T4->fill(cosL,T4);
_h_T5->fill(cosL,T5);
_h_mu->fill(cosL,mu);
_wsum->fill();
_h_cThetaL->fill(cosL);
}
pair<double,pair<double,double> > calcAlpha0(Histo1DPtr hist) {
if(hist->numEntries()==0.) return make_pair(0.,make_pair(0.,0.));
double d = 3./(pow(hist->xMax(),3)-pow(hist->xMin(),3));
double c = 3.*(hist->xMax()-hist->xMin())/(pow(hist->xMax(),3)-pow(hist->xMin(),3));
double sum1(0.),sum2(0.),sum3(0.),sum4(0.),sum5(0.);
for (auto bin : hist->bins() ) {
double Oi = bin.area();
if(Oi==0.) continue;
double a = d*(bin.xMax() - bin.xMin());
double b = d/3.*(pow(bin.xMax(),3) - pow(bin.xMin(),3));
double Ei = bin.areaErr();
sum1 += a*Oi/sqr(Ei);
sum2 += b*Oi/sqr(Ei);
sum3 += sqr(a)/sqr(Ei);
sum4 += sqr(b)/sqr(Ei);
sum5 += a*b/sqr(Ei);
}
// calculate alpha
double alpha = (-c*sum1 + sqr(c)*sum2 + sum3 - c*sum5)/(sum1 - c*sum2 + c*sum4 - sum5);
// and error
double cc = -pow((sum3 + sqr(c)*sum4 - 2*c*sum5),3);
double bb = -2*sqr(sum3 + sqr(c)*sum4 - 2*c*sum5)*(sum1 - c*sum2 + c*sum4 - sum5);
double aa = sqr(sum1 - c*sum2 + c*sum4 - sum5)*(-sum3 - sqr(c)*sum4 + sqr(sum1 - c*sum2 + c*sum4 - sum5) + 2*c*sum5);
double dis = sqr(bb)-4.*aa*cc;
if(dis>0.) {
dis = sqrt(dis);
return make_pair(alpha,make_pair(0.5*(-bb+dis)/aa,-0.5*(-bb-dis)/aa));
}
else {
return make_pair(alpha,make_pair(0.,0.));
}
}
pair<double,double> calcCoeff(unsigned int imode,Histo1DPtr hist) {
if(hist->numEntries()==0.) return make_pair(0.,0.);
double sum1(0.),sum2(0.);
for (auto bin : hist->bins() ) {
double Oi = bin.area();
if(Oi==0.) continue;
double ai(0.),bi(0.);
if(imode==0) {
bi = (pow(1.-sqr(bin.xMin()),1.5) - pow(1.-sqr(bin.xMax()),1.5))/3.;
}
else if(imode>=2 && imode<=4) {
bi = ( pow(bin.xMin(),3)*( -5. + 3.*sqr(bin.xMin())) +
pow(bin.xMax(),3)*( 5. - 3.*sqr(bin.xMax())))/15.;
}
else
assert(false);
double Ei = bin.areaErr();
sum1 += sqr(bi/Ei);
sum2 += bi/sqr(Ei)*(Oi-ai);
}
return make_pair(sum2/sum1,sqrt(1./sum1));
}
/// Normalise histograms etc., after the run
void finalize() {
normalize(_h_cThetaL);
scale(_h_T1, 1./ *_wsum);
scale(_h_T2, 1./ *_wsum);
scale(_h_T3, 1./ *_wsum);
scale(_h_T4, 1./ *_wsum);
scale(_h_T5, 1./ *_wsum);
scale(_h_mu, 2./ *_wsum);
// histos for J/psi or psi(2s)
int ih = isCompatibleWithSqrtS(3.1,1e-2) ? 1 : 2;
// calculate alpha0
pair<double,pair<double,double> > alpha0 = calcAlpha0(_h_cThetaL);
Scatter2DPtr _h_alpha0;
book(_h_alpha0,4,1,ih);
_h_alpha0->addPoint(0.5, alpha0.first, make_pair(0.5,0.5),
make_pair(alpha0.second.first,alpha0.second.second) );
double s2 = -1. + sqr(alpha0.first);
double s3 = 3 + alpha0.first;
double s1 = sqr(s3);
// alpha- and alpha+ from proton data
pair<double,double> c_T2 = calcCoeff(2,_h_T2);
pair<double,double> c_T3 = calcCoeff(3,_h_T3);
pair<double,double> c_T4 = calcCoeff(4,_h_T4);
