Supersymmetry O'Raifeartaigh model negative fermionic masses

[Eisenhorn]

Greetings,

I calculated a basic O'Raifeartaigh model, using the following potential
$$f = \lambda Y_1 (X^2 - M^2) + \mu Y_2 X$$, where $$Y_1$$, $$Y_2$$ and $$X$$ are chiral superfields. Assuming that the vacuum expectation value of $$y_1$$ is zero (where $$y_1$$ is the scalar component of $$Y_1$$), I get a fermionic mass matrix like
$$\left(\begin{array}{ccc}0 & 0 & 0 \\0 & 0 & \mu \\0 & \mu &0\end{array}\right)$$.

My problem is that the eigenvalues of this fermionic mass matrix are $$\mu$$ and $$-\mu$$, and I don't understand the later. Why do I get a negative mass and how can I interpet it?

Eisenhorn.

 

[AndyW]

Hello Eisenhorn,
Thank you for sharing your results with us. Your calculations are correct, and the negative eigenvalue is not an error. In fact, it is a key feature of the O'Raifeartaigh model.

The negative eigenvalue arises due to the spontaneous breaking of supersymmetry in the model. This means that the scalar and fermionic components of the chiral superfields do not have the same mass, and this leads to the negative eigenvalue in the fermionic mass matrix. This is a common occurrence in supersymmetric theories and is known as the "Goldstino" mode.

The interpretation of this negative mass is that it represents a massless particle, known as the Goldstino. This particle is the remnant of the broken supersymmetry and is a crucial component in understanding the dynamics of the O'Raifeartaigh model.

I hope this helps to clarify your results. Let me know if you have any further questions.

 

[Entropia]

Hello Eisenhorn,

Thank you for sharing your findings on the O'Raifeartaigh model and the issue of negative fermionic masses. Supersymmetry is a theoretical framework that predicts a symmetry between bosons and fermions, which are two types of fundamental particles in the Standard Model of particle physics. The O'Raifeartaigh model is a simple supersymmetric model that has been studied extensively in the past.

In your calculation, you have correctly identified that the fermionic mass matrix has eigenvalues of \mu and -\mu. This may seem strange at first, but it is actually a common feature in supersymmetric models. The negative eigenvalue arises due to the presence of a negative mass term in the potential, which is a consequence of supersymmetry breaking. This breaking of supersymmetry is necessary to explain why we do not observe supersymmetric particles in nature at the energy scales accessible to current experiments.

Interpreting the negative mass eigenvalue can be challenging, as it goes against our intuition of positive masses for fundamental particles. One possible explanation is that this negative mass term is a result of a more complex underlying theory, such as string theory, which is believed to provide a more fundamental description of the universe. Another interpretation is that the negative mass term is a sign of new physics beyond the Standard Model, which could potentially be probed by future experiments.

In conclusion, your findings are consistent with the O'Raifeartaigh model and highlight the importance of supersymmetry breaking in understanding the properties of fundamental particles. Further research and experiments are needed to fully understand the implications of negative fermionic masses in supersymmetric models. Thank you for your contribution to this field of study.