We study transverse momentum anisotropies, in particular, the elliptic flow
v2β due to the interference effect sourced by valence quarks in high-energy
hadron-hadron collisions. Our main formula is derived as the high-energy
(eikonal) limit of the impact-parameter dependent cross section in quantum
field theory, which agrees with that in terms of the impact parameter in the
classical picture. As a quantitative assessment of the interference effect, we
calculate v2β in the azimuthal distribution of gluons at a comprehensive
coverage of the impact parameter and the transverse momentum in high-energy
pion-pion collisions. In a broad range of the impact parameter, a sizable
amount of v2β, comparable with that produced due to saturated dense gluons or
final-state interactions, is found to develop. In our calculations, the valence
sector of the pion wave function is obtained numerically from the Basis
Light-Front Quantization, a non-perturbative light-front Hamiltonian approach.
And our formalism is generic and can be applied to other small collision
systems like proton-proton collisions