Rivet analyses referenceBESIII_2023_I2655292Analysis of $J/\psi\to\Sigma^+\bar\Sigma^-$Experiment: BESIII (BEPC) Inspire ID: 2655292 Status: VALIDATED Authors:
Beam energies: (1.6, 1.6) GeV Run details:
Analysis of the angular distribution of the baryons, and decay products, produced in $e^+e^-\to J/\psi \to \Sigma^+\bar\Sigma^-$. The decay modes $\Sigma^+\to p\pi^0$ and $\bar\Sigma^-\to \bar{n}\pi^-$ or their charge conjugates are used to extract the decay asymmetry for $\Sigma^+\to n\pi^+$. Gives information about the decay and is useful for testing correlations in hadron decays. Source code: BESIII_2023_I2655292.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 J/Psi -> Sigma+ Sigmabar-
11 class BESIII_2023_I2655292 : public Analysis {
12 public:
13
14 /// Constructor
15 RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2023_I2655292);
16
17 /// @name Analysis methods
18 /// @{
19
20 /// Book histograms and initialise projections before the run
21 void init() {
22
23 // Initialise and register projections
24 declare(Beam(), "Beams");
25 declare(UnstableParticles(), "UFS");
26 declare(FinalState(), "FS");
27 for(unsigned int ix=0;ix<2;++ix) {
28 book(_h_T1[ix], "/TMP/T1_"+toString(ix),20,-1.,1.);
29 book(_h_T2[ix], "/TMP/T2_"+toString(ix),20,-1.,1.);
30 book(_h_T3[ix], "/TMP/T3_"+toString(ix),20,-1.,1.);
31 book(_h_T4[ix], "/TMP/T4_"+toString(ix),20,-1.,1.);
32 book(_h_T5[ix], "/TMP/T5_"+toString(ix),20,-1.,1.);
33 book(_wsum[ix],"/TMP/wsum_"+toString(ix));
34 }
35 book(_h_cThetaL,"/TMP/cThetaL",20,-1.,1.);
36 }
37
38 void findChildren(const Particle & p,map<long,int> & nRes, int &ncount) {
39 for (const Particle &child : p.children()) {
40 if (child.children().empty()) {
41 nRes[child.pid()]-=1;
42 --ncount;
43 }
44 else {
45 findChildren(child,nRes,ncount);
46 }
47 }
48 }
49
50 /// Perform the per-event analysis
51 void analyze(const Event& event) {
52 // get the axis, direction of incoming electron
53 const ParticlePair& beams = apply<Beam>(event, "Beams").beams();
54 Vector3 axis;
55 if (beams.first.pid()>0) axis = beams.first.mom().p3().unit();
56 else axis = beams.second.mom().p3().unit();
57 // types of final state particles
58 const FinalState& fs = apply<FinalState>(event, "FS");
59 map<long,int> nCount;
60 int ntotal(0);
61 for (const Particle& p : fs.particles()) {
62 nCount[p.pid()] += 1;
63 ++ntotal;
64 }
65 // loop over Sigma+ baryons
66 const UnstableParticles & ufs = apply<UnstableParticles>(event, "UFS");
67 Particle Sigma,SigBar;
68 bool matched(false);
69 for (const Particle& p : ufs.particles(Cuts::abspid==3222)) {
70 if (p.children().empty()) continue;
71 map<long,int> nRes=nCount;
72 int ncount = ntotal;
73 findChildren(p,nRes,ncount);
74 matched=false;