double s4 = sqr(c_T2.first);
double s5 = sqr(c_T3.first);
double s6 = sqr(c_T4.first);
double disc = s1*s5*s6*(-9.*s2*s4 + 4.*s1*s5*s6);
if(disc>=0.) {
disc = sqrt(disc);
double aM = -sqrt(-1./s2/s6*(2.*s1*s5*s6+disc));
double aP = c_T4.first/c_T3.first*aM;
double aM_P = (2*(alpha0.first*c_T4.first*alpha0.second.first + c_T4.second*s2)*(disc + 2*s1*s5*s6)
- c_T4.first*s2*(4*s3*c_T3.first*c_T4.first*(c_T3.first*c_T4.first*alpha0.second.first +s3*c_T4.first*c_T3.second +s3*c_T3.first*c_T4.second) +
(disc*(- 9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
+ 9*((1 - alpha0.first*(3 + 2*alpha0.first))* c_T3.first*c_T4.first*alpha0.second.first - s2*s3*c_T4.first*c_T3.second
- s2*s3*c_T3.first*c_T4.second)* s4
+ 8*(c_T3.first*c_T4.first*alpha0.second.first + s3*c_T4.first*c_T3.second + s3*c_T3.first*c_T4.second)* s1*s5*s6))
/(4*pow(3 + alpha0.first,3)*pow(c_T3.first,3)*pow(c_T4.first,3) -9*s2*s3*c_T3.first*c_T4.first*s4)))/
(2.*pow(c_T4.first,3)*pow(s2,2)*sqrt(-((disc + 2*s1*s5*s6)/(s2*s6))));
double aM_M = (2*(alpha0.first*c_T4.first*alpha0.second.second + c_T4.second*s2)*(disc + 2*s1*s5*s6)
- c_T4.first*s2*(4*s3*c_T3.first*c_T4.first*(c_T3.first*c_T4.first*alpha0.second.second +s3*c_T4.first*c_T3.second +s3*c_T3.first*c_T4.second) +
(disc*(- 9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
+ 9*((1 - alpha0.first*(3 + 2*alpha0.first))* c_T3.first*c_T4.first*alpha0.second.second - s2*s3*c_T4.first*c_T3.second
- s2*s3*c_T3.first*c_T4.second)* s4
+ 8*(c_T3.first*c_T4.first*alpha0.second.second + s3*c_T4.first*c_T3.second + s3*c_T3.first*c_T4.second)* s1*s5*s6))
/(4*pow(3 + alpha0.first,3)*pow(c_T3.first,3)*pow(c_T4.first,3) -9*s2*s3*c_T3.first*c_T4.first*s4)))/
(2.*pow(c_T4.first,3)*pow(s2,2)*sqrt(-((disc + 2*s1*s5*s6)/(s2*s6))));
double aP_M = (c_T4.first*sqrt(-((disc + 2*s1*s5*s6)/ (s2*s6)))*
(-2*c_T3.second - (2*alpha0.first*c_T3.first*alpha0.second.first)/s2 + (c_T3.first*(4*s3*c_T3.first*c_T4.first*(c_T3.first*c_T4.first*alpha0.second.first + s3*c_T4.first*c_T3.second + s3*c_T3.first*c_T4.second)
+ (disc*(-9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
+ 9*((1 - alpha0.first*(3 + 2*alpha0.first))* c_T3.first*c_T4.first*alpha0.second.first - s2*s3*c_T4.first*c_T3.second
- s2*s3*c_T3.first*c_T4.second)* s4 +
8*(c_T3.first*c_T4.first*alpha0.second.first + s3*c_T4.first*c_T3.second + s3*c_T3.first*c_T4.second)* s1*s5*s6))/
(4* pow(3 + alpha0.first,3)* pow(c_T3.first,3)* pow(c_T4.first,3) - 9*s2*s3*c_T3.first*c_T4.first*s4)))/
(disc + 2*s1*s5*s6)))/(2.*pow(c_T3.first,2));
double aP_P = (c_T4.first*sqrt(-((disc + 2*s1*s5*s6)/ (s2*s6)))*
(-2*c_T3.second - (2*alpha0.first*c_T3.first*alpha0.second.second)/s2 + (c_T3.first*(4*s3*c_T3.first*c_T4.first*(c_T3.first*c_T4.first*alpha0.second.second + s3*c_T4.first*c_T3.second + s3*c_T3.first*c_T4.second)
