Chapter 1
Symmetries in the Standard Model
Jose Bernabeu
Abstract Symmetries in the Physical Laws of Nature lead to observable effects.
Beyond the regularities and conserved magnitudes, the last decades in Particle
Physics have seen the identification of symmetries, and their well-defined breaking,
as the guiding principle for the elementary constituents of matter and their interactions. Flavour SU(3) symmetry of hadrons led to the Quark Model and the
antisymmetry requirement under exchange of identical fermions led to the colour
degree of freedom. Colour became the generating charge for flavour-independent
strong interactions of quarks and gluons in the exact Colour SU(3) local gauge
symmetry. Parity violation in weak interactions led to consider the chiral fields of
fermions as the objects with definite transformation properties under the weak
isospin SU(2) gauge group of the unifying electroweak SU(2) Â U(1) symmetry,
which predicted novel weak neutral current interactions. CP violation led to three
families of quarks opening the field of Flavour Physics. Time-reversal violation has
recently been observed with entangled neutral mesons, compatible with
CPT-invariance. The cancellation of gauge anomalies, that would invalidate the
gauge symmetry of the quantum field theory, leads to quark-lepton symmetry. The
experimental discovery of quarks and leptons and the mediators of their interactions,
with physical observables in spectacular agreement with this standard theory, is the
triumph of symmetries. The gauge symmetry is exact only when the particles are
massless. One needs a subtle breaking of the symmetry, providing the origin of mass,
without affecting the excellent description of the interactions. This is the Brout–
Englert–Higgs mechanism which produces the Higgs boson as a remnant discovered
at CERN in 2012. Open present problems are addressed with the search of New
Physics Beyond-the-Standard-Model.
J. Bernabeu (*)
Department of Theoretical Physics, University of Valencia, Valencia, Spain
IFIC, Joint Centre UV-CSIC, Burjassot, Spain
e-mail: Jose.Bernabeu@uv.es
© Springer Nature Switzerland AG 2021
B. G. Sidharth et al. (eds.), Fundamental Physics and Physics Education Research,
https://doi.org/10.1007/978-3-030-52923-9_1
3
Symmetries in the Standard Model
Jose Bernabeu
Abstract Symmetries in the Physical Laws of Nature lead to observable effects.
Beyond the regularities and conserved magnitudes, the last decades in Particle
Physics have seen the identification of symmetries, and their well-defined breaking,
as the guiding principle for the elementary constituents of matter and their interactions. Flavour SU(3) symmetry of hadrons led to the Quark Model and the
antisymmetry requirement under exchange of identical fermions led to the colour
degree of freedom. Colour became the generating charge for flavour-independent
strong interactions of quarks and gluons in the exact Colour SU(3) local gauge
symmetry. Parity violation in weak interactions led to consider the chiral fields of
fermions as the objects with definite transformation properties under the weak
isospin SU(2) gauge group of the unifying electroweak SU(2) Â U(1) symmetry,
which predicted novel weak neutral current interactions. CP violation led to three
families of quarks opening the field of Flavour Physics. Time-reversal violation has
recently been observed with entangled neutral mesons, compatible with
CPT-invariance. The cancellation of gauge anomalies, that would invalidate the
gauge symmetry of the quantum field theory, leads to quark-lepton symmetry. The
experimental discovery of quarks and leptons and the mediators of their interactions,
with physical observables in spectacular agreement with this standard theory, is the
triumph of symmetries. The gauge symmetry is exact only when the particles are
massless. One needs a subtle breaking of the symmetry, providing the origin of mass,
without affecting the excellent description of the interactions. This is the Brout–
Englert–Higgs mechanism which produces the Higgs boson as a remnant discovered
at CERN in 2012. Open present problems are addressed with the search of New
Physics Beyond-the-Standard-Model.
J. Bernabeu (*)
Department of Theoretical Physics, University of Valencia, Valencia, Spain
IFIC, Joint Centre UV-CSIC, Burjassot, Spain
e-mail: Jose.Bernabeu@uv.es
© Springer Nature Switzerland AG 2021
B. G. Sidharth et al. (eds.), Fundamental Physics and Physics Education Research,
https://doi.org/10.1007/978-3-030-52923-9_1
3