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25 // 22 //
26 // G4MuonDecayChannelWithSpin class implementa << 23 // ------------------------------------------------------------
>> 24 // GEANT 4 class header file
>> 25 //
>> 26 // History:
>> 27 // 17 August 2004 P.Gumplinger and T.MacPhail
>> 28 // samples Michel spectrum including 1st order
>> 29 // radiative corrections
>> 30 // Reference: Florian Scheck "Muon Physics", in Physics Reports
>> 31 // (Review Section of Physics Letters) 44, No. 4 (1978)
>> 32 // 187-248. North-Holland Publishing Company, Amsterdam
>> 33 // at page 210 cc.
>> 34 //
>> 35 // W.E. Fisher and F. Scheck, Nucl. Phys. B83 (1974) 25.
>> 36 //
>> 37 // ------------------------------------------------------------
27 // 38 //
28 // References: <<
29 // - Florian Scheck "Muon Physics", in Physics <<
30 // (Review Section of Physics Letters) 44, N <<
31 // 187-248. North-Holland Publishing Company <<
32 // - W.E. Fisher and F. Scheck, Nucl. Phys. B8 <<
33 <<
34 // Authors: P.Gumplinger and T.MacPhail, 17 Au <<
35 // ------------------------------------------- <<
36 <<
37 #include "G4MuonDecayChannelWithSpin.hh" 39 #include "G4MuonDecayChannelWithSpin.hh"
38 40
>> 41 #include "Randomize.hh"
39 #include "G4DecayProducts.hh" 42 #include "G4DecayProducts.hh"
40 #include "G4LorentzVector.hh" 43 #include "G4LorentzVector.hh"
41 #include "G4PhysicalConstants.hh" <<
42 #include "G4SystemOfUnits.hh" <<
43 #include "Randomize.hh" <<
44 44
45 G4MuonDecayChannelWithSpin::G4MuonDecayChannel << 45 G4MuonDecayChannelWithSpin::G4MuonDecayChannelWithSpin(const G4String& theParentName,
46 << 46 G4double theBR)
47 : G4MuonDecayChannel(theParentName, theBR) << 47 : G4MuonDecayChannel(theParentName,theBR)
48 {} << 48 {
>> 49 }
49 50
50 G4MuonDecayChannelWithSpin& << 51 G4MuonDecayChannelWithSpin::~G4MuonDecayChannelWithSpin()
51 G4MuonDecayChannelWithSpin::operator=(const G4 <<
52 { 52 {
53 if (this != &right) { <<
54 kinematics_name = right.kinematics_name; <<
55 verboseLevel = right.verboseLevel; <<
56 rbranch = right.rbranch; <<
57 <<
58 // copy parent name <<
59 delete parent_name; <<
60 parent_name = new G4String(*right.parent_n <<
61 <<
62 // clear daughters_name array <<
63 ClearDaughtersName(); <<
64 <<
65 // recreate array <<
66 numberOfDaughters = right.numberOfDaughter <<
67 if (numberOfDaughters > 0) { <<
68 daughters_name = new G4String*[numberOfD <<
69 // copy daughters name <<
70 for (G4int index = 0; index < numberOfDa <<
71 daughters_name[index] = new G4String(* <<
72 } <<
73 } <<
74 } <<
75 return *this; <<
76 } 53 }
77 54
78 G4DecayProducts* G4MuonDecayChannelWithSpin::D << 55 G4DecayProducts *G4MuonDecayChannelWithSpin::DecayIt(G4double)
79 { 56 {
80 // This version assumes V-A coupling with 1s 57 // This version assumes V-A coupling with 1st order radiative correctons,
81 // the standard model Michel pa 58 // the standard model Michel parameter values, but
82 // gives incorrect energy spect 59 // gives incorrect energy spectrum for neutrinos
