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0001 // -*- C++ -*- 0002 // 0003 // YFSFormFactors.h is a part of Herwig - A multi-purpose Monte Carlo event generator 0004 // Copyright (C) 2002-2019 The Herwig Collaboration 0005 // 0006 // Herwig is licenced under version 3 of the GPL, see COPYING for details. 0007 // Please respect the MCnet academic guidelines, see GUIDELINES for details. 0008 // 0009 #ifndef HERWIG_YFSFormFactors_H 0010 #define HERWIG_YFSFormFactors_H 0011 // 0012 // This is the declaration of the YFSFormFactors class. 0013 // 0014 0015 #include "ThePEG/Config/ThePEG.h" 0016 #include "Herwig/Utilities/Maths.h" 0017 0018 namespace Herwig { 0019 0020 using namespace ThePEG; 0021 0022 /** 0023 * The YFSFormFactors class is a pure static class which implements the various YFS 0024 * form factors we need for the decays. 0025 */ 0026 class YFSFormFactors { 0027 0028 public: 0029 0030 /** 0031 * The value of \f$\alpha\f$ at \f$q^2=0\f$. 0032 */ 0033 static const double _alpha; 0034 0035 private: 0036 /** 0037 * The default value of the photon mass 0038 */ 0039 static const Energy _mgamma; 0040 0041 /** 0042 * The cut-off on the value of \f$t\f$ for the switch to the $t=0$ result 0043 */ 0044 static const Energy2 _tcut; 0045 0046 /** 0047 * The cut-off on the energy of a particle for it to be considered in its rest frame 0048 */ 0049 static const Energy _ecut; 0050 0051 public: 0052 0053 /** 0054 * Exponentials of the YFS form factors 0055 */ 0056 //@{ 0057 /** 0058 * The exponential of the YFS form factor for the initial-final dipole 0059 * @param beta0 Velocity of the incoming charged particle, \f$\beta_0\f$ 0060 * @param beta1 Velocity of the outgoing charged particle, \f$\beta_1\f$. 0061 * @param ombeta0 One minus the velocity of the incoming particle, \f$1-\beta_0\f$ 0062 * @param ombeta1 One minus the velocity of the outgoing particle, \f$1-\beta_1\f$ 0063 * @param en0 The energy of the incoming particle 0064 * @param en1 The energy of the outgoing particle 0065 * @param m0 The mass of the incoming particle 0066 * @param m1 The mass of the outgoing particle 0067 * @param t The invariant mass of the charged particles 0068 * @param charge The product of the charges of the particles in the dipole 0069 * @param emin The minimum photon energy 0070 */ 0071 static double exponentialYFSIF(double beta0,double ombeta0, 0072 double beta1,double ombeta1, 0073 Energy en0 ,Energy en1 , 0074 Energy m0 ,Energy m1 , 0075 Energy2 t ,double charge , 0076 Energy emin) { 0077 return exp(YFSIF(beta0,ombeta0,beta1,ombeta1,en0,en1,m0,m1,t,charge,emin)); 0078 } 0079 /** 0080 * The exponential of the YFS form factor for the final-final dipole 0081 * The \f$2\alpha\tilde{B}\f$ function for the final-final dipole 0082 * @param beta1 Velocity of the first charged particle, \f$\beta_1\f$ 0083 * @param beta2 Velocity of the second charged particle, \f$\beta_2\f$. 0084 * @param ombeta1 One minus the velocity of the first particle, \f$1-\beta_1\f$ 0085 * @param ombeta2 One minus the velocity of the second particle, \f$1-\beta_2\f$ 0086 * @param en1 The energy of the first particle 0087 * @param en2 The energy of the second particle 0088 * @param m1 The mass of the first particle 0089 * @param m2 The mass of the second particle 0090 * @param s The invariant mass of the charged particles 0091 * @param charge The product of the charges of the particles in the dipole 0092 * @param emin The minimum photon energy 0093 */ 0094 static double