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2, 12, 117, 1959, 45171, 1170086, ...: a Hilbert series for the QCD chiral Lagrangian


Graf,  Lukas
Division Prof. Dr. Manfred Lindner, MPI for Nuclear Physics, Max Planck Society;

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Graf, L., Henning, B., Lu, X., Melia, T., & Murayama, H. (2021). 2, 12, 117, 1959, 45171, 1170086,..: a Hilbert series for the QCD chiral Lagrangian. Journal of high energy physics: JHEP, 2021(1): 142. doi:10.1007/JHEP01(2021)142.

Cite as: https://hdl.handle.net/21.11116/0000-000A-3A30-F
We apply Hilbert series techniques to the enumeration of operators in
the mesonic QCD chiral Lagrangian. Existing Hilbert series technologies
for non-linear realizations are extended to incorporate the external
fields. The action of charge conjugation is addressed by folding the su
n Dynkin diagrams, which we detail in an appendix that can be read
separately as it has potential broader applications. New results include
the enumeration of anomalous operators appearing in the chiral
Lagrangian at order p(8), as well as enumeration of CP-even, CP-odd,
C-odd, and P-odd terms beginning from order p(6). The method is
extendable to very high orders, and we present results up to order
p(16).(The title sequence is the number of independent C-even and P-even
operators in the mesonic QCD chiral Lagrangian with three light flavors
of quarks, at chiral dimensions p(2), p(4), p(6), ...)