Rivet analyses referenceBESIII_2023_I2634735Analysis of $\psi(2S)$ decays to $\Xi^0\bar{\Xi}^0$Experiment: BESIII (BEPC) Inspire ID: 2634735 Status: VALIDATED NOHEPDATA Authors:
Beam energies: (1.8, 1.8) GeV Run details:
Analysis of the angular distribution of the baryons, and decay products, produced in $e^+e^-\to \psi(2S) \to \Xi^0\bar{\Xi}^0$. Gives information about the decay and is useful for testing correlations in hadron decays. The phase and $\alpha$ parameters were taken from the tables in the paper. Source code: BESIII_2023_I2634735.cc 1// -*- C++ -*-
2#include "Rivet/Analysis.hh"
3#include "Rivet/Projections/Beam.hh"
4#include "Rivet/Projections/FinalState.hh"
5#include "Rivet/Projections/UnstableParticles.hh"
6
7namespace Rivet {
8
9
10 /// @brief psi(2S) -> Xi0 Xibar0
11 class BESIII_2023_I2634735 : public Analysis {
12 public:
13
14 /// Constructor
15 RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2023_I2634735);
16
17
18 /// @name Analysis methods
19 /// @{
20
21 /// Book histograms and initialise projections before the run
22 void init() {
23 // Initialise and register projections
24 declare(Beam(), "Beams");
25 declare(UnstableParticles(), "UFS");
26 declare(FinalState(), "FS");
27 // Book histograms
28 book(_h_T1, "TMP/T1",20,-1.,1.);
29 book(_h_T2, "TMP/T2",20,-1.,1.);
30 book(_h_T3, "TMP/T3",20,-1.,1.);
31 book(_h_T4, "TMP/T4",20,-1.,1.);
32 book(_h_T5, "TMP/T5",20,-1.,1.);
33 book(_h_cTheta,"TMP/cTheta",20,-1.,1.);
34 for (unsigned int ix=0; ix<2; ++ix) {
35 book(_h_cProton[ix],"TMP/cProton_"+toString(ix+1), 20, -1., 1.);
36 }
37 book(_wsum,"TMP/wsum");
38 }
39
40 void findChildren(const Particle& p,map<long,int>& nRes, int& ncount) {
41 for (const Particle& child : p.children()) {
42 if (child.children().empty()) {
43 nRes[child.pid()]-=1;
44 --ncount;
45 }
46 else {
47 findChildren(child,nRes,ncount);
48 }
49 }
50 }
51
52 /// Perform the per-event analysis
53 void analyze(const Event& event) {
54 // get the axis, direction of incoming electron
55 const ParticlePair& beams = apply<Beam>(event, "Beams").beams();
56 Vector3 axis;
57 if (beams.first.pid()>0) {
58 axis = beams.first .mom().p3().unit();
59 }
60 else {
61 axis = beams.second.mom().p3().unit();
62 }
63 // types of final state particles
64 const FinalState& fs = apply<FinalState>(event, "FS");
65 map<long,int> nCount;
66 int ntotal(0);
67 for (const Particle& p : fs.particles()) {
68 nCount[p.pid()] += 1;
69 ++ntotal;
70 }
71 // loop over Xi baryons
72 const UnstableParticles& ufs = apply<UnstableParticles>(event, "UFS");
73 Particle Xi,XiBar;
74 bool matched(false);
75 for (const Particle& p : ufs.particles(Cuts::abspid==3322)) {
76 if (p.children().empty()) continue;
77 map<long,int> nRes=nCount;
78 int ncount = ntotal;
79 findChildren(p,nRes,ncount);
80 matched=false;
81 // check for antiparticle
82 for (const Particle& p2 : ufs.particles(Cuts::pid==-p.pid())) {
83 if (p2.children().empty()) continue;
84 map<long,int> nRes2=nRes;
85 int ncount2 = ncount;
86 findChildren(p2,nRes2,ncount2);
87 if (ncount2==0) {
