Speaker
Description
We construct Collinear Chiral Perturbation Theory, useful in the context of highly boosted pseudo-Goldstone systems, like heavy-to-light transitions at large meson recoil. We introduce the purely collinear Lagrangian based on two observations: A boosted Goldstone boson remains a low-virtuality degree of freedom, and the Lorentz contractions of the strong chiral Lagrangian pair its large light-cone derivative with a parametrically small one, so the boosted strong sector still follows the ordinary chiral expansion. External currents, however, are different: they supply a preferred light-like direction, so arbitrary $\bar n$ derivatives are unsuppressed and must be collected into light-ray operators. We build a tower of unsuppressed operators using the usual non-linear representation, but dressed with Wilson lines $\Sigma_\infty=W_{\ell_c}^\dagger\Sigma_c W_{r_c}$, where the Wilson lines are built from the external sources alone. By exploiting the unitarity of this field, we employ a subtraction procedure to arrive at a new basis that is triangular in collinear-meson multiplicity.