Higher Order Calculations for Low Energy Precision Physics

Abstract: This thesis concerns higher order calculations needed for precision physics in the low energy region of particlephysics. Of the four papers it contains, the first two introduce calculations at order p8 in the power countingof chiral perturbation theory, which is an effective field theory of QCD at low energies. The remaining twopapers concern the hadronic contributions to the muon anomalous magnetic moment, or muon g − 2, which areresponsible for the main uncertainty in the theoretical prediction of the quantity.Paper I. The pion mass and decay constant are calculated at order p8 within two-flavour chiral perturbationtheory. A small numerical study of the quark mass dependence is performed, and there is good agreement withlower order results at the physical point.Paper II. The order p8 mesonic chiral Lagrangian is derived for two, three as well as a general number of flavours.This is done by explicitly creating all operators allowed by the relevant symmetries, and finding a minimal basis ofoperators. Special cases where some of the external fields are set to zero are also considered.Paper III. The finite volume effects from the next-to-leading order electromagnetic corrections to the hadronicvacuum polarisation are here calculated in QEDL. This is needed for precision calculations of the muon g − 2on the lattice. The analytic results are compared to lattice simulations as well as numerical lattice perturbationtheory. There is good agreement between the methods, and it is found that the electromagnetic corrections aresuppressed to such an extent that they for moderately sized lattices and pion masses in principle can be neglectedfor the currently sought precision on the hadronic vacuum polarisation.Paper IV. Short-distance constraints on the hadronic light-by-light contribution to the muon g − 2 are herederived. Such constraints are useful for the matching of hadronic models valid at low energies to the high energyregion. In particular, the 4-point function entering into the hadronic light-by-light piece is calculated as a 3-pointfunction in the presence of an external electromagnetic field. We show that the quark loop is the first term in anoperator product expansion, and also consider the next term containing the condensate ⟨q σαβ q⟩ which is relatedto the magnetic susceptibility of the QCD vacuum. This latter contribution is found to be negligible due to thesuppression in quark masses and sizes of the condensates.