A search for leptoquark signals is performed in final states with a hadronically decaying τ -lepton and missing transverse momentum, using data from proton–proton collisions at a centre-of-mass energy of s = 13 TeV recorded by the ATLAS detector at the Large Hadron Collider during Run 2 (2015–18), corresponding to an integrated luminosity of 140 fb − 1 . The analysis is designed to probe both resonant production and non-resonant t -channel exchange of the leptoquark, covering a wide range of coupling scenarios. No excess above the Standard Model background prediction is observed. Limits are set on the couplings in the benchmark U 1 vector-leptoquark model at 95% confidence level for masses between 1.5 TeV and 3.0 TeV.
In the perturbative formulation of the Hamiltonian of quadratic gravity, a specific gauge condition is required to hold the equivalence of the Hamiltonian equations of motion with the covariant field equations. Here we give robust evidence that this is an effect of perturbations, the exact nonperturbative equations of both formulations are equivalent, with no need of specific gauge conditions. Despite this, the required gauge condition must be imposed in the perturbative approach. We use it, together with other conditions obtained on very broad grounds, to obtain the quantum Lagrangian resulting from the integration on the canonical variables of the BFV quantization of the theory. This allow us to characterize the quantum modes from the Lagrangian perspective.
We demonstrate that the leading IR-renormalon divergence in the perturbative pole mass of a massive quark resides entirely in the contribution from the trace anomaly of the energy-momentum tensor in QCD. Consequently, the recently proposed trace-anomaly-subtracted σ -mass definition for heavy quarks is not only scheme- and scale-invariant, hence unique for each flavor, but also free from the leading IR-renormalon ambiguity. We further derive a formula connecting this σ -mass to the perturbative pole mass, solely in terms of the QCD β -function, quark-mass anomalous dimension γ m and a proper rewritten form of the pole-to- MS ‾ mass conversion factor. Utilizing this formula together with the ingredients available in the literature, we present the explicit five-loop result for the perturbative relationship between the σ -mass and the perturbative pole mass in QCD under the approximation of keeping only a single quark massive. Furthermore, we outline how σ -mass for a heavy quark can in principle be determined from lattice QCD through an intermediate regularization-independent renormalization and continuum perturbative matching, for which we analyze the matching factor through four loops with appealing features revealed. Given the aforementioned theoretical merits of this mass definition and the availability of high-precision conversion relations as well as the feasibility of direct extraction from lattice QCD, it is well suited for acting as a promising candidate reference scheme for comparing or combining quark masses of the same flavor obtained in different schemes.
