  Light pseudoscalar mesons are Janus-type particles: Within quantum
chromodynamics, they must be described as bound states of its fundamental
degrees of freedom and as the (pseudo-) Goldstone bosons of its spontaneously
broken chiral symmetry. This janiform nature of pions and kaons may be easily
accommodated by the Bethe-Salpeter formalism in its instantaneous limit:
Starting from the general behaviour of the Bethe-Salpeter solutions for light
pseudoscalar mesons at large Euclidean momenta, we provide the exact
relationship between the solutions of our bound-state equation and the
underlying interactions, boiled down to a configuration-space potential
depending on the interquark distance: the potential exhibits a logarithmically
softened Coulomb singularity at the origin and, at large interquark distances,
rises beyond bounds for massless quarks but approaches a non-positive finite
limit for too heavy quarks.