exponentialYFSFF(double beta1, double ombeta1, 0095 double beta2, double ombeta2, 0096 Energy en1 , Energy en2 , 0097 Energy m1 , Energy m2 , 0098 Energy2 s , double charge , 0099 Energy emin) { 0100 return exp(YFSFF(beta1,ombeta1,beta2,ombeta2,en1,en2,m1,m2,s,charge,emin)); 0101 } 0102 //@} 0103 /** 0104 * The YFS form factors for the initial-final and final-final dipoles 0105 */ 0106 //@{ 0107 /** 0108 * The YFS form factor for the initial-final dipole 0109 * @param beta0 Velocity of the incoming charged particle, \f$\beta_0\f$ 0110 * @param beta1 Velocity of the outgoing charged particle, \f$\beta_1\f$. 0111 * @param ombeta0 One minus the velocity of the incoming particle, \f$1-\beta_0\f$ 0112 * @param ombeta1 One minus the velocity of the outgoing particle, \f$1-\beta_1\f$ 0113 * @param en0 The energy of the incoming particle 0114 * @param en1 The energy of the outgoing particle 0115 * @param m0 The mass of the incoming particle 0116 * @param m1 The mass of the outgoing particle 0117 * @param t The invariant mass of the charged particles 0118 * @param charge The product of the charges of the particles in the dipole 0119 * @param emin The minimum photon energy 0120 */ 0121 static double YFSIF(double beta0 ,double ombeta0 , 0122 double beta1 ,double ombeta1 , 0123 Energy en0 ,Energy en1 , 0124 Energy m0 ,Energy m1 , 0125 Energy2 t ,double charge , 0126 Energy emin) { 0127 return BtildeIF(beta0,ombeta0,beta1,ombeta1,en0,en1,m0,m1,t,charge,emin,false) 0128 +ReBIF(m0,m1,t,charge,false); 0129 } 0130 /** 0131 * The YFS form factor for the final-final dipole 0132 * The \f$2\alpha\tilde{B}\f$ function for the final-final dipole 0133 * @param beta1 Velocity of the first charged particle, \f$\beta_1\f$ 0134 * @param beta2 Velocity of the second charged particle, \f$\beta_2\f$. 0135 * @param ombeta1 One minus the velocity of the first particle, \f$1-\beta_1\f$ 0136 * @param ombeta2 One minus the velocity of the second particle, \f$1-\beta_2\f$ 0137 * @param en1 The energy of the first particle 0138 * @param en2 The energy of the second particle 0139 * @param m1 The mass of the first particle 0140 * @param m2 The mass of the second particle 0141 * @param s The invariant mass of the charged particles 0142 * @param charge The product of the charges of the particles in the dipole 0143 * @param emin The minimum photon energy 0144 */ 0145 static double YFSFF(double beta1 ,double ombeta1 , 0146 double beta2 ,double ombeta2 , 0147 Energy en1 ,Energy en2 , 0148 Energy m1 ,Energy m2 , 0149 Energy2 s ,double charge , 0150 Energy emin) { 0151 return BtildeFF(beta1,ombeta1,beta2,ombeta2,en1,en2,m1,m2,s,charge,emin,false) 0152 +ReBFF(m1,m2,s,charge,false); 0153 } 0154 //@} 0155 0156 /** 0157 * Crude average multiplicities for initial-final and final-final dipoles 0158 */ 0159 //@{ 0160 /** Crude multiplicity for the final-final dipole 0161 * @param beta1 Velocity of the first charged particle, \f$\beta_1\f$ 0162 * @param beta2 Velocity of the second charged particle, \f$\beta_2\f$. 0163 * @param ombeta1 One minus the velocity of the first particle, \f$1-\beta_1\f$ 0164 * @param ombeta2 One minus the velocity of the second particle, \f$1-\beta_2\f$ 0165 * @param charge The product of the charges of the particles in the dipole 0166 * @param Emin The maximum energy for the integral 0167 * @param Emax The minimum energy for the integral 0168 * @param massterms Whether or not to include the mass terms 0169 */ 0170 static double nbarFF(double beta1, double ombeta1, 0171 double beta2, double ombeta2, 0172 double charge, 0173 Energy Emax , Energy Emin, 0174 bool massterms=false) { 0175 if(!massterms) 0176 return -_alpha/Constants::pi*charge* 0177 ((1.