that short-distance constraints are missing. Nevertheless, resonance saturation provides at least a possible parametrization of the LECs. The most systematic approach is based on factorization (valid to leading order in $1/N_c$) [@Pallante:2001he; @Cirigliano:2003gt], but higher-order corrections in $1/N_c$ may well be sizeable.

A different approach is to use the $1/N_c$ arguments in conjunction with the underlying short-distance physics. This approach was pioneered by [@Bardeen:1986uz] and further pursued in [@Bijnens:1998ee]. A more recent discussion is in [@Buras:2014maa]. One main problem here is to make sure that short- and long-distance matching is performed in a clean fashion [@Bijnens:1999zn; @Peris:1998nj].

Finally, there is a chiral Lagrangian for electromagnetic corrections to nonleptonic weak processes. The single LEC of lowest order, $O(G_F e^2 p^0$), related to the electromagnetic penguin contribution [@Bijnens:1983ye; @Grinstein:1985ut], is reasonably well known [@Cirigliano:1999hj; @Bijnens:2001ps; @Cirigliano:2003gt]. The additional 14 LECs of $O(G_F e^2 p^2)$ [@Ecker:2000zr] have again been estimated to leading order in $1/N_c$ (factorization). In this way, the LECs can be expressed in terms of Wilson coefficients, the strong LECs $L_5,L_8$ and the electromagnetic LECs $K_i$ [@Pallante:2001he; @Cirigliano:2003gt].

Contributions at each order and terminology {#sec:terminology}
-------------------------------------------

[ChPT]{} has been an active field since the early 1980s. As a consequence, the same 