| Abstract [eng] |
Determining the Gauge Dependence of the Loop-corrected Light Neutrino Propagator The Standard Model of particle physics predicts that neutrinos are massless particles. However, it is now a well known fact that neutrinos must have nonzero masses [1], albeit very small ones: currently established limit of the sum of neutrino masses is < 0.12 eV (95% C.L.) [2]. For comparison, the mass of the next lightest particle of the Standard Model, the electron, is ~511 keV, 6 orders of magnitude higher. The question of the origin of this huge mass difference is currently on the frontier of research of theoretical particle physics, and it is one of the most promising paths to the physics beyond the Standard Model. The most ubiquitous explanation is the so-called seesaw mechanism. It has several versions; one of the simplest extends the Standard Model (SM) with an additional right-handed neutrino field and a second Higgs doublet, allowing to generate three massive neutrino fields — one very heavy (possibly of the order of 10^14 GeV), two very light (order of 1 eV) — and one massless [3]. This model (let’s further call it the Grimus-Neufeld (GN) model) seems promising, since it is economical (the SM is extended only slightly) and reproduces the mass hierarchy of the neutrino fields that is compatible with observations. In [4], among other things, it is shown that in the GN model one of the light neutrino fields acquires mass through one-loop corrections to the neutrino propagator. It means that the expressions of one-loop corrections (and, consequently, the parameters of the GN model) can be connected with experimentally measurable quantities (squared mass differences of the neutrinos). This could allow making concrete numerical predictions and testing the validity of the GN model (if, for example, the second Higgs doublet is experimentally discovered at some point in the future). However, first we must be sure that the theory is consistent. One of the most obvious consistency checks of a gauge theory is its gauge invariance: None of the physically observable predictions of the theory should depend on the value of an arbitrary gauge parameter. In [4] the authors concisely show that the one-loop corrections they obtain are gauge invariant. The aim of this work is to check this result using a different approach. This master’s thesis continues and finishes the work of my last three semester’s papers. The first one [5] was an introduction to the quantum field theory and, more specifically, the concept of propagators. Second semester’s work [6] focused on understanding concepts of spinors and gauge invariance, and presented our approach to deriving one-loop corrections of the neutrino propagator in a general model, not tied to any specific particle fields. Third semester’s paper [7] connected the Lagrangian of this general model with the Standard Model extended by one right-handed neutrino field. And, finally, this master’s thesis aimed to (i) make the particle content of our model the same as in the GN model by introducing the second Higgs doublet, and (ii) check, whether the one-loop corrections to the neutrino propagator calculated in our formalism are gauge-invariant. These aims were achieved: In the 2nd section the second Higgs doublet is presented, and in the 4th section — connected with our model; in the 6th section the gauge dependence of one-loop corrections is investigated. It was determined that the mass corrections of the first and the second neutrinos are gauge independent, agreeing with the results of [4]. However, the gauge parameter does not vanish from the expressions of mass corrections of the third neutrino. Possible reasons for this result are briefly discussed in the end of section 6. |