+beta1*beta2)/(beta1+beta2)*(+log((1.+beta1)/ombeta1) 0178 +log((1.+beta2)/ombeta2)))*log(Emax/Emin); 0179 else 0180 return -_alpha/Constants::pi*charge* 0181 ((1.+beta1*beta2)/(beta1+beta2)*(+log((1.+beta1)/ombeta1) 0182 +log((1.+beta2)/ombeta2))-2.)*log(Emax/Emin); 0183 } 0184 0185 /** 0186 * Crude multiplicity for the initial-final dipole 0187 * @param beta Velocity of the outgoing charged particle, \f$\beta\f$ 0188 * @param ombeta One minus the velocity of the outgoing charged particle, 0189 * \f$1-\beta\f$ 0190 * @param charge The product of the charges of the particles in the dipole 0191 * @param Emin The maximum energy for the integral 0192 * @param Emax The minimum energy for the integral 0193 * @param massterms Whether or not to include the mass terms 0194 */ 0195 //@} 0196 static double nbarIF(double beta, double ombeta, 0197 double charge, 0198 Energy Emax , Energy Emin, 0199 bool massterms=false) { 0200 if(!massterms) 0201 return -_alpha/Constants::pi*charge/beta* log((1.+beta)/ombeta) *log(Emax/Emin); 0202 else 0203 return -_alpha/Constants::pi*charge/beta*(log((1.+beta)/ombeta)-2.)*log(Emax/Emin); 0204 } 0205 0206 /** 0207 * The virtual piece for the initial-final and final-final dipoles 0208 */ 0209 //@{ 0210 /** 0211 * The \f$2\alpha\mathcal{R}B\f$ function for the initial-final dipole 0212 * @param m0 The mass of the incoming particle 0213 * @param m1 The mass of the outgoing particle 0214 * @param t The invariant mass of the charged particles 0215 * @param charge The product of the charges of the particles in the dipole 0216 * @param includegamma Include the photon mass terms 0217 * @param mgamma The photon mass, 0218 */ 0219 static double ReBIF(Energy m0 ,Energy m1 , Energy2 t , 0220 double charge ,bool includegamma=true, 0221 Energy mgamma=_mgamma); 0222 0223 /** 0224 * The \f$2\alpha\mathcal{R}B\f$ function for the final-final dipole 0225 * @param m1 The mass of the incoming particle 0226 * @param m2 The mass of the outgoing particle 0227 * @param s The invariant mass of the charged particles 0228 * @param charge The product of the charges of the particles in the dipole 0229 * @param includegamma Include the photon mass terms 0230 * @param mgamma The photon mass, 0231 */ 0232 static double ReBFF(Energy m1,Energy m2,Energy2 s,double charge, 0233 bool includegamma=true,Energy mgamma=_mgamma); 0234 //@} 0235 0236 /** 0237 * The real emission terms for initial-final and final-final dipoles 0238 */ 0239 //@{ 0240 /** 0241 * The \f$2\alpha\tilde{B}\f$ function for the initial-final dipole 0242 * @param beta0 Velocity of the incoming charged particle, \f$\beta_0\f$ 0243 * @param beta1 Velocity of the outgoing charged particle, \f$\beta_1\f$. 0244 * @param ombeta0 One minus the velocity of the incoming particle, \f$1-\beta_0\f$ 0245 * @param ombeta1 One minus the velocity of the outgoing particle, \f$1-\beta_1\f$ 0246 * @param en0 The energy of the incoming particle 0247 * @param en1 The energy of the outgoing particle 0248 * @param m0 The mass of the incoming particle 0249 * @param m1 The mass of the outgoing particle 0250 * @param t The invariant mass of the charged particles 0251 * @param charge The product of the charges of the particles in the dipole 0252 * @param emin The minimum photon energy 0253 * @param