Elements of ∞-Category Theory

The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what exactly an ∞-category is requires various technical models, raising the question of how they might be compared. To overcome this, a model-independent approach is desired, so that theorems proven with any model would apply to them all. This text develops the theory of ∞-categories from first principles in a model-independent fashion using the axiomatic framework of an ∞-cosmos, the universe in which ∞-categories live as objects. An ∞-cosmos is a fertile setting for the formal category theory of ∞-categories, and in this way the foundational proofs in ∞-category theory closely resemble the classical foundations of ordinary category theory. Equipped with exercises and appendices with background material, this first introduction is meant for students and researchers who have a strong foundation in classical 1-category theory.

Dynamical Mass of the Young Substellar Companion HD 984 B

Model-independent masses of substellar companions are critical tools to validate models of planet and brown dwarf cooling, test their input physics, and determine the formation and evolution of these objects. In this work, we measure the dynamical mass and orbit of the young substellar companion HD 984 B. We obtained new high-contrast imaging of the HD 984 system with Keck/NIRC2 that expands the baseline of relative astrometry from 3 to 8 yr. We also present new radial velocities of the host star with the Habitable-Zone Planet Finder spectrograph at the Hobby-Eberly Telescope. Furthermore, HD 984 exhibits a significant proper motion difference between Hipparcos and Gaia EDR3. Our joint orbit fit of the relative astrometry, proper motions, and radial velocities yields a dynamical mass of 61 ± 4 M Jup for HD 984 B, placing the companion firmly in the brown dwarf regime. The new fit also reveals a higher eccentricity for the companion (e = 0.76 ± 0.05) compared to previous orbit fits. Given the broad age constraint for HD 984, this mass is consistent with predictions from evolutionary models. HD 984 B’s dynamical mass places it among a small but growing list of giant planet and brown dwarf companions with direct mass measurements.

Long-lived heavy neutral leptons at the LHC: four-fermion single-NR operators

Interest in searches for heavy neutral leptons (HNLs) at the LHC has increased considerably in the past few years. In the minimal scenario, HNLs are produced and decay via their mixing with active neutrinos in the Standard Model (SM) spectrum. However, many SM extensions with HNLs have been discussed in the literature, which sometimes change expectations for LHC sensitivities drastically. In the NRSMEFT, one extends the SM effective field theory with operators including SM singlet fermions, which allows to study HNL phenomenology in a “model independent” way. In this paper, we study the sensitivity of ATLAS to HNLs in the NRSMEFT for four-fermion operators with a single HNL. These operators might dominate both production and decay of HNLs, and we find that new physics scales in excess of 20 TeV could be probed at the high-luminosity LHC.

Electromagnetic finite-size effects beyond the point-like approximation

We present a model-independent and relativistic approach to analytically derive electromagnetic finite-size effects beyond the point-like approximation. The key element is the use of electromagnetic Ward identities to constrain vertex functions, and structure-dependence appears via physical form-factors and their derivatives. We apply our general method to study the leading finitesize structure-dependence in the pseudoscalar mass (at order 1/L3) as well as in the leptonic decay amplitudes of pions and kaons (at order 1/L2). Knowledge of the latter is essential for Standard Model precision tests in the flavour physics sector from lattice simulations.

Short-distance constraints for HLbL in muon g-2

Model-independent short-distance constraints allow for a reduction of theoretical uncertainties associated to the analytic evaluation of Hadronic Light-by-Light contributions to the muon g-2. In this talk we focus on the region where the three loop virtualities are large. Even when the fourth photon leg is soft, we show how a precise Operator Product Expansion can be applied in that region. The leading contribution is found to be given by the quark loop, while the evaluation of both gluonic and power corrections show how the expansion is well behaved at relatively low energies, where significant contributions to the muon g-2 remain. Numerical values for them are also presented.

Maximum latent heat of neutron star matter without GR

We show how the specific latent heat is relevant to characterize the first-order phase transitions in neutron stars. Our current knowledge of this dynamical quantity strongly depends on the uncertainty bands of Chiral Perturbation Theory and of pQCD calculations and can be used to diagnose progress on the equation of state. We state what is known to be hadron-model independent and without feedback from neutron star observations and, therefore, they can be used to test General Relativity as well as theories beyond GR, such as modified gravity.

Kaonic atoms measurements at the DAΦNE collider: the SIDDHARTA-2 experiment

The X-ray spectroscopy measurements of light kaonic atoms’ deexcitation towards the fundamental level provide unique information on the low-energy Quantum ChromoDynamics (QCD) in the strangeness sector, being a direct probe of the kaon/nucleon interaction at threshold, unobtainable through the scattering experiments. In this framework, the SIDDHARTA-2 collaboration is going to perform the first kaonic deuterium 2p → 1s transition measurement at the DAΦNE collider of Istituto Nazionale di Fisica Nucleare – Laboratori Nazionali di Frascati. Combining this measurement with the kaonic hydrogen one performed by SIDDHARTA in 2009 it will be possible to obtain, in a model-independent way, the isospin-dependent antikaon-nucleon scattering lengths. The paper introduces the SIDDHARTA-2 setup, an upgraded version with respect to the one used for the kaonic hydrogen measurement, dedicated to the ambitious kaonic deuterium measurement, together with the preliminary results obtained during the kaonic helium run, preparatory for the SIDDHARTA-2 data taking campaign.

Variants of Homomorphism Polynomials Complete for Algebraic Complexity Classes

We present polynomial families complete for the well-studied algebraic complexity classes VF, VBP, VP, and VNP. The polynomial families are based on the homomorphism polynomials studied in the recent works of Durand et al. (2014) and Mahajan et al. (2018). We consider three different variants of graph homomorphisms, namely injective homomorphisms , directed homomorphisms , and injective directed homomorphisms , and obtain polynomial families complete for VF, VBP, VP, and VNP under each one of these. The polynomial families have the following properties: • The polynomial families complete for VF, VBP, and VP are model independent, i.e., they do not use a particular instance of a formula, algebraic branching programs, or circuit for characterising VF, VBP, or VP, respectively. • All the polynomial families are hard under p -projections.