int main()
{
// -- Declaring Cuba variables -- //
int comp, nregions, neval, fail;
cubareal integral[NCOMP], error[NCOMP], prob[NCOMP];
// -- ThreeBodyDecay initialization-- //
muon.SetMotherMPThetaPhi(M,muon_p,muon_theta,muon_phi);
muon.SetBitBoostBack(BitBoostBack);
// -- Set up pointers to the momenta
P = muon.P;
p1 = muon.p[0];
p2 = muon.p[1];
p3 = muon.p[2];
// -- Get muon kinematics
double P_gamma = P->Gamma();
double P_beta = P->Beta();
double P_M = P->M();
double P_MomMag = P->P();
// -- Polarization vector -- //
// -- Custom vector construction
k0_custom = TLorentzVector(1.0, 0.0, 0.0, 1.0);
// k0_custom = TLorentzVector(3, 2, 0.0, 1.0);
// k0_custom = TLorentzVector(1.0, 0.0, 0.0, 1.0);
double alpha = 1;
// -- Phyicsal vector construction
k0_physical[3] = 1;
for (int i = 0; i<3; i++)
{ k0_physical[i] = (*P)[i]/P_MomMag; }
for (int nu = 0; nu<4; nu++)
{ k0_physical[nu] = alpha*k0_physical[nu]/(P_M*P_gamma*(1+P_beta)); }
// -- Choosing k0 auxiliary vector
if ( k0_flag == 1)
{ k0 = k0_custom; }
if ( k0_flag == 2)
{ k0 = k0_physical; }
// Get pk0 scalar product
double Pk0 = P->Dot(k0);
// Custom spin polarization vector with p and k0
if (polvec_flag == 1)
{
for(int nu = 0; nu<4; nu++)
{ polvec[nu] = ( (*P)[nu]/M) - (M/Pk0)*k0[nu]; }
}
// Helicity spin ampltiude vector
// Note:
// This should be equivalent to the custom pol. vector
// when choosing physical k0
// Default:
if (polvec_flag == 2)
{
TVector3 phat(1.0,0.0,0.0);
phat.SetPhi(phat_phi);
phat.SetTheta(phat_theta);
polvec = TLorentzVector(phat,P->Beta());
for(int nu = 0; nu<4; nu++)
{ polvec[nu] = polvec[nu]*P_gamma; }
}
phat34 = TVector3(1.0,0.0,0.0);
phat34.SetPhi(phat34_phi);
phat34.SetTheta(phat34_theta);
polvec34 = TLorentzVector(phat34,0);
/////////////////////////////////////////////////////////////////////////
#if 1
printf("-------------------- Vegas test --------------------\n");
Vegas(NDIM, NCOMP, Integrand, USERDATA, NVEC,
EPSREL, EPSABS, VERBOSE, SEED,
MINEVAL, MAXEVAL, NSTART, NINCREASE, NBATCH,
GRIDNO, STATEFILE, SPIN,
&neval, &fail, integral, error, prob);
printf("VEGAS RESULT:\tneval %d\tfail %d\n",
neval, fail);
comp = 0;
printf("VEGAS RESULT:\t%.8f +- %.8f\tp = %.3f\n",
(double)integral[comp], (double)error[comp], (double)prob[comp]);
#endif
#if 0
printf("\n-------------------- Suave test --------------------\n");
Suave(NDIM, NCOMP, Integrand, USERDATA, NVEC,
EPSREL, EPSABS, VERBOSE | LAST, SEED,
MINEVAL, MAXEVAL, NNEW, NMIN, FLATNESS,
STATEFILE, SPIN,
&nregions, &neval, &fail, integral, error, prob);
printf("SUAVE RESULT:\tnregions %d\tneval %d\tfail %d\n",
nregions, neval, fail);
comp = 0;
printf("SUAVE RESULT:\t%.8f +- %.8f\tp = %.3f\n",
(double)integral[comp], (double)error[comp], (double)prob[comp]);
#endif
#if 0
printf("\n------------------- Divonne test -------------------\n");
Divonne(NDIM, NCOMP, Integrand, USERDATA, NVEC,
EPSREL, EPSABS, VERBOSE, SEED,
MINEVAL, MAXEVAL, KEY1, KEY2, KEY3, MAXPASS,
BORDER, MAXCHISQ, MINDEVIATION,
NGIVEN, LDXGIVEN, NULL, NEXTRA, NULL,
STATEFILE, SPIN,
&nregions, &neval, &fail, integral, error, prob);
