When the backwards evolution of initial-state radiation traces the prehistory to hard interactions, two partons participating in two separate hard scatterings may turn out to have a common ancestor, joined interactions (JI).
The joined interactions are well-known in the context of the evolution of multiparton densities [Kon79], but have not been applied to a multiple-interactions framework. A full implementation of the complete kinematics, intertwining MI, ISR and JI all possible ways, is a major undertaking, worth the effort only if the expected effects are non-negligible. Given the many uncertainties in all the other processes at play, one would otherwise expect that the general tuning of MI/ISR/FSR/...to data would hide the effects of JI.
The current program can simulate the joining term in the evolution equations, and thereby estimate how often and at what values joinings should occur. However, the actual kinematics has not been worked out, so the suggested joinings are never performed. Instead the evolution is continued as if nothing had happened. Therefore this facility is more for general guidance than for detailed studies.
To see how it works, define the two-parton density
as the probability to have a parton
at energy fraction and a parton at energy fraction
when the proton is probed at a scale . The evolution equation for
this distribution is
Rewriting this into a backwards-evolution probability, the last term