Next Generation Higgs Bosons: Theory, Constraints and Discovery Prospects at the Large Hadron Collider

Particle physics model building within the context of string theory suggests that further copies of the Higgs boson sector may be expected. Concerns regarding tree-level flavor changing neutral currents are easiest to allay if little or no couplings of next generation Higgs bosons are allowed to Standard Model fermions. We detail the resulting general Higgs potential and mass spectroscopy in both a Standard Model extension and a supersymmetric extension. We present the important experimental constraints from meson-meson mixing, loop-induced $b\to s\gamma$ decays and LEP2 direct production limits. We investigate the energy range of valid perturbation theory of these ideas. In the supersymmetric context we present a class of examples that marginally aids the fine-tuning problem for parameter space where the lightest Higgs boson mass is greater than the Standard Model limit of 114 GeV. Finally, we study collider physics signatures generic to next generation Higgs bosons, with special emphasis on $Ah\to hhZ\to 4b+2l$ signal events, and describe the capability of discovery at the Large Hadron Collider.Comment: 43 pages, 12 figures; v3: minor corrections, published in Physical Review

Non-Medical Prescription Pain Reliever Use as a Risk Factor for Suicidal Ideation

Research has shown a positive association between depression and non-medical prescription pain reliever use. Given the connection of depression to suicidality, the current research question evaluates non-medical prescription pain reliever use as an indicator of suicidal thought. Using the 2011 National Survey on Drug Use and Health, our analysis found that non-medical use of pain relievers increased the odds for suicidal ideation (O.R. = 2.36). Future research is needed to understand the mechanisms underlying this link. Potential mechanisms include substance induced depression and non-medical pain reliever use in the context of conditions such as chronic pain

Nondestructive Evaluation of Foam Insulation for the External Tank Return to Flight

Nondestructive evaluation methods have been developed to identify defects in the foam thermal protection system (TPS) of the Space Shuttle External Tank (ET). Terahertz imaging and backscatter radiography have been brought from prototype lab systems to production hardened inspection tools in just a few years. These methods have been demonstrated to be capable of detecting void type defects under many inches of foam which, if not repaired, could lead to detrimental foam loss. The evolution of these methods from lab tools to implementation on the ET will be discussed

Group of Homography in Real Projective Plane

Using the Mizar system [2], we formalized that homographies of the projective real plane (as defined in [5]), form a group. Then, we prove that, using the notations of Borsuk and Szmielew in [3] “Consider in space ℝℙ2 points P1, P2, P3, P4 of which three points are not collinear and points Q1,Q2,Q3,Q4 each three points of which are also not collinear. There exists one homography h of space ℝℙ2 such that h(Pi) = Qi for i = 1, 2, 3, 4. ”(Existence Statement 52 and Existence Statement 53) [3]. Or, using notations of Richter [11] “Let [a], [b], [c], [d] in ℝℙ2 be four points of which no three are collinear and let [a′],[b′],[c′],[d′] in ℝℙ2 be another four points of which no three are collinear, then there exists a 3 × 3 matrix M such that [Ma] = [a′], [Mb] = [b′], [Mc] = [c′], and [Md] = [d′] ”Makarios has formalized the same results in Isabelle/Isar (the collineations form a group, lemma statement52-existence and lemma statement 53-existence) and published it in Archive of Formal Proofs [10], [9].Rue de la Brasserie 5, 7100, La Louvière, BelgiumGrzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Grzegorz Bancerek, Czesław Bylinski, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pak, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261-279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1.Karol Borsuk and Wanda Szmielew. Foundations of Geometry. North Holland, 1960.Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.Roland Coghetto. Homography in RP2. Formalized Mathematics, 24(4):239-251, 2016.Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.Kanchun, Hiroshi Yamazaki, and Yatsuka Nakamura. Cross products and tripple vector products in 3-dimensional Euclidean space. Formalized Mathematics, 11(4):381-383, 2003.Wojciech Leończuk and Krzysztof Prazmowski. A construction of analytical projective space. Formalized Mathematics, 1(4):761-766, 1990.Timothy James McKenzie Makarios. The independence of Tarski’s Euclidean Axiom. Archive of Formal Proofs, October 2012.Timothy James McKenzie Makarios. A mechanical verification of the independence of Tarski’s Euclidean Axiom. Victoria University of Wellington, New Zealand, 2012. Master’s thesis.Jürgen Richter-Gebert. Perspectives on projective geometry: a guided tour through real and complex geometry. Springer Science & Business Media, 2011

Exact and Estimated Exact Tests Using the Rank Transform in Designed Experiments

Statistic