PurposeLeksell Gamma Knife® is a stereotactic radiosurgery system that allows fine‐grained control of the delivered dose distribution. We describe a new inverse planning approach that both resolves shortcomings of earlier approaches and unlocks new capabilities.MethodsWe fix the isocenter positions and perform sector‐duration optimization using linear programming, and study the effect of beam‐on time penalization on the trade‐off between beam‐on time and plan quality. We also describe two techniques that reduce the problem size and thus further reduce the solution time: dualization and representative subsampling.ResultsThe beam‐on time penalization reduces the beam‐on time by a factor 2–3 compared with the naïve alternative. Dualization and representative subsampling each leads to optimization time‐savings by a factor 5–20. Overall, we find in a comparison with 75 clinical plans that we can always find plans with similar coverage and better selectivity and beam‐on time. In 44 of these, we can even find a plan that also has better gradient index. On a standard GammaPlan workstation, the optimization times ranged from 2.3 to 26 s with a median time of 5.7 s.ConclusionWe present a combination of techniques that enables sector‐duration optimization in a clinically feasible time frame.

We study the general Zee model, which includes an extra Higgs scalar doublet and a new singly-charged scalar singlet. Neutrino masses are generated at one-loop level, and in order to describe leptonic mixing, both the Standard Model and the extra Higgs scalar doublets need to couple to leptons (in a type-III two-Higgs doublet model), which necessarily generates large lepton flavor violating signals, also in Higgs decays. Imposing all relevant phenomenological constraints and performing a full numerical scan of the parameter space, we find that both normal and inverted neutrino mass orderings can be fitted, although the latter is disfavored with respect to the former. In fact, inverted ordering can only be accommodated if θ 23 turns out to be in the first octant. A branching ratio for h → τ µ of up to 10 −2 is allowed, but it could be as low as 10 −6 . In addition, if future expected sensitivities of τ → µγ are achieved, normal ordering can be almost completely tested. Also, µe conversion is expected to probe large parts of the parameter space, excluding completely inverted ordering if no signal is observed. Furthermore, non-standard neutrino interactions are found to be smaller than 10 −6 , which is well below future experimental sensitivity. Finally, the results of our scan indicate that the masses of the additional scalars have to be below 2.5 TeV, and typically they are lower than that and therefore within the reach of the LHC and future colliders.

We investigate the renormalization group evolution of fermion masses, mixings and quartic scalar Higgs self-couplings in an extended non-supersymmetric SO(10) model, where the Higgs sector contains the 10 H , 120 H , and 126 H representations. The group SO(10) is spontaneously broken at the GUT scale to the Pati-Salam group and subsequently to the Standard Model (SM) at an intermediate scale M I . We explicitly take into account the effects of the change of gauge groups in the evolution. In particular, we derive the renormalization group equations for the different Yukawa couplings. We find that the computed physical fermion observables can be successfully matched to the experimental measured values at the electroweak scale. Using the same Yukawa couplings at the GUT scale, the measured values of the fermion observables cannot be reproduced with a SM-like evolution, leading to differences in the numerical values up to around 80%. Furthermore, a similar evolution can be performed for a minimal SO(10) model, where the Higgs sector consists of the 10 H and 126 H representations only, showing an equally good potential to describe the low-energy fermion observables. Finally, for both the extended and the minimal SO(10) models, we present predictions for the three Dirac and Majorana CPviolating phases as well as three effective neutrino mass parameters.