Applications of non-perturbative renormalisation for lattice QCD

Abstract

The Standard Model (SM) of particle physics, despite proving to be the most robust framework for our current understanding of fundamental particles and their interactions in nature, fails to account for several observed phenomena. In order to uncover the New Physics beyond the SM and further our theoretical understanding of nature, it is important to perform precision tests on its predictions, and also explore theories beyond the Standard Model (BSM). Lattice quantum chromodynamics (QCD) is an ab initio framework for testing the SM in the non-perturbative regime of QCD; observables on the discrete lattice can be related to their continuum counterparts by performing a continuum extrapolation. An important corequisite for this procedure is the renormalisation of bare quantities computed on the lattice. In this thesis we present two studies that aim to make high precision predictions for SM and BSM parameters with the use of regularisation-independent momentum subtraction schemes for the non-perturbative renormalisation of lattice quantities.

We present non-perturbative results for BSM kaon mixing matrix elements in the isospin symmetric limit of QCD, including a complete estimate of all dominant sources of systematic error. Our results are obtained from numerical simulations of lattice QCD with 2 + 1 flavours of dynamical domain wall fermions. We include data at three lattice spacings in the range 0.11 – 0.07 fm and with pion masses ranging from the physical value up to 450 MeV. This improves upon earlier studies by including direct calculations at physical quark masses and a third lattice spacing, therefore making the removal of discretisation effects significantly more precise and eliminating the need for any significant mass extrapolation beyond the range of simulated data. We renormalise the lattice operators non-perturbatively using RI/SMOM off-shell schemes. These schemes eliminate the need to model and subtract non-perturbative pion poles that arise in the RI/MOM scheme. Furthermore, since the calculations are performed with domain wall fermions, the unphysical mixing between chirality sectors is suppressed. Our results for the bag parameters in the MS scheme at 3 GeV are BK ≡ B1 = 0.5240(17)(54), B2 = 0.4794(25)(35), B3 = 0.746(13)(17), B4 = 0.897(02)(10) and B5 = 0.6882(78)(94),where the first error is from lattice uncertainties and the second is the uncertainty due to the perturbative matching to MS-bar.

We also present the first numerical implementation of a massive momentum subtraction (RI/mSMOM) renormalisation scheme and use it to calculate the charm quark mass. This scheme aims to curb discretisation effects in the study of heavy quark observables on the lattice. Based on ensembles with 2 + 1 flavours of dynamical domain wall fermions with lattice spacings in the range 0.11 – 0.08 fm, we demonstrate that the mass scale which defines the RI/mSMOM scheme can be chosen such that the extrapolation has significantly smaller discretisation effects than the RI/SMOM scheme which is defined in the massless limit. Converting our results to the MS-bar scheme we obtain mc(3 GeV) = 1.008(13) GeV and mc(mc) = 1.292(12) GeV.

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Identifiers

ORCID for Rajnandini Mukherjee: orcid.org/0000-0003-1015-8533

ORCID for Jonathan Flynn: orcid.org/0000-0002-6280-1677

ORCID for Andreas Juttner: orcid.org/0000-0002-3978-0927

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