88 matched = true;
89 for (const auto& val : nRes2) {
90 if (val.second!=0) {
91 matched = false;
92 break;
93 }
94 }
95 // found baryon and antibaryon
96 if (matched) {
97 if (p.pid()>0) {
98 Xi = p;
99 XiBar = p2;
100 }
101 else {
102 Xi = p2;
103 XiBar = p;
104 }
105 break;
106 }
107 }
108 }
109 if (matched) break;
110 }
111 if (!matched) vetoEvent;
112 // find the lambda and antilambda
113 Particle Lambda,LamBar;
114 if (Xi.children()[0].pid() ==3122 && Xi.children()[1].pid()==111) {
115 Lambda = Xi.children()[0];
116 }
117 else if (Xi.children()[1].pid() ==3122 && Xi.children()[0].pid()==111) {
118 Lambda = Xi.children()[1];
119 }
120 else {
121 vetoEvent;
122 }
123 if (XiBar.children()[0].pid() ==-3122 && XiBar.children()[1].pid()==111) {
124 LamBar = XiBar.children()[0];
125 }
126 else if (XiBar.children()[1].pid() ==-3122 && XiBar.children()[0].pid()==111) {
127 LamBar = XiBar.children()[1];
128 }
129 else {
130 vetoEvent;
131 }
132 // boost to the Xi rest frame
133 LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Xi.mom().betaVec());
134 Vector3 e1z = Xi.mom().p3().unit();
135 Vector3 e1y = e1z.cross(axis).unit();
136 Vector3 e1x = e1y.cross(e1z).unit();
137 FourMomentum pLambda = boost1.transform(Lambda.mom());
138 Vector3 axis1 = pLambda.p3().unit();
139 double n1x(e1x.dot(axis1)),n1y(e1y.dot(axis1)),n1z(e1z.dot(axis1));
140 Particle proton;
141 if (Lambda.children().size()!=2) vetoEvent;
142 if (Lambda.children()[0].pid()== 2212 && Lambda.children()[1].pid()==-211) {
143 proton = Lambda.children()[0];
144 }
145 else if (Lambda.children()[1].pid()== 2212 && Lambda.children()[0].pid()==-211) {
146 proton = Lambda.children()[1];
147 }
148 else {
149 vetoEvent;
150 }
151 LorentzTransform boost3 = LorentzTransform::mkFrameTransformFromBeta(pLambda.betaVec());
152 FourMomentum pProton = boost3.transform(boost1.transform(proton.mom()));
153 const double cProton = pProton.p3().unit().dot(axis1);
154 _h_cProton[0]->fill(cProton);
155 // boost to the Xi bar rest frame
156 LorentzTransform boost2 = LorentzTransform::mkFrameTransformFromBeta(XiBar.mom().betaVec());
157 FourMomentum pLamBar = boost2.transform(LamBar.mom());
158 Vector3 axis2 = pLamBar.p3().unit();
159 double n2x(e1x.dot(axis2)),n2y(e1y.dot(axis2)),n2z(e1z.dot(axis2));
160 double cosX = axis.dot(Xi.mom().p3().unit());
161 double sinX = sqrt(1.-sqr(cosX));
162 Particle pbar;
163 if (LamBar.children().size()!=2) vetoEvent;
164 if (LamBar.children()[0].pid()==-2212 && LamBar.children()[1].pid()== 211) {
165 pbar = LamBar.children()[0];
166 }
167 else if (LamBar.children()[1].pid()==-2212 && LamBar.children()[0].pid()== 211) {
168 pbar = LamBar.children()[1];
169 }
170 else {
171 vetoEvent;
172 }
173 LorentzTransform boost4 = LorentzTransform::mkFrameTransformFromBeta(pLamBar.betaVec());
174 FourMomentum pPbar = boost4.transform(boost2.transform(pbar.mom()));
175 double cPbar = pPbar.p3().unit().dot(axis2);
176 _h_cProton[1]->fill(cPbar);
177 // moments
178 double T1 = sqr(sinX)*n1x*n2x+sqr(cosX)*n1z*n2z;
