Exploiting the substructure of jets observed at the LHC to better understand and interpret the experimental data has recently been a very active area of research. In this thesis we study the substructure of high-pt QCD jets, which form a background to many new physics searches. In particular, we explore in detail the perturbative distributions of a certain class of observables known as non-global jet shapes. More specifically, we identify and present state-of-the-art calculations, both at fixed-order and to all-orders in the perturbative expansion, of a set of large logarithms known as non-global logarithms. Hitherto, these logarithms have been largely mis-treated, and in many cases ignored, in the literature despite being first pointed out more than a decade ago. Our work has triggered the interest of many groups, particularly Soft and Collinear Effective Theory (SCET) groups, and led to a flurry of papers on non-global logarithms and related issues. Although our primary aim is to provide analytical results for hadron-hadron scattering environments, it is theoretically instructive to consider the simpler case of e+e- annihilation. We thus examine, in chapters 4, 5 and 6, the the said jet shapes in the latter environment and compute the full next-to-leading logarithmic resummation of the large logarithms present in the distribution for various jet definitions. We exploit the gained experience to extend our calculations to the more complex hadronic environment in chapter 7. We provide state-of-the-art resummation of the jet mass observable in vector boson + jet and dijet QCD processes at the LHC up to next-to-leading logarithmic accuracy. The resultant distribution of the former (vector boson + jet) process agrees well, after accounting for hadronisation corrections, with standard Monte Carlo event generators and potential comparisons to data from the LHC will be made soon.

The thesis instructively presents axions and axion-like particles as a plau- sible extension of the Standard Model of particle physics and discusses also the cosmological implications in the case of their existence as they present one of the most favourable dark matter candidates at given circumstances. The main part of the thesis is concerned with a search for axion-like particles at the NA62 experiment at CERN and a study of the gathered data and its impact on the data analysis.

The CKM matrix element |Vus| can be extracted from the experimental measurement of semileptonic K → π decays and theoretical input for the corresponding vector form factor in QCD. The thesis performs a major improvement of the RBC/UKQCD programme to calculate Kl3 form factor in Nf = 2+1 Lattice QCD using domain wall fermions. We use data from several lattice spacings and dfferent quark masses with lightest pion mass of about 170MeV. Systematic error corresponding to interpolation in the momentum transfer is avoided using partially twisted boundary conditions. Using simulated quark masses near the physical point, reduce the systematic error due to the mass extrapolation. This work explores different kinematic arrangements of pion and Kaon momenta for twisted boundary conditions. This thesis proposes a new ansatz for mass extrapolation. Analysing three sets of simulation data allows for a detailed study of systematic effects leading to the prediction f+kπ (0) = 0:9671(17)(+18-46), where the first error is statistical and the second error systematic. The result allows us to extract the CKM matrix element |Vus| = 0:2237(+13-8) and confirm unitarity of the first row CKM matrix in the Standard Model. Also in this thesis, we discuss porting of Clover Lattice fermion action to Blue Gene-Q architecture. Clover action achieves maximum efficiency of 29.1% for single precision with good weak scaling. Strong scaling shows local volume dependency. In a study of different iterative solvers for Domain Wall Fermion action (DWF), we find that Modified Conjugate Residual(MCR) and Multishift MCR as the most efficient solver compared to CG and GCR. A new probing technique for estimating the diagonal of the inverse Dirac operator in Lattice QCD is introduced and this method is found to be closer to the exact solution than stochastic methods.

