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Flavor structure in magnetized orbifold and blow-up manifold compactification

内田, 光 北海道大学

2023.03.23

概要

In the particle physics, the standard model (SM) is the successful theory to explain a lot of
observations related to the strong and electroweak (EW) interactions by GSM = SU (3)C ×
SU (2)L × U (1)Y gauge symmetry for their gauge bosons and the local symmetry for matter
fermions as well as Higgs fields in four-dimensional (4D) space-time. The SM particle contents
are listed in Table 1.1. Among them, there are three types of renormalizable couplings: gauge
couplings among gauge bosons and matter fermions as well as Higgs fields, Yukawa couplings
among matter fermions and Higgs fields, and Higgs self-couplings. Note that weak boson
masses and matter fermion masses are obtained by the EW spontaneously symmetry breaking
(SSB) of Higgs fields through the gauge couplings and Yukawa couplings with the Higgs fields,
respectively. On the other hand, before the EW symmetry breaking, gauge bosons and chiral
matter fermions cannot have their masses because of the gauge symmetries and the chiral
symmetries, respectively. Although neutrinos have much tinier masses than the other quarks
and charged leptons, they can be explained by considering the Weinberg operators among
lepton doublets and Higgs doublets with mass dimension 5 if neutrinos are Majorana neutrinos.
Then, by appropriately fitting their SM parameters: gauge coupling constants, Yukawa coupling
constants (as well as Weinberg operator coefficients), and Higgs self-coupling constants, the SM
predictions are consistent with a lot of observations.
However, there remain a lot of issues to be solved: quantum gravitational phenomena cannot be explained in the SM, there are still some discrepancies between the SM predictions
and the experimental results, there are some mysteries such as the origins of the values of the
SM parameters to explain observations, and so on. In particular, to clear the origins of the
SM parameters may give us hints to discover more fundamental theories. For example, the
three gauge coupling constants may be unified around O(1016 )GeV, (see Ref. [1] for the current
renormalization group (RG) flows of the SM parameters,) which implies that there is a more
fundamental theory to unify the three gauge symmetries into one larger gauge symmetry including GSM such as SU (5) and SO(10) with one gauge coupling constant above the scale and
the large gauge symmetry is spontaneously broken at the scale like the EW symmetry breaking
by the SM Higgs fields. Such a fundamental theory is called a grand unified theory (GUT) [2–4]. ...

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