New Detectors to Explore the Lifetime Frontier

Long-lived particles (LLPs) are a common feature in many beyond the Standard Model theories, including supersymmetry, and are generically produced in exotic Higgs decays. Unfortunately, no existing or proposed search strategy will be able to observe the decay of non-hadronic electrically neutral LLPs with masses above $\sim$ GeV and lifetimes near the limit set by Big Bang Nucleosynthesis (BBN), $c \tau \lesssim 10^7 - 10^8$~m. We propose the MATHUSLA surface detector concept (MAssive Timing Hodoscope for Ultra Stable neutraL pArticles), which can be implemented with existing technology and in time for the high luminosity LHC upgrade to find such ultra-long-lived particles (ULLPs), whether produced in exotic Higgs decays or more general production modes. We also advocate for a dedicated LLP detector at a future 100 TeV collider, where a modestly sized underground design can discover ULLPs with lifetimes at the BBN limit produced in sub-percent level exotic Higgs decays.Comment: 7 pages, 4 figures. Added more detail to discussion of backgrounds. Various minor clarifications. Results and conclusions unchange

Fermi Liquids and the Luttinger Integral

The Luttinger Theorem, which relates the electron density to the volume of the Fermi surface in an itinerant electron system, is taken to be one of the essential features of a Fermi liquid. The microscopic derivation of this result depends on the vanishing of a certain integral, the Luttinger integral $I_{\rm L}$, which is also the basis of the Friedel sum rule for impurity models, relating the impurity occupation number to the scattering phase shift of the conduction electrons. It is known that non-zero values of $I_{\rm L}$ with $I_{\rm L}=\pm\pi/2$, occur in impurity models in phases with non-analytic low energy scattering, classified as singular Fermi liquids. Here we show the same values, $I_{\rm L}=\pm\pi/2$, occur in an impurity model in phases with regular low energy Fermi liquid behavior. Consequently the Luttinger integral can be taken to characterize these phases, and the quantum critical points separating them interpreted as topological.Comment: 5 pages 7 figure

On the Surface Area of Scalene Cones and Other Conical Bodies

This paper first appeared in the Novi Commentarii academiae scientiarum Petropolitanae vol. 1, 1750, pp. 3-19 and is reprinted in the Opera Omnia: Series 1, Volume 27, pp. 181–199. Its Eneström number is E133. This translation and the Latin original are available from the Euler Archive

The Surface Area of a Scalene Cone as Solved by Varignon, Leibniz, and Euler

In a 1727 mathematical compendium, Pierre Varignon (1654-1722) published his solution to the problem of finding the surface area of a scalene (oblique) cone, one whose base is circular but whose vertex is off-center. The article after Varignon\u27s in that publication was by Gottfried Leibniz (1646-1716), who proposed improvements and even extended the solution to a base with any curve. When Leonhard Euler (1707-1783) published on the subject [E133] in 1750, he gently pointed out an error in Leibniz\u27s solution, which he corrected, after extending Varignon\u27s solution in the case of circular base. Euler then used Leibniz\u27s approach to solve the general problem. This paper examines all three articles, including English translations