Izbrane teme sodobne fizike in matematike
The Standard Model (SM) of particle physics provides a robust framework for understanding the electromagnetic, weak, and strong interactions of fundamental particles. Despite its many experimental successes, it leaves several important phenomena unexplained, such as flavor mixing and the pronounced hierarchies in fermion masses; collectively referred to as the flavor puzzle. This article explores how fermions within the SM acquire hierarchical masses through the Higgs mechanism and Yukawa couplings, which in turn give rise to the Cabibbo-Kobayashi-Maskawa (CKM) matrix that plays a central role in flavor mixing. As one possible approach to understanding this hierarchical structure, the Froggatt-Nielsen (FN) mechanism is presented, introducing a horizontal \(U(1)_{\text{X}}\) flavor symmetry together with a new scalar field, the flavon. The spontaneous breaking of this symmetry through higher-dimensional operators leads to new FN couplings that yield a natural explanation for the observed fermion mass hierarchy. Finally, the article examines the phenomenological implications of generic FN models at low energies, such as meson mixing, and discusses possible UV completions of the theory through introduction of vector-like fermions. The analysis indicates that consistency with experimental constraints requires a high energy FN scale, thereby providing insights into possible extensions beyond the SM.
Standardni model (SM) fizike delcev predstavlja dober okvir za razumevanje elektromagnetnih, šibkih in močnih interakcij osnovnih delcev. Kljub številnim eksperimentalnim uspehom pa ta ne pojasni nekaterih pomembnih pojavov, kot sta mešanje kvarkovskih okusov in izrazita hierarhija mas fermionov; skupaj znana kot problem okusa (flavor puzzle). Članek obravnava, kako fermioni v okviru SM pridobijo hierarhične mase preko Higgsovega mehanizma in Yukawinih sklopitev, pri čemer le-te vodijo do nastanka matrike Cabibbo-Kobayashi-Maskawa (CKM), ki igra ključno vlogo pri mešanju okusov. Kot eden izmed možnih pristopov k razumevanju te hierarhične strukture, je predstavljen Froggatt-Nielsenov (FN) mehanizem, ki uvaja horizontalno simetrijo okusov \(U(1)_{\text{X}}\) in novo skalarno polje, flavon. Spontani zlom te simetrije preko operatorjev višjih dimenzij vodi do novih FN sklopitev, ki nudijo naravno razlago opažene masne hierarhije. V nadaljevanju so obravnavane tudi fenomenološke posledice splošnih FN modelov pri nizkih energijah, kot je mešanje mezonov, ter možne UV razširitve teorije (UV completion) z vpeljavo vektorskih fermionov. Analiza pokaže, da skladnost teorije z obstoječimi eksperimentalnimi omejitvami zahteva visoko energijsko FN skalo, kar odpira vpogled v potencialne razširitve teorije onkraj SM.