Effective Field Theory Methods Applied to Two-Body and Three-Body Systems
Effective Field Theory Methods Applied to Two-Body and Three-Body Systems
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DissertationPrüfungsdatum
17.12.2025Datum der Veröffentlichung
27.01.2026Erstgutachter
Rusetsky, AkakiZweitgutachter
Meißner, Ulf-G.Metadaten
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Inhalt
Quantum Chromodynamics is the fundamental theory of strong interactions. However, at low energies QCD strong coupling becomes very large and perturbative techniques are no more applicable. Lattice QCD offers an ab-initio non-perturbative method of solving QCD in this region. Since LQCD simulations are performed on a finite-dimensional Euclidean lattice, the result is contaminated with finite-volume effects. Moreover, establishing the relation between the finite-volume energy levels obtained from simulations and the continuum physical observables is highly non-trivial.
In this thesis, methods for extraction of two-body and three-body observables from lattice data are developed with the help of the non-relativistic effective field theory approach. The basic principles of LQCD are outlined while also detailing the methods used for extraction of two-body parameters from lattice data. The NREFT formalism is introduced and its application to both the two-body and three-body sectors is discussed, with special focus on methods for analysis of lattice data.
A formalism, the modified Luscher equation, is developed and derived for extraction of physical scattering parameters in the presence of short- plus long-range interaction in the two-body case based on the modified effective-range expansion. This method allows one to analyze finite-volume energy levels that lie in the left-hand cut region while also addressing the issue of slow convergence of partial-wave expansion in the presence of long-range interactions.
Moreover, an efficient numerical algorithm is detailed for working with the modified Luscher equation. Analysis of synthetic data generated from a toy model is carried out to test the accuracy of the approach. Various numerical and technical issues are described in detail.
In the three-body sector, results from the perturbative calculation of the three-nucleon ground state energy shift up to and including O(L-6), where L is the size of the finite-volume box, are presented. The convergence of the calculation for physical nucleon scattering lengths is discussed. The box size L required for convergence is very large and highly impractical.
Finally, the Lellouch-Luscher factor for K → 3π decay is evaluated numerically and its sensitivity to the three-pion amplitude is studied. It is found that the LL factor shows negligible dependence on the three-pion amplitude, and hence one can use a rough estimate of this amplitude from chiral perturbation theory instead of extracting it from LQCD.
In this thesis, methods for extraction of two-body and three-body observables from lattice data are developed with the help of the non-relativistic effective field theory approach. The basic principles of LQCD are outlined while also detailing the methods used for extraction of two-body parameters from lattice data. The NREFT formalism is introduced and its application to both the two-body and three-body sectors is discussed, with special focus on methods for analysis of lattice data.
A formalism, the modified Luscher equation, is developed and derived for extraction of physical scattering parameters in the presence of short- plus long-range interaction in the two-body case based on the modified effective-range expansion. This method allows one to analyze finite-volume energy levels that lie in the left-hand cut region while also addressing the issue of slow convergence of partial-wave expansion in the presence of long-range interactions.
Moreover, an efficient numerical algorithm is detailed for working with the modified Luscher equation. Analysis of synthetic data generated from a toy model is carried out to test the accuracy of the approach. Various numerical and technical issues are described in detail.
In the three-body sector, results from the perturbative calculation of the three-nucleon ground state energy shift up to and including O(L-6), where L is the size of the finite-volume box, are presented. The convergence of the calculation for physical nucleon scattering lengths is discussed. The box size L required for convergence is very large and highly impractical.
Finally, the Lellouch-Luscher factor for K → 3π decay is evaluated numerically and its sensitivity to the three-pion amplitude is studied. It is found that the LL factor shows negligible dependence on the three-pion amplitude, and hence one can use a rough estimate of this amplitude from chiral perturbation theory instead of extracting it from LQCD.
