T_{0xy}+\hat{P}_{23}\left(V_{1xy}+V_{1xx}-A_{1xy}-A_{1xx}\right)+\hat{P}_{13}\left(V_{1xy}+V_{1yy}+A_{1xy}+A_{1yy}\right)=0.$
(D.22)

From these equations it follows that the relations between the chiral-odd and
chiral-even auxiliary DAs have the following form

$\displaystyle T_{0xx}$ $\displaystyle=$ $\displaystyle P_{13}\left(\
V_{1xx}+V_{1yy}+2V_{1xy}+A_{1xx}+A_{1yy}+2A_{1xy}\right)+P_{23}\left(V_{1xx}-A_{1xx}\right),$
(D.23) $\displaystyle T_{0yy}$ $\displaystyle=$ $\displaystyle
P_{13}\left(V_{1yy}+A_{1yy}\right)+P_{23}\left(V_{1xx}+V_{1yy}+2V_{1xy}-A_{1xx}-A_{1yy}-2A_{1xy}\right),$
(D.24) $\displaystyle T_{0xy}$ $\displaystyle=$ $\displaystyle-
P_{13}\left(V_{1xy}+V_{1yy}+A_{1xy}+A_{1yy}\right)-P_{23}\left(V_{1xy}+V_{1xx}-A_{1xy}-A_{1xx}\right),$
(D.25) $\displaystyle\tilde{T}_{2xy}$ $\displaystyle=$ $\displaystyle-
P_{13}\left(T_{xy}+G_{xy}\right)-P_{23}\left(T_{xy}-G_{xy}\right).$ (D.26)

These equations are very helpful for the analytical check of the $SU(3)$ limit
for the calculated amplitudes.

##  Appendix E Expressions for the projections onto higher twist matrix
elements

Here we give expressions for the projections $P$ and $\bar{P}$ that enter
Eq.(140). In the following we assume the matrix element with the baryon in the
initial state as in the definitions in Sec.2.1. This is convenient for a
comparison of definitions of baryon DAs, which exist in the literature. This
also implies that one calculates the amplitude of the time reversal process
$B+\bar{B}\rightarrow J/\psi$. Since the corresponding amplitude is real this
also gives the correct result. The antibaryon projectors can be obtained from
the baryon ones using the charge conjugation.

For partonic diagrams we assume the configuration of the external momenta as
shown in Fig.2.

Figure 2:  The diagram, which illustrates the choice of external momenta for
the light quarks. The timeline is going to left.

After differentiations with respect to momenta $k_{i}$ and $k^{\prime}_{i}$ we
set

$k_{i}=x_{i}k_{+}\frac{\bar{n}}{2},\
k_{i}^{\prime}=y_{i}k_{-}^{\prime}\frac{n}{2}.$ (E.1)

The derived projectors depend on the auxiliary DAs, which are defined in
Sec.2.2.

The twist-4 projectors have already been derived in Ref.[19]. The chiral-even
projection reads

$\displaystyle\left.\left[P_{\text{tw4}}(x_{i})\right]_{123}\right|_{\text{even}}=\frac{m_{B}}{4}\left\\{\mathcal{V}_{1}^{B}(x_{i})\left[C_{\mathcal{V}1}\right]_{123}+\mathcal{A}_{1}^{B}(x_{i})\left[C_{\mathcal{A}1}\right]_{123}\right.$
$\displaystyle\left.+\mathcal{V}_{2}^{B}(x_{i})\left[C_{\mathcal{V}2}\right]_{123}+\mathcal{A}_{2}^{B}(x_{i})\left[C_{\mathcal{A}2}\right]_{123}\right\\},$
(E.2)

where ($i=1,2$)

$\left[C_{\mathcal{V}i}\right]_{123}=\left[C_{i\bot}^{\alpha}C^{\top}\right]_{21}\left[\gamma_{\bot}^{\alpha}\gamma_{5}N_{\bar{n}}\right]_{3}+\left[C_{i}^{\|}C^{\top}\right]_{21}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{5}N_{\bar{n}}\right]_{3},$
(E.3)
$\left[C_{\mathcal{A}i}\right]_{123}=\left[\gamma_{5}C_{i\bot}^{\alpha}C^{\top}\right]_{21}\left[\gamma_{\bot}^{\alpha}N_{\bar{n}}\right]_{3}+\left[\gamma_{5}C_{i}^{\|}C^{\top}\right]_{21}\left[\hbox
to0.0pt{\hbox to5.52084pt{\hfil/\hfil}\hss}k^{\prime}N_{\bar{n}}\right]_{3},$
(E.4) $C_{i\bot}^{\alpha}=\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\right]\frac{\partial}{\partial
k_{i\bot}^{\alpha}}-\frac{\delta_{i1}}{2(kk^{\prime})}\frac{1}{x_{1}}\left[\hbox
to0.0pt{\hbox to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\alpha}\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\right]-\frac{\delta_{i2}}{2(kk^{\prime})}\frac{1}{x_{2}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\hbox
to0.0pt{\hbox to5.52084pt{\hfil/\hfil}\hss}k\right],\ ~{}\ \
C_{i}^{\|}=\frac{1}{(kk^{\prime})}\frac{1}{x_{3}}\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\right].$ (E.5)

The chiral-odd projection reads

$\displaystyle\left.\left[P_{\text{tw4}}(x_{i})\right]_{123}\right|_{\text{odd}}$
$\displaystyle=\frac{m_{B}}{4}\left\\{T_{2}^{B}(x_{i})\left[C_{T}\right]_{123}+\mathcal{T}_{21}^{B}(x_{i})\left[C_{\mathcal{T}21}\right]_{123}+\mathcal{T}_{22}^{B}(x_{i})\left[C_{\mathcal{T}22}\right]_{123}\right.$
$\displaystyle\left.+\mathcal{T}_{41}^{B}(x_{i})\left[C_{\mathcal{T}41}\right]_{123}+\mathcal{T}_{42}^{B}(x_{i})\left[C_{\mathcal{T}42}\right]_{123}\right\\},$
(E.6)

where

$C_{T}=\frac{1}{2(kk^{\prime})}\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot\alpha}C\right]_{12}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\gamma_{5}N_{\bar{n}}\right]_{3},$
(E.7) $\displaystyle C_{\mathcal{T}2i}$
$\displaystyle=\left[C_{i}^{\|}C\right]_{12}\left[\gamma_{5}N_{\bar{n}}\right]_{3},\
\ C_{\mathcal{T}4i}=\left[C_{i}^{\|}\gamma_{5}C\right]_{12}\
\left[N_{\bar{n}}\right]_{3},$ (E.8) $\displaystyle C_{i}^{\|}$
$\displaystyle=\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot\alpha}\right]~{}\frac{\partial}{\partial
k_{i\bot}^{\alpha}}+\frac{\delta_{i1}}{(kk^{\prime})}\frac{1}{x_{1}}\left[\hbox
to0.0pt{\hbox to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\right]-\frac{\delta_{i2}}{(kk^{\prime})}\frac{1}{x_{2}}\left[\hbox
to0.0pt{\hbox to5.52084pt{\hfil/\hfil}\hss}k\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\right].$ (E.9)

We assume that derivatives in these formulas are applied to the expressions on
the right side, i.e. the derivatives are not applied to the momenta from the
left side and therefore corresponding momenta can be simplified neglecting the
power suppressed components. For a convenience, we also show the Dirac
matrices in the square brackets: $[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k]$, $\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\alpha}\right]$ etc.

