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Federica Piazza

Publications and source records attributed to Federica Piazza.

5 recordsLinked to original sources

On actions and split extensions in varieties of hoops: the case of strong section

The aim of this article is to investigate internal actions and split extensions in the variety of hoops. We provide a characterization of split extensions with strong section in terms of strong external actions. Beyond the general setting of hoops, the study is extended to the subvarieties of basic hoops, Wajsberg hoops, G\"odel hoops and product hoops. Within the setting of basic hoops and their bounded counterparts, BL-algebras, the double negation yields a significant example of split extension with strong section, thus motivating our approach. A connection between strong external actions of hoops and the semidirect product construction introduced by W. Rump in the cateogory of L-algebras is established.

math.CT

Coherent and ideal actions in ideally exact categories

In the context of ideally exact categories, we introduce the notions of internal coherent action and internal ideal action that generalise different aspects of unital actions of rings and algebras. We prove that every ideal action is coherent, and that the converse statement holds in some relevant ideally exact contexts. Furthermore, a connection with G. Janelidze's notion of semidirect product in ideally exact categories is analysed.

math.CT

On the representability of actions of unital algebras

Working in the setting of ideally exact categories, we investigate the representability of actions of unital non-associative algebras over a field. We show that, in general, such categories fail to be action representable: for instance, the category of all unital algebras is not even action accessible. We then consider this problem in the context of operadic, action accessible, unit-closed varieties. Using the construction of the external weak actor, we prove that for any algebra $X$ in such a variety $\mathsf{V}$, the canonical map into its external weak actor is an isomorphism if and only if $X$ is unital. Consequently, the ideally exact category $\mathsf{V}_1$ of unital algebras in $\mathsf{V}$ is action representable, and the actor of $X$ is $X$ itself. Finally, we prove action representability for unital Poisson algebras via an explicit construction of the universal strict general actor.

math.CT

A flexible and efficient approach for missing transverse momentum reconstruction

Missing transverse momentum is a crucial observable for physics at hadron colliders, being the only constraint on the kinematics of "invisible" objects such as neutrinos and hypothetical dark matter particles. Computing missing transverse momentum at the highest possible precision, particularly in experiments at the energy frontier, can be a challenging procedure due to ambiguities in the distribution of energy and momentum between many reconstructed particle candidates. This paper describes a novel solution for efficiently encoding information required for the computation of missing transverse momentum given arbitrary selection criteria for the constituent reconstructed objects. Pileup suppression using information from both the calorimeter and the inner detector is an integral component of the reconstruction procedure. Energy calibration and systematic variations are naturally supported. Following this strategy, the ATLAS Collaboration has been able to optimise the use of missing transverse momentum in diverse analyses throughout Runs 2 and 3 of the Large Hadron Collider and for future analyses.

hep-ex

Displaying dark matter constraints from colliders with varying simplified model parameters

The search for dark matter is one of the main science drivers of the particle and astroparticle physics communities. Determining the nature of dark matter will require a broad approach, with a range of experiments pursuing different experimental hypotheses. Within this search program, collider experiments provide insights on dark matter which are complementary to direct/indirect detection experiments and to astrophysical evidence. To compare results from a wide variety of experiments, a common theoretical framework is required. The ATLAS and CMS experiments have adopted a set of simplified models which introduce two new particles, a dark matter particle and a mediator, and whose interaction strengths are set by the couplings of the mediator. So far, the presentation of LHC and future hadron collider results has focused on four benchmark scenarios with specific coupling values within these simplified models. In this work, we describe ways to extend those four benchmark scenarios to arbitrary couplings, and release the corresponding code for use in further studies. This will allow for more straightforward comparison of collider searches to accelerator experiments that are sensitive to smaller couplings, such as those for the US Community Study on the Future of Particle Physics (Snowmass 2021), and will give a more complete picture of the coupling dependence of dark matter collider searches when compared to direct and indirect detection searches. By using semi-analytical methods to rescale collider limits, we drastically reduce the computing resources needed relative to traditional approaches based on the generation of additional simulated signal samples.

hep-ph