66 research outputs found
Nucleon in a periodic magnetic field
The energy shift of a nucleon in a static periodic magnetic field is
evaluated at second order in the external field strength in perturbation
theory. It is shown that the measurement of this energy shift on the lattice
allows one to determine the unknown subtraction function in the forward doubly
virtual Compton scattering amplitude. The limits of applicability of the
obtained formula for the energy shift are discussed.Comment: The explicit factor is restored in the equations. The conclusions
are unchange
Nucleon in a periodic magnetic field: Finite-volume aspects
The paper presents an extension and a refinement of our previous work on the
extraction of the doubly virtual forward Compton scattering amplitude on the
lattice by using the background field technique, Phys. Rev. D 95, 031502 (2017)
(arXiv:1610.05545). The zero frequency limit for the periodic background field
is discussed, in which the well-known result is reproduced. Further, an upper
limit for the magnitude of the external field is established for which the
perturbative treatment is still possible. Finally, the framework is set for the
evaluation of the finite-volume corrections allowing for the analysis of
upcoming lattice results.Comment: 42 pages, 5 figures; version accepted for publication in Physical
Review
Partial twisting for scalar mesons
The possibility of imposing partially twisted boundary conditions is
investigated for the scalar sector of lattice QCD. According to the commonly
shared belief, the presence of quark-antiquark annihilation diagrams in the
intermediate state generally hinders the use of the partial twisting. Using
effective field theory techniques in a finite volume, and studying the scalar
sector of QCD with total isospin I=1, we however demonstrate that partial
twisting can still be performed, despite the fact that annihilation diagrams
are present. The reason for this are delicate cancellations, which emerge due
to the graded symmetry in partially quenched QCD with valence, sea and ghost
quarks. The modified Luescher equation in case of partial twisting is given.Comment: 35 pages, 4 figure
Exploring exotic states with twisted boundary conditions
The goal of this thesis is to develop methods to study the nature and properties of exotic hadrons from lattice simulations. The main focus lies in the application of twisted boundary conditions. The thesis consists of a general introduction and the collection of three papers, represented respectively in three chapters. The introduction of the thesis reviews the theoretical background, which is further used in the rest of the thesis. Further, in Chapter 1, implementing partially twisted boundary conditions in the scalar sector of lattice QCD is studied. In Chapter 2, we develop a method to study the content of the exotic hadrons by determining the wave function renormalization constant from lattice simulations, exploiting the dependence of the spectrum on the twisted boundary conditions. Finally, Chapter 3 deals with a novel method to study the multi-channel scattering problem in a finite volume, which is relevant for exotic states. Its key idea is to extract the complex hadron-hadron optical potential, avoiding the difficulties, associated with the solution of the multi-channel Lüscher equation
Bound states on the lattice with partially twisted boundary conditions
We propose a method to study the nature of exotic hadrons by determining the
wave function renormalization constant from lattice simulations. It is
shown that, instead of studying the volume-dependence of the spectrum, one may
investigate the dependence of the spectrum on the twisting angle, imposing
twisted boundary conditions on the fermion fields on the lattice. In certain
cases, e.g., the case of the bound state which is addressed in detail, it
is demonstrated that the partial twisting is equivalent to the full twisting up
to exponentially small corrections
Hadronic Electroweak Processes in a Finite Volume
In the present thesis, we study a number of hadronic electroweak processes in a finite volume. Our work is motivated by the ongoing and future lattice simulations of the strong interaction theory called quantum chromodynamics. According to the available computational resources, the numerical calculations are necessarily performed on lattices with a finite spatial extension. The first part of the thesis is based on the finite volume formalism which is a standard method to investigate the processes with the final state interactions, and in particular, the elastic hadron resonances, on the lattice. Throughout the work, we systematically apply the non-relativistic effective field theory. The great merit of this approach is that it encodes the low-energy dynamics directly in terms of the effective range expansion parameters. After a brief introduction into the subject in Chapter 1, we formulate a framework for the extraction of the (Chapter 2) as well as the (Chapter 3) transition form factors from lattice data. Both processes are of substantial phenomenological interest, including the search for physics beyond the Standard Model. Moreover, we provide a proper field-theoretical definition of the resonance matrix elements, and advocate it in comparison to the one based on the infinitely narrow width approximation. In the second part, which includes Chapter 4, we consider certain aspects of the doubly virtual nucleon Compton scattering. The main objective of the work is to answer the question whether there is, in the Regge language, a so-called fixed pole in the process. To answer this question, the unknown subtraction function, which enters one of the dispersion relations for the invariant amplitudes, has to be determined. The external field method provides a feasible approach to tackle this problem on the lattice. Considering the nucleon in a periodic magnetic field, we derive a simple relation for the ground state energy shift up to a second order in the field strength. The obtained result encodes the value of the subtraction function at nonzero photon virtuality. The knowledge of the latter is also important to constrain the two-photon exchange contribution to the Lamb shift in a muonic hydrogen
The form factors on the lattice
The extraction of the transition form factors from lattice data is
studied, applying non-relativistic effective field theory in a finite volume.
The possible mixing of and states is taken into account. The
two-channel analogue of the Lellouch-L\"uscher formula is reproduced. Due to
the resonance nature of the , an equation is derived, which allows to
determine the form factors at the pole position in a process-independent
manner. The infinitely-narrow width approximation of the results is discussed.Comment: 29 pages, 4 figure
The Optical Potential on the Lattice
The extraction of hadron-hadron scattering parameters from lattice data by
using the L\"uscher approach becomes increasingly complicated in the presence
of inelastic channels. We propose a method for the direct extraction of the
complex hadron-hadron optical potential on the lattice, which does not require
the use of the multi-channel L\"uscher formalism. Moreover, this method is
applicable without modifications if some inelastic channels contain three or
more particles.Comment: 26 pages, 12 figure
Finite volume corrections to forward Compton scattering off the nucleon
We calculate the spin-averaged amplitude for doubly virtual forward Compton
scattering off nucleons in the framework of manifestly Lorentz invariant baryon
chiral perturbation theory at complete one-loop order . The
calculations are carried out both in the infinite and in a finite volume. The
obtained results allow for a detailed estimation the finite-volume corrections
to the amplitude which can be extracted on the lattice using the background
field technique.Comment: 35 pages, 8 figure
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