# A puzzle about the higgs mechanism

1. Mar 18, 2012

### Accidently

I might misunderstand the higgs mechanism. And I have a puzzle.

Consider an electron in an accelerater. It is massive at low energy and its speed is something lower than the speed of light. However when it is accelerated to the electroweak scale, su(2) becomes unbroken and the electron turns to be massless and its speed turns into the speed of light at this point.

It seems there is an infinite acceleration when the electron energy reaches electroweak scale.

I just feel this is unnatural, or I missed something there.

2. Mar 19, 2012

### kurros

The Higgs mechanism only gives rest masses to particles, it has nothing (else) to do with their relativistic mass.

3. Mar 19, 2012

### DrDu

In some way, electrons always move at the speed of light, although only for very short distances. Look up "Zitterbewegung".

4. Mar 19, 2012

### humanino

I think what the original poster is missing is that they think in terms of "speed", and they should re-formulate their question in terms of energy transfered to the electron after some finite potential difference. Thinking in terms of "speed" is not wrong, but also it is not very helpful because the "speed" of the electron in an accelerator can become equal to the speed of light "for all practical purposes" (to be specifically defined) although the energy of the electron remains finite. This happens as soon as the mass is negligible compared to the total energy, and it is merely special relativity. Also, it happens much sooner than required to restore electroweak symmetry, and has nothing to do at this point with electroweak symmetry, because the electroweak scale is much higher than the electron mass. Once the original poster reformulate their problem in terms of energy scales, they may not need further clarification.

5. Mar 19, 2012

### DrDu

No, that is not the case. You would have to increase the energy of all particles in the universe to the electroweak scale to un-break the electroweak symmetry.

6. Mar 19, 2012

### kurros

Also they have to collide with each other. A particle in an accelerator that is just zooming around a storage ring just feels like a normal, non-moving version of itself (synchrotron radiation aside), since relative to itself it is not moving. However, if it collides with something, the centre of mass energy is a relativistic invariant, so you cannot make it go away by changing reference frame. It is only at this point that some symmetry breaking voodoo can happen.

7. Mar 19, 2012

### humanino

I am not sure I quite understand what is being claimed in this thread. If a collision occurs at high enough energy, there will be electroweak symmetry restoration. This is not a controversial claim, it is a measured fact. For instance, the H1 and ZEUS combined plot clearly show that the neutral and charged current cross-sections in deep inclusive electron (positron) proton scattering become equal at short distances, as predicted by the standard model :

8. Mar 20, 2012

### DrDu

Very interesting in deed! Could you explain a little bit more in detail what is shown in the plot?

9. Mar 20, 2012

### Bill_K

Neither am I. I think most people would be surprised to learn that the equality of neutral and charged current cross-sections amounts to the restoration of electroweak symmetry, and that this restoration happens at only 100 GeV.

10. Mar 20, 2012

### kurros

Sure, but this is 100 GeV centre of mass energy, i.e. something that happens during a collision, not something that happens to a 100 GeV beam, which seemed to be the assumption the OP was making when they suggested that the particles in the beam would become massless and accelerate themselves up to c.

11. Mar 20, 2012

### humanino

Sure, those are cross-sections as a function of virtuality of the probe for electron (triangles and circles) and positron (stars and squares) deep inclusive scattering on protons, charged (red) and neutral (blue) currents.

For the neutral currents, the lepton remains unchanged and is detected in the final state. The probe is a superposition of photon and Z0. For charged currents, the initial lepton turns into a neutrino which escapes detection and is tagged by requiring a large missing transverse momentum. Detailed simulation had to be carried out, as reported in
Measurement of charged current deep inelastic scattering cross sections with a longitudinally polarised electron beam at HERA
The probe is a superposition of W+ and W-.

There is more than one aspect to electroweak symmetry, and certainly the scattering of high energy leptons on protons in the standard model (without neutrino mass) does not create right handed neutrinos or left handed antineutrinos. This being said, one aspect to electroweak symmetry restoration is indeed in the equality of cross-section for neutral and charged currents (in other words, it is a necessary albeit not sufficient condition), which we naturally expect to happen right above the boson masses.

Last edited: Mar 20, 2012
12. Mar 21, 2012

One thing I don't understand here: why do the charged and neutral current cross-sections become the same even if symmetry is restored? The former are mediated by W fields only, while the latter is a combination of a W and a B and these have different pre-symmetry-breaking coupling constants.

13. Mar 21, 2012

### kurros

I am not sure what you are saying here. There are no right handed neutrinos in the Standard Model, so what could they possibly have to do with electroweak symmetry?

14. Mar 21, 2012

### humanino

The term "equal" was definitely too strong. It was merely appealing to the gross qualitative feature on a logarithmical plot. Quantitatively, as you can see from the graph there are some numerical factors remaining, first off the electric charges. The coupling constants run and converge at high energy.

The reason I mentioned right handed neutrinos is because their absence (in the textbook old standard model) in the lepton sector prevents the electroweak SU(2) to apply non-trivially to the right handed electron singlet, so there cannot be anything to "restore" there, very high energy will not create right handed neutrinos.

15. Mar 21, 2012

### kurros

Sure, but are we not talking about restoring the symmetries of the textbook Standard Model? So won't we be happy just to see that the ordinary left-handed SU(2) is restored (and the orignal hypercharge U(1))?

16. Mar 22, 2012

### DrDu

I think the original question was not whether some scattering cross sections become equal at some scale, but that electrons owe their mass to the constant scattering from the Higgs field which has a non-vanishing vacuum expectation value $\langle \phi \rangle$. The question is whether electrons would become massless again, once one goes to so high energies, or better temperatures, that the vacuum expectation value of the Higgs field vanishes. I don't think this to be the case as at high temperatures the variance of the Higgs field $\langle \phi^2 \rangle$ will even be larger than at T=0, so that electrons will never decouple from the Higgs field.