printf("DIVONNE RESULT:\tnregions %d\tneval %d\tfail %d\n",
nregions, neval, fail);
for( comp = 0; comp < NCOMP; ++comp )
printf("DIVONNE RESULT:\t%.8f +- %.8f\tp = %.3f\n",
(double)integral[comp], (double)error[comp], (double)prob[comp]);
#endif
#if 0
printf("\n-------------------- Cuhre test --------------------\n");
Cuhre(NDIM, NCOMP, Integrand, USERDATA, NVEC,
EPSREL, EPSABS, VERBOSE | LAST,
MINEVAL, MAXEVAL, KEY,
STATEFILE, SPIN,
&nregions, &neval, &fail, integral, error, prob);
printf("CUHRE RESULT:\tnregions %d\tneval %d\tfail %d\n",
nregions, neval, fail);
for( comp = 0; comp < NCOMP; ++comp )
printf("CUHRE RESULT:\t%.8f +- %.8f\tp = %.3f\n",
(double)integral[comp], (double)error[comp], (double)prob[comp]);
#endif
double result = (double)integral[comp];
// If result is unpolarized divide by 2.0
if ( (ampltiude == 0) || (ampltiude == 34) )
{ result = result / 2.0;}
double PSConst = muon.GetPSConst();
double result_wogamma = result * PSConst * G_Fermi * G_Fermi / M / 2.0 ;
result = result * PSConst * G_Fermi * G_Fermi / P->E() / 2.0 ;
double ratio_formula = result/gamma_formula;
double ratio_PDG = result/gamma_PDG;
double tau = hbar/result;
double ctau = tau*c;
double tau_wogamma = hbar/result_wogamma;
double ctau_wogamma = tau_wogamma*c;
// -- Displaying info -- //
printf("\n");
printf("###############################################\n");
printf("### --- Muon decay lifetime calculation --- ###\n");
printf("###############################################\n");
printf("\n");
printf("--------------------------\n");
printf("--- Physical constants ---\n");
printf("--------------------------\n");
printf("\n");
printf("hbar: %12.6e [GeV s]\n", hbar);
printf("c: %12.6e [m/s]\n", c);
printf("hbar*c: %12.6e [GeV fm]\n", hbar_c);
printf("G_Fermi: %12.6e [GeV^{-2}]\n", G_Fermi);
printf("\n");
printf("Muon constants:\n");
printf("m (muon): %12.6f [GeV]\n", M);
printf("c_tau: %12.6e [fm]\n", c_tau_muon);
printf("Gamma(PDG) = hbarc/c_tau = %12.6e [GeV]\n", gamma_PDG);
printf("\n");
printf("Other masses:\n");
printf("m (elec): %12.6f [GeV]\n", m1);
printf("m (nu_e): %12.6f [GeV]\n", m2);
printf("m (nu_m): %12.6f [GeV]\n", m3);
printf("\n");
printf("-------------------------\n");
printf("--- Decay process ---\n");
printf("-------------------------\n");
printf("\n");
printf("(muon)- ---> (electron)- (nu_mu) (nu_electronbar)\n");
printf(" p ---> q k k' \n");
printf(" p ---> q k1 k2 \n");
printf(" P ---> p1 p2 p3 \n");
printf("\n");
printf("-------------------------\n");
printf("--- Configuration ---\n");
printf("-------------------------\n");
printf("\n");
printf("############\n");
printf("### Muon ###\n");
printf("############\n");
printf("\n");
printf("|mom|: %12.6f [GeV/c]\n", muon_p);
printf("theta: %12.6f [rad]\n", muon_theta);
printf("phi: %12.6f [rad]\n", muon_phi);
printf("gamma: %12.6f \n", P->Gamma());
printf("beta: %12.6f \n", P->Beta());
printf("\n");
printf("Momentum:\n");
displayTLorentzVector(P);
printf("\n");
printf("Unitvector pointing in the direction of momentum:\n");
printf("x: %12.6f\n", (*P)[0]/P->P());
printf("y: %12.6f\n", (*P)[1]/P->P());