179 double T2 = -sinX*cosX*(n1x*n2z+n1z*n2x);
180 double T3 = -sinX*cosX*n1y;
181 double T4 = -sinX*cosX*n2y;
182 double T5 = n1z*n2z-sqr(sinX)*n1y*n2y;
183 _h_T1->fill(cosX,T1);
184 _h_T2->fill(cosX,T2);
185 _h_T3->fill(cosX,T3);
186 _h_T4->fill(cosX,T4);
187 _h_T5->fill(cosX,T5);
188 _h_cTheta->fill(cosX);
189 _wsum->fill();
190 }
191
192 pair<double,pair<double,double> > calcAlpha0(Histo1DPtr hist) {
193 if (hist->numEntries()==0.) return make_pair(0.,make_pair(0.,0.));
194 double d = 3./(pow(hist->xMax(),3)-pow(hist->xMin(),3));
195 double c = 3.*(hist->xMax()-hist->xMin())/(pow(hist->xMax(),3)-pow(hist->xMin(),3));
196 double sum1(0.),sum2(0.),sum3(0.),sum4(0.),sum5(0.);
197 for (const auto& bin : hist->bins() ) {
198 double Oi = bin.sumW();
199 if (Oi==0.) continue;
200 double a = d*(bin.xMax() - bin.xMin());
201 double b = d/3.*(pow(bin.xMax(),3) - pow(bin.xMin(),3));
202 double Ei = bin.errW();
203 sum1 += a*Oi/sqr(Ei);
204 sum2 += b*Oi/sqr(Ei);
205 sum3 += sqr(a)/sqr(Ei);
206 sum4 += sqr(b)/sqr(Ei);
207 sum5 += a*b/sqr(Ei);
208 }
209 // calculate alpha
210 double alpha = (-c*sum1 + sqr(c)*sum2 + sum3 - c*sum5)/(sum1 - c*sum2 + c*sum4 - sum5);
211 // and error
212 double cc = -pow((sum3 + sqr(c)*sum4 - 2*c*sum5),3);
213 double bb = -2*sqr(sum3 + sqr(c)*sum4 - 2*c*sum5)*(sum1 - c*sum2 + c*sum4 - sum5);
214 double aa = sqr(sum1 - c*sum2 + c*sum4 - sum5)*(-sum3 - sqr(c)*sum4 + sqr(sum1 - c*sum2 + c*sum4 - sum5) + 2*c*sum5);
215 double dis = sqr(bb)-4.*aa*cc;
216 if (dis>0.) {
217 dis = sqrt(dis);
218 return make_pair(alpha,make_pair(0.5*(-bb+dis)/aa,-0.5*(-bb-dis)/aa));
219 }
220 else {
221 return make_pair(alpha,make_pair(0.,0.));
222 }
223 }
224
225 pair<double,double> calcAlpha(Histo1DPtr hist) {
226 if (hist->numEntries()==0.) return make_pair(0.,0.);
227 double sum1(0.), sum2(0.);
228 for (const auto& bin : hist->bins() ) {
229 double Oi = bin.sumW();
230 if (Oi==0.) continue;
231 double ai = 0.5*(bin.xMax()-bin.xMin());
232 double bi = 0.5*ai*(bin.xMax()+bin.xMin());
233 double Ei = bin.errW();
234 sum1 += sqr(bi/Ei);
235 sum2 += bi/sqr(Ei)*(Oi-ai);
236 }
237 return make_pair(sum2/sum1,sqrt(1./sum1));
238 }
239
240 pair<double,double> calcCoeff(unsigned int imode, Histo1DPtr hist) {
241 if (hist->numEntries()==0.) return make_pair(0.,0.);
242 double sum1(0.),sum2(0.);
243 for (const auto& bin : hist->bins()) {
244 double Oi = bin.sumW();
245 if (Oi==0.) continue;
246 double ai(0.), bi(0.);
247 if (imode==0) {
248 bi = (pow(1.-sqr(bin.xMin()),1.5) - pow(1.-sqr(bin.xMax()),1.5))/3.0;
249 }
250 else if (imode>=2 && imode<=4) {
251 bi = (pow(bin.xMin(),3)*(-5. + 3.*sqr(bin.xMin())) + pow(bin.xMax(),3)*(5. - 3.*sqr(bin.xMax())))/15.;
252 }
253 else {
254 assert(false);
255 }
256 const double Ei = bin.errW();
257 sum1 += sqr(bi/Ei);
258 sum2 += bi/sqr(Ei)*(Oi-ai);
259 }
260 return make_pair(sum2/sum1,sqrt(1./sum1));
261 }
262
263 /// Normalise histograms etc., after the run
264 void finalize() {
265 const double aLambda = 0.754;
266 normalize(_h_cTheta);
267 normalize(_h_cProton);
268 scale(_h_T1, 1.0/ *_wsum);
