In this talk, I will briefly discuss my research to test the Standard Model (SM) of particle physics with high precision and look for signs of new physics using first principle lattice QCD calculations, particularly, in the low energy (~ 1 GeV) regime of QCD, the SU(3) component of the SM. The anomalous magnetic moment of the muon (a_μ), measured with an impressive accuracy of 0.54 parts per million in experiment, provides one of the most stringent tests of the SM. Intriguingly, the experimentally measured anomaly disagrees by around 3 standard deviations with the calculated value from the SM. The current theoretical uncertainty is dominated by that from the calculation of the lowest order "hadronic vacuum polarisation (HVP)". Improvements in the experimental uncertainty by a factor of 4 in the upcoming experiments at Fermilab and J-PARC are expected and improvements in the theoretical determination would make the discrepancy (if it remains) really compelling. I will present my results for improving the theoretical calculation of the HVP contribution to the anomaly using our (HPQCD) new lattice QCD method (Phys.Rev. D89 (2014) 11, 114501; arXiv:1511.05870; arXiv:1512.03270).
The quark flavour sector of the SM is also known to be potentially very sensitive to new physics effects. Studying different flavour-changing processes like leptonic and semi-leptonic decays of mesons and over-constraining the elements of the Cabibbo-Kobayashi-Maskawa (CKM) unitary matrix may lead to an internal inconsistency signalling beyond Standard Model (BSM) physics. In the second part of this talk I will focus on the progress of my calculation of V_cs, the central CKM matrix element, by comparing the lattice QCD results for the scalar and vector form factors associated with D → Klν semi-leptonic decay and the experimental decay rate.