La scoperta del bosone di Higgs a LHC e la determinazione del valore della sua massa ha aperto la possibilità di studiare il Modello Standard (MS) fino ad alte energie, rendendo possibile la verifica della consistenza della teoria e del suo range di validità, dal momento che lo consideriamo come un modello effettivo. In questo scenario, facendo uso dei dati sperimentali più aggiornati, molto interesse è stato riposto nello studio della stabilità del vuoto elettrodebole del MS e le sue particolari implicazioni sia nella fisica delle particelle che, soprattutto, in cosmologia. Il nostro lavoro si inserisce in questo contesto con un doppio fine: da un lato, proviamo a raffinare i più recenti calcoli dei vincoli di stabilità, alla luce dei dati sperimentali e degli approcci teorici più aggiornati, soprattutto relativi alla tecnica del potenziale effettivo; mentre, dall'altro lato, usiamo i risultati di questa analisi per studiare e porre vincoli ad alcune realizzazioni di inflazione cosmica nel contesto del puro MS e di sue estensioni minime. In particolare, abbiamo studiato alcune osservabili \emph{gauge}-indipendenti legate a due configurazioni stazionarie del potenziale del MS, estrapolato ad alte energie grazie all'approccio che fa uso del potenziale effettivo e delle equazioni del gruppo di rinormalizzazione, nella loro forma più aggiornata, vale a dire il NNLO: il valore della massa del quark top in corrispondenza del quale si ha la stabilità dle vuoto elettrodebole (criticality) e il potenziale valutato nel suo punto di flesso. Dimostrata l'indipendenza dalla scelta del gauge di queste osservabili, sono state stimate le incertezze relative. Il primo risultato rilevante, in accordo con la letteratura (con qualche discrepanza), è che la stabilità assoluta del MS non è completamente esclusa, data l'attuale finestra sperimentale: è, in linea di principio, possibile assumere il MS valido fino alla scala di Planck, dove ci aspettiamo che l'interazione gravitazionale cominci a diventare rilevante, senza alcuna inclusione di nuova fisica a basse scale energetiche ("desert scenario"). Partendo da questo punto, abbiamo provato a spiegare la fase inflazionaria primordiale all'interno del puro MS, sfruttando la configurazione del punto di flesso. Tuttavia, mostriamo che diventa in questi casi molto difficile riprodurre gli attuali vincoli sul rapporto tensore/scalare. Vista la necessità di introdurre nuovi gradi di libertà per includere nella teoria un ragionevole meccanismo per l'inflazione cosmica e, in maniera consistente, una stabilizzazione per il potenziale del MS, proviamo a passare in rassegna le principali caratteristiche di una delle possibili estensioni minime al MS, attraverso una simmetria globale U(1)_B-L, e a porre dei vincoli ai parametri propri del nuovo modello, in maniera tale da riuscire a raggiungere entrambi gli obiettivi. Lo scalare extra associato alla rottura di questa nuova simmetria, oltre a garantire la stabilizzazione mediante un effetto di soglia al tree-level, sarebbe responsabile della generazione della massa di un neutrino right-handed, che, a sua volta, fornisce, attraverso il meccanismo see saw di tipo I, le masse dei neutrini di bassa energia. In questo contesto, troviamo la finestra dei parametri accessibile sia per una fase inflazionaria funzionale, guidata dallo stesso scalare massivo, che per la stabilizzazione del modello: confermiamo i risultati riportati in letteratura, nonostante i lavori rilevanti svolgono le loro analisi o in configurazioni leggermente differenti, oppure raffrontano i loro risultati con vincoli sperimentali più datati, giungendo poi dunque a conclusioni diverse. Ad ogni modo, facendo riferimento allo stato dell'arte attuale dal punto di vista sperimentale, questa semplice realizzazione di estensione con nuova fisica del MS sembra non essere sufficiente. Una applicazione allo scenario con accoppiamento non minimale viene anche considerata.

