1 //--------------------------------------------------------------------------
4 // This software is part of the EvtGen package developed jointly
5 // for the BaBar and CLEO collaborations. If you use all or part
6 // of it, please give an appropriate acknowledgement.
8 // Copyright Information: See EvtGen/COPYRIGHT
9 // Copyright (C) 2003 Caltech
11 // Module: EvtGen/EvtBBScalar
13 // Description:Implementation of the decay B- -> lambda p_bar pi according to
14 // hep-ph/0204185, hep-ph/0211240
15 // This model is intended to be applicable to all decays of the type B-> baryon baryon scalar
17 // Modification history:
19 // Jan Strube March 24, 2006 Module created
21 //------------------------------------------------------------------------
22 #include "EvtGenBase/EvtPatches.hh"
24 #include "EvtGenModels/EvtBBScalar.hh"
25 #include "EvtGenBase/EvtGammaMatrix.hh"
26 #include "EvtGenBase/EvtDiracSpinor.hh"
27 #include "EvtGenBase/EvtSpinType.hh"
28 #include "EvtGenBase/EvtTensor4C.hh"
33 const float pi = 3.14159;
34 const EvtComplex EvtBBScalar::I = EvtComplex(0, 1);
35 const EvtComplex EvtBBScalar::V_ub = EvtComplex(3.67e-3*cos(60/180*pi), 3.67e-3*cos(60/180*pi));
36 const EvtComplex EvtBBScalar::V_us_star = EvtComplex(0.22, 0);
37 const EvtComplex EvtBBScalar::a1 = EvtComplex(1.05, 0);
38 const EvtComplex EvtBBScalar::V_tb = EvtComplex(0.99915, 0);
39 const EvtComplex EvtBBScalar::V_ts_star = EvtComplex(-0.04029-0.000813*cos(60/180*pi), -0.000813*cos(60/180*pi));
40 const EvtComplex EvtBBScalar::a4 = EvtComplex(-387.3e-4, -121e-4);
41 const EvtComplex EvtBBScalar::a6 = EvtComplex(-555.3e-4, -121e-4);
42 const double EvtBBScalar::x[] = {420.96, -10485.50, 100639.97, -433916.61, 613780.15};
43 const double EvtBBScalar::y[] = {292.62, -735.73};
44 const double EvtBBScalar::m_s = 0.120;
45 const double EvtBBScalar::m_u = 0.029 * 0.120;
46 const double EvtBBScalar::m_b = 4.88;
49 EvtBBScalar::EvtBBScalar()
58 _f1Map.insert(make_pair(string("K"), dummy));
61 _f0Map.insert(make_pair(string("K"), dummy));
66 _f1Map.insert(make_pair(string("pi"), dummy));
69 _f0Map.insert(make_pair(string("pi"), dummy));
74 std::string EvtBBScalar::getName(){
75 return "B_TO_2BARYON_SCALAR";
78 EvtDecayBase* EvtBBScalar::clone(){
79 return new EvtBBScalar;
83 void EvtBBScalar::setKnownBaryonTypes(const EvtId& baryon) {
84 int baryonId = EvtPDL::getStdHep(baryon);
85 if (EvtPDL::getStdHep(EvtPDL::getId("Lambda0")) == baryonId
86 or EvtPDL::getStdHep(EvtPDL::getId("anti-Lambda0")) == baryonId ) {
87 _baryonCombination.set(Lambda);
88 } else if (EvtPDL::getStdHep(EvtPDL::getId("p+")) == baryonId
89 or EvtPDL::getStdHep(EvtPDL::getId("anti-p-")) == baryonId ) {
90 _baryonCombination.set(Proton);
91 } else if (EvtPDL::getStdHep(EvtPDL::getId("n0")) == baryonId
92 or EvtPDL::getStdHep(EvtPDL::getId("anti-n0")) == baryonId) {
93 _baryonCombination.set(Neutron);
94 } else if (EvtPDL::getStdHep(EvtPDL::getId("Sigma0")) == baryonId
95 or EvtPDL::getStdHep(EvtPDL::getId("anti-Sigma0")) == baryonId ) {
96 _baryonCombination.set(Sigma0);
97 } else if (EvtPDL::getStdHep(EvtPDL::getId("Sigma-")) == baryonId
98 or EvtPDL::getStdHep(EvtPDL::getId("anti-Sigma+")) == baryonId ) {
99 _baryonCombination.set(Sigma_minus);
100 } else if (EvtPDL::getStdHep(EvtPDL::getId("Xi0")) == baryonId
