Kavli Affiliate: Tom Melia
| First 5 Authors: Lukas Graf, Brian Henning, Xiaochuan Lu, Tom Melia, Hitoshi Murayama
| Summary:
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 $frak{su}(n)$ 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 $P$-even operators
in the mesonic QCD chiral Lagrangian with three light flavors of quarks, at
chiral dimensions $p^2$, $p^4$, $p^6$, …)
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