In this tutorial we demonstrate RVec helpers for physics computations such as angle differences $\Delta \phi$, the distance in the $\eta$-$\phi$ plane $\Delta R$ and the invariant mass.
Author: Stefan Wunsch
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Wednesday, July 16, 2025 at 05:09 AM.
The DeltaPhi helper computes the closest angle between angles. This means that the resulting value is in the range [-pi, pi].
Note that the helper also supports to compute the angle difference of an RVec and a scalar and two scalars. In addition, the computation of the difference and the behaviour at the boundary can be adjusted to radian and degrees.
ROOT::RVecF phis = {0.0, 1.0, -0.5, M_PI + 1.0};
auto idx = Combinations(phis, 2);
auto phi1 = Take(phis, idx[0]);
auto phi2 = Take(phis, idx[1]);
auto dphi = DeltaPhi(phi1, phi2);
std::cout << "DeltaPhi(phi1 = " << phi1 << ",\n"
<< " phi2 = " << phi2 << ")\n"
<< " = " << dphi << "\n";
input_line_47:3:12: error: cannot deduce 'auto' from unknown expression
auto idx = Combinations(phis, 2);
^
The DeltaR helper is similar to the DeltaPhi helper and computes the distance in the $\eta$-$\phi$ plane.
ROOT::RVecF etas = {2.4, -1.5, 1.0, 0.0};
auto eta1 = Take(etas, idx[0]);
auto eta2 = Take(etas, idx[1]);
auto dr = DeltaR(eta1, eta2, phi1, phi2);
std::cout << "\nDeltaR(eta1 = " << eta1 << ",\n"
<< " eta2 = " << eta2 << ",\n"
<< " phi1 = " << phi1 << ",\n"
<< " phi2 = " << phi2 << ")\n"
<< " = " << dr << "\n";
input_line_56:4:13: error: cannot deduce 'auto' from unknown expression
auto eta1 = Take(etas, idx[0]);
^
The InvariantMasses helper computes the invariant mass of a two particle system given the properties transverse momentum (pt), rapidity (eta), azimuth (phi) and mass.
ROOT::RVecF pt3 = {40, 20, 30};
ROOT::RVecF eta3 = {2.5, 0.5, -1.0};
ROOT::RVecF phi3 = {-0.5, 0.0, 1.0};
ROOT::RVecF mass3 = {10, 10, 10};
ROOT::RVecF pt4 = {20, 10, 40};
ROOT::RVecF eta4 = {0.5, -0.5, 1.0};
ROOT::RVecF phi4 = {0.0, 1.0, -1.0};
ROOT::RVecF mass4 = {2, 2, 2};
auto invMass = InvariantMasses(pt3, eta3, phi3, mass3, pt4, eta4, phi4, mass4);
std::cout << "\nInvariantMass(pt1 = " << pt3 << ",\n"
<< " eta1 = " << eta3 << ",\n"
<< " phi1 = " << phi3 << ",\n"
<< " mass1 = " << mass3 << ",\n"
<< " pt2 = " << pt4 << ",\n"
<< " eta2 = " << eta4 << ",\n"
<< " phi2 = " << phi4 << ",\n"
<< " mass2 = " << mass4 << ")\n"
<< " = " << invMass << "\n";
input_line_57:12:16: error: cannot deduce 'auto' from unknown expression
auto invMass = InvariantMasses(pt3, eta3, phi3, mass3, pt4, eta4, phi4, mass4);
^
The InvariantMass helper also accepts a single set of (pt, eta, phi, mass) vectors. Then, the invariant mass of all particles in the collection is computed.
auto invMass2 = InvariantMass(pt3, eta3, phi3, mass3);
std::cout << "\nInvariantMass(pt = " << pt3 << ",\n"
<< " eta = " << eta3 << ",\n"
<< " phi = " << phi3 << ",\n"
<< " mass = " << mass3 << ")\n"
<< " = " << invMass2 << "\n";
input_line_58:2:18: error: cannot deduce 'auto' from unknown expression
auto invMass2 = InvariantMass(pt3, eta3, phi3, mass3);
^