83 60
84 #ifdef G4VERBOSE 61 #ifdef G4VERBOSE
85 if (GetVerboseLevel() > 1) G4cout << "G4Muon << 62 if (GetVerboseLevel()>1) G4cout << "G4MuonDecayChannelWithSpin::DecayIt ";
86 #endif 63 #endif
87 64
88 CheckAndFillParent(); << 65 if (parent == 0) FillParent();
89 CheckAndFillDaughters(); << 66 if (daughters == 0) FillDaughters();
90 67
91 // parent mass 68 // parent mass
92 G4double parentmass = G4MT_parent->GetPDGMas << 69 G4double parentmass = parent->GetPDGMass();
93 70
94 G4double EMMU = parentmass; << 71 EMMU = parentmass;
95 72
96 // daughters'mass << 73 //daughters'mass
97 G4double daughtermass[3]; << 74 G4double daughtermass[3];
98 // G4double sumofdaughtermass = 0.0; << 75 G4double sumofdaughtermass = 0.0;
99 for (G4int index = 0; index < 3; ++index) { << 76 for (G4int index=0; index<3; index++){
100 daughtermass[index] = G4MT_daughters[index << 77 daughtermass[index] = daughters[index]->GetPDGMass();
101 // sumofdaughtermass += daughtermass[index << 78 sumofdaughtermass += daughtermass[index];
102 } 79 }
103 80
104 G4double EMASS = daughtermass[0]; << 81 EMASS = daughtermass[0];
105 82
106 // create parent G4DynamicParticle at rest << 83 //create parent G4DynamicParticle at rest
107 G4ThreeVector dummy; 84 G4ThreeVector dummy;
108 auto parentparticle = new G4DynamicParticle( << 85 G4DynamicParticle * parentparticle = new G4DynamicParticle( parent, dummy, 0.0);
109 // create G4Decayproducts << 86 //create G4Decayproducts
110 auto products = new G4DecayProducts(*parentp << 87 G4DecayProducts *products = new G4DecayProducts(*parentparticle);
111 delete parentparticle; 88 delete parentparticle;
112 89
113 // calculate electron energy << 90 // calcurate electron energy
114 91
115 G4double michel_rho = 0.75; // Standard Mod << 92 G4double michel_rho = 0.75; //Standard Model Michel rho
116 G4double michel_delta = 0.75; // Standard M << 93 G4double michel_delta = 0.75; //Standard Model Michel delta
117 G4double michel_xsi = 1.00; // Standard Mod << 94 G4double michel_xsi = 1.00; //Standard Model Michel xsi
118 G4double michel_eta = 0.00; // Standard Mod << 95 G4double michel_eta = 0.00; //Standard Model eta
119 96
120 G4double rndm, x, ctheta; 97 G4double rndm, x, ctheta;
121 98
122 G4double FG; << 99 G4double FG;
123 G4double FG_max = 2.00; 100 G4double FG_max = 2.00;
124 101
125 G4double W_mue = (EMMU * EMMU + EMASS * EMAS << 102 G4double W_mue = (EMMU*EMMU+EMASS*EMASS)/(2.*EMMU);
126 G4double x0 = EMASS / W_mue; << 103 G4double x0 = EMASS/W_mue;
127 104
128 G4double x0_squared = x0 * x0; << 105 G4double x0_squared = x0*x0;
129 106
130 // ***************************************** 107 // ***************************************************
131 // x0 <= x <= 1. and -1 <= y <= 1 108 // x0 <= x <= 1. and -1 <= y <= 1
132 // 109 //
133 // F(x,y) = f(x)*g(x,y); g(x,y) = 1.+g 110 // F(x,y) = f(x)*g(x,y); g(x,y) = 1.+g(x)*y
134 // ***************************************** 111 // ***************************************************
135 112
