The Standard Model (SM) of particle physics provides the theoretical framework to describe the fundamental interactions among elementary constituents of matter. SM is supported by experiments to a high degree of accuracy, up to parts per-mil for the electroweak (EW) sector and parts-per-trillion for QED alone, but it still remains incomplete. Many observed phenomena lack explanation in the framework of the SM and its particles. They indicate the possibility of existence of particles and interactions beyond the SM (BSM). These phenomena include dark matter (DM), dark energy and baryonic asymmetry of the universe. In addition, a quantum description of gravity is still lacking. The top quark has the largest mass among the SM particles. Due to it’s heavy mass, top quark is the only colored particle which does not hadronize and hence its properties are directly accessible by studying it’s decay particles. The order one Yukawa coupling of the top quark also imbibes it with an important role in the behavior of the SM couplings at higher energy scales where possible BSM physics may contribute. As a result, precision measurements of top quark properties may provide a glimpse into BSM physics and hence making these measurements is one of the core aims of the Large Hadron Collider. In stark contrast with top quark physics is the elusive, dark matter (DM) of the universe. There exists a lot of observational evidence for it but, as of yet, with no clue with regards to its particle properties and interactions. Compelling evidence for the existence of DM comes from measurements based on cosmic microwave background radiation, astrophysical observations of distribution of visible matter in galaxy clusters, galactic cluster collisions (e.g. bullet cluster), gravitational lensing, galactic rotation curves, structure formation simulations, to name a few. It is interesting to investigate the possibility that there may be a connection between top quark and DM. In this thesis, we extend the SM with simplified models to study BSM physics at colliders and also to explain the DM puzzle. Here, we use the Top quark as a laboratory for constructing generic probes of BSM and also of the dark sector physics. In Chapter 1, we introduce some relevant background and salient aspects of the SM framework on which the following BSM theories are built. In Chapter 2 we explore an s channel and a t-channel simplified model in the context of top quark pair production using asymmetries constructed with kinematic variables of the top decay products. In Chapter 3, we then propose a simplified model which includes a colored scalar as the mediator between DM and SM particles, termed gluphillic scalar dark matter (GSDM). Monojet process is one of the primary channels to probe DM at hadron colliders. In Chapter 3, the discussion of monojet process at the Large Hadron Collider (LHC) is limited to the effective field theory (EFT) framework. In Chapter 4 we discuss collider processes in GSDM model with complete loop calculations for the diagrams involving the mediating colored scalar. We also compare the loop calculation with the EFT results to find the range of applicability of the EFT. The top quark study in Chapter 2 was initially inspired from an interesting observation made in 2008 which suggested a deviation from the SM in the forward-backward asymmetry (FBA) of a pair produced top quark. The value of FBA measured at the time was 18% ±12%. This value deviated by more than 1σ with respect to the SM leading order (LO) value of 5%. The deviation was observed by both the detectors at Tevatron, D0 and CDF, and it’s significance increased with additional data in 2012. Recent analyses of the data by D0 is now in better agreement with the latest effective-NNNLO calculations. However, the FBA measurements by CDF are still in tension with those by D0 and the value predicted by theoretical calculations. Inspired by this puzzle, which may be on its way to getting solved, we have been able to construct effective probes of BSM physics for the on-going and future searches of BSM in the top quark sector. In our analyses, we studied correlations among observables which can distinguish between different sources of BSM contributions in the top quark pair production. As a template, we use an s-channel and a t-channel mediator, both of which leave very different signatures in the kinematic asymmetry correlations. The simplified models considered by us also included parity breaking interactions which lead to polarized top quarks, providing another probe into the underlying production process. We find that all the kinematic distributions of the decay lepton get influenced by the polarization of the top quark. We show that these correlations can distinguish well between the template models of axigluon and diquark. In general, all of these observables also provide a probe into the polarization of the top quark and therefore any chiral couplings with the mediator. However, the lepton polar angle asymmetry measured in the lab frame is special in that it can not only probe the longitudinal polarization as other observables but is also sensitive to the transverse polarization of the top quark. We also show the effectiveness of the proposed top