Threshold resummation for Drell-Yan production: theory and phenomenology

We present a phenomenological study of Drell-Yan pair production at hadron colliders based on the NNLO fixed order calculation and on NNLL resummation of threshold logarithms. We give an argument to prove that resummation effects are relevant also for values of x=M^2/s far from threshold. We compare different prescriptions for the calculation of resummed quantities, emphasizing the differences coming from subleading terms, which are important when x is small. We present phenomenological predictions for Drell-Yan rapidity distributions at the LHC, we study the ambiguity related to the resummation prescription, and we compare it to that coming from scale variation.Comment: 6 pages, 3 figure

Small-xx phenomenology at the LHC and beyond: HELL 3.0 and the case of the Higgs cross section

Small-$x$ resummation has been proven recently to be a crucial ingredient for describing small-$x$ HERA data, and the inclusion of small-$x$ resummation in parton distribution function (PDF) determination has a sizeable effect on the PDFs even at the electroweak scale. In this work we explore the implications of small-$x$ resummation at the Large Hadron Collider (LHC) and at a Future Circular Collider (FCC). We construct the theoretical machinery for resumming physical inclusive observables at hadron colliders, and describe its implementation in the public code HELL 3.0. We focus on Higgs production in gluon fusion as a prototypical example, both because it is sensitive to small-$x$ gluons and because of its importance for the LHC physics programme. We find that adding small-$x$ resummation to the N$^3$LO Higgs production cross section can lead to an increase of up to 10% at FCC, while the effect is smaller (+1%) at LHC but still important to achieve a high level of precision.Comment: 42 pages, 8 figures. Added new Fig 6 and some discussions. Final version published in EPJ

Small-xx resummation from HELL

Small-$x$ logarithmic enhancements arising from high-energy gluon emissions affect both the evolution of collinearly-factorized parton densities and partonic coefficient functions. With the higher collider energy reached by the LHC, the prospect of a future high-energy collider, and the recent deep-inelastic scattering (DIS) results at small-$x$ from HERA, providing phenomenological tools for performing small-$x$ resummation has become of great relevance. In this paper we discuss a framework to perform small-$x$ resummation for both parton evolution and partonic coefficient functions and we describe its implementation in a computer code named High-Energy Large Logarithms (HELL). We present resummed and matched results for the DGLAP splitting functions and, as a proof of principle, for the massless structure functions in DIS.Comment: Version accepted by EPJ C. 26 pages, 7 figures. Section 2.4 largely re-written. Added estimate of theoretical uncertainty and comparison to CCS

Resummation and Matching of bb-quark Mass Effects in bbˉHb\bar{b}H Production

We use a systematic effective field theory setup to derive the $b\bar{b}H$ production cross section. Our result combines the merits of both fixed 4-flavor and 5-flavor schemes. It contains the full 4-flavor result, including the exact dependence on the $b$-quark mass, and improves it with a resummation of collinear logarithms of $m_b/m_H$. In the massless limit, it corresponds to a reorganized 5-flavor result. While we focus on $b\bar{b}H$ production, our method applies to generic heavy-quark initiated processes at hadron colliders. Our setup resembles the variable flavor number schemes known from heavy-flavor production in deep-inelastic scattering, but also differs in some key aspects. Most importantly, the effective $b$-quark PDF appears as part of the perturbative expansion of the final result where it effectively counts as an $O(\alpha_s)$ object. The transition between the fixed-order (4-flavor) and resummation (5-flavor) regimes is governed by the low matching scale at which the $b$-quark is integrated out. Varying this scale provides a systematic way to assess the perturbative uncertainties associated with the resummation and matching procedure and reduces by going to higher orders. We discuss the practical implementation and present numerical results for the $b\bar{b}H$ production cross section at NLO+NLL. We also provide a comparison to the corresponding predictions in the fixed 4-flavor and 5-flavor results and the Santander matching prescription. Compared to the latter, we find a slightly reduced uncertainty and a larger central value, with its central value lying at the lower edge of our uncertainty band.Comment: 54 pages, 16 figures. Final version to be published in JHEP (one ref added