75 // check for antiparticle
76 for (const Particle& p2 : ufs.particles(Cuts::pid==-p.pid())) {
77 if (p2.children().empty()) continue;
78 map<long,int> nRes2=nRes;
79 int ncount2 = ncount;
80 findChildren(p2,nRes2,ncount2);
81 if(ncount2==0) {
82 matched = true;
83 for(const auto& val : nRes2) {
84 if (val.second!=0) {
85 matched = false;
86 break;
87 }
88 }
89 // fond baryon and antibaryon
90 if (matched) {
91 if (p.pid()>0) {
92 Sigma = p;
93 SigBar = p2;
94 }
95 else {
96 Sigma = p2;
97 SigBar = p;
98 }
99 break;
100 }
101 }
102 }
103 if (matched) break;
104 }
105 if (!matched) vetoEvent;
106 // scattering angle
107 const double cosL = axis.dot(Sigma.mom().p3().unit());
108 const double sinL = sqrt(1.-sqr(cosL));
109 _h_cThetaL->fill(cosL);
110 // decay of the Sigma+
111 Particle baryon;
112 int imode[2]={-1,-1};
113 if (Sigma.children()[0].pid()==2212 && Sigma.children()[1].pid()==111) {
114 baryon = Sigma.children()[0];
115 imode[0] = 0;
116 }
117 else if (Sigma.children()[1].pid()==2212 && Sigma.children()[0].pid()==111) {
118 baryon = Sigma.children()[1];
119 imode[0] = 0;
120 }
121 else if (Sigma.children()[0].pid()==2112 && Sigma.children()[1].pid()==211) {
122 baryon = Sigma.children()[0];
123 imode[0] = 1;
124 }
125 else if (Sigma.children()[1].pid()==2112 && Sigma.children()[0].pid()==211) {
126 baryon = Sigma.children()[1];
127 imode[0] = 1;
128 }
129 if (imode[0]<0) vetoEvent;
130 // decay of the Sigmabar-
131 Particle abaryon;
132 if (SigBar.children()[0].pid()==-2212 && SigBar.children()[1].pid()==111) {
133 abaryon = SigBar.children()[0];
134 imode[1] = 0;
135 }
136 else if (SigBar.children()[1].pid()==-2212 && SigBar.children()[0].pid()==111) {
137 abaryon = SigBar.children()[1];
138 imode[1] = 0;
139 }
140 else if (SigBar.children()[0].pid()==-2112 && SigBar.children()[1].pid()==-211) {
141 abaryon = SigBar.children()[0];
142 imode[1] = 1;
143 }
144 else if (SigBar.children()[1].pid()==-2112 && SigBar.children()[0].pid()==-211) {
145 abaryon = SigBar.children()[1];
146 imode[1] = 1;
147 }
148 if (imode[1]<0) vetoEvent;
149 if (imode[0]==imode[1]) vetoEvent;
150 // boost to the Sigma rest frame
151 LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Sigma.mom().betaVec());
152 Vector3 e1z = Sigma.mom().p3().unit();
153 Vector3 e1y = e1z.cross(axis).unit();
154 Vector3 e1x = e1y.cross(e1z).unit();
155 Vector3 axis1 = boost1.transform(baryon.mom()).p3().unit();
156 double n1x(e1x.dot(axis1)),n1y(e1y.dot(axis1)),n1z(e1z.dot(axis1));
157 // boost to the Sigma bar
158 LorentzTransform boost2 = LorentzTransform::mkFrameTransformFromBeta(SigBar.mom().betaVec());
159 Vector3 axis2 = boost2.transform(abaryon.mom()).p3().unit();
160 double n2x(e1x.dot(axis2)),n2y(e1y.dot(axis2)),n2z(e1z.dot(axis2));
