Renormalization of Chiral Perturbation Theory to Order p6

Abstract

The renormalization of chiral perturbation theory is carried out to next-tonext-to-leading order in the meson sector. We calculate the divergent part of the generating functional of Green functions of quark currents to O(p 6 ) for chiral SU (n), involving one-and two-loop diagrams. The renormalization group equations for the renormalized low-energy constants of O(p 6 ) are derived. We compare our results with previous two-loop calculations in chiral perturbation theory.

Revisiting at low energies

“…In particular, we have verified that the counterterms from the Lagrangian L 6 [12] remove all ultraviolet divergences, which is a very non-trivial check on our calculation. Furthermore, we have checked that the (ultra-violet finite) amplitude so obtained is scale independent.…”

“…The coefficients γ i are given in [2], and γ (1,2,L) i are tabulated in [12]. In order to compare the present calculation with the result of [4], we shall use the scale independent quantitiesl i introduced in [2],…”

“…We have made use of the techniques developed in Ref. [5,23], and of the effective Lagrangian L 6 constructed in [11,12]. 2.…”

The chiral logs of the K→ππ amplitude

“…Since the wavefunction renormalization at this order is not available in the literature so far , I use the counterterm Lagrangian provided in [24] …”

Renormalization group equations

“…The use of the background field method and the heat-kernel techniques are particularly convenient in cases where a local symmetry is present, like for gauge theories or CHPT. Concrete examples of calculations of A (n) k up to n = 2 for gauge theories and CHPT can be found in [11] and [7], respectively.…”