4 where the hard part is given by, After carrying out the trace, we obtain, where the twist-3 parton distribution f A q $_{⊥}$( x$_{B}$, k$_{⊥}$ ) is defined as The contribution ˜ W (1 ,R ) and ˜ W (1 ,L ) are the same in unpolarized SIDIS and are given by, where ω ρ ′ ≡ g ρ ′ − ¯ n$_{ρ}$n ρ $^{′}$, ˆ h (1) ρ µν = γ$_{µ}$n /γ $^{ρ}$¯ n /γ$_{ν}$ and the matrix element has two independent terms contributing to the hadronic tensor where ϵ$_{⊥}$$_{ργ}$ ≡ ϵ$_{αβργ}$ ¯ n $^{α}$n$^{β}$. After carrying out the traces and make the Lorentz contraction with k$_{⊥}$$_{ρ}$ or ϵ$_{⊥}$$_{ργ}$k γ ⊥ respectively, we obtain, where the parton correlation functions are given by, Equation of motion relates [ d 2 ˜ W (1) µν d $^{2}$k$_{⊥}$ ]$_{Twist}$$_{−}$$_{3}$ = − 1 p · q ( p$_{µ}$k$_{⊥}$$_{ν}$ + p$_{ν}$k$_{⊥}$$_{µ}$ )[ ϕ (1) A ⊥ ( x$_{B}$, k$_{⊥}$ ) − ˜ ϕ (1) A ⊥ ( x$_{B}$, k$_{⊥}$ )] , (25) k 2 $_{⊥}$ϕ (1) A ⊥ ( x, k$_{⊥}$ ) = n $^{α}$k ρ $_{⊥}$ϕ (1) A ρα ( x, ⃗ k$_{⊥}$ ) , (26) ik 2 $_{⊥}$˜ ϕ (1) A ⊥ ( x, k$_{⊥}$ ) = n $^{α}$ϵ ρβ ⊥ k$_{⊥}$$_{β}$ ˜ ϕ (1) A ρα ( x, ⃗ k$_{⊥}$ ) , (27) ϕ (1) A ρα ( x, ⃗ k$_{⊥}$ ) = ∫ dy $^{−}$d $^{2}$y$_{⊥}$ (2 π ) 3 e ixp $^{+}$y $^{−}$− i⃗ y$_{⊥}$ · ⃗ $^{k$_{⊥}$}$〈 A | ¯ ψ (0) γ$_{α}$ 2 L (0 , y ) D$_{ρ}$ ( y ) ψ ( y ) | A 〉 (28) ˜ ϕ (1) A ρα ( x, ⃗ k$_{⊥}$ ) = ∫ dy $^{−}$d $^{2}$y$_{⊥}$ (2 π ) 3 e ixp $^{+}$y $^{−}$− i⃗ y$_{⊥}$ · ⃗ $^{k$_{⊥}$}$〈 A | ¯ ψ (0) γ$_{5}$γ$_{α}$ 2 L (0 , y ) D$_{ρ}$ ( y ) ψ ( y ) | A 〉 (29) xf A q $_{⊥}$( x, k$_{⊥}$ ) = − ϕ (1) A ⊥ ( x, k$_{⊥}$ ) + ˜ ϕ (1) A ⊥ ( x, k$_{⊥}$ ) , (30) [ d 2 ˜ W (1) µν d $^{2}$k$_{⊥}$ ]$_{Twist}$$_{−}$$_{3}$ = 1 4 p · q { Tr[ p / ˆ h (1) ρ µν ] k$_{⊥}$$_{ρ}$ϕ (1) A ⊥ ( x$_{B}$, k$_{⊥}$ ) + i Tr[ γ$_{5}$p / ˆ h (1) ρ µν ] ϵ$_{⊥}$$_{ργ}$k γ $_{⊥}$˜ ϕ (1) A ⊥ ( x$_{B}$, k$_{⊥}$ ) } , (24) ˆ ϕ (1) A ρ ( x, ⃗ k$_{⊥}$ ) = ∫ p $^{+}$dy $^{−}$d $^{2}$y$_{⊥}$ (2 π ) 3 e ixp $^{+}$y $^{−}$− i⃗ y$_{⊥}$ · ⃗ $^{k$_{⊥}$}$〈 A | ¯ ψ (0) L (0 , y ) D$_{ρ}$ ( y ) ψ ( y ) | A 〉 , (23) d 2 ˜ W (1 ,R ) µν d $^{2}$k$_{⊥}$ = d 2 ˜ W (1 ,L ) µν d $^{2}$k$_{⊥}$ = 1 4 p · q Tr[ ˆ h (1) ρ µν ω ρ ′ ˆ ϕ (1) A ρ ′ ( x$_{B}$, ⃗ k$_{⊥}$ )] , (22) k α $_{⊥}$f A q $_{⊥}$( x$_{B}$, k$_{⊥}$ ) = d $^{αβ}$Φ (0) A β ( x, ⃗ k$_{⊥}$ ) . (21) [ d 2 ˜ W (0) µν d $^{2}$k$_{⊥}$ ]$_{Twist}$$_{−}$$_{3}$ = ( k$_{⊥}$$_{µ}$n$_{ν}$ + k$_{⊥}$$_{ν}$n$_{µ}$ ) f A q $_{⊥}$( x$_{B}$, k$_{⊥}$ ) , (20) H (0) $_{µν,ρ}$( x ) = 1 4 p · q Tr [ γ$_{ρ}$γ$_{µ}$ ( xp / + q / ) γ$_{ν}$ ] , (18) Φ (0) A σ ( x, ⃗ k$_{⊥}$ ) = ∫ p $^{+}$dy $^{−}$d $^{2}$y$_{⊥}$ (2 π ) 3 e ixp $^{+}$y $^{−}$− i ⃗ k$_{⊥}$ · ⃗ $^{y$_{⊥}$}$〈 A | ¯ ψ (0) γ$_{σ}$ 2 L (0 , y ) ψ ( y ) | A 〉 . (19) and the TMD parton correlation is defined as,