The expressions for the twist-5 projectors are more complicated and include
some special contribution, which is completely defined in terms of twist-3
DAs.

The chiral-even projector is defined as

$\displaystyle\left.\left[P_{\text{tw5}}(x_{i})\right]_{123}\right|_{\text{even}}=\frac{m_{B}^{2}}{8}\left\\{\
x_{1}x_{2}\left(V_{5}^{B}(x_{i})\
\left[C_{V5}\right]_{123}+A_{5}^{B}(x_{i})\left[C_{A5}\right]_{123}\right)\right.$
$\displaystyle+V_{1xy}^{B}(x_{i})\left[C_{V1xy}\right]_{123}+A_{1xy}^{B}(x_{i})\left[C_{A1xy}\right]_{123}$
$\displaystyle+V_{1xx}^{B}(x_{i})\left[C_{V1xx}\right]_{123}+A_{1xx}^{B}(x_{i})\left[C_{A1xx}\right]_{123}+V_{1yy}^{B}(x_{i})\left[C_{V1yy}\right]_{123}+A_{1yy}^{B}(x_{i})\left[C_{A1yy}\right]_{123}$
$\displaystyle\left.+V_{1}^{B}(x_{i})\left[C_{V1}\right]_{123}+A_{1}^{B}(x_{i})\left[C_{A1}\right]_{123}\right\\},$
(E.10)

where

$\left[C_{V5}\right]_{123}=\left[C_{5}^{\alpha\beta}\gamma_{5}C\right]_{12}\left[i\sigma_{\bot\bot}^{\alpha\beta}N_{\bar{n}}\right]_{3}+\left[C_{5}^{\alpha}\gamma_{5}C\right]_{12}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}N_{\bar{n}}\right]_{3},$
(E.11)
$\left[C_{A5}\right]_{123}=\left[C_{5}^{\alpha\beta}C\right]_{12}\left[i\sigma_{\bot\bot}^{\alpha\beta}\gamma_{5}N_{\bar{n}}\right]_{3}+\left[C_{5}^{\alpha}C\right]_{12}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\gamma_{5}N_{\bar{n}}\right]_{3},$
(E.12)

with

$\displaystyle C_{5}^{\alpha\beta}$ $\displaystyle=-\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\right]\ \frac{\partial}{\partial
k_{1\bot}^{\alpha}}\frac{\partial}{\partial
k_{2\bot}^{\beta}}+\frac{1}{2(kk^{\prime})}\left(\frac{1}{x_{2}}\left[\hbox
to0.0pt{\hbox to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\beta}\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\right]\frac{\partial}{\partial
k_{1\bot}^{\alpha}}+\frac{1}{x_{1}}\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\hbox
to0.0pt{\hbox to5.52084pt{\hfil/\hfil}\hss}k\right]\frac{\partial}{\partial
k_{2\bot}^{\beta}}\right)$
$\displaystyle+\frac{1}{2(kk^{\prime})}\frac{1}{x_{1}x_{2}}\left[\gamma_{\bot}^{\alpha}\gamma_{\bot}^{\beta}\hbox
to0.0pt{\hbox to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\right],$ (E.13)
$C_{5}^{\alpha}=\frac{1}{x_{3}}\frac{1}{2(kk^{\prime})}\left\\{\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\right]\left(\frac{\partial}{\partial
k_{2\bot}^{\alpha}}-\frac{\partial}{\partial
k_{1\bot}^{\alpha}}\right)+\frac{1}{2(kk^{\prime})}\left(\frac{1}{x_{1}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\right]-\frac{1}{x_{2}}~{}\left[\hbox
to0.0pt{\hbox to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\alpha}\hbox
to0.0pt{\hbox to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\right]\right)\right\\}.$
(E.14)

The terms in the second line of Eq.(E.10) read

$\left[C_{V1xy}\right]_{123}=\left[C_{1xy}C\right]_{12}\left[\gamma_{5}N_{\bar{n}}\right]_{3}+\left[C_{1xy}^{\beta}C\right]_{12}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\beta}\gamma_{5}N_{\bar{n}}\right]_{3},$
(E.15)
$\left[C_{A1xy}\right]_{123}=\left[C_{1xy}\gamma_{5}C\right]_{12}\left[N_{\bar{n}}\right]_{3}+\left[C_{1xy}^{\beta}\gamma_{5}C\right]_{12}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\beta}N_{\bar{n}}\right]_{3},$
(E.16) $C_{1xy}=-~{}\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot\beta}\gamma_{\bot\alpha}\right]\frac{\partial}{\partial
k_{1\bot}^{\alpha}}\frac{\partial}{\partial k_{2\bot}^{\beta}},$ (E.17)
$C_{1xy}^{\beta}=-\frac{1}{2}\frac{1}{(kk^{\prime})}\frac{1}{x_{3}}\left(\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot\beta}\gamma_{\bot\alpha}\right]\frac{\partial}{\partial
k_{1\bot}^{\alpha}}+\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot\alpha}\gamma_{\bot\beta}\right]\frac{\partial}{\partial
k_{2\bot}^{\alpha}}\right).$ (E.18)

The terms from the third line of Eq.(E.10)

$\left[C_{V1xx}\right]_{123}=\left[C_{1xx}C\right]_{12}~{}~{}\left[\gamma_{5}N\right]_{3}+\left[C_{1xx}^{\alpha}C\right]_{12}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\gamma_{5}N_{\bar{n}}\right]_{3},$
(E.19)
$\left[C_{A1xx}\right]_{123}=~{}\left[C_{1xx}\gamma_{5}C\right]_{12}~{}~{}\left[N\right]_{3}+\left[C_{1xx}^{\alpha}\gamma_{5}C\right]_{12}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}N_{\bar{n}}\right]_{3},$
(E.20)

with

$C_{1xx}=-\frac{1}{2}\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\right]\frac{\partial}{\partial
k_{1\bot}^{\alpha}}\frac{\partial}{\partial
k_{1\bot\alpha}}+\frac{1}{(kk^{\prime})}\frac{1}{x_{1}}\left(\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\right]k_{\alpha}^{\prime}\frac{\partial}{\partial
k_{1}^{\alpha}}+\frac{1}{2}\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot\alpha}\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\right]\frac{\partial}{\partial
k_{1\bot}^{\alpha}}\right),$ (E.21)
$C_{1xx}^{\alpha}=\frac{1}{2(kk^{\prime})}\frac{1}{x_{3}}\left(-\left[\hbox
to0.0pt{\hbox to5.52084pt{\hfil/\hfil}\hss}k\right]\frac{\partial}{\partial
k_{1\bot}^{\alpha}}+\frac{1}{2(kk^{\prime})}\frac{1}{x_{1}}~{}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\hbox
to0.0pt{\hbox to5.52084pt{\hfil/\hfil}\hss}k\right]\right).$ (E.22)
$\left[C_{V1yy}\right]_{123}=\left[C_{1yy}^{(1)}C\right]_{12}\left[\gamma_{5}N\right]_{3}+\left[C_{1yy}^{\alpha}C\right]_{12}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\gamma_{5}N\right]_{3}\
,$ (E.23)
$\left[C_{A1yy}\right]_{123}=\left[C_{1yy}^{(1)}\gamma_{5}C\right]_{12}\left[N\right]_{3}+\left[C_{1yy}^{\alpha}\gamma_{5}C\right]_{12}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}N\right]_{3}\ ,$
(E.24)