This thesis presents a first study of the continuum limit of light hadronic physics using a lattice gauge theory simulation with good chiral symmetry. The results are interpreted and extrapolated using both the chiral effective theory and analytic models. Matrix elements of operators of the effective weak Hamiltonian are calculated. The thesis details a combined chiral and continuum extrapolation of two ensemble sets of 2+1 flavour Domain Wall QCD data with inverse lattice spacings around 1.73 and 2.32 GeV. A novel procedure of matching lattice data at unphysical quark masses is used to define the scaling trajectory to the continuum limit. Quantities studied include the pion and kaon masses and decay constants, the average up/down quark mass, the strange quark mass, and the neutral kaon mixing parameter BK. The latter is an important theoretical input to the K band in the unitarity triangle of the CKM matrix. A subset of recent results of ref. [1] in the chiral effective theory needed to perform our fits are re-derived. New methods for the improved determination of the BK matrix element (and other correlation functions), and also for the renormalisation of the relevant four-quark operator for BK are presented.

We evaluate the prompt atmospheric neutrino flux at high energies using three different frameworks for calculating the heavy quark production cross section in QCD: NLO perturbative QCD, k(T) factorization including low-x resummation, and the dipole model including parton saturation. We use QCD parameters, the value for the charm quark mass and the range for the factorization and renormalization scales that provide the best description of the total charm cross section measured at fixed target experiments, at RHIC and at LHC. Using these parameters we calculate differential cross sections for charm and bottom production and compare with the latest data on forward charm meson production from LHCb at 7TeV and at 13TeV, finding good agreement with the data. In addition, we investigate the role of nuclear shadowing by including nuclear parton distribution functions (PDF) for the target air nucleus using two different nuclear PDF schemes. Depending on the scheme used, we find the reduction of the flux due to nuclear effects varies from 10% to 50% at the highest energies. Finally, we compare our results with the IceCube limit on the prompt neutrino flux, which is already providing valuable information about some of the QCD models.

In the first part of the thesis, theoretical uncertainties of jet cross-section have been calculated for proton-proton collision at the center of mass energy of 8 TeV. For jet identification the anti-kT algorithm with scale parameter R = 0.6 was used. As the calculations showed, the major contribution to the total theoretical uncertainty comes from the uncertainty of parton distribution function parameters. In the second part of the thesis, the angular distribution of dijet events produced in proton-proton collisions at the center of mass energy 8 TeV were simulated using Pythia 8 Monte Carlo event generator. New physics model of quark compositeness that should manifest itself by quark contact interaction was studied using angular distribution of dijet events. Three angular variables were discussed and these variables were used to calculate 95% CL lower limit on contact interaction scale. The results were compared and it emerged that the sensitivity to contact interaction signals varies for these variables.

Title: Partonic showers and jets Author: Ondřej Hladík Department: Institute of Theoretical Physics MFF UK Supervisor: Mgr. Alexander Kupčo, Ph.D., Institute of Physics ASCR, v. v. i. Abstract: In the present thesis we compare experimentally measured differential and integrated jets shapes with predictions of quantum chromodynamics (QCD) at the second order (NLO) of perturbative expansion. The measured jet sha- pes were taken from ATLAS experiment at LHC in proton-proton collisions at a center-of-mass energy √ s = 7 TeV and were compared with these predictions. The jets were reconstructed by means of anti-kT jet algorithm with R = 0.6. The predictions at NLO QCD agree with data in wider kinematics region than predictions at leading order (LO). The agreement, however, is still in some kine- matical regions not satisfactory. Keywords: QCD, jets, jet shapes, LHC