The discovery of the Higgs boson at LHC and the determination of its mass value have opened up the possibility to study the Standard Model (SM) up to very high energies, in order to probe the consistency of the theory and its range of validity, considering the model as an effective one. In this framework, equipped with the latest experimental data, a lot of interest has been devoted to the study of the stability of the SM electroweak vacuum and the peculiar implications both in particle physics and, mostly, in cosmology. Our work fits in this scenario with a two-fold aim: on one side, we try to refine the latest calculations of the stability bounds, in the light of the updated experimental data and the new theoretical approaches in the improved effective potential technique; while, on the other side, we take advantage of this analysis in order to investigate and constrain some realisation of the primordial inflationary phase within the pure SM and its some minimal extensions. In particular, we studied the gauge-independent observables related to two interesting stationary configurations of the SM potential, extrapolated up to high energies by means of the state-of-the-art RGE-improved effective potential approach, namely the Next-to-Next-to-Leading Order: the value of the top quark mass which ensures the electroweak vacuum stability (criticality) and the potential evaluated at the inflection point. Proved the gauge independence of these observables, there were estimated in detail the uncertainties related. The first main result, in agreement with the well-known literature (with some minor discrepancies), is that the SM absolute stability is not completely excluded, given the current experimental data: it is possible to assume the theory valid up to the Planck scale, at which we suppose that the gravitational interaction starts to be relevant, without any inclusion of new physics at low energy ("desert scenario"). Starting from this point, we tried to explain the inflationary phase embedded in a pure SM scenario, exploiting the inflection point configuration. However, we showed that it turns out to be impossible to reproduce the most recent bounds on the primordial tensor-to-scalar-ratio in the sight of SM inflection point models. Being necessary the introduction of new degrees of freedom, in order to include a reasonable inflationary expansion and, consistently, the stabilisation of the SM potential, we try to review the main features of a minimal extension of the SM, through a global U(1)_{B-L} symmetry and try to constrain its parameters so as to achieve both our goals. The extra scalar singlet associated with the breaking of this new symmetry, granting the stabilisation through an induced tree-level threshold effect, would be responsible of the generation of the right-handed neutrino mass, which in turn would provide, via the type I see-saw mechanism, the masses of the low-energy neutrinos. In this framework, we found the parameter window attainable for both a successfully inflationary phase, driven by the same heavy scalar, and the stabilisation of the model: we confirm the results reported in the literature, although the related works carry out the analysis in slightly different setups and often comparing the results to different experimental bounds, leading to different conclusions. However, the overall outcome is perfectly compatible: sticking with the current experimental state-of-the-art, this very simple realisation of new-physics extension of the SM seems to be insufficient, wth some troubles which arise if we try to achieve our initial tasks in one single shot. The other modification of the SM that we consider deals with the inclusion of a non-minimal coupling between the Higgs field, still playing the role of inflaton, and gravity. Here, we put some weak constraints on the tensor-to-scalar-ratio in the low-\xi parameter space, in order to evade the intrinsic unitarity issues of the model.

### Higgs connections: Electroweak Vacuum Stability and Cosmology

#### Abstract

The discovery of the Higgs boson at LHC and the determination of its mass value have opened up the possibility to study the Standard Model (SM) up to very high energies, in order to probe the consistency of the theory and its range of validity, considering the model as an effective one. In this framework, equipped with the latest experimental data, a lot of interest has been devoted to the study of the stability of the SM electroweak vacuum and the peculiar implications both in particle physics and, mostly, in cosmology. Our work fits in this scenario with a two-fold aim: on one side, we try to refine the latest calculations of the stability bounds, in the light of the updated experimental data and the new theoretical approaches in the improved effective potential technique; while, on the other side, we take advantage of this analysis in order to investigate and constrain some realisation of the primordial inflationary phase within the pure SM and its some minimal extensions. In particular, we studied the gauge-independent observables related to two interesting stationary configurations of the SM potential, extrapolated up to high energies by means of the state-of-the-art RGE-improved effective potential approach, namely the Next-to-Next-to-Leading Order: the value of the top quark mass which ensures the electroweak vacuum stability (criticality) and the potential evaluated at the inflection point. Proved the gauge independence of these observables, there were estimated in detail the uncertainties related. The first main result, in agreement with the well-known literature (with some minor discrepancies), is that the SM absolute stability is not completely excluded, given the current experimental data: it is possible to assume the theory valid up to the Planck scale, at which we suppose that the gravitational interaction starts to be relevant, without any inclusion of new physics at low energy ("desert scenario"). Starting from this point, we tried to explain the inflationary phase embedded in a pure SM scenario, exploiting the inflection point configuration. However, we showed that it turns out to be impossible to reproduce the most recent bounds on the primordial tensor-to-scalar-ratio in the sight of SM inflection point models. Being necessary the introduction of new degrees of freedom, in order to include a reasonable inflationary expansion and, consistently, the stabilisation of the SM potential, we try to review the main features of a minimal extension of the SM, through a global U(1)_{B-L} symmetry and try to constrain its parameters so as to achieve both our goals. The extra scalar singlet associated with the breaking of this new symmetry, granting the stabilisation through an induced tree-level threshold effect, would be responsible of the generation of the right-handed neutrino mass, which in turn would provide, via the type I see-saw mechanism, the masses of the low-energy neutrinos. In this framework, we found the parameter window attainable for both a successfully inflationary phase, driven by the same heavy scalar, and the stabilisation of the model: we confirm the results reported in the literature, although the related works carry out the analysis in slightly different setups and often comparing the results to different experimental bounds, leading to different conclusions. However, the overall outcome is perfectly compatible: sticking with the current experimental state-of-the-art, this very simple realisation of new-physics extension of the SM seems to be insufficient, wth some troubles which arise if we try to achieve our initial tasks in one single shot. The other modification of the SM that we consider deals with the inclusion of a non-minimal coupling between the Higgs field, still playing the role of inflaton, and gravity. Here, we put some weak constraints on the tensor-to-scalar-ratio in the low-\xi parameter space, in order to evade the intrinsic unitarity issues of the model.
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MASINA, Isabella
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Descrizione: Tesi dottorato Iacobellis Giuseppe
Tipologia: Tesi di dottorato
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2487829