with

$C_{1yy}=-\frac{1}{2}\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\right]\frac{\partial}{\partial
k_{2\bot}^{\alpha}}\frac{\partial}{\partial
k_{2\bot\alpha}}~{}+\frac{1}{\left(kk^{\prime}\right)}\frac{1}{x_{2}}\left(\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\right]k_{\alpha}^{\prime}\frac{\partial}{\partial
k_{2}^{\alpha}}+\frac{1}{2}\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot\alpha}\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\right]\frac{\partial}{\partial
k_{2\bot}^{\alpha}}\right),$ (E.25)
$C_{1yy}^{\alpha}=\frac{1}{2(kk^{\prime})}\frac{1}{x_{3}}\left(-\left[\hbox
to0.0pt{\hbox to5.52084pt{\hfil/\hfil}\hss}k\right]\frac{\partial}{\partial
k_{2\bot}^{\alpha}}+\frac{1}{2(kk^{\prime})}\frac{1}{x_{2}}\left[\hbox
to0.0pt{\hbox to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\alpha}\hbox
to0.0pt{\hbox to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\right]\right).$ (E.26)

The terms from the last line of Eq.(E.10)

$\left[C_{V1}\right]_{123}=\frac{1}{(kk^{\prime})}~{}\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}kC\right]_{12}\left[\gamma_{5}N_{\bar{n}}\right]_{3}\
k_{\alpha}^{\prime}\frac{\partial}{\partial P^{\alpha}},\ \ \
\left[C_{A1}\right]_{123}=\frac{1}{(kk^{\prime})}~{}\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{5}C\right]_{12}\left[N_{\bar{n}}\right]_{3}\
k_{\alpha}^{\prime}\frac{\partial}{\partial P^{\alpha}}.$ (E.27)

Notice that terms $C_{V1}$ and $C_{A1}$ include the derivatives with respect
to initial momentum $P$, see a more detailed explanation below.

The twist-5 chiral-odd projector is defined as

$\displaystyle\left.\left[P_{\text{tw5}}(x_{i})\right]_{123}\right|_{\text{odd}}$
$\displaystyle=\frac{m_{B}^{2}}{16}\left(\
\left[C_{0xx}\right]_{123}T_{0xx}^{B}(x_{i})+\left[C_{2xx}\right]_{123}T_{0xx}^{B}(x_{i})\right.$
$\displaystyle+\left[C_{0yy}\right]_{123}T_{0yy}^{B}(x_{i})+\left[C_{2yy}\right]_{123}T_{0yy}^{B}(x_{i})$
$\displaystyle+\
\left[C_{0xy}\right]_{123}T_{0xy}^{B}(x_{i})+\left[C_{2xy}\right]_{123}T_{2xy}^{B}(x_{i})+\left[\tilde{C}_{2xy}\right]_{123}\tilde{T}_{2xy}^{B}(x_{i})$
$\displaystyle\left.+\left[C_{T}\right]_{123}T_{1}\right)$ (E.28)

where the coefficients read

$\left[C_{T}\right]_{123}=\frac{2}{(kk^{\prime})}\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\mu}C\right]_{12}\left[\gamma_{\bot}^{\mu}\gamma_{5}N\right]_{3}\
k_{\alpha}^{\prime}\frac{\partial}{\partial P^{\alpha}}.$ (E.29)
$\displaystyle C_{0xx}$ $\displaystyle=-\frac{1}{2}\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\alpha}C\right]_{12}~{}\left[\gamma_{\bot}^{\alpha}\gamma_{5}N_{\bar{n}}\right]_{3}\frac{\partial}{\partial
k_{1\bot}^{\alpha}}\frac{\partial}{\partial
k_{1\bot\alpha}}+\frac{1}{(kk^{\prime})}\frac{1}{x_{1}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\alpha}C\right]_{12}~{}\left[\gamma_{\bot}^{\alpha}\gamma_{5}N_{\bar{n}}\right]_{3}\
k_{\alpha}^{\prime}\frac{\partial}{\partial k_{1}^{\alpha}}$
$\displaystyle+\frac{1}{2(kk^{\prime})}\left(\frac{1}{x_{1}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}C\right]_{12}~{}\left[\gamma_{\bot}^{\sigma}\gamma_{5}N_{\bar{n}}\right]_{3}-\frac{1}{x_{3}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}C\right]_{12}~{}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\gamma_{\bot}^{\sigma}\gamma_{5}N_{\bar{n}}\right]_{3}\right)\frac{\partial}{\partial
k_{1\bot}^{\alpha}}$
$\displaystyle+\frac{1}{4(kk^{\prime})^{2}}\frac{1}{x_{1}x_{3}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\beta}C\right]_{12}~{}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\gamma_{\bot}^{\beta}\gamma_{5}N_{\bar{n}}\right]_{3}\
.$ (E.30) $\displaystyle C_{0yy}=-\frac{1}{2}\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\alpha}C\right]_{12}~{}\left[\gamma_{\bot}^{\alpha}\gamma_{5}N_{\bar{n}}\right]_{3}\frac{\partial}{\partial
k_{2\bot}^{\alpha}}\frac{\partial}{\partial
k_{2\bot\alpha}}+\frac{1}{(kk^{\prime})}\frac{1}{x_{2}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\alpha}C\right]_{12}~{}\left[\gamma_{\bot}^{\alpha}\gamma_{5}N_{\bar{n}}\right]_{3}k_{\alpha}^{\prime}\frac{\partial}{\partial
k_{2}^{\alpha}}$
$\displaystyle+\frac{1}{2(kk^{\prime})}\left(\frac{1}{x_{2}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}\gamma_{\bot}^{\alpha}k^{\prime}C\right]_{12}~{}\left[\gamma_{\bot}^{\sigma}\gamma_{5}N_{\bar{n}}\right]_{3}-\frac{1}{x_{3}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}C\right]_{12}~{}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\gamma_{\bot}^{\sigma}\gamma_{5}N_{\bar{n}}\right]_{3}\right)\frac{\partial}{\partial
k_{2\bot}^{\alpha}}$
$\displaystyle+\frac{1}{4(kk^{\prime})^{2}}\frac{1}{x_{2}x_{3}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}\gamma_{\bot}^{\alpha}\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}C\right]_{12}~{}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\gamma_{\bot}^{\sigma}\gamma_{5}N_{\bar{n}}\right]_{3}\
.$ (E.31)