Exotic mesons are mesons that cannot be described as a quark-antiquark pair. The number of exotic mesons has been growing every year in the charm sector and the theoretical understanding of them is often conflicted amongst the community. Some possible explanations include hybrid mesons where the quark-antiquark pair is coupled to a gluonic excitation, compact tetraquarks where four quarks are bound into a localised state and molecules which consist of pairs of extended mesons. To study exotic mesons from first principles, lattice QCD provides the framework to perform spectroscopy calculations numerically. I will give a review and describe the relevant techniques used in this thesis. After doing so, I will calculate masses of charmonium with angular momentum up to four. The results show QCD permits states with exotic quantum numbers that are not accessible by a quark-antiquark pair. I will identify states that are consistent with the quark-antiquark picture and then show that the remaining states in the extracted spectra can be interpreted to be the lightest and first excited hybrid meson supermultiplet. Whilst the mass is one quantity that can be computed, hadron spectroscopy is also concerned with the calculation of the unstable properties of resonances which can decay into meson-meson states. These meson-meson states have four quarks and could also mix with tetraquarks. I will describe how to correctly extract the energies of four quark states within lattice QCD by reviewing operators resembling meson-mesons and then constructing a general class of operators resembling tetraquarks. I will then calculate a variety of spectra in the isospin-1 hidden charm sector and the doubly charmed sector. No evidence of a bound state or narrow resonance is found in these channels. Having described how to include multi-meson states in lattice QCD, I will describe how to relate the lattice QCD spectrum to the scattering amplitudes and perform a calculation of elastic $DK$ scattering amplitudes which is relevant for the exotic $D_{s0}(2317)$. By analytically continuing the scattering amplitudes into the complex plane, I find a bound state pole near threshold which is in good agreement with what is found experimentally.

Superstring theory is one current, promising attempt at unifying gravity with the other three known forces: the electromagnetic force, and the weak and strong nuclear forces. Though this is still a work in progress, much effort has been put forth toward this goal. A set of specific tools which are used are gauge/gravity dualities. This thesis consists of a specific implementation of gauge/gravity dualities to describe k-strings of strongly coupled gauge theories as objects dual to Dpbranes embedded in confining supergravity backgrounds from low energy superstring field theory. Along with superstring theory, k-strings are also commonly investigated with lattice gauge theory and Hamiltonian methods. A k$string is a colorless combination of quark-anti-quark source pairs, between which a color flux tube develops. The two most notable terms of the k-string energy are, for large quark anti-quark separation L, the tension term, proportional to L, and the Coulombic 1/L correction, known as the Luscher term. This thesis provides an overview of superstring theories and how gauge/gravity dualities emerge from them. It shows in detail how these dualities can be used for the specific problem of calculating the k-string energy in 2+1 and 3+1 space-time dimensions as the energy of Dp-branes in the dual gravitational theory. A detailed review of k-string tension calculations is given where good agreement is found with lattice gauge theory and Hamiltonian methods. In reviewing the k-string tension, we also touch on how different representations of k-strings can be described with Dp-branes through gauge/gravity dualities. The main result of this thesis is how the Luscher term is found to emerge from the energy calculation of Dp-branes. In 2+1 space-time dimensions, we have Luscher term data to compare with from lattice gauge theory, where we find good agreement.

This thesis deals with the study of baryon spectra in the context of the $1/N_c$ expansion. The standard tool to study baryon properties is the constituent quark model. The results are naturally model dependent. The $1/N_c$ expansion generates a new perturbative approach to QCD, convenient for low momentum transfer. It provides a new theoretical method that is quantitative, systematic and predictive. In the first part of the thesis, the $1/N_c$ expansion is introduced as well as the baryon structure at large $N_c$. A summary of important results for ground-state baryons is provided. The second part of the thesis is devoted to excited baryon states. The symmetric orbital states are treated by analogy to the ground state. For mixed symmetric states, two approaches are presented. The traditional one starts from the decoupling of the wave function into an excited quark and a symmetric core. To make the problem tractable the wave function is treated approximately, justified by a Hartree scheme. This approach is applied to the study of the $[{f 70},ell^+] (ell=0,2)$ multiplets (nonstrange and strange cases) and of the $[{f 56},4^+]$ multiplet. An important physical result is the dependence of the spin dependent terms of the mass operator on the excitation energy. Recently we suggested a new approach based on a rigorous group theoretical treatment of the matrix elements of SU(4). No decoupling and no approximations are necessary. When applied to the $[{f 70},1^-]$ nonstrange multiplet, it is found that the leading corrections to the mass operator are of order $1/N_c$ instead of $N_c^0$, as predicted by the decoupling procedure.