136 // ***** sampling F(x,y) directly (brute for 113 // ***** sampling F(x,y) directly (brute force) *****
137 114
138 const std::size_t MAX_LOOP = 10000; << 115 do{
139 for (std::size_t loop_count = 0; loop_count << 116
140 // Sample the positron energy by sampling 117 // Sample the positron energy by sampling from F
141 118
142 rndm = G4UniformRand(); 119 rndm = G4UniformRand();
143 120
144 x = x0 + rndm * (1. - x0); << 121 x = x0 + rndm*(1.-x0);
145 122
146 G4double x_squared = x * x; << 123 G4double x_squared = x*x;
147 124
148 G4double F_IS, F_AS, G_IS, G_AS; 125 G4double F_IS, F_AS, G_IS, G_AS;
149 126
150 F_IS = 1. / 6. * (-2. * x_squared + 3. * x << 127 F_IS = 1./6.*(-2.*x_squared+3.*x-x0_squared);
151 F_AS = 1. / 6. * std::sqrt(x_squared - x0_ << 128 F_AS = 1./6.*std::sqrt(x_squared-x0_squared)*(2.*x-2.+std::sqrt(1.-x0_squared));
152 129
153 G_IS = 2. / 9. * (michel_rho - 0.75) * (4. << 130 G_IS = 2./9.*(michel_rho-0.75)*(4.*x_squared-3.*x-x0_squared);
154 G_IS = G_IS + michel_eta * (1. - x) * x0; << 131 G_IS = G_IS + michel_eta*(1.-x)*x0;
155 132
156 G_AS = 3. * (michel_xsi - 1.) * (1. - x); << 133 G_AS = 3.*(michel_xsi-1.)*(1.-x);
157 G_AS = << 134 G_AS = G_AS+2.*(michel_xsi*michel_delta-0.75)*(4.*x-4.+std::sqrt(1.-x0_squared));
158 G_AS + 2. * (michel_xsi * michel_delta - << 135 G_AS = 1./9.*std::sqrt(x_squared-x0_squared)*G_AS;
159 G_AS = 1. / 9. * std::sqrt(x_squared - x0_ <<
160 136
161 F_IS = F_IS + G_IS; 137 F_IS = F_IS + G_IS;
162 F_AS = F_AS + G_AS; 138 F_AS = F_AS + G_AS;
163 139
164 // *** Radiative Corrections *** 140 // *** Radiative Corrections ***
165 141
166 const G4double omega = std::log(EMMU / EMA << 142 G4double R_IS = F_c(x,x0);
167 G4double R_IS = F_c(x, x0, omega); <<
168 143
169 G4double F = 6. * F_IS + R_IS / std::sqrt( << 144 G4double F = 6.*F_IS + R_IS/std::sqrt(x_squared-x0_squared);
170 145
171 // *** Radiative Corrections *** 146 // *** Radiative Corrections ***
172 147
173 G4double R_AS = F_theta(x, x0, omega); << 148 G4double R_AS = F_theta(x,x0);
174 149
175 rndm = G4UniformRand(); 150 rndm = G4UniformRand();
176 151
177 ctheta = 2. * rndm - 1.; << 152 ctheta = 2.*rndm-1.;
178 153
179 G4double G = 6. * F_AS - R_AS / std::sqrt( << 154 G4double G = 6.*F_AS - R_AS/std::sqrt(x_squared-x0_squared);
180 155
181 FG = std::sqrt(x_squared - x0_squared) * F << 156 FG = std::sqrt(x_squared-x0_squared)*F*(1.+(G/F)*ctheta);
182 157
183 if (FG > FG_max) { << 158 if(FG>FG_max){
184 G4Exception("G4MuonDecayChannelWithSpin: << 159 G4cout<<"***Problem in Muon Decay *** : FG > FG_max"<<G4endl;
185 "Problem in Muon Decay: FG > <<
186 FG_max = FG; 160 FG_max = FG;
187 } 161 }
188 162
189 rndm = G4UniformRand(); 163 rndm = G4UniformRand();
190 164
191 if (FG >= rndm * FG_max) break; << 165 }while(FG<rndm*FG_max);
192 } <<
193 166
194 G4double energy = x * W_mue; 167 G4double energy = x * W_mue;
195 168
196 rndm = G4UniformRand(); 169 rndm = G4UniformRand();
197 170
198 G4double phi = twopi * rndm; 171 G4double phi = twopi * rndm;