Below we use the short notation

$G_{\bot}^{\alpha\beta\sigma\rho}=g_{\bot}^{\alpha\sigma}g_{\bot}^{\beta\rho}+g_{\bot}^{\alpha\rho}g_{\bot}^{\beta\sigma}-g_{\bot}^{\sigma\rho}g_{\bot}^{\alpha\beta}.$
(E.32) $\displaystyle
C_{2yy}=-\frac{1}{2}G_{\bot}^{\alpha\beta\sigma\rho}\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}C\right]_{12}~{}\left[\gamma_{\bot}^{\rho}\gamma_{5}N_{\bar{n}}\right]_{3}\frac{\partial}{\partial
k_{2\bot}^{\alpha}}\frac{\partial}{\partial k_{2\bot}^{\beta}}\hskip
150.00023pt$
$\displaystyle+G_{\bot}^{\alpha\beta\sigma\rho}\frac{1}{2(kk^{\prime})}\left(\frac{1}{x_{2}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}\gamma_{\bot}^{\beta}\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}C\right]_{12}~{}\left[\gamma_{\bot}^{\rho}\gamma_{5}N_{\bar{n}}\right]_{3}-\frac{1}{x_{3}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}C\right]_{12}~{}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\beta}\gamma_{\bot}^{\rho}\gamma_{5}N_{\bar{n}}\right]_{3}\right)\frac{\partial}{\partial
k_{2\bot}^{\alpha}}$
$\displaystyle+G_{\bot}^{\alpha\beta\sigma\rho}\frac{1}{4(kk^{\prime})^{2}}\frac{1}{x_{2}x_{3}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}\gamma_{\bot}^{\alpha}\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}C\right]_{12}~{}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\beta}\gamma_{\bot}^{\rho}\gamma_{5}N_{\bar{n}}\right]_{3}.$
(E.33) $\displaystyle
C_{2xx}=-\frac{1}{2}G_{\bot}^{\alpha\beta\sigma\rho}\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}C\right]_{12}~{}\left[\gamma_{\bot}^{\rho}\gamma_{5}N_{\bar{n}}\right]_{3}\frac{\partial}{\partial
k_{1\bot}^{\alpha}}\frac{\partial}{\partial k_{1\bot}^{\beta}}\hskip
150.00023pt$
$\displaystyle+G_{\bot}^{\alpha\beta\sigma\rho}\frac{1}{2(kk^{\prime})}\left(\frac{1}{x_{1}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\beta}\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}C\right]_{12}~{}\left[\gamma_{\bot}^{\rho}\gamma_{5}N_{\bar{n}}\right]_{3}-\frac{1}{x_{3}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}C\right]_{12}~{}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\beta}\gamma_{\bot}^{\rho}\gamma_{5}N_{\bar{n}}\right]_{3}\right)\frac{\partial}{\partial
k_{1\bot}^{\alpha}}$
$\displaystyle+G_{\bot}^{\alpha\beta\sigma\rho}\frac{1}{4(kk^{\prime})^{2}}\frac{1}{x_{1}x_{3}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}C\right]_{12}~{}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\beta}\gamma_{\bot}^{\rho}\gamma_{5}N_{\bar{n}}\right]_{3}.$
(E.34) $\displaystyle C_{0xy}=-\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}C\right]_{12}~{}\left[\gamma_{\bot}^{\sigma}\gamma_{5}N_{\bar{n}}\right]_{3}\frac{\partial}{\partial
k_{1\bot}^{\alpha}}\frac{\partial}{\partial k_{2\bot\alpha}}\hskip
150.00023pt$
$\displaystyle+\frac{1}{2(kk^{\prime})}\left(\frac{1}{x_{2}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}\gamma_{\bot}^{\alpha}\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}C\right]_{12}~{}\left[\gamma_{\bot}^{\sigma}\gamma_{5}N_{\bar{n}}\right]_{3}-\frac{1}{x_{3}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}C\right]_{12}~{}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\beta}\gamma_{\bot}^{\sigma}\gamma_{5}N_{\bar{n}}\right]_{3}\right)\frac{\partial}{\partial
k_{1\bot}^{\alpha}}$
$\displaystyle+\frac{1}{2(kk^{\prime})}\left(\frac{1}{x_{1}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}C\right]_{12}~{}\left[\gamma_{\bot}^{\sigma}\gamma_{5}N_{\bar{n}}\right]_{3}-\frac{1}{x_{3}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}C\right]_{12}~{}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\gamma_{\bot}^{\sigma}\gamma_{5}N_{\bar{n}}\right]_{3}\right)\frac{\partial}{\partial
k_{2\bot}^{\alpha}}$
$\displaystyle+\frac{1}{4(kk^{\prime})^{2}}\left(\frac{1}{x_{1}x_{3}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}C\right]_{12}~{}+\frac{1}{x_{2}x_{3}}~{}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}\gamma_{\bot}^{\alpha}\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}C\right]_{12}~{}\right)\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\gamma_{\bot}^{\sigma}\gamma_{5}N_{\bar{n}}\right]_{3}.$
(E.35) $C_{2xy}=\tilde{C}_{\alpha\beta\sigma\rho}\
G_{\bot}^{\alpha\beta\sigma\rho},\ \
\tilde{C}_{2xy}=\tilde{C}_{\alpha\beta\sigma\rho}\left(g_{\bot}^{\alpha\rho}g_{\bot}^{\beta\sigma}-g_{\bot}^{\alpha\sigma}g_{\bot}^{\beta\rho}\right),$
(E.36)

where

$\displaystyle\tilde{C}_{\alpha\beta\sigma\rho}=-\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}C\right]_{12}~{}\left[\gamma_{\bot}^{\rho}\gamma_{5}N_{\bar{n}}\right]_{3}\frac{\partial}{\partial
k_{1\bot}^{\alpha}}\frac{\partial}{\partial k_{2\bot\alpha}}\hskip
150.00023pt$
$\displaystyle+\frac{1}{2(kk^{\prime})}\left(\frac{1}{x_{2}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}\gamma_{\bot}^{\beta}\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}C\right]_{12}~{}\left[\gamma_{\bot}^{\rho}\gamma_{5}N_{\bar{n}}\right]_{3}-\frac{1}{x_{3}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}C\right]_{12}~{}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\beta}\gamma_{\bot}^{\rho}\gamma_{5}N_{\bar{n}}\right]_{3}\right)\frac{\partial}{\partial
k_{1\bot}^{\alpha}}$
$\displaystyle+\frac{1}{2(kk^{\prime})}\left(\frac{1}{x_{1}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}C\right]_{12}~{}\left[\gamma_{\bot}^{\rho}\gamma_{5}N_{\bar{n}}\right]_{3}-\frac{1}{x_{3}}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}C\right]_{12}~{}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\gamma_{\bot}^{\rho}\gamma_{5}N_{\bar{n}}\right]_{3}\right)\frac{\partial}{\partial
k_{2\bot}^{\beta}}$
$\displaystyle+\frac{1}{4(kk^{\prime})^{2}}\left(-\frac{1}{x_{1}x_{2}}~{}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}\gamma_{\bot}^{\beta}\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}C\right]_{12}~{}\left[\gamma_{\bot}^{\rho}\gamma_{5}N_{\bar{n}}\right]_{3}\right.$
$\displaystyle\left.+\frac{1}{x_{1}x_{3}}\left[\hbox to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}C\right]_{12}~{}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\beta}\gamma_{\bot}^{\rho}\gamma_{5}N_{\bar{n}}\right]_{3}+\frac{1}{x_{2}x_{3}}~{}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k\gamma_{\bot}^{\sigma}\gamma_{\bot}^{\beta}\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}C\right]_{12}~{}\left[\hbox
to0.0pt{\hbox
to5.52084pt{\hfil/\hfil}\hss}k^{\prime}\gamma_{\bot}^{\alpha}\gamma_{\bot}^{\rho}\gamma_{5}N_{\bar{n}}\right]_{3}\right).\
$ (E.37)

The described projectors depend on the derivatives with respect to quark
momenta $\partial/\partial k_{1,2}$ and also include the terms with derivative
with respect to charmonium momentum $\partial/\partial P$. These terms only
depend on the twist-3 DAs $V_{1}^{B}$, $A_{1}^{B}$ and $T_{1}^{B}$ and they
are related to the matrix element of the leading-twist operator with the total
derivative

$(z_{3}n)\left\langle
0\right|(\bar{n}\partial)\left[\xi_{1}\xi_{2}\xi_{3}\right]\left|B(k)\right\rangle=-i(\bar{n}k)(z_{3}n)\left\langle
0\right|\xi_{1}\xi_{2}\xi_{3}\left|B(k)\right\rangle,$ (E.38)

where $(\bar{n}k)\equiv k_{-}=2m_{B}^{2}/k_{+}$. This contribution does not
vanish, in contrast to an operator with the total transverse derivative. It is
clear that such contributions generate power corrections associated with the
power suppressed component of the total baryon momentum $k$. Notice, that the
calculation of the contributions with derivatives $\partial/\partial k_{1,2}$
implies that $k_{3}=k-k_{1}-k_{2}$ as it follows from the momentum
conservation. The contributions with the matrix elements as in Eq.(E.38) can
be rewritten in a special way. This is related with the details of the Fourier
transformation and with the derivation of the momentum conservation
$\delta$-function.