includegamma Include the photon mass terms 0254 * @param mgamma The photon mass, 0255 */ 0256 static double BtildeIF(double beta0 ,double ombeta0 , 0257 double beta1 ,double ombeta1 , 0258 Energy en0 ,Energy en1 , 0259 Energy m0 ,Energy m1 , 0260 Energy2 t ,double charge , 0261 Energy emin ,bool includegamma=true, 0262 Energy mgamma=_mgamma); 0263 0264 /** 0265 * The \f$2\alpha\tilde{B}\f$ function for the final-final dipole 0266 * @param beta1 Velocity of the first charged particle, \f$\beta_1\f$ 0267 * @param beta2 Velocity of the second charged particle, \f$\beta_2\f$. 0268 * @param ombeta1 One minus the velocity of the first particle, \f$1-\beta_1\f$ 0269 * @param ombeta2 One minus the velocity of the second particle, \f$1-\beta_2\f$ 0270 * @param en1 The energy of the first particle 0271 * @param en2 The energy of the second particle 0272 * @param m1 The mass of the first particle 0273 * @param m2 The mass of the second particle 0274 * @param s The invariant mass of the charged particles 0275 * @param charge The product of the charges of the particles in the dipole 0276 * @param emin The minimum photon energy 0277 * @param includegamma Include the photon mass terms 0278 * @param mgamma The photon mass, 0279 */ 0280 static double BtildeFF(double beta1 ,double ombeta1 , 0281 double beta2 ,double ombeta2 , 0282 Energy en1 ,Energy en2 , 0283 Energy m1 ,Energy m2 , 0284 Energy2 s ,double charge , 0285 Energy emin ,bool includegamma=true, 0286 Energy mgamma=_mgamma); 0287 //@} 0288 0289 /** 0290 * Access to the photon mass 0291 */ 0292 static Energy photonMass() {return _mgamma;} 0293 0294 private: 0295 0296 /** 0297 * Various special cases of the \f$A_4\f$ functions of hep-ph/0302065 for 0298 * the initial-final dipole 0299 */ 0300 //@{ 0301 /** 0302 * The \f$A_4\f$ function for the full final-final dipole 0303 * @param inen1 The energy of the first particle 0304 * @param inen2 The energy of the second particle 0305 * @param beta1 Velocity of the first particle, \f$\beta_1\f$ 0306 * @param beta2 Velocity of the second particle, \f$\beta_2\f$. 0307 * @param inm1 The mass of the first particle 0308 * @param inm2 The mass of the second particle 0309 * @param s The invariant mass of the charged particles 0310 */ 0311 static InvEnergy2 A4FFFull(Energy inen1 ,Energy inen2, 0312 double beta1,double beta2, 0313 Energy inm1 ,Energy inm2,Energy2 s ); 0314 0315 /** 0316 * The \f$A_4\f$ function of hep-ph0302065 using the special cases where 0317 * necessary for numerical stability 0318 * @param beta0 Velocity of the incoming charged particle, \f$\beta_0\f$ 0319 * @param beta1 Velocity of the outgoing charged particle, \f$\beta_1\f$. 0320 * @param ombeta0 One minus the velocity of the incoming particle, \f$1-\beta_0\f$ 0321 * @param ombeta1 One minus the velocity of the outgoing particle, \f$1-\beta_1\f$ 0322 * @param en0 The energy of the incoming particle 0323 * @param en1 The energy of the outgoing particle 0324 * @param m0 The mass of the incoming particle 0325 * @param m1 The mass of the outgoing particle 0326 * @param t The invariant mass of the charged particles 0327 */ 0328 static InvEnergy2 A4IF(double beta0 ,double ombeta0 , 0329 double beta1 ,double ombeta1 , 0330 Energy en0 ,Energy en1 , Energy m0 ,Energy m1 , 0331 Energy2 t); 0332 0333 /** 0334 * The \f$A_4\f$ function of hep-ph/0302065 for a single particle, without the \f$1/p^2\f$ 0335 * pre-factor 0336 */ 0337 static double A4single(double beta,double ombeta) { 0338 if(beta>0.01) return log(ombeta/(1.