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Mayank Jately

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- Thread starter Mayank Jately
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Mayank Jately

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mfb

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And spin, helicity, isospin, strangeness, weak hypercharge, lepton flavor numbers, color, and many more. You'll rarely see them in popular science but they exist.After all their are two properties of matter - mass and charge.

Mass is fundamentally different from all the other properties. It is not a multiple of some elementary number, it is directly linked to the rest energy of the particle (unlike all others), and so on.

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Zz.

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Jeffery Winkler

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The Higgs field itself has a generic mass term by its own, but with the “wrong sign”, so that the local SU(2) x U(1) gauge symmetry is broken to U(1). The great discovery of Brout and Englert, Higgs, and Guralnik, Hagen, Kibble (all three articles in PRL 13, 1964) was that in the case of such a spontaneous breaking of a local gauge symmetry is an exception to Goldstone’s theorem that applies to global gauge symmetries only. In the case of a spontaneously broken local gauge symmetry the “would-be Goldstone bosons” are lumped into the gauge fields of the broken part of the symmetry group and thus provide the longitudinal third component of a massive vector boson, i.e., these gauge bosons become massive. In the case of the electroweak standard model that means that the SU(2) weak-isospin gauge bosons become massive (these are the three W and Z bosons), while the unbroken electromagnetic U(1) keeps its massless gauge boson (the photon). Excitations of the Higgs field above its vacuum expectation value (VEV) appear as physical particles in the theory, and that’s the Higgs boson. It gets its mass from the generic mass term and part of the Higgs-self interaction around the VEV. This leads to an effective mass term for the Higgs boson with the right sign. For the usual choice of a “minimal Higgs sector”, where the Higgs field is a SU(2) weak-isospin doublet (4 real field-degrees of freedom, of which 3 are providing the longitudinal components of the W and Z bosons and 1 describes Higgs-boson particles after spontaneous symmetry breaking).

In the original version of the Standard Model, the fermions are massless. When you try to add a mass term by hand, it violates gauge invariance. If there is a Higgs boson, there would have to be an interaction term between the Higgs boson and the fermions, and that interaction term has the same mathematical form as a mass term for the fermions would have, if there were a mass term, and so therefore you can use the interaction term between the Higgs boson and the fermions for the mass term for the fermions, and thus you end up with a mass term for the fermions.

The Higgs boson mass is given by m_H = √ λ/2 v, where λ is the Higgs self-coupling parameter and v is the vacuum expectation value of the Higgs field, v = (√ 2G_F )^ {−1/2} ≈ 246 GeV, fixed by the Fermi coupling G_F , which is determined with a precision of 0.6 ppm from muon decay measurements. λ is presently unknown. Therefore, the Higgs boson mass depend on the Higgs VeV.

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