Let us consider, as example, the contribution with $V_{1}(x)$ and
$V_{1}(y_{i})$ and the diagram as in Fig.1$(a)$. The following discussion is
also applicable for other cases. Performing the standard steps of the
calculation one obtains the following result

$\delta(k+k^{\prime}-P)\
iM[V_{1}V_{1}]_{\text{tw5}}=~{}\bar{V}_{n}\gamma_{\bot}^{\rho}N_{\bar{n}}\int
Dy_{i}V_{1}(y_{i})\int Dx_{i}~{}V_{1}(x_{i})\ T_{V1V1}(x_{i},y_{i}),$ (E.39)

where

$\displaystyle T_{V1V1}(x_{i},y_{i})$ $\displaystyle=\int
dz_{1}^{\prime}dz_{2}^{\prime}dz_{3}^{\prime}e^{iP\cdot(z_{1}^{\prime}+z_{2}^{\prime})/2}~{}e^{-i(k_{1}^{\prime}z_{1})-i(k_{2}^{\prime}z_{2})-i(k_{3}^{\prime}z_{3})}~{}$
$\displaystyle\int dz_{1}dz_{2}dz_{3}~{}k_{-}(-iz_{3}\cdot
n)~{}e^{-i\left(k_{1}z_{1}\right)-i\left(k_{2}z_{2}\right)-i\left(k_{3}z_{3}\right)}~{}\tilde{D}[z_{123},z_{123}^{\prime}],$
(E.40)

where $\tilde{D}[z_{123},z_{123}^{\prime}]$ denotes the analytical expression
for the diagram in the position space with the requiered operator vertices,
$z_{i}^{\prime}$ and $z_{i}$ describe the coordinates of the QCD vertices, see
Fig.2. The various Fourier exponents in the lhs appear from the hadronic
matrix elements. The quark momenta $k_{i}^{\prime}$ and $k_{i}$ in Eq.(E.40)
the same as in Eq.(E.1).

In order to extract the momentum conservation $\delta$-function from the
expression for $T_{V1V1}$ one uses that $x_{3}=1-x_{1}-x_{2}$,
$y_{3}=1-y_{1}-y_{2}$ and the translation invariance of the diagram
$\tilde{D}[z_{123},z_{123}^{\prime}]$. Performing redefinition
$z_{i}\rightarrow z_{i}+z_{3}$ and $z_{i}^{\prime}\rightarrow
z_{i}^{\prime}+z_{3}^{\prime}$ for $i=1,2$ one defines the Fourier exponent
with the coordinate $z_{3}$

$\displaystyle
e^{iP\cdot(z_{1}^{\prime}+z_{2}^{\prime})/2}~{}e^{-i(k_{1}^{\prime}z_{1})-i(k_{2}^{\prime}z_{2})-i(k_{3}^{\prime}z_{3})}~{}e^{-i\left(k_{1}z_{1}\right)-i\left(k_{2}z_{2}\right)-i\left(k_{3}z_{3}\right)}$
$\displaystyle\rightarrow\left\\{e^{i(Pz_{3})-i(k_{-}^{\prime}z_{3+})/2-i(k_{+}z_{3-})/2}\right\\}~{}e^{iP\cdot(z_{1}^{\prime}+z_{2}^{\prime})/2}~{}e^{-i(k_{1}^{\prime}z_{1})-i(k_{2}^{\prime}z_{2})}~{}e^{-i\left(k_{1}z_{1}\right)-i\left(k_{2}z_{2}\right)},$
(E.41)

and

$\tilde{D}[z_{123},z_{123}^{\prime}]\rightarrow\tilde{D}[z_{12},z_{12}^{\prime}].$
(E.42)

Therefore

$\displaystyle T_{V1V1}(x_{i},y_{i})$ $\displaystyle=\int
dz_{3}~{}k_{-}(-iz_{3}\cdot
n)e^{i(Pz_{3})-i(k_{-}^{\prime}z_{3+})/2-i(k_{+}z_{3-})/2}$
$\displaystyle\times\int
dz_{1}^{\prime}dz_{2}^{\prime}dz_{3}^{\prime}e^{iP\cdot(z_{1}^{\prime}+z_{2}^{\prime})/2}~{}e^{-i(k_{1}^{\prime}z_{1})-i(k_{2}^{\prime}z_{2})}$
$\displaystyle\times\int
dz_{1}dz_{2}~{}e^{-i\left(k_{1}z_{1}\right)-i\left(k_{2}z_{2}\right)}~{}\tilde{D}[z_{12},z_{12}^{\prime}].$
(E.43)

The integrals over $dz^{\prime}_{i}dz_{j}$ in this expression can be
understood as FT of the diagram $\tilde{D}$

$\displaystyle\int
dz_{1}^{\prime}dz_{2}^{\prime}dz_{3}^{\prime}e^{iP\cdot(z_{1}^{\prime}+z_{2}^{\prime})/2}~{}e^{-i(k_{1}^{\prime}z_{1})-i(k_{2}^{\prime}z_{2})}\int
dz_{1}dz_{2}~{}e^{-i\left(k_{1}z_{1}\right)-i\left(k_{2}z_{2}\right)}~{}\tilde{D}[z_{12},z_{12}^{\prime}]$
$\displaystyle=D(k_{12},k_{12}^{\prime},P).$ (E.44)

The first line in Eq.(E) gives the $\delta$-function if the factor
$k_{-}(-iz_{3}\cdot n)$ is rewritten as

$k_{-}(-iz_{3}\cdot n)=k_{-}\left.n_{\alpha}\frac{\partial}{\partial
l^{\alpha}}e^{-i\left(l\cdot z_{3}\right)}\right|_{l=0},$ (E.45)

where $l$ is just an auxiliary momentum. This gives

$T_{V1V1}(x_{i},y_{i})=k_{-}\left.\left[n_{\alpha}\frac{\partial}{\partial
l^{\alpha}}\delta(P-k_{-}^{\prime}n/2-k_{+}\bar{n}/2-l)\right]D(k_{12},k_{12}^{\prime},P)\right|_{l=0}$
(E.46) $=k_{-}\left.\left[-n_{\alpha}\frac{\partial}{\partial
P^{\alpha}}\delta(P-k_{-}^{\prime}n/2-k_{+}\bar{n}/2)\right]D(k_{12},k_{12}^{\prime},P)\right|_{P=2m_{c}\omega}$
(E.47) $=\delta(P-k_{-}^{\prime}n/2-k_{+}\bar{n}/2)\
\frac{2m_{B}^{2}}{k_{+}}\left.n_{\alpha}\frac{\partial}{\partial
P^{\alpha}}D(k_{12},k_{12}^{\prime},P)\right|_{P=2m_{c}\omega}$ (E.48)
$\simeq\delta(P-k^{\prime}-k)\
\frac{2m_{B}^{2}}{(kk^{\prime})}\left.k_{\alpha}^{\prime}\frac{\partial}{\partial
P^{\alpha}}D(k_{12},k_{12}^{\prime},P)\right|_{P=2m_{c}\omega},$ (E.49)

where one assumes that $P^{2}$ is not fixed before the differentiation. This
result explains the computational prescription for the terms with derivatives
$\partial/\partial P$ .

