Speaker
Description
An open problem that the Standard Model does not solve is about the ori-
gin of the mass hierarchy among fermions. Different alternatives have been
proposed by adding extra groups to the Gauge group of the Standard Model or
by building hybrid models with some of them. It has been shown that the S3
symmetry has given good results if, in addition, three Higgs doublets with their
invariant potential of S3 are introduced. However, when taking into account
the minimization conditions of the Higgs potential, the resulting matrix VCKM
exhibits a residual symmetry with zeros in some entries. Following the success
of S3, an extension of the Standard Model is proposed by means of the same
group, but obtained from modular symmetry. In doing so, certain special func-
tions known as modular forms are taken into account, which have a particular
transformation under the application of the modular group. By considering a
modular symmetry, it is possible to assign to the quark fields and Higgs fields
a new quantity known as the modular weight which, together with the symme-
try of S3, produces new constraints on the way the Yukawa sector Lagrangian
is built and hence the couplings, which will be in terms of modular forms. A
proper assignment of the quark and Higgs fields in S3 and their modular weights
allows a mass matrix with texture zeros to be written. When calculating the
elements of the quark mixing matrix VCKM, it is found that, indeed, the VCKM
matrix does not exhibit zeros in any of its inputs and they are comparable to
the data provided by the PDG.