The threshold region for Higgs production in gluon fusion

We provide a quantitative determination of the effective partonic kinematics for Higgs production in gluon fusion in terms of the collider energy at the LHC. We use the result to assess, as a function of the Higgs mass, whether the large top mass approximation is adequate and whether Sudakov resummation is advantageous. We argue that our results hold to all perturbative orders. Based on it, we conclude that the full inclusion of finite top mass corrections is likely to be important for accurate phenomenology for a light Higgs with m_H ~ 125 GeV at the LHC with sqrt{s} = 14 TeV.Comment: 5 pages, 3 figures. Refs 9 and 15 added, several small textual improvements. Final version, to be published in Physical Review Letter

Top Quark Pair Production beyond NNLO

We construct an approximate expression for the total cross section for the production of a heavy quark-antiquark pair in hadronic collisions at next-to-next-to-next-to-leading order (N$^3$LO) in $\alpha_s$. We use a technique which exploits the analyticity of the Mellin space cross section, and the information on its singularity structure coming from large N (soft gluon, Sudakov) and small N (high energy, BFKL) all order resummations, previously introduced and used in the case of Higgs production. We validate our method by comparing to available exact results up to NNLO. We find that N$^3$LO corrections increase the predicted top pair cross section at the LHC by about 4% over the NNLO.Comment: 34 pages, 9 figures; final version, to be published in JHEP; reference added, minor improvement

Efficient modelling and simulation techniques for energy related system level studies in buildings