Let us also to note that such terms also include the endpoint singularities,
which cancel in the sum of the all twist-5 contributions. Therefore, it is
important to take them into account properly.

##  Appendix F Analytical expressions for the hard kernels $K_{XY}$

In these section we provide the analytical expressions for the hard kernels
$K_{XY}(x_{i},y_{i})$ in the integrals $J[X,Y]$ defined in Eq.(147). In the
following we use convenient notation

$\displaystyle D_{i}$ $\displaystyle=x_{i}(1-y_{i})+y_{i}(1-x_{i}),$ (F.1)
$\displaystyle f(x_{i})$ $\displaystyle\equiv f(x_{123})\equiv
f(x_{1},x_{2},x_{3}).$ (F.2)

The integrals, which describe twist-4$\times$twist-4 contribution read

$\left.J_{44}^{B}\right|_{\text{even}}=J[\mathcal{V}^{B}_{1},\mathcal{V}^{B}_{1}]+J[\mathcal{V}^{B}_{2},\mathcal{V}^{B}_{1}]+J[\mathcal{A}^{B}_{1},\mathcal{A}^{B}_{1}]+J[\mathcal{A}^{B}_{2},\mathcal{A}^{B}_{1}]+J[\mathcal{A}^{B}_{1},\mathcal{V}^{B}_{1}]+J[\mathcal{A}^{B}_{2},\mathcal{V}^{B}_{1}],$
(F.3)

where

$K_{\mathcal{V}_{1}\mathcal{V}_{1}}(x_{i},y_{i})=K_{\mathcal{A}_{1}\mathcal{A}_{1}}(x_{i},y_{i})=\frac{1}{2}\frac{x_{2}y_{2}}{D_{1}D_{2}D_{3}},$
(F.4)
$K_{\mathcal{V}_{2}\mathcal{V}_{1}}(x_{i},y_{i})=K_{\mathcal{A}_{2}\mathcal{A}_{1}}(x_{i},y_{i})=\frac{1}{4}\frac{x_{1}y_{1+}x_{2}y_{2}}{D_{1}D_{2}D_{3}},$
(F.5)
$K_{\mathcal{A}_{1}\mathcal{V}_{1}}(x_{i},y_{i})=\frac{x_{2}y_{2}}{D_{1}D_{2}D_{3}},$
(F.6)
$K_{\mathcal{A}_{2}\mathcal{V}_{1}}(x_{i},y_{i})=\frac{1}{2}\frac{x_{2}y_{2}-x_{1}y_{1}}{D_{1}D_{2}D_{3}}.$
(F.7)

$\left.J_{44}^{B}\right|_{\text{odd}}=J[\mathcal{T}^{B}_{21}+\mathcal{T}^{B}_{41},\mathcal{T}^{B}_{21}+\mathcal{T}^{B}_{41}]+J[\mathcal{T}^{B}_{22}-\mathcal{T}^{B}_{42},\mathcal{T}^{B}_{21}-\mathcal{T}^{B}_{41}]+J[\mathcal{T}^{B}_{22}+\mathcal{T}^{B}_{42},\mathcal{T}^{B}_{21}+\mathcal{T}^{B}_{41}],$
(F.8)

where

$K_{\mathcal{T}_{21}+\mathcal{T}_{41},\mathcal{T}_{21}+\mathcal{T}_{41}}(x_{i},y_{i})=-\frac{1}{2}\frac{x_{2}+y_{2}-3x_{2}y_{2}}{D_{1}D_{2}D_{3}},$
(F.9)
$K_{\mathcal{T}_{22}+\mathcal{T}_{42},\mathcal{T}_{21}+\mathcal{T}_{41}}(x_{i},y_{i})=-\frac{1}{4}\frac{1-2x_{1}-2y_{2}+6x_{1}y_{2}}{D_{1}D_{2}D_{3}},$
(F.10)
$K_{\mathcal{T}_{22}-\mathcal{T}_{42},\mathcal{T}_{21}-\mathcal{T}_{41}}(x_{i},y_{i})=-\frac{1}{4}\frac{x_{3}y_{3}}{D_{1}D_{2}D_{3}}.$
(F.11)

The twist-3$\times$twist-5 integrals have the following kernels.

$\displaystyle\left.J_{35}^{B}\right|_{\text{even}}=J[V^{B}_{5},V^{B}_{1}]+J[V^{B}_{5},A^{B}_{1}]+J[A^{B}_{5},A^{B}_{1}]+J[A^{B}_{5},V^{B}_{1}]$
(F.12)
$\displaystyle\phantom{J[V_{5},V_{1}]]}+J_{B}[V^{B}_{Z},V^{B}_{1}]+J_{B}[A^{B}_{Z},V^{B}_{1}]+J_{B}[A^{B}_{Z},A^{B}_{1}]+J_{B}[V^{B}_{Z},A^{B}_{1}].$
(F.13)

The first four integrals have relatively simple structure

$K_{V5V1}(x_{i},y_{i})=K_{A5A1}(x_{i},y_{i})=\frac{1}{16}\frac{x_{1}x_{2}}{D_{1}D_{2}D_{3}}(-1+2y_{3}+x_{3}y_{3}+x_{1}y_{2}+x_{2}y_{1}),$
(F.14)
$K_{A5V1}(x_{i},y_{i})=K_{V5A1}(x_{i},y_{i})=\frac{1}{16}\frac{x_{1}x_{2}}{D_{1}D_{2}D_{3}}\left(y_{1}-y_{2}+x_{1}(y_{2}-y_{3})-x_{2}(y_{1}-y_{3})\right).$
(F.15)

The integrals $J_{Z}$ defined in Eqs.(154)-(157) are also well defined, but
they are given by the sum of the singular terms $J[X,Y]$. The analytical
expression for the total sum is quite complicated and it is more constructive
to describe the expressions for the individual kernels in $J[X,Y]$. Then

$J_{Z}[V^{B}_{Z},V^{B}_{1}]=J[V^{B}_{1xx},V^{B}_{1}]+J[V^{B}_{1yy},V^{B}_{1}]+J[V^{B}_{1xy},V^{B}_{1}]+(1-\delta_{B\Lambda})J[V^{B}_{1},V^{B}_{1}].$
(F.16)

Each term in Eq.(F.16) has the following kernel

$K_{V1xxV1}(x_{i},y_{i})=\frac{1}{32}\left(\frac{A}{D_{1}D_{3}}+\frac{B}{D_{1}D_{2}}+\frac{C}{D_{2}D_{3}}\right),$
(F.17)

where

$A=-\frac{1}{x_{1}}\left(\frac{1}{D_{1}}+\frac{1-2x_{2}}{D_{3}}\right)(x_{3}y_{1}+x_{1}y_{3})+1-\frac{1}{2x_{1}}+\frac{1}{2x_{3}}-\frac{1}{2x_{1}x_{3}}+\frac{y_{1}}{y_{3}}+\frac{x_{3}y_{1}}{x_{1}y_{3}},$
(F.18)