+ (disc*(-9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
+ 9*((1 - alpha0.first*(3 + 2*alpha0.first))* c_T3.first*c_T4.first*alpha0.second.second - s2*s3*c_T4.first*c_T3.second
- s2*s3*c_T3.first*c_T4.second)* s4 +
8*(c_T3.first*c_T4.first*alpha0.second.second + s3*c_T4.first*c_T3.second + s3*c_T3.first*c_T4.second)* s1*s5*s6))/
(4* pow(3 + alpha0.first,3)* pow(c_T3.first,3)* pow(c_T4.first,3) - 9*s2*s3*c_T3.first*c_T4.first*s4)))/
(disc + 2*s1*s5*s6)))/(2.*pow(c_T3.first,2));
Scatter2DPtr _h_alphaM;
book(_h_alphaM,2,1,1);
_h_alphaM->addPoint(0.5, aM, make_pair(0.5,0.5),
make_pair(-aM_M , -aM_P ) );
Scatter2DPtr _h_alphaP;
book(_h_alphaP,2,1,2);
_h_alphaP->addPoint(0.5, aP, make_pair(0.5,0.5),
make_pair(-aP_M , -aP_P ) );
Scatter2DPtr _h_alphabar;
book(_h_alphabar,2,1,3);
_h_alphabar->addPoint(0.5, 0.5*(aM-aP), make_pair(0.5,0.5),
make_pair(0.5*sqrt(sqr(aM_M)+sqr(aP_P)) ,
0.5*sqrt(sqr(aM_P)+sqr(aP_M))) );
// now for Delta
double sDelta = (-2.*(3. + alpha0.first)*c_T3.first)/(aM*sqrt(1 - sqr(alpha0.first)));
double cDelta = (-3*(3 + alpha0.first)*c_T2.first)/(aM*aP*sqrt(1 - sqr(alpha0.first)));
double Delta = asin(sDelta);
if(cDelta<0.) Delta = M_PI-Delta;
double ds_P = (-9*c_T2.first*((-1 + alpha0.first)*(1 + alpha0.first)* (3 + alpha0.first)*c_T3.first*c_T4.first*c_T2.second + c_T2.first*c_T4.first*(c_T3.first*(alpha0.second.first + 3*alpha0.first*alpha0.second.first) -(-1 + alpha0.first)*(1 + alpha0.first)*(3 + alpha0.first)*c_T3.second)
- (-1 + alpha0.first)*(1 + alpha0.first)* (3 + alpha0.first)*c_T2.first*c_T3.first*c_T4.second)*disc)/
(pow(1 - pow(alpha0.first,2),1.5)*pow(c_T4.first,3)*pow(-((disc + 2*s1*s5*s6)/ (s2*s6)),1.5)*(-9*s2*s4 + 4*s1*s5*s6));
double ds_M = (-9*c_T2.first*((-1 + alpha0.first)*(1 + alpha0.first)* (3 + alpha0.first)*c_T3.first*c_T4.first*c_T2.second + c_T2.first*c_T4.first*(c_T3.first*(alpha0.second.second + 3*alpha0.first*alpha0.second.second) -(-1 + alpha0.first)*(1 + alpha0.first)*(3 + alpha0.first)*c_T3.second)
- (-1 + alpha0.first)*(1 + alpha0.first)* (3 + alpha0.first)*c_T2.first*c_T3.first*c_T4.second)*disc)/
(pow(1 - pow(alpha0.first,2),1.5)*pow(c_T4.first,3)*pow(-((disc + 2*s1*s5*s6)/ (s2*s6)),1.5)*(-9*s2*s4 + 4*s1*s5*s6));
ds_P /= sqrt(1.-sqr(sDelta));
ds_M /= sqrt(1.-sqr(sDelta));
Scatter2DPtr _h_sin;
book(_h_sin,3,1,ih);
_h_sin->addPoint(0.5, Delta/M_PI*180., make_pair(0.5,0.5), make_pair( -ds_P/M_PI*180., -ds_M/M_PI*180. ) );
}
}
///@}
/// @name Histograms
///@{
Histo1DPtr _h_T1,_h_T2,_h_T3,_h_T4,_h_T5;
Histo1DPtr _h_cThetaL;
Histo1DPtr _h_mu;
CounterPtr _wsum;
///@}
};
RIVET_DECLARE_PLUGIN(BESIII_2020_I1791570);
}
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