199 172
200 if (energy < EMASS) energy = EMASS; << 173 if(energy < EMASS) energy = EMASS;
201 174
202 // Calculate daughter momentum << 175 // calculate daughter momentum
203 G4double daughtermomentum[3]; 176 G4double daughtermomentum[3];
204 177
205 daughtermomentum[0] = std::sqrt(energy * ene << 178 daughtermomentum[0] = std::sqrt(energy*energy - EMASS*EMASS);
206 179
207 G4double stheta = std::sqrt(1. - ctheta * ct << 180 G4double stheta = std::sqrt(1.-ctheta*ctheta);
208 G4double cphi = std::cos(phi); 181 G4double cphi = std::cos(phi);
209 G4double sphi = std::sin(phi); 182 G4double sphi = std::sin(phi);
210 183
211 // Coordinates of the decay positron with re << 184 //Coordinates of the decay positron with respect to the muon spin
212 G4double px = stheta * cphi; << 185
213 G4double py = stheta * sphi; << 186 G4double px = stheta*cphi;
>> 187 G4double py = stheta*sphi;
214 G4double pz = ctheta; 188 G4double pz = ctheta;
215 189
216 G4ThreeVector direction0(px, py, pz); << 190 G4ThreeVector direction0(px,py,pz);
217 191
218 direction0.rotateUz(parent_polarization); 192 direction0.rotateUz(parent_polarization);
219 193
220 auto daughterparticle0 = << 194 G4DynamicParticle * daughterparticle0
221 new G4DynamicParticle(G4MT_daughters[0], d << 195 = new G4DynamicParticle( daughters[0], daughtermomentum[0]*direction0);
222 196
223 products->PushProducts(daughterparticle0); 197 products->PushProducts(daughterparticle0);
224 198
>> 199
225 // daughter 1 ,2 (neutrinos) 200 // daughter 1 ,2 (neutrinos)
226 // create neutrinos in the C.M frame of two 201 // create neutrinos in the C.M frame of two neutrinos
227 G4double energy2 = parentmass - energy; << 202 G4double energy2 = parentmass*(1.0 - x/2.0);
228 G4double vmass = std::sqrt((energy2 - daught << 203 G4double vmass = std::sqrt((energy2-daughtermomentum[0])*(energy2+daughtermomentum[0]));
229 G4double beta = -1.0 * daughtermomentum[0] / << 204 G4double beta = -1.0*daughtermomentum[0]/energy2;
230 G4double costhetan = 2. * G4UniformRand() - << 205 G4double costhetan = 2.*G4UniformRand()-1.0;
231 G4double sinthetan = std::sqrt((1.0 - costhe << 206 G4double sinthetan = std::sqrt((1.0-costhetan)*(1.0+costhetan));
232 G4double phin = twopi * G4UniformRand() * ra << 207 G4double phin = twopi*G4UniformRand()*rad;
233 G4double sinphin = std::sin(phin); 208 G4double sinphin = std::sin(phin);
234 G4double cosphin = std::cos(phin); 209 G4double cosphin = std::cos(phin);
235 210
236 G4ThreeVector direction1(sinthetan * cosphin << 211 G4ThreeVector direction1(sinthetan*cosphin,sinthetan*sinphin,costhetan);
237 auto daughterparticle1 = new G4DynamicPartic << 212 G4DynamicParticle * daughterparticle1
238 auto daughterparticle2 = << 213 = new G4DynamicParticle( daughters[1], direction1*(vmass/2.));
239 new G4DynamicParticle(G4MT_daughters[2], d << 214 G4DynamicParticle * daughterparticle2
>> 215 = new G4DynamicParticle( daughters[2], direction1*(-1.0*vmass/2.));
240 216
241 // boost to the muon rest frame 217 // boost to the muon rest frame
