Neutrinoless double beta decay derivation

In summary, the decay rate for neutrinoless double beta decay can be calculated using the formula $$\Gamma_{\beta\beta}^{0\nu} = G^{0\nu}|M^{0\nu}|^2<m_{\beta\beta}>^2$$ and there are several resources available for further understanding. These include a review article by the Particle Data Group and a Wikipedia article with additional references. A preprint from March 2021 also provides background information, with two references offering a more detailed analysis.
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Malamala
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Hello! Can someone point me towards a derivation (whether with Fermi Golden rule, or full QFT calculations) of the decay rate for the neutrinoless double beta decay:

$$\Gamma_{\beta\beta}^{0\nu} = G^{0\nu}|M^{0\nu}|^2<m_{\beta\beta}>^2$$

Thank you!
 
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There is a short review article at the Particle Data Group. And there is a fairly well written Wikipedia article on the topic, together with the references that it cites, which is probably the best place to start.

Most of the details are spelled out in a summary manner as background in this March 11, 2021 preprint at pages 2-6. And, two references in that paper provide a more in depth analysis (with the arXiv open access preprint number in square brackets at the end of each citation):

* F. F. Deppisch, M. Hirsch and H. Pas, Neutrinoless Double Beta Decay and Physics Beyond the Standard Model, J. Phys. G 39 (2012) 124007, [1208.0727], and

* M. J. Dolinski, A. W. P. Poon and W. Rodejohann, Neutrinoless Double-Beta Decay: Status and Prospects, Ann. Rev. Nucl. Part. Sci. 69 (2019) 219–251, [1902.04097].

[Mentors' note: A digression sparked by the wikipedia reference has been moved to a thread in General Discussion]
 
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1. What is neutrinoless double beta decay?

Neutrinoless double beta decay is a hypothetical nuclear process in which two neutrons in a nucleus simultaneously transform into two protons while emitting two electrons and no neutrinos.

2. Why is neutrinoless double beta decay important?

Neutrinoless double beta decay is important because it could provide evidence for the existence of Majorana particles, which are particles that are their own antiparticles. This would have significant implications for our understanding of the fundamental building blocks of the universe.

3. How is neutrinoless double beta decay derived?

The derivation of neutrinoless double beta decay involves the use of quantum field theory and the Standard Model of particle physics. It also takes into account the conservation laws of energy, momentum, and lepton number.

4. What is the current status of the search for neutrinoless double beta decay?

The search for neutrinoless double beta decay is an ongoing effort in the field of particle physics. Many experiments have been conducted and are still being conducted to try to observe this process, but so far, there has been no definitive evidence for its existence.

5. How does the observation of neutrinoless double beta decay impact our understanding of the universe?

If neutrinoless double beta decay is observed, it would provide evidence for new physics beyond the Standard Model and could help us better understand the origin of matter and the nature of the neutrino, which is one of the most elusive particles in the universe.

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