101 or EvtPDL::getStdHep(EvtPDL::getId("anti-Xi0")) == baryonId) {
102 _baryonCombination.set(Xi0);
103 } else if (EvtPDL::getStdHep(EvtPDL::getId("Xi-")) == baryonId
104 or EvtPDL::getStdHep(EvtPDL::getId("anti-Xi+")) == baryonId) {
105 _baryonCombination.set(Xi_minus);
107 report(ERROR, "EvtGen")
108 << "EvtBBScalar::init: Don't know what to do with this type as the first or second baryon\n";
113 const double EvtBBScalar::baryonF1F2(double t) {
114 // check for known form factors for combination of baryons
115 if (_baryonCombination.test(Lambda) and _baryonCombination.test(Proton)) {
116 return -sqrt(1.5) * G_p(t);
117 } else if (_baryonCombination.test(Sigma0) and _baryonCombination.test(Proton)) {
118 return -sqrt(0.5) * (G_p(t) + 2* G_n(t));
119 } else if (_baryonCombination.test(Sigma_minus) and _baryonCombination.test(Neutron)) {
120 return -G_p(t) - 2* G_n(t);
121 } else if (_baryonCombination.test(Xi0) and _baryonCombination.test(Sigma_minus)) {
122 return G_p(t) - G_n(t);
123 } else if (_baryonCombination.test(Xi_minus) and _baryonCombination.test(Sigma0)) {
124 return sqrt(0.5) * (G_p(t) - G_n(t));
125 } else if (_baryonCombination.test(Xi_minus) and _baryonCombination.test(Lambda)) {
126 return sqrt(1.5) * (G_p(t) + G_n(t));
128 report(ERROR, "EvtGen")
129 << "EvtBBScalar::baryonF1F2: Don't know what to do with this type as the first or second baryon\n";
134 const double EvtBBScalar::formFactorFit(double t, const vector<double>& params) {
135 static const double gamma = 2.148;
136 static const double Lambda_0 = 0.3;
138 for (size_t i=0; i<params.size(); ++i) {
139 result += params[i]/pow(t, static_cast<int>(i+1));
141 return result * pow(log(t/pow(Lambda_0, 2)), -gamma);
145 const double EvtBBScalar::G_p(double t) {
146 const vector<double> v_x(x, x+5);
147 return formFactorFit(t, v_x);
151 const double EvtBBScalar::G_n(double t) {
152 const vector<double> v_y(y, y+2);
153 return -formFactorFit(t, v_y);
158 const double EvtBBScalar::baryon_gA(double t) {
159 // check for known form factors for combination of baryons
160 if (_baryonCombination.test(Lambda) and _baryonCombination.test(Proton)) {
161 return -1/sqrt(6.) * (D_A(t) + 3*F_A(t));
162 } else if (_baryonCombination.test(Sigma0) and _baryonCombination.test(Proton)) {
163 return 1/sqrt(2.) * (D_A(t) - F_A(t));
164 } else if (_baryonCombination.test(Sigma_minus) and _baryonCombination.test(Neutron)) {
165 return D_A(t) - F_A(t);
166 } else if (_baryonCombination.test(Xi0) and _baryonCombination.test(Sigma_minus)) {
167 return D_A(t) + F_A(t);
168 } else if (_baryonCombination.test(Xi_minus) and _baryonCombination.test(Sigma0)) {
169 return 1/sqrt(2.) * (D_A(t) + F_A(t));
170 } else if (_baryonCombination.test(Xi_minus) and _baryonCombination.test(Lambda)) {
171 return -1 / sqrt(6.) * (D_A(t) - 3*F_A(t));
173 report(ERROR, "EvtGen")
174 << "EvtBBScalar::baryon_gA: Don't know what to do with this type as the first or second baryon\n";
180 const double EvtBBScalar::baryon_gP(double t) {
181 // check for known form factors for combination of baryons
182 if (_baryonCombination.test(Lambda) and _baryonCombination.test(Proton)) {
183 return -1/sqrt(6.) * (D_P(t) + 3*F_P(t));
184 } else if (_baryonCombination.test(Sigma0) and _baryonCombination.test(Proton)) {