$B=\frac{x_{2}(1-2x_{1})}{2x_{1}x_{3}},\,\,C=-\frac{(1-2x_{2})}{x_{1}D_{3}}(x_{2}y_{3}+x_{3}y_{2})+\frac{y_{2}}{y_{3}}+\frac{x_{2}}{2x_{1}x_{3}}+\frac{x_{3}y_{2}}{x_{1}y_{3}}.$
(F.19) $K_{V1yyV1}(x_{i},y_{i})=K_{V1xxV1}(x_{213},y_{213}).$ (F.20)
$K_{V1xyV1}(x_{i},y_{i})=\frac{1}{8}\left(\frac{A}{D_{1}D_{3}}+\frac{C}{D_{2}D_{3}}\right),$
(F.21)

where

$A=-\frac{1}{D_{3}}(x_{1}y_{3}+x_{3}y_{1})+\frac{y_{1}}{2y_{3}},\ \
C=-\frac{1}{D_{3}}(x_{3}y_{2}+x_{2}y_{3})+\frac{y_{2}}{2y_{3}}.$ (F.22)
$K_{V1V1}(x_{i},y_{i})=\frac{1}{64}\left(\frac{A}{D_{1}D_{3}}+\frac{C}{D_{2}D_{3}}\right),$
(F.23)

where

$A=\left(\frac{1-2x_{1}}{D_{1}}-\frac{1-2x_{3}}{D_{3}}\right)(y_{1}x_{3}+y_{3}x_{1})-\bar{x}_{2}-\frac{2y_{1}x_{3}}{y_{3}},$
(F.24)
$C=\left(\frac{1-2x_{2}}{D_{2}}-\frac{1-2x_{3}}{D_{3}}\right)(y_{2}x_{3}+y_{3}x_{2})-\bar{x}_{1}-\frac{2y_{2}x_{3}}{y_{3}}.$
(F.25)

The next integral reads

$J_{Z}[V^{B}_{Z},A^{B}_{1}]=J[V^{B}_{1xx},A^{B}_{1}]+J[V^{B}_{1yy},A^{B}_{1}]+J[V^{B}_{1xy},A^{B}_{1}]+(1-\delta_{B\Lambda})J[V^{B}_{1},A^{B}_{1}].$
(F.26)

The kernels of the individual integrals read

$K_{V1xxA1}(x_{i},y_{i})=\frac{1}{32}\left(\frac{A}{D_{1}D_{3}}+\frac{B}{D_{1}D_{2}}+\frac{C}{D_{2}D_{3}}\right),$
(F.27)

where

$A=\frac{1}{x_{1}}\left(\frac{1}{D_{1}}+\frac{1-2x_{2}}{D_{3}}\right)(x_{3}y_{1}+x_{1}y_{3})+1-\frac{1}{2x_{1}}+\frac{1}{2x_{3}}-\frac{y_{1}}{y_{3}}-\frac{1}{2x_{1}x_{3}}-\frac{x_{3}y_{1}}{x_{1}y_{3}},$
(F.28)
$B=\frac{2x_{2}(1-2x_{1})}{x_{1}x_{3}},\,\,C=-\frac{1-2x_{2}}{x_{1}D_{3}}(x_{3}y_{2}+x_{2}y_{3})+\frac{\bar{x}_{2}y_{2}}{x_{1}y_{3}}+\frac{x_{2}}{2x_{1}x_{3}}.$
(F.29) $K_{V1yyA1}(x_{i},y_{i})=K_{V1xxA1}(x_{213},y_{213}).$ (F.30)
$K_{V1xyA1}(x_{i},y_{i})=\frac{1}{8}\left(\frac{A}{D_{1}D_{3}}+\frac{C}{D_{2}D_{3}}\right),$
(F.31)

where

$A=\frac{1}{D_{3}}(x_{1}y_{3}+x_{3}y_{1})-\frac{y_{1}}{2y_{3}},\ \ \
C=-\frac{1}{D_{3}}(x_{2}y_{3}+x_{3}y_{2})+\frac{y_{2}}{2y_{3}}.$ (F.32)
$K_{V1A1}(x_{i},y_{i})=\frac{1}{64}\left(\frac{A}{D_{1}D_{3}}+\frac{C}{D_{2}D_{3}}\right),$
(F.33)

where

$A=-\left(\frac{1-2x_{1}}{D_{1}}-\frac{1-2x_{3}}{D_{3}}\right)(x_{3}y_{1}+x_{1}y_{3})+3x_{1}-x_{3}+2\frac{y_{1}x_{3}}{y_{3}},$
(F.34)
$C=\left(\frac{1-2x_{2}}{D_{2}}-\frac{1-2x_{3}}{D_{3}}\right)(x_{3}y_{2}+x_{2}y_{3})-3x_{2}+x_{3}-2\frac{y_{2}x_{3}}{y_{3}}.$
(F.35)

The next integral reads

$J_{Z}[A^{B}_{Z},V^{B}_{1}]=J[A^{B}_{1xx},V^{B}_{1}]+J[A^{B}_{1yy},V^{B}_{1}]+J[A^{B}_{1xy},V^{B}_{1}]+\delta_{B\Lambda}J[A^{B}_{1},V^{B}_{1}].$
(F.36)

The kernels of the individual integrals read

$K_{A1xxV1}(x_{i},y_{i})=K_{V1xxA1}(x_{i},y_{i}).$ (F.37)
$K_{A1yyV1}(x_{i},y_{i})=K_{A1xxV1}(x_{213},y_{213}).$ (F.38)
$K_{A1xyV1}(x_{i},y_{i})=K_{V1xyA1}(x_{i},y_{i}).$ (F.39)
$K_{A1V1}(x_{i},y_{i})=K_{V1A1}(x_{i},y_{i}).$ (F.40)

The next integral reads

$J_{Z}[A^{B}_{Z},A^{B}_{1}]=J[A^{B}_{1xx},A^{B}_{1}]+J[A^{B}_{1yy},V^{B}_{1}]+J[A^{B}_{1xy},V^{B}_{1}]+\delta_{B\Lambda}J[A^{B}_{1},A^{B}_{1}].$
(F.41)

The kernels of the individual integrals read

$K_{A1xxA1}(x_{i},y_{i})=K_{V1xxV1}(x_{i},y_{i}).$ (F.42)
$K_{A1yyA1}(x_{i},y_{i})=K_{A1xxA1}(x_{213},y_{213}).$ (F.43)
$K_{A1xyA1}(x_{i},y_{i})=K_{V1xyV1}(x_{i},y_{i}).$ (F.44)
$K_{A1A1}(x_{i},y_{i})=K_{V1V1}(x_{i},y_{i}).$ (F.45)

The last integral reads

$\displaystyle
J_{Z}[T^{B}_{Z},T^{B}_{1}]=J[T^{B}_{0xx},T^{B}_{1}]+J[T^{B}_{0yy},T^{B}_{1}]+J[T^{B}_{0xy},T^{B}_{1}]+J[\tilde{T}^{B}_{2xy},T^{B}_{1}]$
$\displaystyle+(1-\delta_{B\Lambda})J[T^{B}_{1},T^{B}_{1}].$ (F.46)