161 double T1 = sqr(sinL)*n1x*n2x+sqr(cosL)*n1z*n2z;
162 double T2 = -sinL*cosL*(n1x*n2z+n1z*n2x);
163 double T3 = -sinL*cosL*n1y;
164 double T4 = -sinL*cosL*n2y;
165 double T5 = n1z*n2z-sqr(sinL)*n1y*n2y;
166 _h_T1[imode[0]]->fill(cosL,T1);
167 _h_T2[imode[0]]->fill(cosL,T2);
168 _h_T3[imode[0]]->fill(cosL,T3);
169 _h_T4[imode[0]]->fill(cosL,T4);
170 _h_T5[imode[0]]->fill(cosL,T5);
171 _wsum[imode[0]]->fill();
172 }
173
174 pair<double,pair<double,double> > calcAlpha0(Histo1DPtr hist) const {
175 if (hist->numEntries()==0.) return make_pair(0.,make_pair(0.,0.));
176 double d = 3./(pow(hist->xMax(),3)-pow(hist->xMin(),3));
177 double c = 3.*(hist->xMax()-hist->xMin())/(pow(hist->xMax(),3)-pow(hist->xMin(),3));
178 double sum1(0.),sum2(0.),sum3(0.),sum4(0.),sum5(0.);
179 for (const auto& bin : hist->bins()) {
180 double Oi = bin.sumW();
181 if (Oi==0.) continue;
182 double a = d*(bin.xMax() - bin.xMin());
183 double b = d/3.*(pow(bin.xMax(),3) - pow(bin.xMin(),3));
184 double Ei = bin.errW();
185 sum1 += a*Oi/sqr(Ei);
186 sum2 += b*Oi/sqr(Ei);
187 sum3 += sqr(a)/sqr(Ei);
188 sum4 += sqr(b)/sqr(Ei);
189 sum5 += a*b/sqr(Ei);
190 }
191 // calculate alpha
192 double alpha = (-c*sum1 + sqr(c)*sum2 + sum3 - c*sum5)/(sum1 - c*sum2 + c*sum4 - sum5);
193 // and error
194 double cc = -pow((sum3 + sqr(c)*sum4 - 2*c*sum5),3);
195 double bb = -2*sqr(sum3 + sqr(c)*sum4 - 2*c*sum5)*(sum1 - c*sum2 + c*sum4 - sum5);
196 double aa = sqr(sum1 - c*sum2 + c*sum4 - sum5)*(-sum3 - sqr(c)*sum4 + sqr(sum1 - c*sum2 + c*sum4 - sum5) + 2*c*sum5);
197 double dis = sqr(bb)-4.*aa*cc;
198 if (dis>0.) {
199 dis = sqrt(dis);
200 return make_pair(alpha,make_pair(0.5*(-bb+dis)/aa,-0.5*(-bb-dis)/aa));
201 }
202 else {
203 return make_pair(alpha,make_pair(0.,0.));
204 }
205 }
206
207 pair<double,double> calcCoeff(unsigned int imode, Histo1DPtr hist) const {
208 if (hist->numEntries()==0.) return make_pair(0.,0.);
209 double sum1(0.), sum2(0.);
210 for (const auto& bin : hist->bins()) {
211 double Oi = bin.sumW();
212 if (Oi==0.) continue;
213 double ai(0.),bi(0.);
214 if (imode==0) {
215 bi = (pow(1.-sqr(bin.xMin()),1.5) - pow(1.-sqr(bin.xMax()),1.5))/3.;
216 }
217 else if (imode>=2 && imode<=4) {
218 bi = ( pow(bin.xMin(),3) * (-5. + 3.*sqr(bin.xMin()))
219 + pow(bin.xMax(),3) * ( 5. - 3.*sqr(bin.xMax())))/15.;
220 }
221 else {
222 assert(false);
223 }
224 double Ei = bin.errW();
225 sum1 += sqr(bi/Ei);
226 sum2 += bi/sqr(Ei)*(Oi-ai);
227 }
228 return make_pair(sum2/sum1,sqrt(1./sum1));
229 }
230
231 /// Normalise histograms etc., after the run
232 void finalize() {
233 normalize(_h_cThetaL);
234 for (unsigned int ix=0;ix<2;++ix) {
235 scale(_h_T1[ix], 1./ *_wsum[ix]);
236 scale(_h_T2[ix], 1./ *_wsum[ix]);