185 return 1/sqrt(2.) * (D_P(t) - F_P(t));
186 } else if (_baryonCombination.test(Sigma_minus) and _baryonCombination.test(Neutron)) {
187 return D_P(t) - F_P(t);
188 } else if (_baryonCombination.test(Xi0) and _baryonCombination.test(Sigma_minus)) {
189 return D_P(t) + F_P(t);
190 } else if (_baryonCombination.test(Xi_minus) and _baryonCombination.test(Sigma0)) {
191 return 1/sqrt(2.) * (D_P(t) + F_P(t));
192 } else if (_baryonCombination.test(Xi_minus) and _baryonCombination.test(Lambda)) {
193 return -1 / sqrt(6.) * (D_P(t) - 3*F_P(t));
195 report(ERROR, "EvtGen")
196 << "EvtBBScalar::baryon_gP: Don't know what to do with this type as the first or second baryon\n";
201 const double EvtBBScalar::baryon_fS(double t) {
202 // check for known form factors for combination of baryons
203 if (_baryonCombination.test(Lambda) and _baryonCombination.test(Proton)) {
204 return -1/sqrt(6.) * (D_S(t) + 3*F_S(t));
205 } else if (_baryonCombination.test(Sigma0) and _baryonCombination.test(Proton)) {
206 return 1/sqrt(2.) * (D_S(t) - F_S(t));
207 } else if (_baryonCombination.test(Sigma_minus) and _baryonCombination.test(Neutron)) {
208 return D_S(t) - F_S(t);
209 } else if (_baryonCombination.test(Xi0) and _baryonCombination.test(Sigma_minus)) {
210 return D_S(t) + F_S(t);
211 } else if (_baryonCombination.test(Xi_minus) and _baryonCombination.test(Sigma0)) {
212 return 1/sqrt(2.) * (D_S(t) + F_S(t));
213 } else if (_baryonCombination.test(Xi_minus) and _baryonCombination.test(Lambda)) {
214 return -1 / sqrt(6.) * (D_S(t) - 3*F_S(t));
216 report(ERROR, "EvtGen")
217 << "EvtBBScalar::baryon_fS: Don't know what to do with this type as the first or second baryon\n";
223 const double EvtBBScalar::D_A(double t) {
224 const double d_tilde[] = {x[0]-1.5*y[0], -478};
225 const vector<double> v_d_tilde(d_tilde, d_tilde+2);
226 return formFactorFit(t, v_d_tilde);
230 const double EvtBBScalar::F_A(double t) {
231 const double f_tilde[] = {2./3*x[0]+0.5*y[0], -478};
232 const vector<double> v_f_tilde(f_tilde, f_tilde+2);
233 return formFactorFit(t, v_f_tilde);
237 const double EvtBBScalar::D_P(double t) {
238 const double d_bar[] = {1.5*y[0]* _massRatio, /*-952*/0};
239 const vector<double> v_d_bar(d_bar, d_bar+2);
240 return formFactorFit(t, v_d_bar);
244 const double EvtBBScalar::F_P(double t) {
245 const double f_bar[] = {(x[0]-0.5*y[0]) * _massRatio, /*-952*/0};
246 const vector<double> v_f_bar(f_bar, f_bar+2);
247 return formFactorFit(t, v_f_bar);
251 const double EvtBBScalar::D_S(double t) {
252 return -1.5 * _massRatio * G_n(t);
256 const double EvtBBScalar::F_S(double t) {
257 return (G_p(t) + 0.5*G_n(t)) * _massRatio;
261 const double EvtBBScalar::baryon_hA(double t) {
262 return (1/_massRatio*baryon_gP(t)-baryon_gA(t))*pow(_baryonMassSum, 2)/t;
266 void EvtBBScalar::init() {
267 // no arguments, daughter lambda p_bar pi
268 // charge conservation is checked by base class
271 checkSpinParent(EvtSpinType::SCALAR);
272 checkSpinDaughter(0, EvtSpinType::DIRAC);
273 checkSpinDaughter(1, EvtSpinType::DIRAC);
274 checkSpinDaughter(2, EvtSpinType::SCALAR);
275 EvtId baryon1 = getDaug(0);
276 EvtId baryon2 = getDaug(1);
277 EvtId scalar = getDaug(2);
278 int scalarId = EvtPDL::getStdHep(scalar);
280 // Different form factors for the B-pi or B-K transition.