quark kinematic observables, to distinguish between s and t-channel BSM physics models, in future searches for BSM particles at the run-II LHC. In a large verity of dark matter (DM) models the simplest candidate is the model of a singlet scalar particle. The scalar may couple to the standard model in a number of ways via any of the SM particles. Such models with BSM Yukawa interactions or gauge sector extensions are strongly constrained from both the direct detection and collider precision measurements. The remaining models either predict a very heavy dark matter, completely out of reach of collider searches or introduce an unnaturally weak coupling with the SM particles giving no justifications for the small numbers. An interesting corner of the space of possible DM models which has been under-explored so far includes interactions of DM particles with gluons. Although DM particles cannot themselves be charged or colored, a colored scalar mediator can allow this interaction. One such model arises when we consider the scalar DM in presence of a colored scalar particle, for example the one from t-channel model above. Such colored scalars are generically present in a number of BSM theories including SUSY and GUT. How-ever, without the need for any additional gauge symmetries, the two scalars would interact with each other via the marginal operators. In Chapter 3 we study a SM singlet scalar DM candidate which couples to SM via a colored scalar particle. In the GSDM model, DM and mediator interact via the quartic, marginal operator. DM annihilation cross-section of the order of weak interactions (∼ 0.1pb) is predicted to explain the observed dark matter relic density if arising from thermal production of a WIMP DM candidate of mass ∼ 100 GeV. On investigating the GSDM model, we find that it allows a large annihilation cross-section and is still compatible with direct detection bounds. This is so because the annihilation cross-section to a pair of colored scalars proceeds via a tree-level interaction, whereas the interaction with SM particles proceeds via loop diagrams involving the colored scalars. Our work shows that this model is compatible with the observed relic density of DM when the mediating particle is lighter than DM for a large range of the couplings. For masses of the DM and the mediator less then ∼ 50 GeV, the DM can also be lighter than the mediator where the annihilation then proceeds via loop interactions. This region of parameter space is strongly constrained from the collider physics bounds on a colored scalar particle. These bounds become much weaker in the case where the colored scalar does not couple to quarks and hence cannot decay. The bounds coming from long-lived colored scalars become relevant in those cases and also constrain the light mass window. A colored scalar interacting with quarks must do so without violating the strong flavor constraints. We consider the scalar in the framework of a class of models termed minimally flavor violating (MFV) and also assume that it couples only to the right handed up-sector quarks. Such a particle would couple to the top quark and would be observable at the LHC pair production of the top quark. We find constraints on a color triplet particle in such a case and show the coupling and mass regions allowed. Constraints from the decays to light quarks are interpreted from dijet process searches and limit the mass of a color-triplet scalar above 350 GeV. The primary process for direct search of stable particles produced at a collider is a single jet in association with missing transverse energy (MET). We find that in an effective field theory (EFT) framework, very weak bounds are obtained on the mediating scale. In Chapter 4, we perform complete loop calculations for processes involving colored scalar particles and DM at LHC in order to explore the GSDM model at LHC and FCC (Future Circular Collider). The EFT is valid only for mediator masses much heavier than the momentum transfer or the MET cuts. We show the region of applicability of the EFT by comparing it with respect to the loop induced calculation. We analyze the monojet + missing transverse energy (MET) process to find the expected bounds from LHC 13 TeV run-II. We calculate the reach of the LHC in the high luminosity run in the future and also the reach of the FCC to explore the GSDM model. We perform all our calculations for a number of representations of the colored mediator from a triplet to dimension 15. As expected, collider constraints are only significant when the dark matter is light enough (mDM ∼ 10 GeV) to be copiously produced at the LHC. We find that in the high luminosity run, LHC can probe the scalar triplet particle up-to 50 GeV mass in the monojet process though a dimension 15 particle can be probed up to 150 GeV. With an order of magnitude higher beam energy, FCC can rule out much larger parameter space or provide observational evidence for TeV scale mediating particles. In conclusion, this thesis adds to the growing body of literature which points towards BSM discoveries around the corner at high luminosity LHC in the top physics and in dark sector physics. We have also proposed avenues for precision BSM studies at the next generation colliders.

