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arXiv · 1812.03005

Covariant chiral nucleon-nucleon contact Lagrangian up to order $\mathcal{O}(q^4)$

Yang Xiao·Li-Sheng Geng·Xiu-Lei Ren
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Abstract

We adopt a covariant version of the naive dimensional analysis and construct the chiral two-nucleon contact Lagrangian constrained by Lorentz, parity, charge conjugation, hermitian conjugation, and chiral symmetries. We show that at $\mathcal{O}(q^0)$, $\mathcal{O}(q^2)$, $\mathcal{O}(q^4)$, where $q$ denotes a generic small quantity, there are 4, 13, and 23 terms, respectively. We find that by performing $1/m_N$ expansions, the covariant Lagrangian reduces to the conventional non-relativistic one, which includes 2, 7, and 15 terms at each corresponding order.

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Yang Xiao, Li-Sheng Geng, Xiu-Lei Ren. 2018-12-07. Covariant chiral nucleon-nucleon contact Lagrangian up to order $\mathcal{O}(q^4)$. https://doi.org/10.1103/physrevc.99.024004

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