Connecting the Quenched and Unquenched Worlds via the Large N_c World

TL;DR

This paper explores the relationship between quenched and unquenched QCD in the large N_c limit, highlighting how quenched calculations can approximate unquenched results with certain corrections, especially for weak matrix elements.

Contribution

It demonstrates that quenched QCD and full QCD are equivalent at large N_c, providing insights into the corrections needed for accurate weak decay calculations.

Findings

Quenched and unquenched QCD are identical at large N_c.

Corrections for nonleptonic kaon decays are of order 1/N_c.

Quenched calculations are valuable for poorly known weak matrix elements.

Abstract

In the large N_c(number of colors) limit, quenched QCD and QCD are identical. This implies that, in the effective field theory framework, some of the low energy constants in (N_c=3) quenched QCD and QCD are the same up to higher-order corrections in the 1/N_c expansion. Thus the calculation of the nonleptonic kaon decays relevant for the Delta I=1/2 rule in the quenched approximation is expected to differ from the unquenched one by an O(1/N_c) correction. However, the calculation relevant to the CP-violation parameter epsilon'/epsilon would have a relatively big higher-order correction due to the large cancellation in the leading order. Some important weak matrix elements are poorly known that even constraints with 100% errors are interesting. In those cases, quenched calculations will be very useful.