L’étude des mécanismes de production des quarkonia (J/ψ or Υ) dans les collisions proton-proton (pp) est intéressante car elle nécessite de prendre en compte les aspects perturbatifs et non perturbatifs de la ChromoDynamique Quantique (QCD). La production de quarkonia en fonction de la multiplicité des particules chargées a été mesurée pour la première fois dans les collisions pp avec le détecteur ALICE au Grand collisionneur de hadrons (LHC). Ces mesures présentent une corrélation non triviale qui peut conduire à une meilleure compréhension du mécanisme d’interaction partonique multiple dans l’état initial de la collision ainsi que des effets collectifs possibles dans les petits systèmes. L’étude du dernier échantillon de données enregistré au LHC en collisions pp aux énergies les plus élevées jamais atteintes en laboratoire (√s=13 TeV) permettra d’étudier des événements à forte multiplicité. Avec ALICE, les quarkonia sont mesurés jusqu’à des impulsions transverses nulles. Les charmonia (J/ψ, cc̄ ) sont détectés par leur désintégration en diélectrons à mi-rapidité (|y|< 0.9) et en dimuons en rapidité vers l’avant (2.5 < y < 4). Les bottomonia (Υ, bb̄) sont détectées par leur décroissance en dimuons en rapidité vers l’avant. La multiplicité des particules chargées est mesurée à l’aide de segments de traces avec le détecteur de silicium à pixels pour |η|< 1. Dans cette thèse, nous présenterons les premières mesures réalisées avec ALICE des productions relatives d’Υ(1S) et Υ(2S) en fonction de la multiplicité des collisions pp à √s =13 TeV. Nous discuterons du rapport relatif des Υ(2S) par rapport aux Υ(1S) en fonction de la multiplicité des particules chargées. La comparaison entre les J/ψ et les Υ(1S) mesurés en rapidité avant en fonction de la multiplicité sera également examinée. Ces études permettront d’examiner la dépendance possible de la corrélation mesurée avec les différentes masses des quarkonia considérés et les différents types de contenus en quark. La dépendance du domaine en rapidité et de l’énergie de la collision sera également considérée. / The study of quarkonium (J/ψ or Υ) in proton-proton (pp) collisions is interesting as both perturbative and non perturbative aspects of Quantum ChromoDynamics (QCD) are involved in the production mechanism. The quarkonium production as a function of charged-particle multiplicity has been measured in a pp collisions with ALICE detector at the Large Hadron Collider (LHC). They exhibit a non-trivial correlation that can lead to a better understanding of the multi-parton interaction mechanism in the initial state of the collision as well as possible collective effects in small systems. Thestudy of latest data sample recorded at the LHC in pp collisions at the highest collision energies everreached in the laboratory (√s = 13 TeV) will allow to investigate high multiplicity events. In ALICE,quarkonia are measured down to zero transverse momentum. Charmonia (J/ψ, cc̄) are detected viatheir decay into di-electrons at mid-rapidity (|y|< 0.9) and dimuons at forward rapidity (2.5 < y < 4).Bottomonia (Υ, bb̄) are detected via their decay into dimuons at forward rapidity. Charged-particlemultiplicity is measured using track segments in the silicon pixel detector in |η|< 1. In this thesis, we will present the first ALICE measurements of relative Υ(1S) and Υ(2S) productions as a function of multiplicity in pp collisions at √s =13 TeV. We will discuss the ratio of the relative Υ(2S) overΥ(1S) as a function of charged-particle multiplicity. The comparison between the relative J/ψ andΥ(1S) yields measured at forward rapidity as a function of multiplicity will also be discussed. This will provide insight of possible dependence of the measured correlation with different mass and quark contents as well as the evolution with rapidity range and the collision energy.