printf("z: %12.6f\n", (*P)[1]/P->P());
printf("\n");
printf("################################\n");
printf("### Spin Polarization vector ###\n");
printf("################################\n");
printf("### - Denoted by s^{mu} \n");
printf("\n");
if ( (ampltiude == -1) || (ampltiude == 0) || (ampltiude == 1) )
{
if ( polvec_flag == 1 )
{
printf("polvec_flag: %d\n", polvec_flag);
printf("Spin polarization defined with auxiliary vector k0:\n");
printf("s^{mu} = P^{mu}/M - (m/Pk0)*k0^{mu}\n");
printf("\n");
printf("k0_flag: %d\n", k0_flag);
if ( k0_flag == 1 )
{ printf("Custom k0:\n"); }
if ( k0_flag == 2 )
{
printf("Choice of k0, yielding helicity polarization vector.\n");
printf("Physical k0:\n");
}
displayTLorentzVector(&k0);
printf("\n");
}
if ( polvec_flag == 2 )
{
printf("polvec_flag: %d\n", polvec_flag);
printf("Spin polarization vector = helicity polarization vector\n");
printf("s^{mu} = ( |pvec|^2 , p0 pvec) / (m |pvec|)) = \n");
printf(" = gamma (beta,phat vector)\n");
printf("\n");
}
printf("Spin polarization vector components:\n");
displayTLorentzVector(&polvec);
}
if ( (ampltiude == 3) || (ampltiude == 4) || (ampltiude == 34) )
{
printf("Spin polarization vector defined in rest frame of the muon\n");
printf("s^{mu} = (0,phat34)\n");
printf("\n");
printf("where the phat34 is pointing towards:\n");
printf("phat34 theta: %12.6f\n", phat34_theta);
printf("phat34 phi: %12.6f\n", phat34_phi);
printf("\n");
printf("phat34 components:\n");
printf("x: %12.6f\n", phat34[0]);
printf("y: %12.6f\n", phat34[1]);
printf("z: %12.6f\n", phat34[2]);
}
printf("\n");
printf("--------------------------\n");
printf("--- Consistency checks ---\n");
printf("--------------------------\n");
printf("\n");
printf("- Lorentz scalar product (ps) = 0 (orthogonality check)\n");
printf("(ps): %12.6e (should give really small value)\n", (*P)*polvec);
printf("\n");
printf("- k0^{2} = 0 (massless auxuliary vector)\n");
printf("(k0)^2: %12.6e (should give really small value)\n", k0.M2());
printf("\n");
printf("------------------\n");
printf("--- Ampltidude ---\n");
printf("------------------\n");
printf("\n");
printf("Amplitude formula chosen: ---> %d <--- \n", ampltiude);
printf("\n");
printf("Amplitude formula list:\n");
printf("(No): ---------------------- Formula ---------------------------- (polarization)\n");
printf("- Default case: \n");
printf(" (0): 128 * (p k') * (q k) (unpolarized)\n");
printf("(-1): 64 * (p k') * (q k) + 64 * M * (s k') * (q k) (polarized)\n");
printf("(+1): 64 * (p k') * (q k) - 64 * M * (s k') * (q k) (polarized)\n");
printf("- Custom: \n");
printf(" (+3): 64 * gamma * ( 1 - beta ) * (M * (k')^{0}) * (q k) - (polarized)\n");
printf(" -64 * gamma * ( 1 - beta ) * M * (s k') * (q k) \n");
printf(" (+4): 64 * gamma * ( 1 + beta ) * (M * (k')^{0}) * (q k) + (polarized)\n");
printf(" +64 * gamma * ( 1 + beta ) * M * (s k') * (q k) \n");
printf("(+34): sum of (+3) and (+4) (unpolarized)\n");
printf("\n");
printf("Notations:\n");
printf("(muon)- ---> (electron)- (nu_mu) (nu_electronbar)\n");
printf(" p ---> q k k' \n");
