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Higher Order Calculations for Low Energy Precision Physics

Hermansson Truedsson, Nils LU (2019)
Abstract (Swedish)
Denna sammanläggningsavhandling berör beräkningar som behövs för precisionsfysik vid låga energier inom Standardmodellen, särskilt högre ordningars korrektioner. I avhandlingens två första artiklar introduceras beräkningar på ordning p8 i kiral störningsräkning, vilket är en effektiv fältteori för QCD vid låga energier. De sista två artiklarna handlar om myonens anomala magnetiska moment och de hadronbidrag som står för den största delen av osäkerheten i den teoretiska förutsägelsen av nämnda magnetiska moment.

Artikel I: Här beräknas pionens massa och sönderfallskonstant på ordning p8 i kiral störningsräkning. En mindre numerisk studie visar att dessa överensstämmer väl med lägre ordningars beräkningar för fysikaliska... (More)
Denna sammanläggningsavhandling berör beräkningar som behövs för precisionsfysik vid låga energier inom Standardmodellen, särskilt högre ordningars korrektioner. I avhandlingens två första artiklar introduceras beräkningar på ordning p8 i kiral störningsräkning, vilket är en effektiv fältteori för QCD vid låga energier. De sista två artiklarna handlar om myonens anomala magnetiska moment och de hadronbidrag som står för den största delen av osäkerheten i den teoretiska förutsägelsen av nämnda magnetiska moment.

Artikel I: Här beräknas pionens massa och sönderfallskonstant på ordning p8 i kiral störningsräkning. En mindre numerisk studie visar att dessa överensstämmer väl med lägre ordningars beräkningar för fysikaliska kvarkmassor.

Artikel II: I denna artikel härleds Lagrangefunktionen för mesoner på ordning p8 i kiral störningsräkning. Detta görs för två, tre samt ett godtyckligt antal kvarksmaker. Detta görs genom att explicit konstruera alla av symmetrin tillåtna operatorer samt generera alla möjliga relationer mellan dessa. Från detta system av relationer tas därefter en minimal bas fram.

Artikel III: Här undersöks de korrektioner från ändlig-volymapproximationen inom gitterstudier som uppkommer när elektromagnetiska effekter inkluderas till vakuumpolarisationens hadronbidrag. Detta är viktigt för att minska det teoretiska felet på myonens anomala magnetiska moment. Vi visar att ändlig-volymkorrektionerna är mindre än förväntade, och i princip inte behöver korrigeras för givet nuvarande eftersökta precision.

Artikel IV: I denna artikel härleder vi modelloberoende begränsningar för lågenergimodeller av en viss typ av hadronbidrag till myonens magnetiska moment, detta från störningsmässig QCD. Detta görs genom att introducera en operatorproduktexpansion i ett externt elektromagnetiskt fält, vars första term är en kvarkloop och nästa innehåller ett kondensat relaterat till magnetiska egenskaper hos QCD-vakuumet. Detta senare bidrag visas vara undertryckt med nästan en faktor tusen, och är därför försumbart. (Less)
Abstract
This thesis concerns higher order calculations needed for precision physics in the low energy region of particle
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... (More)
This thesis concerns higher order calculations needed for precision physics in the low energy region of particle
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.
(Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Associate Professor Pineda, Antonio, Grup de Física Teòrica, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain
organization
alternative title
Högre ordningars beräkningar för precisionsfysik vid låga energier
publishing date
type
Thesis
publication status
published
subject
keywords
Effective Field Theory, Chiral Perturbation Theory, The Muon Anomalous Magnetic Moment, Lattice Gauge Theory, Finite Volume Effects, Effektiv fältteori, Kiral störningsräkning, Myonens anomala magnetiska moment, Gitter-gaugeteori, Ändlig-volymkorrektioner
pages
176 pages
defense location
Lundmarksalen, Astronomihuset, Sölvegatan 27, Lund
defense date
2019-09-20 10:00
ISBN
978-91-7895-213-7
978-91-7895-214-4
language
English
LU publication?
yes
id
e8cc22f5-8ed6-4d4f-85e0-84fa82419cc6
date added to LUP
2019-08-12 14:50:57
date last changed
2019-08-22 02:18:13
@phdthesis{e8cc22f5-8ed6-4d4f-85e0-84fa82419cc6,
  abstract     = {This thesis concerns higher order calculations needed for precision physics in the low energy region of particle<br/>physics. Of the four papers it contains, the first two introduce calculations at order p8 in the power counting<br/>of chiral perturbation theory, which is an effective field theory of QCD at low energies. The remaining two<br/>papers concern the hadronic contributions to the muon anomalous magnetic moment, or muon g − 2, which are<br/>responsible for the main uncertainty in the theoretical prediction of the quantity.<br/><br/>Paper I. The pion mass and decay constant are calculated at order p8 within two-flavour chiral perturbation<br/>theory. A small numerical study of the quark mass dependence is performed, and there is good agreement with<br/>lower order results at the physical point.<br/><br/>Paper II. The order p8 mesonic chiral Lagrangian is derived for two, three as well as a general number of flavours.<br/>This is done by explicitly creating all operators allowed by the relevant symmetries, and finding a minimal basis of<br/>operators. Special cases where some of the external fields are set to zero are also considered.<br/><br/>Paper III. The finite volume effects from the next-to-leading order electromagnetic corrections to the hadronic<br/>vacuum polarisation are here calculated in QEDL. This is needed for precision calculations of the muon g − 2<br/>on the lattice. The analytic results are compared to lattice simulations as well as numerical lattice perturbation<br/>theory. There is good agreement between the methods, and it is found that the electromagnetic corrections are<br/>suppressed to such an extent that they for moderately sized lattices and pion masses in principle can be neglected<br/>for the currently sought precision on the hadronic vacuum polarisation.<br/><br/>Paper IV. Short-distance constraints on the hadronic light-by-light contribution to the muon g − 2 are here<br/>derived. Such constraints are useful for the matching of hadronic models valid at low energies to the high energy<br/>region. In particular, the 4-point function entering into the hadronic light-by-light piece is calculated as a 3-point<br/>function in the presence of an external electromagnetic field. We show that the quark loop is the first term in an<br/>operator product expansion, and also consider the next term containing the condensate ⟨q σαβ q⟩ which is related<br/>to the magnetic susceptibility of the QCD vacuum. This latter contribution is found to be negligible due to the<br/>suppression in quark masses and sizes of the condensates.<br/>},
  author       = {Hermansson Truedsson, Nils},
  isbn         = {978-91-7895-213-7 },
  keyword      = {Effective Field Theory, Chiral Perturbation Theory, The Muon Anomalous Magnetic Moment, Lattice Gauge Theory, Finite Volume Effects,Effektiv fältteori, Kiral störningsräkning, Myonens anomala magnetiska moment, Gitter-gaugeteori, Ändlig-volymkorrektioner},
  language     = {eng},
  pages        = {176},
  school       = {Lund University},
  title        = {Higher Order Calculations for Low Energy Precision Physics},
  year         = {2019},
}