Light Quarks at Large $N$

Daniel Davies; Michael Dine; Benjamin V. Lehmann

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arXiv · 2201.05719

Light Quarks at Large $N$

Daniel Davies·Michael Dine·Benjamin V. Lehmann

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Abstract

Lattice gauge theory simulations are our principal probe of the masses of the light quarks. Results from such computations are the primary evidence against the $m_u=0$ solution to the strong CP problem. The large-$N$ approximation offers an independent approach to light quarks. We extend existing literature, noting that one can determine the parameters of the non-linear sigma model through second order in quark mass, rule out the $m_u=0$ hypothesis, and make predictions for outputs of lattice calculations and phenomenological fits. A crucial feature of this analysis is a Wilsonian effective action at scales above the $\eta^\prime$ mass. One can self-consistently test the validity of aspects of this framework, and it may well be good to the part-in-three level. We also note consistency with some phenomenological fits and existing lattice results.

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Daniel Davies, Michael Dine, Benjamin V. Lehmann. 2022-01-15. Light Quarks at Large $N$. https://arxiv.org/abs/2201.05719

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