Klassifikation (DDC)
530 PhysikBubna, Rishabh: Effective Field Theory Methods Applied to Two-Body and Three-Body Systems. - Bonn, 2026. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-87087
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-87087
@phdthesis{handle:20.500.11811/13851,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-87087,
author = {{Rishabh Bubna}},
title = {Effective Field Theory Methods Applied to Two-Body and Three-Body Systems},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2026,
month = jan,
note = {Quantum Chromodynamics is the fundamental theory of strong interactions. However, at low energies QCD strong coupling becomes very large and perturbative techniques are no more applicable. Lattice QCD offers an ab-initio non-perturbative method of solving QCD in this region. Since LQCD simulations are performed on a finite-dimensional Euclidean lattice, the result is contaminated with finite-volume effects. Moreover, establishing the relation between the finite-volume energy levels obtained from simulations and the continuum physical observables is highly non-trivial.
In this thesis, methods for extraction of two-body and three-body observables from lattice data are developed with the help of the non-relativistic effective field theory approach. The basic principles of LQCD are outlined while also detailing the methods used for extraction of two-body parameters from lattice data. The NREFT formalism is introduced and its application to both the two-body and three-body sectors is discussed, with special focus on methods for analysis of lattice data.
A formalism, the modified Luscher equation, is developed and derived for extraction of physical scattering parameters in the presence of short- plus long-range interaction in the two-body case based on the modified effective-range expansion. This method allows one to analyze finite-volume energy levels that lie in the left-hand cut region while also addressing the issue of slow convergence of partial-wave expansion in the presence of long-range interactions.
Moreover, an efficient numerical algorithm is detailed for working with the modified Luscher equation. Analysis of synthetic data generated from a toy model is carried out to test the accuracy of the approach. Various numerical and technical issues are described in detail.
In the three-body sector, results from the perturbative calculation of the three-nucleon ground state energy shift up to and including O(L-6), where L is the size of the finite-volume box, are presented. The convergence of the calculation for physical nucleon scattering lengths is discussed. The box size L required for convergence is very large and highly impractical.
Finally, the Lellouch-Luscher factor for K → 3π decay is evaluated numerically and its sensitivity to the three-pion amplitude is studied. It is found that the LL factor shows negligible dependence on the three-pion amplitude, and hence one can use a rough estimate of this amplitude from chiral perturbation theory instead of extracting it from LQCD.},
url = {https://hdl.handle.net/20.500.11811/13851}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-87087,
author = {{Rishabh Bubna}},
title = {Effective Field Theory Methods Applied to Two-Body and Three-Body Systems},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2026,
month = jan,
note = {Quantum Chromodynamics is the fundamental theory of strong interactions. However, at low energies QCD strong coupling becomes very large and perturbative techniques are no more applicable. Lattice QCD offers an ab-initio non-perturbative method of solving QCD in this region. Since LQCD simulations are performed on a finite-dimensional Euclidean lattice, the result is contaminated with finite-volume effects. Moreover, establishing the relation between the finite-volume energy levels obtained from simulations and the continuum physical observables is highly non-trivial.
In this thesis, methods for extraction of two-body and three-body observables from lattice data are developed with the help of the non-relativistic effective field theory approach. The basic principles of LQCD are outlined while also detailing the methods used for extraction of two-body parameters from lattice data. The NREFT formalism is introduced and its application to both the two-body and three-body sectors is discussed, with special focus on methods for analysis of lattice data.
A formalism, the modified Luscher equation, is developed and derived for extraction of physical scattering parameters in the presence of short- plus long-range interaction in the two-body case based on the modified effective-range expansion. This method allows one to analyze finite-volume energy levels that lie in the left-hand cut region while also addressing the issue of slow convergence of partial-wave expansion in the presence of long-range interactions.
Moreover, an efficient numerical algorithm is detailed for working with the modified Luscher equation. Analysis of synthetic data generated from a toy model is carried out to test the accuracy of the approach. Various numerical and technical issues are described in detail.
In the three-body sector, results from the perturbative calculation of the three-nucleon ground state energy shift up to and including O(L-6), where L is the size of the finite-volume box, are presented. The convergence of the calculation for physical nucleon scattering lengths is discussed. The box size L required for convergence is very large and highly impractical.
Finally, the Lellouch-Luscher factor for K → 3π decay is evaluated numerically and its sensitivity to the three-pion amplitude is studied. It is found that the LL factor shows negligible dependence on the three-pion amplitude, and hence one can use a rough estimate of this amplitude from chiral perturbation theory instead of extracting it from LQCD.},
url = {https://hdl.handle.net/20.500.11811/13851}
}
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