242 G4LorentzVector p4; 218 G4LorentzVector p4;
243 p4 = daughterparticle1->Get4Momentum(); 219 p4 = daughterparticle1->Get4Momentum();
244 p4.boost(direction0.x() * beta, direction0.y << 220 p4.boost( direction0.x()*beta, direction0.y()*beta, direction0.z()*beta);
245 daughterparticle1->Set4Momentum(p4); 221 daughterparticle1->Set4Momentum(p4);
246 p4 = daughterparticle2->Get4Momentum(); 222 p4 = daughterparticle2->Get4Momentum();
247 p4.boost(direction0.x() * beta, direction0.y << 223 p4.boost( direction0.x()*beta, direction0.y()*beta, direction0.z()*beta);
248 daughterparticle2->Set4Momentum(p4); 224 daughterparticle2->Set4Momentum(p4);
249 products->PushProducts(daughterparticle1); 225 products->PushProducts(daughterparticle1);
250 products->PushProducts(daughterparticle2); 226 products->PushProducts(daughterparticle2);
251 daughtermomentum[1] = daughterparticle1->Get 227 daughtermomentum[1] = daughterparticle1->GetTotalMomentum();
252 daughtermomentum[2] = daughterparticle2->Get 228 daughtermomentum[2] = daughterparticle2->GetTotalMomentum();
253 229
254 // output message 230 // output message
255 #ifdef G4VERBOSE 231 #ifdef G4VERBOSE
256 if (GetVerboseLevel() > 1) { << 232 if (GetVerboseLevel()>1) {
257 G4cout << "G4MuonDecayChannelWithSpin::Dec 233 G4cout << "G4MuonDecayChannelWithSpin::DecayIt ";
258 G4cout << " create decay products in rest << 234 G4cout << " create decay products in rest frame " <<G4endl;
259 G4double TT = daughterparticle0->GetTotalE << 235 products->DumpInfo();
260 + daughterparticle2->GetTota <<
261 G4cout << "e " << daughterparticle0->GetT <<
262 G4cout << "nu1" << daughterparticle1->GetT <<
263 G4cout << "nu2" << daughterparticle2->GetT <<
264 G4cout << "total" << (TT - parentmass) / k <<
265 if (GetVerboseLevel() > 2) { <<
266 products->DumpInfo(); <<
267 } <<
268 } 236 }
269 #endif 237 #endif
270 <<
271 return products; 238 return products;
272 } 239 }
273 240
274 G4double G4MuonDecayChannelWithSpin::R_c(G4dou << 241 G4double G4MuonDecayChannelWithSpin::R_c(G4double x){
275 { <<
276 auto n_max = (G4int)(100. * x); <<
277 242
278 if (n_max < 10) n_max = 10; << 243 G4int n_max = (int)(100.*x);
>> 244
>> 245 if(n_max<10)n_max=10;
279 246
280 G4double L2 = 0.0; 247 G4double L2 = 0.0;
281 248
282 for (G4int n = 1; n <= n_max; ++n) { << 249 for(G4int n=1; n<=n_max; n++){
283 L2 += std::pow(x, n) / (n * n); << 250 L2 += std::pow(x,n)/(n*n);
284 } 251 }
285 252
>> 253 G4double omega = std::log(EMMU/EMASS);
>> 254
286 G4double r_c; 255 G4double r_c;
287 256
288 r_c = 2. * L2 - (pi * pi / 3.) - 2.; << 257 r_c = 2.*L2-(pi*pi/3.)-2.;
289 r_c = r_c + omega * (1.5 + 2. * std::log((1. << 258 r_c = r_c + omega * (1.5+2.*std::log((1.-x)/x));
290 r_c = r_c - std::log(x) * (2. * std::log(x) << 259 r_c = r_c - std::log(x)*(2.*std::log(x)-1.);
291 r_c = r_c + (3. * std::log(x) - 1. - 1. / x) << 260 r_c = r_c + (3.*std::log(x)-1.-1./x)*std::log(1.-x);
292 261
293 return r_c; 262 return r_c;
294 } 263 }
295 264