237 scale(_h_T3[ix], 1./ *_wsum[ix]);
238 scale(_h_T4[ix], 1./ *_wsum[ix]);
239 scale(_h_T5[ix], 1./ *_wsum[ix]);
240 }
241 // first calculate alpha for J/psi -> Sigma+ Sigmabar-
242 pair<double,pair<double,double> > alphaPsi = calcAlpha0(_h_cThetaL);
243 Estimate0DPtr h_alphaPsi;
244 book(h_alphaPsi,1,1,1);
245 h_alphaPsi->set(alphaPsi.first, alphaPsi.second);
246 double s2 = -1. + sqr(alphaPsi.first);
247 double s3 = 3 + alphaPsi.first;
248 double s1 = sqr(s3);
249 pair<double,pair<double,double> > alpha0 = make_pair(0.,make_pair(0.,0.));
250 pair<double,pair<double,double> > alphabar0 = make_pair(0.,make_pair(0.,0.));
251 pair<double,pair<double,double> > alphaplus = make_pair(0.,make_pair(0.,0.));
252 pair<double,pair<double,double> > alphaminus = make_pair(0.,make_pair(0.,0.));
253 pair<double,pair<double,double> > delta = make_pair(0.,make_pair(0.,0.));
254
255 // now for the Sigma decays
256 for (unsigned int ix=0; ix<2; ++ix) {
257 pair<double,double> c_T2 = calcCoeff(2,_h_T2[ix]);
258 pair<double,double> c_T3 = calcCoeff(3,_h_T3[ix]);
259 pair<double,double> c_T4 = calcCoeff(4,_h_T4[ix]);
260 double s4 = sqr(c_T2.first);
261 double s5 = sqr(c_T3.first);
262 double s6 = sqr(c_T4.first);
263 double disc = s1*s5*s6*(-9.*s2*s4 + 4.*s1*s5*s6);
264 if (disc<0.) continue;
265 disc = sqrt(disc);
266 double aM = -sqrt(-1./s2/s6*(2.*s1*s5*s6+disc));
267 if (ix==1) aM *=-1;
268 double aP = c_T4.first/c_T3.first*aM;
269 double aM_P = (2*(alphaPsi.first*c_T4.first*alphaPsi.second.first + c_T4.second*s2)*(disc + 2*s1*s5*s6)
270 - c_T4.first*s2*(4*s3*c_T3.first*c_T4.first*(c_T3.first*c_T4.first*alphaPsi.second.first
271 +s3*c_T4.first*c_T3.second +s3*c_T3.first*c_T4.second) +
272 (disc*(- 9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
273 + 9*((1 - alphaPsi.first*(3 + 2*alphaPsi.first))* c_T3.first*c_T4.first*alphaPsi.second.first
274 - s2*s3*c_T4.first*c_T3.second - s2*s3*c_T3.first*c_T4.second)* s4
275 + 8*(c_T3.first*c_T4.first*alphaPsi.second.first + s3*c_T4.first*c_T3.second
276 + s3*c_T3.first*c_T4.second)* s1*s5*s6))
277 /(4*pow(3 + alphaPsi.first,3)*pow(c_T3.first,3)*pow(c_T4.first,3)
278 - 9*s2*s3*c_T3.first*c_T4.first*s4)))
279 / (2.*pow(c_T4.first,3)*pow(s2,2)*sqrt(-((disc + 2*s1*s5*s6)/(s2*s6))));
280 double aM_M = (2*(alphaPsi.first*c_T4.first*alphaPsi.second.second + c_T4.second*s2)*(disc + 2*s1*s5*s6)
281 - c_T4.first*s2*(4*s3*c_T3.first*c_T4.first*(c_T3.first*c_T4.first*alphaPsi.second.second
282 + s3*c_T4.first*c_T3.second +s3*c_T3.first*c_T4.second) +
283 (disc*(- 9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
284 + 9*((1 - alphaPsi.first*(3 + 2*alphaPsi.first))* c_T3.first*c_T4.first*alphaPsi.second.second
285 - s2*s3*c_T4.first*c_T3.second - s2*s3*c_T3.first*c_T4.second)* s4
