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  1. Abstract Webs are planar graphs with boundary that describe morphisms in a diagrammatic representation category for $\mathfrak{sl}_k$. They are studied extensively by knot theorists because braiding maps provide a categorical way to express link diagrams in terms of webs, producing quantum invariants like the well-known Jones polynomial. One important question in representation theory is to identify the relationships between different bases; coefficients in the change-of-basis matrix often describe combinatorial, algebraic, or geometric quantities (e.g., Kazhdan–Lusztig polynomials). By ”flattening” the braiding maps, webs can also be viewed as the basis elements of a symmetric group representation. In this paper, we define two new combinatorial structures for webs: band diagrams and their one-dimensional projections, shadows, which measure depths of regions inside the web. As an application, we resolve an open conjecture that the change of basis between the so-called Specht basis and web basis of this symmetric group representation is unitriangular for $\mathfrak{sl}_3$-webs ([ 33] and [ 29].) We do this using band diagrams and shadows to construct a new partial order on webs that is a refinement of the usual partial order. In fact, we prove that for $\mathfrak{sl}_2$-webs, our new partial order coincides with the tableau partial order on webs studied by the authors and others [ 12, 17, 29, 33]. We also prove that though the new partial order for $\mathfrak{sl}_3$-webs is a refinement of the previously studied tableau order, the two partial orders do not agree for $\mathfrak{sl}_3$. 
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  2. Abstract

    Particles beyond the Standard Model (SM) can generically have lifetimes that are long compared to SM particles at the weak scale. When produced at experiments such as the Large Hadron Collider (LHC) at CERN, these long-lived particles (LLPs) can decay far from the interaction vertex of the primary proton–proton collision. Such LLP signatures are distinct from those of promptly decaying particles that are targeted by the majority of searches for new physics at the LHC, often requiring customized techniques to identify, for example, significantly displaced decay vertices, tracks with atypical properties, and short track segments. Given their non-standard nature, a comprehensive overview of LLP signatures at the LHC is beneficial to ensure that possible avenues of the discovery of new physics are not overlooked. Here we report on the joint work of a community of theorists and experimentalists with the ATLAS, CMS, and LHCb experiments—as well as those working on dedicated experiments such as MoEDAL, milliQan, MATHUSLA, CODEX-b, and FASER—to survey the current state of LLP searches at the LHC, and to chart a path for the development of LLP searches into the future, both in the upcoming Run 3 and at the high-luminosity LHC. The work is organized around the current and future potential capabilities of LHC experiments to generally discover new LLPs, and takes a signature-based approach to surveying classes of models that give rise to LLPs rather than emphasizing any particular theory motivation. We develop a set of simplified models; assess the coverage of current searches; document known, often unexpected backgrounds; explore the capabilities of proposed detector upgrades; provide recommendations for the presentation of search results; and look towards the newest frontiers, namely high-multiplicity ‘dark showers’, highlighting opportunities for expanding the LHC reach for these signals.

     
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  3. Abstract The semiconductor tracker (SCT) is one of the tracking systems for charged particles in the ATLAS detector. It consists of 4088 silicon strip sensor modules.During Run 2 (2015–2018) the Large Hadron Collider delivered an integrated luminosity of 156 fb -1 to the ATLAS experiment at a centre-of-mass proton-proton collision energy of 13 TeV. The instantaneous luminosity and pile-up conditions were far in excess of those assumed in the original design of the SCT detector.Due to improvements to the data acquisition system, the SCT operated stably throughout Run 2.It was available for 99.9% of the integrated luminosity and achieved a data-quality efficiency of 99.85%.Detailed studies have been made of the leakage current in SCT modules and the evolution of the full depletion voltage, which are used to study the impact of radiation damage to the modules. 
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