Renormalisation I: Perturbation theory

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Perturbation Theory ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Power Counting

After giving an overview about regularisation and renormalisation methods, this chapter shows the calculation of the anomalous magnetic moment of the electron in QED. Using a power counting argument, non-, super- and renormalisable theories are distinguish from one another. The structure of the divergences and perturbative renormalisation is discussed for the case of the λϕ‎4 theory. regularisation methods, renormalisation schemes, anomalous magnetic moment of the electron, power counting, renormalisation of the λϕ‎4 theory.

scholarly journals Stochastic computation of g − 2 in QED

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ryuichiro Kitano ◽  
Hiromasa Takaura ◽  
Shoji Hashimoto
Keyword(s):  
Perturbation Theory ◽  
Numerical Computation ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Stochastic Perturbation ◽  
Higher Order ◽  
Feynman Diagrams ◽  
Perturbative Series ◽  
Physical Quantities

Abstract We perform a numerical computation of the anomalous magnetic moment (g − 2) of the electron in QED by using the stochastic perturbation theory. Formulating QED on the lattice, we develop a method to calculate the coefficients of the perturbative series of g − 2 without the use of the Feynman diagrams. We demonstrate the feasibility of the method by performing a computation up to the α3 order and compare with the known results. This program provides us with a totally independent check of the results obtained by the Feynman diagrams and will be useful for the estimations of not-yet-calculated higher order values. This work provides an example of the application of the numerical stochastic perturbation theory to physical quantities, for which the external states have to be taken on-shell.

scholarly journals Pion mass dependence of the HVP contribution to muon g – 2

2018 ◽  
Vol 175 ◽  
pp. 06010
Author(s):  
Maarten Golterman ◽  
Kim Maltman ◽  
Santiago Peris
Keyword(s):  
Perturbation Theory ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Pion Mass ◽  
Systematic Errors ◽  
Mass Dependence ◽  
Chiral Perturbation ◽  
Muon Anomalous Magnetic Moment ◽  
Chiral Extrapolation ◽  
Pion Mass Dependence

One of the systematic errors in some of the current lattice computations of the HVP contribution to the muon anomalous magnetic moment g – 2 is that associated with the extrapolation to the physical pion mass. We investigate this extrapolation assuming lattice pion masses in the range of 220 to 440 MeV with the help of two-loop chiral perturbation theory, and find that such an extrapolation is unlikely to lead to control of this systematic error at the 1% level. This remains true even if various proposed tricks to improve the chiral extrapolation are taken into account.

Über den magnetischen Formfaktor des Nukleons

1959 ◽  
Vol 14 (8) ◽  
pp. 699-707
Author(s):  
H. Eisenlohr ◽  
H. Salecker
Keyword(s):  
Perturbation Theory ◽  
Form Factor ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Form Factors ◽  
Sufficient Accuracy ◽  
Mean Square ◽  
Vector Form ◽  
High Q ◽  
Moment Distribution

This article deals with the form factor of the anomalous magnetic moment distribution of proton and neutron. It is first shown with three examples that the magnetic root mean square radius cannot be taken from the existing experiments with sufficient accuracy. Satisfactory agreement with the experimental results can be obtained with arbitrary values of rm2. We calculate the magnetic moment form factors depending on the energy momentum transfer q2 in perturbation theory and the 2 π meson contribution to the isotopic vector form factor with dispersion relations also in relation to q2, with and without π meson form factor. We get better agreement of the shape of the form factor with the phenomenological form factor of HOFSTADTER at the expense of the static magnetic moment. But the contribution of the high q2 values is still too large i.e. the structure is somewhat too concentrated **

TENTH-ORDER QED CONTRIBUTION TO THE ELECTRON g-2 AND HIGH PRECISION TEST OF QUANTUM ELECTRODYNAMICS

2014 ◽  
Vol 29 (02) ◽  
pp. 1430003 ◽  
Author(s):  
TOICHIRO KINOSHITA
Keyword(s):  
Perturbation Theory ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Quantum Electrodynamics ◽  
Feynman Diagrams ◽  
Current Status ◽  
Complete Evaluation ◽  
Code Generator ◽  
Parametric Integrals ◽  
Precision Test

This paper presents the current status of the theory of electron anomalous magnetic moment ae ≡(g-2)/2, including a complete evaluation of 12,672 Feynman diagrams in the tenth-order perturbation theory. To solve this problem, we developed a code-generator which converts Feynman diagrams automatically into fully renormalized Feynman-parametric integrals. They are evaluated numerically by an integration routine VEGAS. The preliminary result obtained thus far is 9.16 (58) (α/π)5, where (58) denotes the uncertainty in the last two digits. This leads to ae( theory ) = 1.159 652 181 78 (77) ×10-3, which is in agreement with the latest measurement ae ( exp :2008) = 1.159 652 180 73 (28) ×10-3. It shows that the Feynman–Dyson method of perturbative QED works up to the precision of 10-12.

scholarly journals CHIRAL LAGRANGIANS

2002 ◽  
Vol 17 (23) ◽  
pp. 3154-3169
Author(s):  
JOHAN BIJNENS
Keyword(s):  
Perturbation Theory ◽  
Chiral Lagrangians ◽  
Chiral Perturbation Theory ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Chiral Perturbation ◽  
Muon Anomalous Magnetic Moment

An overview of the field of Chiral Lagrangians is given. This includes Chiral Perturbation Theory and resummations to extend it to higher energies, applications to the muon anomalous magnetic moment, ∊′/∊ and others.

scholarly journals The axion-baryon coupling in SU(3) heavy baryon chiral perturbation theory

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Thomas Vonk ◽  
Feng-Kun Guo ◽  
Ulf-G. Meißner
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Heavy Baryon ◽  
Power Counting ◽  
Flavor Symmetry ◽  
Chiral Perturbation ◽  
Third Order ◽  
Stellar Objects ◽  
The Past ◽  
Dense Nuclear Matter

Abstract In the past, the axion-nucleon coupling has been calculated in the framework of SU(2) heavy baryon chiral perturbation theory up to third order in the chiral power counting. Here, we extend these earlier studies to the case of heavy baryon chiral perturbation theory with SU(3) flavor symmetry and derive the axion coupling to the full SU(3) baryon octet, showing that the axion also significantly couples to hyperons. As studies on dense nuclear matter suggest the possible existence of hyperons in stellar objects such as neutron stars, our results should have phenomenological implications related to the so-called axion window.

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