286 + 8*(c_T3.first*c_T4.first*alphaPsi.second.second + s3*c_T4.first*c_T3.second
287 + s3*c_T3.first*c_T4.second)* s1*s5*s6))
288 / (4*pow(3 + alphaPsi.first,3)*pow(c_T3.first,3)*pow(c_T4.first,3)
289 - 9*s2*s3*c_T3.first*c_T4.first*s4)))
290 /(2.*pow(c_T4.first,3)*pow(s2,2)*sqrt(-((disc + 2*s1*s5*s6)/(s2*s6))));
291 double aP_M = (c_T4.first*sqrt(-((disc + 2*s1*s5*s6)
292 / (s2*s6)))* (-2*c_T3.second - (2*alphaPsi.first*c_T3.first*alphaPsi.second.first)/s2
293 + (c_T3.first*(4*s3*c_T3.first*c_T4.first*(c_T3.first*c_T4.first*alphaPsi.second.first
294 + s3*c_T4.first*c_T3.second + s3*c_T3.first*c_T4.second)
295 + (disc*(-9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
296 + 9*((1 - alphaPsi.first*(3 + 2*alphaPsi.first))* c_T3.first*c_T4.first*alphaPsi.second.first
297 - s2*s3*c_T4.first*c_T3.second - s2*s3*c_T3.first*c_T4.second)* s4
298 + 8*(c_T3.first*c_T4.first*alphaPsi.second.first + s3*c_T4.first*c_T3.second
299 + s3*c_T3.first*c_T4.second)* s1*s5*s6))
300 / (4* pow(3 + alphaPsi.first,3)* pow(c_T3.first,3)* pow(c_T4.first,3)
301 - 9*s2*s3*c_T3.first*c_T4.first*s4)))
302 / (disc + 2*s1*s5*s6)))/(2.*pow(c_T3.first,2));
303 double aP_P = (c_T4.first*sqrt(-((disc + 2*s1*s5*s6)/(s2*s6)))
304 * (-2*c_T3.second - (2*alphaPsi.first*c_T3.first*alphaPsi.second.second)/s2
305 + (c_T3.first*(4*s3*c_T3.first*c_T4.first*(c_T3.first*c_T4.first*alphaPsi.second.second
306 + s3*c_T4.first*c_T3.second + s3*c_T3.first*c_T4.second)
307 + (disc*(-9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
308 + 9*((1 - alphaPsi.first*(3 + 2*alphaPsi.first))* c_T3.first*c_T4.first*alphaPsi.second.second
309 - s2*s3*c_T4.first*c_T3.second - s2*s3*c_T3.first*c_T4.second)* s4
310 + 8*(c_T3.first*c_T4.first*alphaPsi.second.second + s3*c_T4.first*c_T3.second
311 + s3*c_T3.first*c_T4.second)* s1*s5*s6))
312 / (4* pow(3 + alphaPsi.first,3)* pow(c_T3.first,3) * pow(c_T4.first,3)
313 - 9*s2*s3*c_T3.first*c_T4.first*s4)))
314 / (disc + 2*s1*s5*s6)))/(2.*pow(c_T3.first,2));
315 if (ix==0) {
316 alphaminus = make_pair(aP, make_pair(-aP_M , -aP_P));
317 alpha0 = make_pair(aM, make_pair(-aM_M , -aM_P));
318 }
319 else {
320 alphabar0 = make_pair(aP, make_pair(-aP_M , -aP_P));
321 alphaplus = make_pair(aM, make_pair(-aM_M , -aM_P));
322 }
323 // now for Delta
324 double sDelta = (-2.*(3. + alphaPsi.first)*c_T3.first)/(aM*sqrt(1 - sqr(alphaPsi.first)));
325 double cDelta = (-3*(3 + alphaPsi.first)*c_T2.first)/(aM*aP*sqrt(1 - sqr(alphaPsi.first)));
326
327 double Delta = asin(sDelta);
328 if (cDelta<0.) Delta = M_PI-Delta;
329 double ds_P = (-9*c_T2.first*((-1 + alphaPsi.first)*(1 + alphaPsi.first)
330 * (3 + alphaPsi.first)*c_T3.first*c_T4.first*c_T2.second
331 + c_T2.first*c_T4.first*(c_T3.first*(alphaPsi.second.first
