Title:

Precision tests of the standard model using lattice QCD

The Standard Model of particle physics successfully describes the fundamental particles and their interactions, but suffers from a few critical limitations which raise the intriguing possibility of new physics beyond it. My dissertation focuses on the study of the phenomenologically important quantities in the Standard Model, particularly, involving the high precision first principle calculations in the lowenergy ($\sim1$GeV) regime of Quantum Chromodynamics (QCD), the $SU(3)$ component of the Standard Model. In this regime, since the QCD coupling becomes strong and the quarks and the gluons are confined to bound states called hadrons, a perturbative expansion in the coupling constant is not possible. However, the introduction of a fourdimensional Euclidean spacetime lattice allows for an abinitio treatment of QCD and provides a powerful tool  lattice QCD to study the low energy dynamics of the hadrons using numerical simulations. I have used existing methods of lattice QCD and developed new methods to study the pseudoscalar and the vector mesons (quarkantiquark hadrons) made of valence light (up and down), strange and charm quarks which are important final states in a number of decay processes that are studied in experiments and are sensitive to new physics. From the large time exponential behaviour of the meson correlators generated on lattice, I have extracted the masses and the decay constants (annihilation amplitude) of the mesons. My results include the most accurate lattice QCD calculation to date of the properties of the vector mesons $\phi$ and $\rho$. In lattice QCD calculations, the systematic uncertainty coming from the renormalisation constants relating the lattice results to the continuum results can be crucial and therefore has been determined precisely. Subsequently, we realised that our methods can also be extended to the calculation of the hadronic vacuum polarisation (HVP) contribution to the anomalous magnetic moment of the muon, $a_\mu$. The anomalous magnetic moment of the muon, shows a large discrepancy ($\sim3\sigma$) between theoretical and experimental results, putting the Standard Model to one of its most stringent tests. To complement the plans for a fourfold improvement in its experimental uncertainty, this project aims to improve the dominant contributions in the theoretical uncertainty coming from the hadronic vacuum polarisation to $\sim1\%$. I with my collaborators have developed a new lattice QCD method to calculate the HVP, making a significant progress over previous calculations by achieving an unprecedented precision ($\sim2\%$) in the HVP. The quark flavour sector of the Standard Model is also a fertile ground to test any new physics effect through the Unitarity test of the CabbiboKobayashiMaskawa (CKM) matrix. Therefore, my aim was to perform a lattice QCD calculation of the scalar and the vector form factors (over a large $q^2$ region including $q^2=0$) associated with the $D\rightarrow Kl\nu$ semileptonic decay. The central CKM matrix element, $V_{cs}$ in the Standard Model, is then calculated by comparing the lattice QCD results for the form factors and the experimental decay rate. For my research I have used publicly avalilable MILC HISQ configurations with dynamical up, down, strange and charm quarks. For most of my calculations I have used HISQ valence quarks except for the renormalisation of currents where for the comparison between different lattice formalisms I have also used the clover valence quarks.