Ad oggi, è stato ampiamente riconosciuto che il consumo energetico su scala globale dipende in larga parte dal consumo degli edifici. E' stato anche osservato che il loro consumo possa essere notevolmente ridotto agendo in due direzioni principali: l'utilizzo di materiali più efficienti dal punto di vista energetico, migliorare le tecniche di costruzione, i dispositivi per la climatizzazione, eccetera; mentre la seconda, prevede l'adozione di politiche per il controllo e gestione dell'energia. All'interno dello scenario esposto, la tesi si occupa dello sviluppo di modelli e di paradigmi modellistici che siano in grado di supportare il difficile problema della progettazione di edifici (o raggruppamenti di essi) al alta efficienza energetica; senza precludere la ristrutturazione ed il miglioramento dell'esistente. Una caratteristica distintiva del lavoro è che nonostante si parli di edifici, in realtà l'analisi si rivolge anche agli impianti contenuti al loro interno. Questo aspetto rende i risultati ottenuti applicabili anche ad altri contesti. E' importante sottolineare che uno dei limiti principali nella progettazione (o eventuali riprogettazioni) degli edifici ad elevata efficienza energetica, è la complessità dell'edificio inteso come sistema, le cui performance sono determinate dalle interazioni dei svariati sottosistemi che lo compongono. Pertanto, la progettazione di un sistema così complesso ed eterogeneo, per essere efficace deve essere supportata da strumenti informatici. Per questo motivo, negli ultimi 50 anni sono stati sviluppati molti software per la simulazione delle performance energetiche degli edifici, e molti di questi sono ancora in uso all'interno della comunità dei progettisti. Tuttavia, molti esperti si chiedono se questi strumenti saranno in grado di affrontare le nuove sfide in modo efficace. Negli ultimi anni, nuove tecniche per la modellistica e simulazione hanno preso piede in molti ambiti sia nel campo scientifico che industriale. L'obiettivo della tesi è di sfruttare i principi delle tecniche sopracitate in modo da fornire dei modelli -- e più in astratto metodologie modellistiche -- che siano in grado di risolvere i principali problemi dei software per la simulazione dei consumi energetici degli edifici. Pertanto, i contributi di questo lavoro sono riassunti in seguito. (i) Mostrare come integrare in un unico framework problemi che altrimenti richiederebbero l'ausilio di diversi strumenti di simulazione, a svantaggio della simulazione d'insieme dell'edificio. Le idee proposte sono esemplificate mostrando come integrare uno dei punti più critici, la simulazione dell'aria all'interno di grandi spazi. (ii) Le stesse idee, sebbene applicate in un contesto completamente diverso, si dimostrano in grado di rappresentare in modo realistico i sistemi di controllo. Infatti, le performance energetiche potrebbero essere migliorate significativamente se i sistemi di controllo fossero accuratamente ottimizzati. Tuttavia, l'ottimizzazione risulta impossibile solo se l'edificio ed il sistema di controllo possono essere simulati contemporaneamente. (iii) I principi della modellistica Object-Oriented sono stati sfruttati per la realizzazione di modelli aventi diversi livelli di dettaglio. Tali modelli permettono l'adattamento del modello di simulazione a una qualsiasi delle fasi di progetto, concentrandosi sulla parte in questione e semplificando le altre. E' evidente che la possibilità di adattare il livello di dettaglio dei modelli porti grandi benefici al flusso di progettazione, presentandosi come uno strumento in grado di seguirne il ciclo completo. (iv) Le idee presentate nella tesi sono state supportate da molte applicazioni e simulazioni che esemplificano l'utilizzo delle tecniche proposte, evidenziandone l'applicabilità ed il potenziale.It is universally acknowledged that buildings contribute to a very significant extent to the world energy demand. It is also recognised that said contribution can be dramatically reduced by acting along two main directions: to employ better materials, construction techniques, climatisation devices, lighting, appliances, while the second is to adopt improved control and energy management policies. In such a scenario, this dissertation deals with the definition and realisation of a modelling and simulation paradigm suitable for supporting all the steps of so complex a problem as the design of a new energy efficient building or neighbourhood, and also the refurbishment of an existing one in a view to reducing its energy footprint. As an important peculiarity of the work, it is to be noticed that despite the presented research is said to refer to ``buildings'' for brevity, in fact the installed plants are considered as well. This makes the obtained results applicable also in other domains. In this respect, it is worth noticing right from the beginning that one of the most significant barriers to energy efficient building (re)design is that buildings are complex systems, the energy performance of which is affected by the interaction of several parts and phenomena. The design of such complex and heterogeneous systems apparently needs to be supported by computer aided tools. In fact, during the past 50 years, a wide variety of building energy simulation programs have been developed, and some are nowadays commonly in use throughout the building energy community. However, many experts wonder if these tools will be able to address the future needs in an effective way. In recent years, new modelling and simulation techniques have gained interest in the scientific and professional communities of a variety of fields. The aim of this work is to exploit these techniques so as to provide models, and modelling methodologies, to overcome the main shortcomings of the Energy and Building Performance Simulation tools presently available. As such, the contribution of this dissertation can be summarised as follows. (i) It is shown how to use OOMS to represent in a unitary framework phenomena that would otherwise call for different simulation and analysis tools, to the detriment of a coordinated and whole-system, approach. The proposed general ideas are exemplified by addressing and solving (among others) maybe the toughest problem of this type, i.e., the modelling and simulation of large air volumes. (ii) The same ideas, though differently declined, are shown to be capable of accommodating for a reliable representation of control systems. In fact, if properly optimised can provide significant energy performance improvements, but such an optimisation is hardly possible if the building and its controls cannot be represented and simulated jointly. (iii) The principles of OOMS are exploited so as to allow for models of scalable detail level, which permits to tailor the simulation model complexity to any particular study at hand, concentrating on the relevant parts of the system and employing simple - thus computationally fast - descriptions of the rest. It is worth noticing that the possibility of scaling the detail level is highly beneficial also in a view to have the simulation tool follow the entire life cycle of a project. (iv) Several simulation studies are proposed and discussed, to better explain the presented ideas and to show their actualDIPARTIMENTO DI ELETTRONICA, INFORMAZIONE E BIOINGEGNERIA25SCATTOLINI, RICCARDOFIORINI, CARLO ETTOR