# Johan Rathsman

Senior lecturer

## Higher Order Calculations for Low Energy Precision Physics

Högre ordningars beräkningar för precisionsfysik vid låga energier

Author

## Summary, in English

physics. Of the four papers it contains, the first two introduce calculations at order p8 in the power counting

of chiral perturbation theory, which is an effective field theory of QCD at low energies. The remaining two

papers concern the hadronic contributions to the muon anomalous magnetic moment, or muon g − 2, which are

responsible 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 perturbation

theory. A small numerical study of the quark mass dependence is performed, and there is good agreement with

lower 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 of

operators. 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 hadronic

vacuum polarisation are here calculated in QEDL. This is needed for precision calculations of the muon g − 2

on the lattice. The analytic results are compared to lattice simulations as well as numerical lattice perturbation

theory. There is good agreement between the methods, and it is found that the electromagnetic corrections are

suppressed to such an extent that they for moderately sized lattices and pion masses in principle can be neglected

for 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 here

derived. Such constraints are useful for the matching of hadronic models valid at low energies to the high energy

region. In particular, the 4-point function entering into the hadronic light-by-light piece is calculated as a 3-point

function in the presence of an external electromagnetic field. We show that the quark loop is the first term in an

operator product expansion, and also consider the next term containing the condensate ⟨q σαβ q⟩ which is related

to the magnetic susceptibility of the QCD vacuum. This latter contribution is found to be negligible due to the

suppression in quark masses and sizes of the condensates.

Department/s

- Theoretical Particle Physics

Publishing year

2019

Language

English

Full text

Document type

Dissertation

Publisher

Lund University, Faculty of Science

Topic

- Subatomic Physics

Keywords

- Effective Field Theory, Chiral Perturbation Theory, The Muon Anomalous Magnetic Moment, Lattice Gauge Theory, Finite Volume Effects
- Fysicumarkivet A:2019:Hermansson
- Effektiv fältteori, Kiral störningsräkning, Myonens anomala magnetiska moment, Gitter-gaugeteori, Ändlig-volymkorrektioner

Status

Published

Supervisor

- Johan Bijnens
- Johan Rathsman

ISBN/ISSN/Other

- ISBN: 978-91-7895-214-4
- ISBN: 978-91-7895-213-7

Defence date

20 September 2019

Defence time

10:00

Defence place

Lundmarksalen, Astronomihuset, Sölvegatan 27, Lund

Opponent

- Antonio Pineda (Associate Professor)