# Running constants

1. May 7, 2014

### ChrisVer

Well I am having some difficulty in understanding the running constants... I am not sure if this applies to the Standard Model as well, but I saw that in SUSY recently...
If we take the value of the gaugino masses $m_{\bar{g}},m_{\bar{W}},m_{\bar{B}}$ (by bar I mean Gluino,W-ino and B-ino) to be equal at some energy scale (~MGUT) then we can go to lower energy scales (let's say at TeV) to find their ratio:
$m_{\bar{g}}:m_{\bar{W}}:m_{\bar{B}}≈6:2:1$
I guess this ratio depends on the model.

My problem is that I don't understand how we can do that, in the case the SuSy breakdown occurs at lower energies than M_GUT... While SuSy is unbroken, the gauginos will have to be massless, right? If the breakdown occurs at around 2TeV let's say, then it's meaningless to speak about their masses...

2. May 7, 2014

### Orodruin

Staff Emeritus
The same thing happens with fermion masses in the Standard Model. Typically it is just a matter of sloppy wording and what really is running are the Yukawa couplings (at least above EWSB). I am no SUSY expert, but I suspect there is something similar at work here.

3. May 8, 2014

### kurros

In SUSY models where you have some unification of masses etc. at the GUT scale, then it is at the GUT scale where the SUSY breaking is hypothesised to be happening. So no, that sort of unification doesn't make any sense if the SUSY breaking scale is way below the GUT scale.

4. May 8, 2014

### ChrisVer

yes, the same question I could ask for the Standard Model as well for above the EWSB...
For example do the W and Z bosons we know become massless? I think they do (at least effectively) because you will have energies above the vev energy...

5. May 8, 2014

### kurros

Yeah actually I'd like to know the details of this too. Does anyone have a good reference? The whole point of the Higgs mechanism is that the fermions have no mass before symmetry breaking, but how literally can this be "undone" in high energy collisions? What is happening? If we calculate say the running top mass in some renormalisation scheme or other, does it go to zero above the symmetry breaking scale? What will happen experimentally to reflect this?

6. May 8, 2014

### andrien

Be careful here, it is possible to have a supersymmetric theory of scalars and fermions which does not have gauge interactions. In this case, a supersymmetric multiplet necessarily have the same mass because supercharges commute with the momentum operator, so a supercharge acting on a state does not alter the eigenvalue of pμpμ.

The equality of masses is a result of presence of auxiliary field which has no kinetic term and eliminating it by EOM yields the constraints on fermion boson masses and coupling constant.

7. May 11, 2014

### kurros

I can't say that I understand what your point is.

8. May 12, 2014

### andrien

It is meaningful to talk about masses of particles in a supersymmetric theory even when the SUSY breaking has not taken place if you don't have requirement of gauge invariance.

9. May 12, 2014

### kurros

Ahh I see. Interesting.