Abstract
Models of spontaneous baryogenesis have an interaction term \(\partial _\mu \theta j^\mu _B\) in the Lagrangian, where \(j^\mu _B\) is the baryonic current and \(\theta \) can be a pseudo-Nambu-Goldstone boson. Since the time component of this term, \(\dot{\theta }j^0_B\), equals \(\dot{\theta }n_B\) for a spatially homogeneous current, it is usually argued that this term implies a splitting in the energy of baryons and antibaryons thereby providing an effective chemical potential for baryon number. In thermal equilibrium, one then obtains \(n_B \sim \dot{\theta }T^2\). We however argue that a term of this form in the Lagrangian does not contribute to the single particle energies of baryons and antibaryons. We show this for both fermionic and scalar baryons. But we find that despite the above result the baryon number density obtained from a Boltzmann equation analysis can be proportional to \(\dot{\theta }T^2\). Our arguments are very different from that in the standard literature on spontaneous baryogenesis. This presentation is based on Phys. Rev. D98 (2018) no.8, 083527 with A. Dasgupta and R.K. Jain.
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Notes
- 1.
A similar argument was made in the arXiv version of [7].
- 2.
We would like to thank Prof. A. D. Dolgov for highlighting this to us.
- 3.
This is slightly different from the approach in [6], and we thank Prof. Michael Ratz for pointing out that one may not use \(B+L\) conservation as that symmetry is broken by \(U(\theta )\).
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Rangarajan, R. (2020). Effective Chemical Potential in Spontaneous Baryogenesis. In: Giri, A., Mohanta, R. (eds) Workshop on Frontiers in High Energy Physics 2019. Springer Proceedings in Physics, vol 248. Springer, Singapore. https://doi.org/10.1007/978-981-15-6292-1_2
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DOI: https://doi.org/10.1007/978-981-15-6292-1_2
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