The anomalous chiral Lagrangian of order $p^6$

Abstract

We construct the effective chiral Lagrangian for chiral perturbation theory in the mesonic odd-intrinsic-parity sector at order $p^6$. The Lagrangian contains 24 in principle measurable terms and no contact terms for the general case of $N_f$ light flavours, 23 terms for three and 5 for two flavours. In the two flavour case we need a total of 13 terms if an external singlet vector field is included. We discuss and implement the methods used to reduce to a minimal set. The infinite parts needed for renormalization are calculated and presented as well.Comment: 12 pages, misprint in table 2 correcte

Holography, chiral Lagrangian and form factor relations

“…where C W 22 is an O(p 6 ) LEC in the odd-parity sector [13]. While we have shown before that χPT Lagrangian up to O(p 4 ) can be reproduced directly, no derivation for the higher order terms has been done.…”

Vector-axial vector correlators in weak electric field and the holographic dynamics of the chiral condensate

“…where C W 22 is a coupling constant of the parity odd sector of the low energy chiral Lagrangian, [38]. However, there is no independent calculation of the value of C W 22 in order to verify eq.…”

Towards a determination of the chiral couplings at NLO in 1/NC: L8r(μ) and C38r(μ)

“…The precision required in present phenomenological applications makes necessary to include corrections of O(p 6 ). While many two-loop χPT calculations have been already performed [7,8,9,10,11,12,13,14,15], the large number of unknown low-energy couplings (LECs) appearing at this order puts a clear limit to the achievable accuracy [16].…”