281 if ( scalarId == EvtPDL::getStdHep(EvtPDL::getId("pi+"))
282 or scalarId == EvtPDL::getStdHep(EvtPDL::getId("pi-"))
283 or scalarId == EvtPDL::getStdHep(EvtPDL::getId("pi0"))) {
285 } else if (scalarId == EvtPDL::getStdHep(EvtPDL::getId("K+"))
286 or scalarId == EvtPDL::getStdHep(EvtPDL::getId("K-"))
287 or scalarId == EvtPDL::getStdHep(EvtPDL::getId("K0"))
288 or scalarId == EvtPDL::getStdHep(EvtPDL::getId("anti-K0"))) {
291 report(ERROR, "EvtGen")
292 << "EvtBBScalar::init: Can only deal with Kaons or pions as the third particle\n"
293 << "\tFound: " << scalarId << endl;
296 // check for known particles
297 setKnownBaryonTypes(baryon1);
298 setKnownBaryonTypes(baryon2);
299 double mass1 = EvtPDL::getMass(baryon1);
300 double mass2 = EvtPDL::getMass(baryon2);
301 // This whole model deals only with baryons that differ in s-u
303 _massRatio = (mass1-mass2) / (m_s-m_u);
305 _massRatio = (mass2-mass1) / (m_s-m_u);
306 _baryonMassSum = mass1 + mass2;
310 // initialize phasespace and calculate the amplitude
311 void EvtBBScalar::decay(EvtParticle* p) {
312 p->initializePhaseSpace(getNDaug(), getDaugs());
313 EvtVector4R B_Momentum = p->getP4Lab();
314 EvtDiracParticle* theLambda = dynamic_cast<EvtDiracParticle*>(p->getDaug(0));
315 EvtDiracParticle* theAntiP = dynamic_cast<EvtDiracParticle*>(p->getDaug(1));
316 EvtScalarParticle* theScalar = dynamic_cast<EvtScalarParticle*>(p->getDaug(2));
317 EvtVector4R scalarMomentum = theScalar->getP4Lab();
319 // The amplitude consists of three matrix elements. These will be calculated one by one here.
321 // loop over all possible spin states
322 for (int i=0; i<2; ++i) {
323 EvtDiracSpinor lambdaPol = theLambda->spParent(i);
324 for (int j=0; j<2; ++j) {
325 EvtDiracSpinor antiP_Pol = theAntiP->spParent(j);
326 EvtVector4C theAmplitudePartA = amp_A(B_Momentum, scalarMomentum);
327 EvtComplex amplitude;
328 for (int index=0; index<4; ++index) {
329 amplitude += theAmplitudePartA.get(index)
330 * ( const_B*amp_B(theLambda, lambdaPol, theAntiP, antiP_Pol, index)
331 + const_C*amp_C(theLambda, lambdaPol, theAntiP, antiP_Pol, index) );
333 vertex(i, j, amplitude);
338 void EvtBBScalar::initProbMax()
341 setProbMax(0.2); // found by trial and error
344 // Form factor f1 for B-pi transition
345 const double EvtBBScalar::B_pi_f1(double t)
347 FormFactor f = _f1Map[_scalarType];
348 double mv2 = f.mV*f.mV;
349 return f.value / ((1-t/mv2) * (1-f.sigma1*t/mv2+f.sigma2*t*t/mv2/mv2));
352 // Form factor f0 for B-pi transition
353 const double EvtBBScalar::B_pi_f0(double t)
355 FormFactor f = _f0Map[_scalarType];
356 double mv2 = f.mV*f.mV;
357 return f.value / (1 - f.sigma1*t/mv2 + f.sigma2*t*t/mv2/mv2);
361 // constants of the B and C parts of the amplitude
362 const EvtComplex EvtBBScalar::const_B = V_ub*V_us_star*a1 - V_tb*V_ts_star*a4;
363 const EvtComplex EvtBBScalar::const_C = 2*a6*V_tb*V_ts_star;
365 // part A of the amplitude, see hep-ph/0204185
