double EW_ABC::Mw(const bool bAlternative) const
{
if (!bAlternative)
return NPE.Mw_eps(eps1(), eps2(), eps3());
else {
double delta_alpha = (NPE.alphaMz() - 1.0 / 128.90) / NPE.getAle();
double cW2_Born = 0.768905 * (1.0 - 0.40 * delta_alpha);
double cW2 = cW2_Born * (1.0 + 1.43 * eps1() - 1.00 * eps2() - 0.86 * eps3());
return ( sqrt(cW2) * NPE.getMz());
}
}
double EW_ABC::R_b(const bool bAlternative) const
{
if (!bAlternative)
return ( Gamma_b() / Gamma_had());
else {
double R_b0 = 0.2182355;
return ( R_b0 * (1.0 - 0.06 * eps1() + 0.07 * eps3() + 1.79 * epsb()));
}
}
double EW_ABC::R_l(const bool bAlternative) const
{
if (!bAlternative)
return ( Gamma_had() / Gamma_l(NPE.ELECTRON));
else {
double delta_als = (NPE.Als(NPE.getMz(), FULLNNLO) - 0.119) / M_PI;
double delta_alpha = (NPE.alphaMz() - 1.0 / 128.90) / NPE.getAle();
double R_0 = 20.8228 * (1.0 + 1.05 * delta_als - 0.28 * delta_alpha);
return ( R_0 * (1.0 + 0.28 * eps1() - 0.36 * eps3() + 0.50 * epsb()));
}
}
double EW_ABC::AFB_l(StandardModel::lepton l, const bool bAlternative) const
{
if (!bAlternative) {
double x = gVl_over_gAl(l).real();
return ( 3.0 * x * x / (1.0 + x * x) / (1.0 + x * x));
} else {
double delta_als = (NPE.Als(NPE.getMz(), FULLNNLO) - 0.119) / M_PI;
double AFB_l_Born = 0.01696 * (1.0 - 34.0 * delta_als);
return ( AFB_l_Born * (1.0 + 34.72 * eps1() - 45.15 * eps3()));
}
}
double EW_ABC::sin2thetaEff(const bool bAlternative) const
{
if (!bAlternative) {
double x = gVl_over_gAl(NPE.ELECTRON).real();
return ( (1.0 - x) / 4.0);
} else {
double delta_als = (NPE.Als(NPE.getMz(), FULLNNLO) - 0.119) / M_PI;
double x0 = 0.075619 - 1.32 * delta_als;
double x = x0 * (1.0 + 17.6 * eps1() - 22.9 * eps3());
return ( (1.0 - x) / 4.0);
}
}
double EW_ABC::A_l(StandardModel::lepton l, const bool bAlternative) const
{
if (!bAlternative) {
double x = gVl_over_gAl(l).real();
return ( 2.0 * x / (1.0 + x * x));
} else {
double delta_alpha = (NPE.alphaMz() - 1.0 / 128.90) / NPE.getAle();
double x0 = 0.075619 - 1.32 * delta_alpha;
double x = x0 * (1.0 + 17.6 * eps1() - 22.9 * eps3());
return ( 2.0 * x / (1.0 + x * x));
}
}
double EW_ABC::sigma0_had(const bool bAlternative) const
{
if (!bAlternative)
return ( 12.0 * M_PI / NPE.getMz() / NPE.getMz()
* Gamma_l(NPE.ELECTRON) * Gamma_had()
/ GammaZ(false) / GammaZ(false));
else {
double delta_als = (NPE.Als(NPE.getMz(), FULLNNLO) - 0.119) / M_PI;
double delta_alpha = (NPE.alphaMz() - 1.0 / 128.90) / NPE.getAle();
double sigma_h0 = 41.420 * (1.0 - 0.41 * delta_als + 0.03 * delta_alpha);
return ( sigma_h0 * (1.0 - 0.03 * eps1() + 0.04 * eps3() - 0.20 * epsb()));
}
}
double EW_ABC::GammaZ(const bool bAlternative) const
{
if (!bAlternative)
return ( Gamma_l(NPE.NEUTRINO_1) + Gamma_l(NPE.NEUTRINO_2)
+ Gamma_l(NPE.NEUTRINO_3) + Gamma_l(NPE.ELECTRON)
+ Gamma_l(NPE.MU) + Gamma_l(NPE.TAU)
+ Gamma_had());
else {
double delta_als = (NPE.Als(NPE.getMz(), FULLNNLO) - 0.119) / M_PI;
double delta_alpha = (NPE.alphaMz() - 1.0 / 128.90) / NPE.getAle();
