Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2010-10-13
Phys.Rev.C83:045206,2011
Physics
High Energy Physics
High Energy Physics - Phenomenology
28 pages, 2 figures, RevTeX4, appendix added, version published in Phys. Rev. C
Scientific paper
10.1103/PhysRevC.83.045206
Utilizing the Foldy-Wouthuysen representation, we use a bottom-up approach to construct heavy-baryon Lagrangian terms, without employing a relativistic Lagrangian as the starting point. The couplings obtained this way feature a straightforward $1/m$ expansion, which ensures Lorentz invariance order by order in effective field theories. We illustrate possible applications with two examples in the context of chiral effective field theory: the pion-nucleon coupling, which reproduces the results in the literature, and the pion-nucleon-delta coupling, which does not employ the Rarita-Schwinger field for describing the delta isobar, and hence does not invoke any spurious degrees of freedom. In particular, we point out that one of the subleading $\pi N \Delta$ couplings used in the literature is, in fact, redundant, and discuss the implications of this. We also show that this redundant term should be dropped if one wants to use low-energy constants fitted from $\pi N$ scattering in calculations of $NN\to NN\pi$ reactions.
Lensky Vadim
Long Bingwei
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