# The Wolfenstein potential for ultra-light mediators

**Authors:** Alexei Yu. Smirnov, Xun-Jie Xu  
**arXiv:** [1909.07505](https://arxiv.org/abs/1909.07505)  
**Date:** 2019-09-16  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1909.07505v1/

## Key points

- Study on "The Wolfenstein Potential for Ultra-Light Mediators" by Alexei Yu. Smirnov and Xun-Jie Xu
- Introduction of very light and weakly interacting particles as mediators between neutrinos and ordinary matter
- Analysis of the Wolfenstein potential in neutrino oscillations with ultra-light scalar and vector mediators
- Modification in the conventional dependence of the potential when mediator mass is comparable to the size of the medium
- Conclusion that significant effects on neutrino propagation are unlikely for scalar mediators, but permissible for vector mediators within a specific range of masses and gauge coupling values

## Summary

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In their study "The Wolfenstein Potential for Ultra-Light Mediators," authors Alexei Yu. Smirnov and Xun-Jie Xu delve into the realm of new physics emerging at low energy scales. They introduce very light and weakly interacting particles that can mediate interactions between neutrinos and ordinary matter, playing a crucial role in shaping the Wolfenstein potential in neutrino oscillations. The research focuses on computing this potential with the presence of ultra-light scalar and vector mediators, analyzing how it varies with mediator mass $m_A while considering the finite size of matter distributions such as Earth, Sun, and supernovae. One key finding is that for ultra-light mediators with $m_{A}^{-1}$ comparable to the size of the medium ($R$), there is a modification in the conventional $m_{A}^{-2}$ dependence of the potential. Particularly interesting is when $m_{A}^{-1}\gg R$, as in this scenario, the potential no longer relies on $m_{A$. By incorporating existing constraints on light mediators, it was concluded that significant effects on neutrino propagation are unlikely for scalar mediators. However, for vector mediators within a specific range of masses ($m_{A} \in [2\times10^{-17}, 4\times10^{-14}]$ eV) and a gauge coupling $g\sim 10^{-25}$, substantial matter effects on neutrinos are permissible. This comprehensive analysis sheds light on how ultra-light mediators can influence neutrino behavior and opens up avenues for further exploration in understanding fundamental interactions at low energy scales.