# B Weak force symmetry broken above 250 GeV?

1. Aug 16, 2016

### cube137

I'm reviewing this book Warped Passages by Lisa Randall and a sentence caused me some incomprehension. Somewhere in it she stated:

"The weak gauge boson masses tell us the precise value of the energy at which the weak force symmetry is spontaneously broken. That energy is 250 GeV, the weak scale energy, very close to the masses of the weak gauge bosons, the W-, the W+ and the Z. When particles have energy greater than 250 Gev, interactions occur as if the symmetry is preserved, but when their energy is less than 250 Gev, the symmetry is broken and weak gauge bosons act as if they have mass. With the correct value of the nonvanishing Higgs field, the weak force symmetry is spontaneously broken at the right energy, and the weak gauge bosons get precisely the right mass."

I'd like to know something. Why, if the energy of the accelerator is above 250 GeV. Can they see the weak bosons losing mass and become massless, just like the photons?

And why the 250 GeV value? The mass of the Z is 91.1876 GeV and the Ws is 80.385 GeV. Where did Lisa come up with 250 GeV (which is exactly double the mass of the Higgs.. the book written in 2006, so she didn't know).

2. Aug 17, 2016

### ChrisVer

Well it is ~246GeV, so nothing great with the 250 value.... It is the Higg's vaccuum expectation value.

The rest I guess may refer to the equivalence theorem... http://journals.aps.org/prd/abstract/10.1103/PhysRevD.41.2294 ?
or it may just want to state that since the energy E $E>>M_V$ the mass of the vector boson, the interactions don't depend [at leading order] on the vector boson's mass?

3. Aug 17, 2016

### cube137

Why, at LHC, if the energies are above 245 GeV.. can they detect the weak bosons as massless (before electroweak symmetry breaking)?

4. Aug 18, 2016

### vanhees71

Well, that's a bit tricky. A way to get a world, where the VEV of the Higgs field vanishes, you'd have to have to create ultrahot matter, i.e., matter at temperatures that cannot achieved with our present technology. Nevertheless, even then the vector bosons wouldn't be exactly massless, because all particles get thermal masses and a finite width in the medium.

What has been achieved at the CERN SPS, RHIC, and the LHC, however, is the confinement-deconfinement phase transition. This is done by colliding heavy nuclei (heavy ions) and create a very hot and dense medium, the socalled quark-gluon plasma, which however lasts only for a few $\mathrm{fm}/c$ since the fireballs of a few fm size expand and cool down quickly. Wikipedia has a nice overview on the subject:

https://en.wikipedia.org/wiki/Quark–gluon_plasma

5. Aug 18, 2016

### cube137

The Quark-gluon_plasma is related to QCD. I was asking about Electroweak. Or let me just ask you if the third polarization of the massive weak gauge bosons were gone at high-energy interactions at the LHC. The following is the context of my questions.. quoting from Lisa Randall Warped Passages:

"These two facts together imply something fairly profound: to avoid problematic high-energy predictions, an internal
symmetry is essential—the lessons of the previous chapter still apply. But when the massive gauge bosons have low
energy (low compared with the energy that Einstein's relation E = mc2 associates with its mass), the symmetry should no
longer be preserved. The symmetry must be eliminated so that gauge bosons can have mass and the third polarization can
participate in the low-energy interactions where the mass makes a difference.

In 1964, Peter Higgs and others discovered how theories of forces could incorporate massive gauge bosons by doing
exactly what we just said: keeping an internal symmetry at high energies, but eliminating it at low energies. The Higgs
mechanism, based on spontaneous symmetry breaking, breaks the internal symmetry of the weak interactions, but only at
low energy. That ensures that the extra polarization will be present at low energy, where the theory needs it. But the extra
polarization will not participate in high-energy processes, and the nonsensical high-energy interactions will not appear."

Vanhees71. Is the high-energy processes vs low energies about the accelerator energies at the LHC which can turn on and off the third polarization of the weak bosons?

6. Aug 19, 2016

### ChrisVer

Well nothing is lost/gone, since at the end of the day you can calculate amplitudes without caring about the longitudinal polarization of the vector bosons (you just need to make an appropriate exchange with the Higgs ghosts, which are would-be goldstone bosons). That is how I interpret the equivalence theorem. So it's not like it's "gone". It's not turned on or off as a result.

7. Aug 19, 2016

### vanhees71

I know, and I told you that we don't have any handle on "un-Higgsed" electroweak matter, because for that we'd need ultrahigh energies. In nature, according to our understanding now, this has been present only very very shortly after the Big Bang. The only analogue situation is the QGP and the "melting" of the quark condensate, which however is not a Higgsed local but a spontaneously global symmetry (note that local symmetries cannot be spontaneously broken although it's always said in this way, but that's a mathematical theorem (Elitzur's theorem)).