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 $Delta Ngamma^*$ (Chapter 2) as well as the $Brightarrow K^*$ (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

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 $e$ 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

The B→K∗B\to K^* form factors on the lattice

The extraction of the $B\to K^*$ transition form factors from lattice data is studied, applying non-relativistic effective field theory in a finite volume. The possible mixing of $\pi K$ and $\eta K$ states is taken into account. The two-channel analogue of the Lellouch-L\"uscher formula is reproduced. Due to the resonance nature of the $K^*$, 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

Rare B meson decays on the lattice

We discuss a framework for the measurement of the B → K* transition form factors in lattice simulations, when the K* eventually decays. The possible mixing of πK and ηK states is considered. We reproduce the two-channel analogue of the Lellouch-Lüscher formula, which allows one to extract the B → K*l+l− decay amplitude in the low-recoil region. Since the K* is a resonance, we provide a procedure to determine the form factors at the complex pole position in a process-independent manner. The infinitely-narrow width approximation of the results is also studied

Generating functional for mesonic ChPT with virtual photons in a general covariant gauge

The divergent part of the one-loop effective action in Chiral Perturbation Theory with virtual photons has been evaluated in an arbitrary covariant gauge. The differential operator that emerges in the functional determinant is of non-minimal type, for which the standard heat kernel methods are not directly applicable. Both the SU(2) and SU(3) cases have been worked out. A comparison with existing results in the literature is given

Radiative decays of resonances on the lattice

International audienceWe discuss a generalization of the Lüscher approach to the calculation of the matrix elements of the unstable states. A theoretical framework for the lattice extraction of the ΔNγ* transition form factors is formulated. The procedure to measure the form factors at the resonance pole is given. The current theoretical progress on the B → K*γ* decays is briefly summarized

B→K∗B\to K^* decays in a finite volume

International audienceWe study the extraction of the B → K ∗ transition form factors on the lattice by using the non- relativistic effective field theory in a finite volume. The de termination of the matrix element at the resonance pole is considered in the case of coupled-chan nels. It is shown that, in the limit of the infinitely narrow width, the expected result for the matr ix element is reproduced. The results, contained in this contribution, are discussed at length in R ef. [1]

Resonance matrix elements on the lattice

The notion of resonance matrix elements is discussed. The analogue of the Lellouch-Lüscher formula for the pion photo(electro)production amplitude in the Δ(1232) resonance region is given. A prescription for the pole extraction of the ΔNγ* transition form factors is provided. Theoretical prospects on the lattice calculation of B → K*(892)l+l− form factors are briefly summarized

Resonance matrix elements on the lattice

International audienceThe notion of resonance matrix elements is discussed. The analogue of the Lellouch-Lu K*(892)l^+l^- form factors are briefly summarized