367 EvtBBScalar::amp_A(const EvtVector4R& p4B, const EvtVector4R& p4Scalar)
369 double mB2 = p4B.mass2();
370 double mScalar2 = p4Scalar.mass2();
371 double t = (p4B-p4Scalar).mass2();
372 return ((p4B+p4Scalar) - (mB2-mScalar2)/t * (p4B-p4Scalar)) * B_pi_f1(t)
373 + (mB2-mScalar2)/t * (p4B-p4Scalar) * B_pi_f0(t);
376 // part B of the amplitude, Vector and Axial Vector parts
378 EvtBBScalar::amp_B(const EvtDiracParticle* baryon1, const EvtDiracSpinor& b1Pol
379 , const EvtDiracParticle* baryon2, const EvtDiracSpinor& b2Pol
382 return amp_B_vectorPart(baryon1, b1Pol, baryon2, b2Pol, index)
383 - amp_B_axialPart(baryon1, b1Pol, baryon2, b2Pol, index);
388 EvtBBScalar::amp_B_vectorPart(const EvtDiracParticle* baryon1, const EvtDiracSpinor& b1Pol
389 , const EvtDiracParticle* baryon2, const EvtDiracSpinor& b2Pol
392 double t = (baryon1->getP4Lab() + baryon2->getP4Lab()).mass2();
393 EvtGammaMatrix gamma;
394 for (int i=0; i<4; ++i) {
395 gamma += EvtTensor4C::g().get(index, i) * EvtGammaMatrix::g(i);
397 // The F2 contribution that is written out in the paper is neglected here.
398 // see hep-ph/0204185
399 return b1Pol.adjoint()* (gamma*baryonF1F2(t) *b2Pol);
403 EvtBBScalar::amp_B_axialPart(const EvtDiracParticle* baryon1, const EvtDiracSpinor& b1Pol
404 , const EvtDiracParticle* baryon2, const EvtDiracSpinor& b2Pol
407 EvtGammaMatrix gamma;
408 for (int i=0; i<4; ++i) {
409 gamma += EvtTensor4C::g().get(index, i) * EvtGammaMatrix::g(i);
411 double t = (baryon1->getP4Lab() + baryon2->getP4Lab()).mass2();
412 double mSum = baryon1->mass() + baryon2->mass();
413 EvtVector4C momentum_upper = (baryon1->getP4Lab()+baryon2->getP4Lab());
414 EvtVector4C momentum;
415 for (int mu=0; mu<0; ++mu) {
417 for (int i=0; i<4; ++i) {
418 dummy += EvtTensor4C::g().get(index, i)*momentum_upper.get(i);
420 momentum.set(mu, dummy);
422 return b1Pol.adjoint() * (((baryon_gA(t) * gamma +
423 EvtGammaMatrix::id()*baryon_hA(t)/mSum*momentum.get(index))
424 * EvtGammaMatrix::g5()) * b2Pol);
428 // part C of the amplitude, Scalar and Pseudoscalar parts
430 EvtBBScalar::amp_C(const EvtDiracParticle* baryon1, const EvtDiracSpinor& b1Pol
431 , const EvtDiracParticle* baryon2, const EvtDiracSpinor& b2Pol
434 EvtVector4C baryonSumP4_upper = baryon1->getP4Lab() + baryon2->getP4Lab();
435 EvtVector4C baryonSumP4;
436 for (int mu=0; mu<4; ++mu) {
438 for (int i=0; i<4; ++i) {
439 dummy += EvtTensor4C::g().get(mu, i) * baryonSumP4_upper.get(i);
441 baryonSumP4.set(mu, dummy);
443 double t = (baryon1->getP4Lab() + baryon2->getP4Lab()).mass2();
444 return baryonSumP4.get(index)/(m_b-m_u)*(amp_C_scalarPart(b1Pol, b2Pol, t) + amp_C_pseudoscalarPart(b1Pol, b2Pol, t));
449 EvtBBScalar::amp_C_scalarPart(const EvtDiracSpinor& b1Pol, const EvtDiracSpinor& b2Pol, double t)
451 return baryon_fS(t) * b1Pol.adjoint()*b2Pol;
455 EvtBBScalar::amp_C_pseudoscalarPart(const EvtDiracSpinor& b1Pol, const EvtDiracSpinor& b2Pol, double t)
457 return baryon_gP(t) * b1Pol.adjoint()*(EvtGammaMatrix::g5()*b2Pol);