double Gamma_T0 = 2.48946 * (1.0 + 0.73 * delta_als - 0.35 * delta_alpha);
return ( Gamma_T0 * (1.0 + 1.35 * eps1() - 0.46 * eps3() + 0.35 * epsb()));
}
}
gslpp::complex EW_ABC::gVb() const
{
return NPE.gV_f_eps(NPE.getQuarks(NPE.BOTTOM), eps1(), eps3(), epsb());
}
gslpp::complex EW_ABC::gVq(QCD::quark q) const
{
if (q == QCD::BOTTOM || q == QCD::TOP)
throw std::runtime_error("Error in EW_ABC::gVq()");
return NPE.gV_f_eps(NPE.getQuarks(q), eps1(), eps3());
}
gslpp::complex EW_ABC::gVl(StandardModel::lepton l) const
{
return NPE.gV_f_eps(NPE.getLeptons(l), eps1(), eps3());
}
void pbsolver(Mat<>& eps, Mat<>& phi, Mat<>& bgf, double dcel, double tol, int iter){
size_t nx = eps.nx(), ny = eps.ny(), nz = eps.nz();
double dx = comdata.deltax, dy = comdata.deltay, dz = comdata.deltaz;
Mat<> eps1(nx,ny,nz), eps2(nx,ny,nz), eps3(nx,ny,nz);
for(size_t i=1; i<nx; ++i){
for(size_t j=1; j<ny; ++j){
for(size_t k=1; k<nz; ++k){
eps1(i,j,k) = (eps(i+1,j,k) + eps(i,j,k))/2.0;
eps2(i,j,k) = (eps(i,j+1,k) + eps(i,j,k))/2.0;
eps3(i,j,k) = (eps(i,j,k+1) + eps(i,j,k))/2.0;
}}}
std::vector< Eigen::Triplet<double> > tripletList;
tripletList.reserve(nx*ny*nz);
Eigen::VectorXd phi_flat(nx*ny*nz);
size_t n = nx*ny*nz;
for(size_t i=1; i<=nx; ++i){
for(size_t j=1; j<=ny; ++j){
for(size_t k=1; k<=nz; ++k){
size_t ijk = (i-1)*nz*ny + (j-1)*nz + k-1;
if(i==1 || i==nx || j==1 || j==ny || k==1 || k==nz){
tripletList.push_back( Eigen::Triplet<double>(ijk, ijk, 1.0) );
}else{
double f = -( (eps1(i,j,k) + eps1(i-1,j,k))/dx/dx
+ (eps2(i,j,k) + eps2(i,j-1,k))/dy/dy
+ (eps3(i,j,k) + eps3(i,j,k-1))/dz/dz );
tripletList.push_back( Eigen::Triplet<double>(ijk, ijk, f) );
double weit[6];
weit[0] = eps1(i-1,j,k)/dx/dx;
weit[1] = eps2(i,j-1,k)/dy/dy;
weit[2] = eps3(i,j,k-1)/dz/dz;
weit[3] = eps3(i,j,k)/dz/dz;
weit[4] = eps2(i,j,k)/dy/dy;
weit[5] = eps1(i,j,k)/dx/dx;
size_t jj = ijk - nz*ny;
if(jj>=0){ tripletList.push_back( Eigen::Triplet<double>(ijk, jj, weit[0]) ); }
jj = ijk - nz;
if(jj>=0){ tripletList.push_back( Eigen::Triplet<double>(ijk, jj, weit[1]) ); }
jj = ijk - 1;
if(jj>=0){ tripletList.push_back( Eigen::Triplet<double>(ijk, jj, weit[2]) ); }
jj = ijk + 1;
if(jj<n){ tripletList.push_back( Eigen::Triplet<double>(ijk, jj, weit[3]) ); }
jj = ijk + nz;
if(jj<n){ tripletList.push_back( Eigen::Triplet<double>(ijk, jj, weit[4]) ); }
jj = ijk + nz*ny;
if(jj<n){ tripletList.push_back( Eigen::Triplet<double>(ijk, jj, weit[5]) ); }
}
phi_flat(ijk) = phi(i,j,k);
}}}
Eigen::SparseMatrix<double> A(n, n);
A.setFromTriplets(tripletList.begin(), tripletList.end());
A.makeCompressed();
Eigen::BiCGSTAB<Eigen::SparseMatrix<double>, Eigen::IdentityPreconditioner > solver(A);
solver.setMaxIterations(iter);
solver.setTolerance(tol);
phi_flat = solver.solveWithGuess(bgf.baseInterface(), phi_flat);
for(size_t i=1; i<=nx; ++i){
for(size_t j=1; j<=ny; ++j){
for(size_t k=1; k<=nz; ++k){
size_t ijk = (i-1)*nz*ny + (j-1)*nz + k-1;
phi(i,j,k) = phi_flat(ijk);
}}}
}