m_j')\rangle = 2P^+ (2\pi)^3 \delta^3(P - P')
\delta_{jj'}\delta_{m_j,m_j'} \delta_{hh'},$$ Then, the orthonormalization of the LFWFs reads, $$\label{eqn:normalization}
 \sum_{s, \bar s} \int_0^1\frac{\dd x}{2x(1-x)} \int \frac{\dd^2  k_\perp}{(2\pi)^3} 
\psi^{(m_j')*}_{s \bar s/h'}(\vec k_\perp, x)\psi^{(m_j)}_{s \bar s/h}(\vec k_\perp, x)  = \delta_{hh'}\delta_{m_j,m_j'}.$$ Note that different hadron states with the same quantum numbers, such as $J/\psi$ and $\psi'$, are also orthogonal. It is also useful to introduce LFWFs in the transverse coordinate space: $$\widetilde\psi_{s\bar s} (\vec r_\perp, x) \equiv \frac{1}{\sqrt{x(1-x)}}\int \frac{\dd^2 k_\perp}{(2\pi)^2}  e^{\imag \vec k_\perp \cdot
\vec r_\perp} \psi_{s \bar s} (\vec k_\perp, x).$$ with orthonormalization, $$\sum_{s, \bar s} \int_0^1\frac{\dd x}{4\pi} \int \dd^2 r_\perp \, \widetilde\psi^{(m_j')*}_{s \bar s/h'}(\vec r_\perp, x)
\widetilde\psi^{(m_j)}_{s \bar s/h}(\vec r_\perp, x)  = \delta_{hh'}\delta_{m_j,m_j'}.$$

Parity $\mathcal P$ is a dynamical symmetry on the light front, as it swaps light-front coordinate $x^-$ and light-front time $x^+$. The mirror parity $m_P \equiv \mathcal R_x(\pi)\mathcal P$, which only flips one of the transverse spatial coordinates ($x^1$), survives as a kinematical symmetry in light-front dynamics. The eigenvalue equations related to the mirror parity $\hat m_P$ and the charge conjugation $\hat C$ are [@Krautgartner:1991xz; @Trittmann:1997xz; @Brodsky:2006ez; @Li:2015zda]: $$\label{eqn:parity}
 \hat m_P |\psi_h(P, j, m_j)\rangle = (-i)^{2j}\mathsf{P}|\psi_h(\widetilde P, j, -m_j)\rangle, \quad \hat C |\psi_h(P, j, m_j)\rangle =
\mathsf C |\psi_{\bar h}(P, 