printf(" p ---> q k1 k2 \n");
printf(" P ---> p1 p2 p3 \n");
printf("\n");
printf("Leftover factors multiplying the result:\n");
printf("- Coupling constant\n");
printf(" G_Fermi^{2}\n");
printf("- Initial particle state normalization:\n");
printf(" 1.0/(2*E) = 1.0/2*M (in the rest frame)\n");
printf("- Spin averaging for the muon (only if unpolarized):\n");
printf(" 1.0/2.0\n");
printf("\n");
printf("ThreeBodyDecay class\n");
printf("PSConstant (formula) s23_length/pow(M_PI,3.0)/128.0\n");
printf("PSConstant (numval): %12.6e \n", PSConst);
printf("\n");
printf("---------------------------\n");
printf("--- Other formulas used ---\n");
printf("---------------------------\n");
printf("\n");
printf("Textbook result of the integration:\n");
printf("Gamma: G_Fermi^{2}*m_mu^{5}/(192*pi^{3})\n");
printf("\n");
printf("tau = hbar/Gamma\n");
printf("ctau = c*tau\n");
printf("\n");
printf("-------------------------\n");
printf("--- Numerical results ---\n");
printf("-------------------------\n");
printf("Don't forget: our result are quoted in the LAB frame, while the PDG and\n");
printf(" the textbook formula are calculated in the muon rest frame!\n");
printf("\n");
printf("# Important flags:\n", ampltiude);
printf("- k0_type: %d (see above at 'Spin polarization', 1 = custom, 2 = physical)\n", k0_flag);
printf("- spin_polarization: %d (see above at 'Spin polarization', 1 = computed with k0, 2 = helicity)\n", polvec_flag);
printf("- Amplitude formula chosen: %d (see above at 'Amplitude' )\n", ampltiude);
printf("\n");
printf("Note: Choosing (k0_type = 2) and (spin_polarization = 1) should give the same result as\n");
printf(" choosing (spin_polarization = 2) by definition\n");
printf("\n");
printf("Gamma(PDG): %12.6e [GeV] (note: this is the total gamma!)\n", gamma_PDG);
printf("Gamma(textbook): %12.6e [GeV]\n", gamma_formula);
printf("Gamma(our result w/o gamma factor): %12.6e [GeV]\n", result_wogamma);
printf("Gamma(our result): %12.6e [GeV]\n", result);
printf("\n");
printf("ctau(PDG): %12.6e [m]\n", c_tau_muon*1e-15);
printf("ctau(textbook): %12.6e [m]\n", ctau_formula*1e-15);
printf("ctau(our result w/o gamma factor): %12.6e [m]\n", ctau_wogamma);
printf("ctau(our result): %12.6e [m]\n", ctau);
printf("\n");
printf("# Muon configuration\n");
printf("beta: %12.6f\n", P->Beta());
printf("gamma: %12.6f <-\n", P->Gamma());
printf("\n");
printf("# Ratios\n");
printf("ratio of ctau's: (our result)/(textbook rest frame) %12.6f <-\n", ctau/ctau_formula/1e-15);
printf("ratio of the above two values: %12.6f\n", P->Gamma()/(ctau/ctau_formula/1e-15));
printf("\n");
printf("Note: You should compare the values of 'gamma' with the 'ratio of ctau's',\n");
printf(" as they should be equal.\n");
printf(" The 'ratio of the above two values' gives a measure how well they agree.\n");
printf(" It should be close to unity, but there could be some tiny deviation as\n");
printf(" this is after all a numerical integration.\n");
printf("\n");
printf("VEGAS RESULT:\t%.8f +- %.8f\tp = %.3f\n",
(double)integral[comp], (double)error[comp], (double)prob[comp]);
return 0;
}
