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Life in the Higgs condensate, where electrons have mass
Roland E. Allen
Texas A&M University, Department of Physics and Astronomy, College Station, USA
The particle recently discovered by the CMS and ATLAS collaborations at CERN is almost certainly a Higgs boson, fulfilling a quest that can be traced back to three seminal
high-energy papers of 1964, but which is intimately connected to ideas in other areas
of physics that go back much further. In 1935, Fritz and Heinz London effectively gave
mass to the photon in a superconductor, and thereby provided a macroscopic explanation of the Meissner effect – the expulsion of a magnetic field from a superconductor.
In 1963, Philip Anderson pointed out another important aspect: A would-be zero-mass
Nambu-Goldstone boson in a superconductor is effectively eaten by the photon to become a finite-mass longitudinal mode, which appears as a plasmon in a nonrelativistic
treatment. In 1964, realistic models with Lorentz invariance and nonabelian gauge fields
were formulated by Englert and Brout, by Higgs, and by Guralnik, Hagen, and Kibble. Finally, Weinberg recognized that a Yukawa interaction with the Higgs field would
give masses to fermions like the electron in the fully developed electroweak theory. The
Higgs condensate is thus responsible for the masses both of the gauge bosons which are
carriers of the weak nuclear force and of fermions like electrons, but in different ways.
The radius of an electron’s orbit in the ground state of a hydrogen atom is inversely
proportional to the electron mass, and similar results hold for other atoms. So if the
mass of an electron were zero there would be no atoms, and the formation of ordinary
matter would be impossible without the Higgs condensate. (However, about 99% of the
mass of an atom or human body results from the kinetic energy of quarks and gluons as
they whiz around relativistically inside the protons and neutrons.) It is a true demonstration of the unity of physics that the Meissner effect in a superconducting metal and
the short range of the weak nuclear force in the universe have the same origin: In each
case the vector bosons (photons or W and Z bosons) grow masses because they are
coupled to a field which forms a condensate at low temperature, as the metal is cooled
in the laboratory or the universe expands and cools after the Big Bang. Because of a
quadratic divergence of radiative corrections to its mass, the Higgs boson appears to
require new physics such as supersymmetry, potentially opening the door to a plethora
of new effects and new particles, such as a dark-matter candidate. It is also connected to
grand unification of the forces of nature, with various high-energy symmetry breakings
which presumably involve condensation of Higgs-like fields. Finally, the cosmological
constant and dark energy problems are yet again associated with the Higgs field, whose
condensation should produce an enormous negative vacuum energy. Instead of acting as
an endpoint for physics, and a mere capstone of the Standard Model, the Higgs boson
is thus a harbinger of exciting new physics.