Stabilization of Unstable Procedures: The Recursive Projection Method

Fixed-point iterative procedures for solving nonlinear parameter dependent problems can converge for some interval of parameter values and diverge as the parameter changes. The Recursive Projection Method (RPM), which stabilizes such procedures by computing a projection onto the unstable subspace is presented. On this subspace a Newton or special Newton iteration is performed, and the fixed-point iteration is used on the complement. As continuation in the parameter proceeds, the projection is efficiently updated, possibly increasing or decreasing the dimension of the unstable subspace. The method is extremely effective when the dimension of the unstable subspace is small compared to the dimension of the system. Convergence proofs are given and pseudo-arclength continuation on the unstable subspace is introduced to allow continuation past folds. Examples are presented for an important application of the RPM in which a “black-box” time integration scheme is stabilized, enabling it to compute unstable steady states. The RPM can also be used to accelerate iterative procedures when slow convergence is due to a few slowly decaying modes

Modified Higgs couplings and unitarity violation

Prompted by the recent observation of a Higgs-like particle at the CERN Large Hadron Collider (LHC), we investigate a quantitative correlation between possible departures of the gauge and Yukawa couplings of this particle from their Standard Model expectations and the scale of unitarity violation in the processes $WW \to WW$ and $t\bar t \to WW$.Comment: 6 pages, 6 eps figures, Arrayeq.sty attached; v2: minor updates, version published: PRD 87 (2013) 011702(R), Rapid Communicatio

Scalar sector properties of two-Higgs-doublet models with a global U(1) symmetry

We analyze the scalar sector properties of a general class of two-Higgs-doublet models which has a global U(1) symmetry in the quartic terms. We find constraints on the parameters of the potential from the considerations of unitarity of scattering amplitudes, the global stability of the potential and the $\rho$-parameter. We concentrate on the spectrum of the non-standard scalar masses in the decoupling limit which is preferred by the Higgs data at the LHC. We exhibit charged-Higgs induced contributions to the diphoton decay width of the 125\,GeV Higgs boson and its correlation with the corresponding $Z\gamma$ width.Comment: 12 pages, 15 eps figure files; minor modifications made and a few references adde

New constraints on R-parity violation from proton stability

We derive stringent upper bounds on all the $(\lambda''_{ijk} \mu_l)$-type combinations from the consideration of proton stability, where $\lambda''_{ijk}$ are baryon-number-violating trilinear couplings and $\mu_l$ are lepton-number-violating bilinear mass parameters in a R-parity-violating supersymmetric theory.Comment: 4 pages, Latex, uses axodraw.sty (in the revised version all combinations of the form $\lambda"_{ijk}\mu_l$ have been constrained, using one-loop graphs) To appear in Phys. Lett.

Parallel hybrid textures of lepton mass matrices

We analyse the parallel hybrid texture structures in the charged lepton and the neutrino sector. These parallel hybrid texture structures have physical implications as they cannot be obtained from arbitrary lepton mass matrices through weak basis transformations. The total sixty parallel hybrid texture structures can be grouped into twelve classes, and all the hybrid textures in the same class have identical physical implications. We examine all the twelve classes under the assumption of non-factorizable phases in the neutrino mass matrix. Five out of the total twelve classes are found to be phenomenologically disallowed. We study the phenomenological implications of the allowed classes for 1-3 mixing angle, Majorana and Dirac-type $CP$ violating phases. Interesting constraints on effective Majorana mass are obtained for all the allowed classes.Comment: Physical Review D (To appear