269 scale(_h_T2, 1.0/ *_wsum);
270 scale(_h_T3, 1.0/ *_wsum);
271 scale(_h_T4, 1.0/ *_wsum);
272 scale(_h_T5, 1.0/ *_wsum);
273 // calculate alpha0
274 pair<double,pair<double,double> > alpha0 = calcAlpha0(_h_cTheta);
275 Estimate0DPtr _h_alpha0;
276 book(_h_alpha0,1,1,1);
277 _h_alpha0->set(alpha0.first, alpha0.second);
278 double s2 = -1. + sqr(alpha0.first);
279 double s3 = 3 + alpha0.first;
280 double s1 = sqr(s3);
281 // alpha parameters
282 pair<double,double> alpha[2];
283 for(unsigned int ix=0;ix<2;++ix) {
284 Estimate0DPtr _h_alpha;
285 book(_h_alpha,1,1,3+2*ix);
286 alpha[ix] = calcAlpha(_h_cProton[ix]);
287 alpha[ix].first /= aLambda;
288 if(ix==1) alpha[ix].first *=-1;
289 alpha[ix].second /= aLambda;
290 _h_alpha->set(alpha[ix].first, alpha[ix].second);
291 }
292 // now for Delta
293 pair<double,double> c_T2 = calcCoeff(2,_h_T2);
294 pair<double,double> c_T3 = calcCoeff(3,_h_T3);
295 pair<double,double> c_T4 = calcCoeff(4,_h_T4);
296 double s4 = sqr(c_T2.first);
297 double s5 = sqr(c_T3.first);
298 double s6 = sqr(c_T4.first);
299 double disc = s1*s5*s6*(-9.*s2*s4 + 4.*s1*s5*s6);
300 if (disc<0.) return;
301 disc = sqrt(disc);
302 double sDelta = (-2.*(3. + alpha0.first)*c_T3.first)/(alpha[0].first*sqrt(1 - sqr(alpha0.first)));
303 double cDelta = (-3*(3 + alpha0.first)*c_T2.first)/(alpha[0].first*alpha[1].first*sqrt(1 - sqr(alpha0.first)));
304 double Delta = asin(sDelta);
305 if(cDelta<0.) Delta = M_PI-Delta;
306 double ds_P = (-9*c_T2.first*((-1 + alpha0.first)*(1 + alpha0.first) *
307 (3 + alpha0.first)*c_T3.first*c_T4.first*c_T2.second +
308 c_T2.first*c_T4.first*(c_T3.first*(alpha0.second.first +
309 3*alpha0.first*alpha0.second.first) -(-1 + alpha0.first) *
310 (1 + alpha0.first)*(3 + alpha0.first)*c_T3.second) -
311 (-1 + alpha0.first)*(1 + alpha0.first) *
312 (3 + alpha0.first)*c_T2.first*c_T3.first*c_T4.second)*disc) /
313 (pow(1 - pow(alpha0.first,2),1.5)*pow(c_T4.first,3) *
314 pow(-((disc + 2*s1*s5*s6) / (s2*s6)),1.5)*(-9*s2*s4 + 4*s1*s5*s6));
315 double ds_M = (-9*c_T2.first*((-1 + alpha0.first)*(1 + alpha0.first) *
316 (3 + alpha0.first)*c_T3.first*c_T4.first*c_T2.second +
317 c_T2.first*c_T4.first*(c_T3.first*(alpha0.second.second +
318 3*alpha0.first*alpha0.second.second) - (-1 + alpha0.first) *
319 (1 + alpha0.first)*(3 + alpha0.first)*c_T3.second) -
320 (-1 + alpha0.first)*(1 + alpha0.first) *
321 (3 + alpha0.first)*c_T2.first*c_T3.first * c_T4.second)*disc) /
322 (pow(1 - pow(alpha0.first,2),1.5)*pow(c_T4.first,3) *
323 pow(-((disc + 2*s1*s5*s6) /(s2*s6)),1.5)*(-9*s2*s4 + 4*s1*s5*s6));
324 ds_P /= sqrt(1.-sqr(sDelta));
325 ds_M /= sqrt(1.-sqr(sDelta));
326 Estimate0DPtr _h_sin;
327 book(_h_sin, 1, 1, 2);
328 _h_sin->set(Delta, make_pair( -ds_P, -ds_M));
329 }
330
331 /// @}
332
333
334 /// @name Histograms
335 /// @{
336 Histo1DPtr _h_T1,_h_T2,_h_T3,_h_T4,_h_T5;
337 Histo1DPtr _h_cTheta,_h_cProton[2];
338 CounterPtr _wsum;
339 /// @}
340
341
342 };
343
344
345 RIVET_DECLARE_PLUGIN(BESIII_2023_I2634735);
346
347}
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