Can one see the number of colors?

We formulate the standard model with an arbitrary number of colors N-c. The cancellation of Witten's global SU(2)(L) anomaly requires N-c to be odd, while the cancellation of triangle anomalies determines the consistent N-c-dependent values of the quark charges. In this theory, the width of the decay pi (0) --> gamma gamma is not proportional to N-c(2). In fact, in the case of a single generation and hence for two quark flavors (N-f = 2), N-c does not appear explicitly in the low-energy effective theory of the standard model. Hence, contrary to common lore, it is impossible to see the number of colors in low-energy experiments with just pions and photons. For N-f greater than or equal to 3, on the other hand, N-c explicitly enters the chiral Lagrangian as the quantized prefactor of the Wess-Zumino-Witten term, but the contribution of this term to photon-pion vertices is completely canceled by the N-c-dependent part of a Goldstone-Wilczek term. However, the width of the decay eta --> pi (+)pi (-)gamma survives the cancellation and is indeed proportional to N-c(2). By detecting the emerging photon, this process thus allows one to literally see N-c for N-f greater than or equal to 3. (C) 2001 Elsevier Science B.V. All rights reserved.