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A puzzle about the higgs mechanism 
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#1
Mar1812, 11:32 PM

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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
Mar1912, 02:21 AM

P: 369

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



#3
Mar1912, 02:57 AM

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



#4
Mar1912, 10:41 AM

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A puzzle about the higgs mechanism
I think what the original poster is missing is that they think in terms of "speed", and they should reformulate 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
Mar1912, 01:23 PM

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#6
Mar1912, 03:49 PM

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#7
Mar1912, 10:49 PM

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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 crosssections in deep inclusive electron (positron) proton scattering become equal at short distances, as predicted by the standard model :



#8
Mar2012, 02:42 AM

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#9
Mar2012, 04:14 AM

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#10
Mar2012, 06:10 AM

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#11
Mar2012, 11:22 AM

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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. 


#12
Mar2112, 05:15 PM

P: 136

One thing I don't understand here: why do the charged and neutral current crosssections 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 presymmetrybreaking coupling constants.



#13
Mar2112, 06:21 PM

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#14
Mar2112, 10:11 PM

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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 nontrivially to the right handed electron singlet, so there cannot be anything to "restore" there, very high energy will not create right handed neutrinos. 


#15
Mar2112, 10:47 PM

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#16
Mar2212, 04:43 AM

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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 nonvanishing vacuum expectation value [itex]\langle \phi \rangle [/itex]. 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 [itex]\langle \phi^2 \rangle [/itex] will even be larger than at T=0, so that electrons will never decouple from the Higgs field.



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