Running Constants: Unifying Gaugino Masses in SUSY

In summary: So in summary, the gaugino masses in SUSY models are typically unified at the GUT scale, but if SUSY breaking occurs at a lower energy scale, this unification may not hold. Similarly, in the Standard Model, the W and Z bosons may become effectively massless at high energies above the symmetry breaking scale. However, it is also possible to have a supersymmetric theory without gauge interactions where the masses of particles are not necessarily unified.
  • #1
ChrisVer
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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 [itex]m_{\bar{g}},m_{\bar{W}},m_{\bar{B}}[/itex] (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:
[itex]m_{\bar{g}}:m_{\bar{W}}:m_{\bar{B}}≈6:2:1[/itex]
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...
 
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  • #2
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
ChrisVer said:
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...

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
Orodruin said:
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.

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
ChrisVer said:
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...

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
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
I can't say that I understand what your point is.
 
  • #8
andrien said:
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.
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
andrien said:
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.

Ahh I see. Interesting.
 

1. What is SUSY and why is it important in particle physics?

SUSY, or Supersymmetry, is a theoretical framework that proposes a new symmetry between fermions and bosons. It is important in particle physics because it provides a possible solution to the hierarchy problem, which is the large discrepancy between the mass of the Higgs boson and the expected mass based on the Standard Model of particle physics. SUSY also predicts the existence of new particles that could help explain dark matter.

2. What are gaugino masses and how do they relate to SUSY?

Gaugino masses are the mass parameters of the superpartners of gauge bosons in SUSY. They play a crucial role in the unification of the different gauge couplings in the Standard Model. In SUSY, the masses of these particles are related to each other by a running constant, which is a key concept in this theory.

3. How does "Running Constants" unify gaugino masses in SUSY?

The "Running Constants" method is a theoretical framework that uses the renormalization group equations (RGEs) to relate the gaugino masses at different energy scales. This allows for the prediction of the gaugino mass parameters at high energy scales, such as the Grand Unification scale, based on their values at lower energy scales. This unification of gaugino masses is a key feature of SUSY.

4. What are the implications of the "Running Constants" method in SUSY phenomenology?

The "Running Constants" method has important implications in SUSY phenomenology, as it allows for the prediction of the masses of superpartners, which could be detected at high energy colliders such as the Large Hadron Collider (LHC). It also provides a framework for testing the validity of SUSY models and could help narrow down the possible parameter space of these models.

5. Are there any limitations or challenges in using the "Running Constants" method in SUSY?

Like any theoretical framework, the "Running Constants" method has its limitations and challenges. One major limitation is the complexity of the RGEs, which require precise calculations and assumptions. There are also uncertainties in the experimental measurements of the gauge couplings that could affect the predictions of the gaugino masses. Additionally, the "Running Constants" method relies on the assumption that SUSY is the correct theory, which has not yet been confirmed by experimental evidence.

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