Probing longitudinal dynamics in the pion

We compute the low energy observables for the pion using the light-front holographic Schrödinger Equation for the transverse internal dynamics, together with an ansatz for the equation governing longitudinal dynamics. Our ansatz accommodates ’t Hooft and Li-Vary Equations of ( 1 + 1 ) -dim QCD, as well as an AdS 3 string equation recently derived by Vegh. While the ’t Hooft and Li-Vary Equations are degenerate in describing the data, we find a viable scenario where the data favour the Vegh Equation in the weak string coupling limit. We also find a longitudinal wavefunction that is rather more peaked about x ∼ 1 / 2 than in previous studies.