Jet masses

The particles of an event may be divided into two classes. For each class a squared invariant mass may be calculated, $M_1^2$ and $M_2^2$. If the assignment of particles is adjusted such that the sum $M_1^2 + M_2^2$ is minimized, the two masses thus obtained are called heavy and light jet mass, $M_{\mathrm{H}}$ and $M_{\mathrm{L}}$. It has been shown that these quantities are well behaved in perturbation theory [Cla79]. In $\mathrm{e}^+\mathrm{e}^-$ annihilation, the heavy jet mass obtains a contribution from $\mathrm{q}\overline{\mathrm{q}}\mathrm{g}$ 3-jet events, whereas the light mass is non-vanishing only when 4-jet events also are included. In the c.m. frame of an event one has the limits $0 \leq M_{\mathrm{H}}^2 \leq E_{\mathrm{cm}}^2/3$.

In general, the subdivision of particles tends to be into two hemispheres, separated by a plane perpendicular to an event axis. As with thrust, it is time-consuming to find the exact solution. Different approximate strategies may therefore be used. In the program, the sphericity axis is used to perform a fast subdivision into two hemispheres, and thus into two preliminary jets. Thereafter one particle at a time is tested to determine whether the sum $M_1^2 + M_2^2$ would be decreased if that particle were to be assigned to the other jet. The procedure is stopped when no further significant change is obtained. Often the original assignment is retained as it is, i.e. the sphericity axis gives a good separation. This is not a full guarantee, since the program might get stuck in a local minimum which is not the global one.