# Higgs boson's mechanism for giving mass?

by keepit
Tags: boson, giving, higgs, mass, mechanism
P: 83
 Quote by keepit In general is the technique of renormalization required because of interactions? I know the question is vague. That's because there's a lot i don't know.
That is correct.
P: 1,685
 Quote by my2cts Can you explain the difference?
See the figure in this post: http://dorigo.wordpress.com/2007/11/...-real-dummies/. The values +/- $\nu$ are the vacuum expectation values of the field for the corresponding vacuum. The Higgs starts in the middle, at the local maximum (the false vacuum), and rolls down to one of the minima (true vacua). The energy of the true vacua, $V(\pm \nu)$, is the vacuum energy of the Higgs. So the vacuum expectation value of the field and the vacuum energy are different things. It is generally assumed that $V(\nu)=0$, but this is really just put in by hand. If $V(\nu)<0$, then the universe should collapse if the Higgs field is dominating the energy density of the universe (this might be what Veltmann is talking about). Otherwise, if $V(\nu)>0$, the universe should inflate once the Higgs field dominates.
 P: 533 Here's how I like to explain it. The Higgs particle gets a nonzero field value from interacting with itself. That nonzero field value then makes it always there for particles that interact with it, and that's what gives those particles their masses.
 Sci Advisor P: 1,685 But you should distinguish between the Higgs field and the Higgs particle, which is the excitation of the field. Gauge bosons acquire mass through their coupling to the VEV, not through Yukawa-type couplings to the field directly.
 P: 533 Gauge particles don't just couple to the Higgs VEV, but to the entire Higgs field, as elementary fermions do.
 Sci Advisor P: 1,685 Of course, but the gauge boson mass terms arise specifically from the coupling with the VEV: $M \sim gv$, where $v$ is the VEV and $g$ the coupling.
 P: 533 The elementary-fermion mass terms also arise in that fashion. Rather schematically, $$L = |(g\cdot W)\cdot H|^2 + (y \cdot \psi_R \cdot H \cdot \psi_L) + \text{H.C.}$$ for the gauge particles and the elementary fermions. $$H = v + \phi$$ Higgs particle -> VEV + excitations So it works the same for both: $$L = (m_W)^2 |W|^2 (1 + \phi/v)^2 + (m_f \cdot \psi_R \cdot \psi_L) (1 + \phi/v) + \text{H.C.}$$ where mW = g*v and mf = y*v.
 P: 83 Ok guys, thanks for the explanations. I wonder what Veltman's pov is on this. How does the cosmological constant fit in?
P: 83
 Quote by bapowell That's the energy of the Higgs vacuum; I'm referring to the vacuum expectation value of the field. The latter is definitively nonzero, the former is unknown. I have no idea Veltman thinks there needs to be an energy associated with the Higgs field that would cause the universe to collapse.

In this link there is more detail:
http://igitur-archive.library.uu.nl/...temVeltman.pdf
 P: 533 The cosmological constant is a sort of vacuum energy density, with pressure = - that density. Notice the minus sign. The big problem with it is that its value is much lower than what one might expect from quantum gravity. One naively expects the Planck density, but its observed value is about 10^(-120) that. Relative to electroweak symmetry breaking, that discrepancy is about 10^(-52) - 10^(-50). I think that it's a problem for quantum gravity, and that is still an unsolved problem.
 P: 83 Veltman states that the cosmological constant in the Higgs model takes the form C= m2M2 / 8g2 , which is way too large. http://igitur-archive.library.uu.nl/...temVeltman.pdf
 P: 270 This must be one of the most common questions I have seen on this forum

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