# Mirror fermions / mirror families. How does it work?

• I
• arivero
In summary, the conversation discusses the concept of mirror generations and anti-generations in relation to chiral fermions and the possibility of having an even or odd number of parity-invariant generations. It is suggested that having an anti-generation can remove a generation from low-energy phenomenology and lead to a net total of three light generations. Further discussions on the topic involve the use of heterotic phenomenology and Nir Polonsky's investigations in N=2 phenomenology.
arivero
Gold Member
From time to time we have some minor threads mentioning real vs complex representations of fermions, chiral theories, etc and how a loophole is to use mirror generations, but I do not remember some detailed discussion of how does it work.

For starters, do we need an even number of parity-invariant generations, and then half go to low energy, half remain high? Or can we do it with odd numbers?

I think you have it backwards? The significance of a mirror generation or anti-generation is that, even if you have a generation of chiral fermions, if you also have an anti-generation, they will pair off into non-chiral vector-like fermions. Naturalness arguments then imply that these vector fermions will be heavy unless there is a special "mirror parity" symmetry. So each anti-generation removes a generation from low-energy phenomenology.

For example, in heterotic phenomenology, the net number of generations is half the Euler character of the Calabi-Yau, which is the difference between two Hodge numbers, one of which gives the number of generations and the other the number of anti-generations. (I believe the idea is that you start with a 27 superfield of E6 coming from the string, then you get a copy of that for each fermionic zero mode of that superfield on the Calabi-Yau, and the number of those zero modes equals the number of harmonic forms which is given by the relevant Hodge number; and then something analogous happens for 27bar.)

So you might have four generations and one anti-generation, but the anti-generation will pair off with a generation and become heavy, leading to a net total of three light generations.

If you go the other way, and start with vector-like fermions but try to get light chiral fermions... Nir Polonsky's investigations in N=2 phenomenology would be relevant. But I think that implies a lot of BSM effects that aren't seen.

## 1. What are mirror fermions/mirror families?

Mirror fermions, also known as mirror families, are hypothetical particles that are predicted by certain extensions of the Standard Model of particle physics. These particles are believed to have the same properties as the known fermions (such as electrons and quarks), but with opposite chirality (handedness).

## 2. How do mirror fermions work?

Mirror fermions are thought to interact with the known particles through a mirror version of the weak nuclear force, known as the mirror weak force. This interaction allows for the mirror fermions to mirror the behavior of the known particles, but with opposite handedness.

## 3. What is the significance of mirror fermions in physics?

The existence of mirror fermions would have significant implications for our understanding of the fundamental forces and particles in the universe. It could also help explain the imbalance between matter and antimatter in the universe, as well as provide insights into the nature of dark matter.

## 4. Has there been any evidence for the existence of mirror fermions?

Despite numerous theoretical models predicting the existence of mirror fermions, there has been no direct experimental evidence to confirm their existence. However, some studies have suggested possible indirect evidence, such as anomalies in particle interactions and discrepancies in cosmic ray data.

## 5. Are there any current experiments or research dedicated to studying mirror fermions?

Yes, there are several ongoing experiments and research projects aimed at detecting and studying mirror fermions. These include the Belle II experiment in Japan, the LHCb experiment at CERN, and the PTOLEMY experiment at the Fermi National Accelerator Laboratory. These experiments hope to shed light on the existence and properties of mirror fermions.

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