Royo Amondarain, Eduardo
Azcoiti Pérez, Vicente (dir.) ; Follana Adín, Eduardo (dir.)
Universidad de Zaragoza,
2021
Resumen: A few decades have passed since quantum chromodynamics (QCD) was established
as the theory describing strong interactions. It is broadly accepted as one of
the most successful theories in modern physics, and it has been extensively
tested, both from the theoretical and the experimental perspectives.
At high energies, QCD is asymptotically free, which means that its
fundamental constituents, quarks and gluons, interact with a strength that
decreases as the energy scale reaches higher values. In this regime, it is
feasible to use perturbation theory to resolve short distance interactions.
On the other hand, for not-so-high energies, the strong interaction cannot
be reduced to a converging series of Feynman diagrams. In fact, one of the
characteristic properties of QCD is the so-called color-confinement. In this
purely non-perturbative regime, there are few techniques that can analyze the
theory successfully. Probably the most well-established of them is lattice
QCD. Since the foundational work of Wilson in 1974, the success of the lattice
approach has been growing consistently over time. Many milestones
have already been reached, including precise simulations that account for the
effects of virtual quark loops, the determination of the light hadron spectrum
with fully controlled systematics or, more recently, the computation of the
isospin splittings with great agreement with the experimental data.
For the above reasons, QCD is believed to be the correct theory describing
strong interactions, both for high and low energies, and lattice QCD is
recognized by the community as a trustworthy ab initio approach that
has an useful interaction with experiment, paraphrasing Wilson. However,
there are some fundamental topics that still constitute open questions.
At least two problems share this status: the behavior of matter at finite
baryonic density and the studies involving topological effects in QCD. The
main difficulty behind the modest progress achieved in both areas is the same:
the action of the theory is complex, and there is no known reformulation that can
avoid the appearance of a severe sign problem (SSP).
In this context, the main part of this thesis has been devoted to study models
which suffer from a SSP, such as the two-dimensional Ising model within an
imaginary magnetic field or the massive 1-flavor Schwinger model with a theta
term. In the first case, we study the well-known model by means of analytical
techniques, exploring a region of the parameter space somewhat unattended by
the literature, possibly due to the difficulty of applying either analytical
or numerical techniques. Secondly, and with the aim of engaging with QCD-like
systems with a theta term and to develop further the methods dealing with the
SSP, we have studied the massive 1-flavor Schwinger model with a $\theta$ term,
which corresponds to QED in $1+1$ dimensions, and is in fact broadly used as its
toy model. Moreover, defining the topological charge on the lattice is almost
trivial in this model, in contrast with any of the usual definitions of this
observable in lattice QCD, which are much more involved. As a byproduct of this
line of work, and driven by the necessity of optimizing further our previous
algorithms, we have also analysed the 2-flavor version of the Schwinger model.
In this case, we have bypassed the computation of the full fermionic determinant
by following an approach based on the use of pseudofermions.
Finally, beyond the study of systems afflicted by a SSP, another topic within
lattice QCD has been treated during the development of this thesis: the strong
running coupling alpha_S. Its dependence with the momentum transfer, which
encodes the underlying interactions of quarks and gluons in the QCD framework,
constitutes a very active field of research, that includes a large variety of
approaches. At large momenta, where perturbative QCD can be applied, both
experimental and theoretical methods try to provide the most accurate
approximation. In this context, lattice-based strategies have been capable of
delivering results both in the infrared region and in the high energy regime,
where in fact they provide the most precise determination of the coupling
constant. Our work can be framed precisely into these approaches that come
from lattice QCD, and it relies upon a ghost-gluon vertex computation.
Resumen (otro idioma):
as the theory describing strong interactions. It is broadly accepted as one of
the most successful theories in modern physics, and it has been extensively
tested, both from the theoretical and the experimental perspectives.
At high energies, QCD is asymptotically free, which means that its
fundamental constituents, quarks and gluons, interact with a strength that
decreases as the energy scale reaches higher values. In this regime, it is
feasible to use perturbation theory to resolve short distance interactions.
On the other hand, for not-so-high energies, the strong interaction cannot
be reduced to a converging series of Feynman diagrams. In fact, one of the
characteristic properties of QCD is the so-called color-confinement. In this
purely non-perturbative regime, there are few techniques that can analyze the
theory successfully. Probably the most well-established of them is lattice
QCD. Since the foundational work of Wilson in 1974, the success of the lattice
approach has been growing consistently over time. Many milestones
have already been reached, including precise simulations that account for the
effects of virtual quark loops, the determination of the light hadron spectrum
with fully controlled systematics or, more recently, the computation of the
isospin splittings with great agreement with the experimental data.
For the above reasons, QCD is believed to be the correct theory describing
strong interactions, both for high and low energies, and lattice QCD is
recognized by the community as a trustworthy ab initio approach that
has an useful interaction with experiment, paraphrasing Wilson. However,
there are some fundamental topics that still constitute open questions.
At least two problems share this status: the behavior of matter at finite
baryonic density and the studies involving topological effects in QCD. The
main difficulty behind the modest progress achieved in both areas is the same:
the action of the theory is complex, and there is no known reformulation that can
avoid the appearance of a severe sign problem (SSP).
In this context, the main part of this thesis has been devoted to study models
which suffer from a SSP, such as the two-dimensional Ising model within an
imaginary magnetic field or the massive 1-flavor Schwinger model with a theta
term. In the first case, we study the well-known model by means of analytical
techniques, exploring a region of the parameter space somewhat unattended by
the literature, possibly due to the difficulty of applying either analytical
or numerical techniques. Secondly, and with the aim of engaging with QCD-like
systems with a theta term and to develop further the methods dealing with the
SSP, we have studied the massive 1-flavor Schwinger model with a $\theta$ term,
which corresponds to QED in $1+1$ dimensions, and is in fact broadly used as its
toy model. Moreover, defining the topological charge on the lattice is almost
trivial in this model, in contrast with any of the usual definitions of this
observable in lattice QCD, which are much more involved. As a byproduct of this
line of work, and driven by the necessity of optimizing further our previous
algorithms, we have also analysed the 2-flavor version of the Schwinger model.
In this case, we have bypassed the computation of the full fermionic determinant
by following an approach based on the use of pseudofermions.
Finally, beyond the study of systems afflicted by a SSP, another topic within
lattice QCD has been treated during the development of this thesis: the strong
running coupling alpha_S. Its dependence with the momentum transfer, which
encodes the underlying interactions of quarks and gluons in the QCD framework,
constitutes a very active field of research, that includes a large variety of
approaches. At large momenta, where perturbative QCD can be applied, both
experimental and theoretical methods try to provide the most accurate
approximation. In this context, lattice-based strategies have been capable of
delivering results both in the infrared region and in the high energy regime,
where in fact they provide the most precise determination of the coupling
constant. Our work can be framed precisely into these approaches that come
from lattice QCD, and it relies upon a ghost-gluon vertex computation.
Resumen (otro idioma):
Pal. clave: fisica teorica ; fisica teorica de altas energias ; teoria cuantica de campos
Titulación: Programa de Doctorado en Física
Plan(es): Plan 488
Nota: Presentado: 28 01 2021
Nota: Tesis-Univ. Zaragoza, , 2021
-
Enlace permanente:
Visitas y descargas
Registro creado el 2021-03-24, última modificación el 2021-05-20
