Investigating Multiple Solutions in the Constrained Minimal Supersymmetric Standard Model

Recent work has shown that the Constrained Minimal Supersymmetric Standard Model (CMSSM) can possess several distinct solutions for certain values of its parameters. The extra solutions were not previously found by public supersymmetric spectrum generators because fixed point iteration (the algorithm used by the generators) is unstable in the neighbourhood of these solutions. The existence of the additional solutions calls into question the robustness of exclusion limits derived from collider experiments and cosmological observations upon the CMSSM, because limits were only placed on one of the solutions. Here, we map the CMSSM by exploring its multi-dimensional parameter space using the shooting method, which is not subject to the stability issues which can plague fixed point iteration. We are able to find multiple solutions where in all previous literature only one was found. The multiple solutions are of two distinct classes. One class, close to the border of bad electroweak symmetry breaking, is disfavoured by LEP2 searches for neutralinos and charginos. The other class has sparticles that are heavy enough to evade the LEP2 bounds. Chargino masses may differ by up to around 10% between the different solutions, whereas other sparticle masses differ at the sub-percent level. The prediction for the dark matter relic density can vary by a hundred percent or more between the different solutions, so analyses employing the dark matter constraint are incomplete without their inclusion.Comment: 30 pages, 12 figures, 2 tables; v2: added discussion on speed of shooting method, fixed typos, matches published versio

Identification of nonlinearity in conductivity equation via Dirichlet-to-Neumann map

We prove that the linear term and quadratic nonlinear term entering a nonlinear elliptic equation of divergence type can be uniquely identified by the Dirichlet to Neuman map. The unique identifiability is proved using the complex geometrical optics solutions and singular solutions

Formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential

For the Schrodinger equation at fixed energy with a potential supported in a bounded domain we give formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential. For the case of zero background potential these results were obtained in [R.G.Novikov, Multidimensional inverse spectral problem for the equation -\Delta\psi+(v(x)-Eu(x))\psi=0, Funkt. Anal. i Ego Prilozhen 22(4), pp.11-22, (1988)]

A convergent algorithm for the hybrid problem of reconstructing conductivity from minimal interior data

We consider the hybrid problem of reconstructing the isotropic electric conductivity of a body $\Omega$ from interior Current Density Imaging data obtainable using MRI measurements. We only require knowledge of the magnitude $|J|$ of one current generated by a given voltage $f$ on the boundary $\partial\Omega$. As previously shown, the corresponding voltage potential u in $\Omega$ is a minimizer of the weighted least gradient problem $$u=\hbox{argmin} \{\int_{\Omega}a(x)|\nabla u|: u \in H^{1}(\Omega), \ \ u|_{\partial \Omega}=f\},$$ with $a(x)= |J(x)|$. In this paper we present an alternating split Bregman algorithm for treating such least gradient problems, for $a\in L^2(\Omega)$ non-negative and $f\in H^{1/2}(\partial \Omega)$. We give a detailed convergence proof by focusing to a large extent on the dual problem. This leads naturally to the alternating split Bregman algorithm. The dual problem also turns out to yield a novel method to recover the full vector field $J$ from knowledge of its magnitude, and of the voltage $f$ on the boundary. We then present several numerical experiments that illustrate the convergence behavior of the proposed algorithm

Statistical Patterns of Theory Uncertainties

A comprehensive uncertainty estimation is vital for the precision program of the LHC. While experimental uncertainties are often described by stochastic processes and well-defined nuisance parameters, theoretical uncertainties lack such a description. We study uncertainty estimates for cross-section predictions based on scale variations across a large set of processes. We find patterns similar to a stochastic origin, with accurate uncertainties for processes mediated by the strong force, but a systematic underestimate for electroweak processes. We propose an improved scheme, based on the scale variation of reference processes, which reduces outliers in the mapping from leading order to next-to-leading-order in perturbation theory.Comment: UCI-HEP-TH-2022-2

Arsenic: A Roadblock to Potential Animal Waste Management Solutions

The localization and intensification of the poultry industry over the past 50 years have incidentally created a largely ignored environmental management crisis. As a result of these changes in poultry production, concentrated animal feeding operations (CAFOs) produce far more waste than can be managed by land disposal within the regions where it is produced. As a result, alternative waste management practices are currently being implemented, including incineration and pelletization of waste. However, organic arsenicals used in poultry feed are converted to inorganic arsenicals in poultry waste, limiting the feasibility of waste management alternatives. The presence of inorganic arsenic in incinerator ash and pelletized waste sold as fertilizer creates opportunities for population exposures that did not previously exist. The removal of arsenic from animal feed is a critical step toward safe poultry waste management

Full-wave invisibility of active devices at all frequencies

There has recently been considerable interest in the possibility, both theoretical and practical, of invisibility (or "cloaking") from observation by electromagnetic (EM) waves. Here, we prove invisibility, with respect to solutions of the Helmholtz and Maxwell's equations, for several constructions of cloaking devices. Previous results have either been on the level of ray tracing [Le,PSS] or at zero frequency [GLU2,GLU3], but recent numerical [CPSSP] and experimental [SMJCPSS] work has provided evidence for invisibility at frequency $k\ne 0$. We give two basic constructions for cloaking a region $D$ contained in a domain $\Omega$ from measurements of Cauchy data of waves at \p \Omega; we pay particular attention to cloaking not just a passive object, but an active device within $D$, interpreted as a collection of sources and sinks or an internal current.Comment: Final revision; to appear in Commun. in Math. Physic