332 + 3*alphaPsi.first*alphaPsi.second.first) -(-1 + alphaPsi.first)
333 * (1 + alphaPsi.first)*(3 + alphaPsi.first)*c_T3.second)
334 - (-1 + alphaPsi.first)*(1 + alphaPsi.first)
335 * (3 + alphaPsi.first)*c_T2.first*c_T3.first*c_T4.second)*disc)
336 / (pow(1 - pow(alphaPsi.first,2),1.5)*pow(c_T4.first,3)*pow(-((disc + 2*s1*s5*s6)
337 / (s2*s6)),1.5)*(-9*s2*s4 + 4*s1*s5*s6));
338 double ds_M = (-9*c_T2.first*((-1 + alphaPsi.first)*(1 + alphaPsi.first)
339 * (3 + alphaPsi.first)*c_T3.first*c_T4.first*c_T2.second
340 + c_T2.first*c_T4.first*(c_T3.first*(alphaPsi.second.second
341 + 3*alphaPsi.first*alphaPsi.second.second) -(-1 + alphaPsi.first)
342 * (1 + alphaPsi.first)*(3 + alphaPsi.first)*c_T3.second)
343 - (-1 + alphaPsi.first)*(1 + alphaPsi.first)
344 * (3 + alphaPsi.first)*c_T2.first*c_T3.first*c_T4.second)*disc)
345 / (pow(1 - pow(alphaPsi.first,2),1.5)*pow(c_T4.first,3)*pow(-((disc + 2*s1*s5*s6)
346 / (s2*s6)),1.5)*(-9*s2*s4 + 4*s1*s5*s6));
347 ds_P /= sqrt(1.-sqr(sDelta));
348 ds_M /= sqrt(1.-sqr(sDelta));
349 delta.first += Delta;
350 delta.second.first += sqr(ds_P);
351 delta.second.second += sqr(ds_M);
352 }
353 // delta phi
354 Estimate0DPtr h_delta;
355 book(h_delta,1,1,2);
356 delta.first *= 0.5;
357 delta.second.first = 0.5*sqrt(delta.second.first );
358 delta.second.second = 0.5*sqrt(delta.second.second);
359 h_delta->set(delta.first, delta.second);
360 // alphas
361 Estimate0DPtr h_alphaP;
362 book(h_alphaP,1,1,3);
363 h_alphaP->set(alphaplus.first,alphaplus.second);
364 Estimate0DPtr h_alphaM;
365 book(h_alphaM,1,1,4);
366 h_alphaM->set(alphaminus.first,alphaminus.second);
367 Estimate0DPtr h_alpha0,h_alphabar0;
368 book(h_alpha0,"TMP/h_alpha0");
369 h_alpha0->set(alpha0.first,alpha0.second);
370 book(h_alphabar0,"TMP/h_alphabar0");
371 h_alphabar0->set(alphabar0.first,alphabar0.second);
372 // ratios
373 Estimate0DPtr rplus;
374 book(rplus,1,1,5);
375 divide(h_alphaP,h_alpha0,rplus);
376 rplus->setPath("/"+name()+"/"+mkAxisCode(1,1,5));
377 Estimate0DPtr rminus;
378 book(rminus,1,1,6);
379 divide(h_alphaM,h_alphabar0,rminus);
380 rminus->setPath("/"+name()+"/"+mkAxisCode(1,1,6));
381 //average
382 Estimate0DPtr aver;
383 book(aver,1,1,8);
384 aver->setVal(0.5*(alphaplus.first-alphaminus.first));
385 aver->setErr(make_pair(0.5*sqrt(sqr(alphaplus.second.first )+sqr(alphaminus.second.second)),
386 0.5*sqrt(sqr(alphaplus.second.second)+sqr(alphaminus.second.first ))));
387 }
388
389 /// @}
390
391 /// @name Histograms
392 /// @{
393 Histo1DPtr _h_T1[2],_h_T2[2],_h_T3[2],_h_T4[2],_h_T5[2];
394 Histo1DPtr _h_cThetaL;
395 CounterPtr _wsum[2];
396 /// @}
397
398 };
399
400
401 RIVET_DECLARE_PLUGIN(BESIII_2023_I2655292);
402
403}
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