+beta))/beta; 0339 else return -2.-2./3.*sqr(beta)*(1+0.6*sqr(beta)); 0340 } 0341 0342 /** 0343 * The \f$A_4\f$ function of hep-ph/0302065 for the initial-final dipole with \f$t=0\f$ in the 0344 * rest frame. 0345 * @param m0 The mass of the incoming particle 0346 * @param m1 The mass of the outgoing particle 0347 */ 0348 static InvEnergy2 A4IFRestZero(Energy m0, Energy m1) { 0349 Energy2 mdiff(m0*m0-m1*m1); 0350 return -2./mdiff*(sqr(log(m0/m1))+Math::ReLi2(mdiff/sqr(m0))); 0351 } 0352 0353 /** 0354 * The \f$A_4\f$ function for the initial-final dipole with \f$t=0\f$. 0355 * @param beta0 Velocity of the incoming charged particle, \f$\beta_0\f$ 0356 * @param beta1 Velocity of the outgoing charged particle, \f$\beta_1\f$. 0357 * @param ombeta1 \f$1-\beta_1\f$ for the outgoing charged particle. 0358 * @param en0 The energy of the incoming particle 0359 * @param en1 The energy of the outgoing particle 0360 * @param m0 The mass of the incoming particle 0361 * @param m1 The mass of the outgoing particle 0362 */ 0363 static InvEnergy2 A4IFZero(double beta0, double beta1, 0364 double ombeta1, Energy en0, 0365 Energy en1 , Energy m0 , Energy m1); 0366 0367 /** 0368 * The \f$A_4\f$ function for the initial-final dipole in the rest frame of 0369 * the decaying particle 0370 * @param m0 The mass of the incoming particle 0371 * @param m1 The mass of the outgoing particle 0372 * @param beta1 The velocity of the decay product 0373 * @param ombeta1 \f$1-\beta\f$ for the decay product 0374 * @param E1 The energy of the outgoing particle 0375 */ 0376 static InvEnergy2 A4IFRest(Energy m0 ,Energy m1, double beta1, 0377 double ombeta1, Energy E1); 0378 0379 /** 0380 * The \f$A_4\f$ function for the full initial-final dipole 0381 * @param beta0 Velocity of the incoming charged particle, \f$\beta_0\f$ 0382 * @param beta1 Velocity of the outgoing charged particle, \f$\beta_1\f$. 0383 * @param en0 The energy of the incoming particle 0384 * @param en1 The energy of the outgoing particle 0385 * @param m0 The mass of the incoming particle 0386 * @param m1 The mass of the outgoing particle 0387 * @param t The invariant mass of the charged particles 0388 */ 0389 static InvEnergy2 A4IFFull(Velocity beta0,Velocity beta1, 0390 Energy en0 ,Energy en1 , 0391 Energy m0 ,Energy m1 , Energy2 t); 0392 //@} 0393 0394 /** 0395 * Functions from hep-ph/9606429 for the calculation of the \f$A_4\f$ functions 0396 */ 0397 //@{ 0398 /** 0399 * The function \f$Z_{ij}(\eta)\f$ from hep-ph/9606429 for the evaluation of the \f$A_4\f$ 0400 * function. 0401 * @param eta The value of \f$\eta\f$ 0402 * @param yi The value of \f$y_i\f$ 0403 * @param yj The value of \f$y_j\f$ 0404 */ 0405 template <typename T> 0406 static double Zij(T eta, T yi, T yj) { 0407 return 2.*Math::ReLi2((yj-yi)/(eta-yi))+0.5*sqr(log(abs((eta-yi)/(eta-yj)))); 0408 } 0409 0410 /** 0411 * The function \f$X^{ij}_{kl}(\eta)\f$ from hep-ph/9606429 for the evaluation of the \f$A_4\f$ 0412 * function. 0413 * @param eta The value of \f$\eta\f$ 0414 * @param yi The value of \f$y_i\f$ 0415 * @param yj The value of \f$y_j\f$ 0416 * @param yk The value of \f$y_k\f$ 0417 * @param yl The value of \f$y_l\f$ 0418 */ 0419 template <typename T> 0420 static double Xijkl(T eta,T yi, T yj, T yk, T yl) { 0421 return log(abs((eta-yi)*(eta-yj)/(eta-yk)/(eta-yl))); 0422 } 0423 //@} 0424 0425 }; 0426 0427 } 0428 0429 #endif /* HERWIG_YFSFormFactors_H */
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