The kernels of the individual integrals read

$K_{T0xxT1}(x_{i},y_{i})=\frac{1}{16}\left(\frac{A}{D_{1}D_{3}}+\frac{B}{D_{1}D_{2}}+\frac{C}{D_{2}D_{3}}\right),$
(F.47)

where

$A=1-\frac{1}{x_{3}}+\frac{1}{2x_{1}}+\frac{1}{2x_{3}}-\frac{1}{2x_{1}x_{3}},$
(F.48)
$B=(x_{2}y_{1}+x_{1}y_{2})\left(\frac{1}{x_{3}y_{3}}+\frac{1}{x_{1}y_{3}}-\frac{1}{x_{1}D_{1}}\right)+\frac{x_{2}}{2x_{1}x_{3}},\,\,C=-\frac{x_{2}}{x_{1}}+\frac{x_{2}}{2x_{1}x_{3}}.$
(F.49) $K_{T0yyT1}(x_{i},y_{i})=K_{T0xxT1}(x_{213},y_{213}).$ (F.50)
$K_{T0xyT1}(x_{i},y_{i})=\frac{1}{16}\left(\frac{A}{D_{1}D_{3}}+\frac{B}{D_{1}D_{2}}+\frac{C}{D_{2}D_{3}}\right),$
(F.51)

where

$A=1-\frac{1}{2x_{3}}+\frac{1}{2x_{1}}-\frac{x_{1}}{x_{2}}-\frac{1}{2x_{1}x_{3}}+\frac{x_{1}}{2x_{2}x_{3}},$
(F.52)

$B=\frac{x_{1}}{2x_{2}x_{3}}+\frac{x_{2}}{2x_{1}x_{3}}+\frac{2x_{2}y_{1}}{x_{3}y_{3}}+\frac{2x_{1}y_{2}}{x_{3}y_{3}},$
(F.53)
$C=1-\frac{1}{2x_{3}}+\frac{1}{2x_{2}}-\frac{x_{2}}{x_{1}}-\frac{1}{2x_{2}x_{3}}+\frac{x_{2}}{2x_{1}x_{3}}.$
(F.54)
$K_{\tilde{T}2xyT1}(x_{i},y_{i})=\frac{1}{16}\left(\frac{A}{D_{1}D_{3}}+\frac{B}{D_{1}D_{2}}+\frac{C}{D_{2}D_{3}}\right),$
(F.55)

where

$A=-1+\frac{1}{2x_{3}}-\frac{1}{2x_{1}}-\frac{x_{1}}{x_{2}}+\frac{1}{2x_{1}x_{3}}+\frac{x_{1}}{2x_{2}x_{3}},\,\,B=\frac{x_{1}}{2x_{2}x_{3}}-\frac{x_{2}}{2x_{1}x_{3}}$
(F.56)
$C=1-\frac{1}{2x_{3}}+\frac{1}{2x_{2}}+\frac{x_{2}}{x_{1}}-\frac{1}{2x_{2}x_{3}}-\frac{x_{2}}{2x_{1}x_{3}}.$
(F.57) $\displaystyle K_{T1T1}(x_{i},y_{i})=$
$\displaystyle\frac{1}{16}\frac{1}{D_{1}D_{2}}\left\\{\left(\frac{1-2x_{1}}{D_{1}}+\frac{1-2x_{2}}{D_{2}}\right)(x_{2}y_{1}+x_{1}y_{2})\right.$
$\displaystyle\phantom{\frac{1}{4}\frac{1}{D_{1}D_{2}}\frac{1-2x_{1}}{D_{1}}}\left.-\frac{1}{y_{3}}\left(2y_{1}x_{2}+2x_{1}y_{2}+x_{2}y_{3}+x_{1}y_{3}\right)\right\\}.$
(F.58)

## References

  * [1] S. J. Brodsky and G. P. Lepage, Phys. Rev. D 24 (1981) 2848. doi:10.1103/PhysRevD.24.2848
  * [2] V. L. Chernyak and A. R. Zhitnitsky, Phys. Rept. 112 (1984) 173. doi:10.1016/0370-1573(84)90126-1
  * [3] N. Brambilla et al. [Quarkonium Working Group], hep-ph/0412158.
  * [4] N. Brambilla et al., Eur. Phys. J. C 71 (2011) 1534 doi:10.1140/epjc/s10052-010-1534-9 [arXiv:1010.5827 [hep-ph]].
  * [5] V. L. Chernyak, A. A. Ogloblin and I. R. Zhitnitsky, Z. Phys. C 42 (1989) 583 [Yad. Fiz. 48 (1988) 1398] [Sov. J. Nucl. Phys. 48 (1988) 889]. doi:10.1007/BF01557664
  * [6] N. G. Stefanis and M. Bergmann, Phys. Rev. D 47 (1993), R3685-R3689 doi:10.1103/PhysRevD.47.R3685 [arXiv:hep-ph/9211250 [hep-ph]].
  * [7] J. Bolz and P. Kroll, Eur. Phys. J. C 2 (1998), 545-556 doi:10.1007/s100520050160 [arXiv:hep-ph/9703252 [hep-ph]].
  * [8] M. Ablikim et al. [BES], Phys. Rev. D 78 (2008), 092005 doi:10.1103/PhysRevD.78.092005 [arXiv:0810.1896 [hep-ex]].
  * [9] M. Ablikim et al. [BESIII], Phys. Rev. D 86 (2012), 032014 doi:10.1103/PhysRevD.86.032014 [arXiv:1205.1036 [hep-ex]].
  * [10] M. Ablikim et al. [BESIII], Phys. Rev. D 93 (2016) no.7, 072003 doi:10.1103/PhysRevD.93.072003 [arXiv:1602.06754 [hep-ex]].
  * [11] M. Ablikim et al. [BESIII], Phys. Lett. B 770 (2017), 217-225 doi:10.1016/j.physletb.2017.04.048 [arXiv:1612.08664 [hep-ex]].
  * [12] M. Ablikim et al. [BESIII], Phys. Rev. D 95 (2017) no.5, 052003 doi:10.1103/PhysRevD.95.052003 [arXiv:1701.07191 [hep-ex]].
  * [13] M. Ablikim et al. [BESIII], Phys. Rev. Lett. 125 (2020) no.5, 052004 doi:10.1103/PhysRevLett.125.052004 [arXiv:2004.07701 [hep-ex]].
  * [14] M. Alekseev, A. Amoroso, R. B. Ferroli, I. Balossino, M. Bertani, D. Bettoni, F. Bianchi, J. Chai, G. Cibinetto and F. Cossio, et al. Chin. Phys. C 43 (2019) no.2, 023103 doi:10.1088/1674-1137/43/2/023103 [arXiv:1809.04273 [hep-ph]].
  * [15] R. Baldini Ferroli, A. Mangoni, S. Pacetti and K. Zhu, Phys. Lett. B 799 (2019), 135041 doi:10.1016/j.physletb.2019.135041 [arXiv:1905.01069 [hep-ph]].
  * [16] M. Claudson, S. L. Glashow and M. B. Wise, Phys. Rev. D 25 (1982) 1345. doi:10.1103/PhysRevD.25.1345
  * [17] C. Carimalo, Int. J. Mod. Phys. A 2 (1987) 249. doi:10.1142/S0217751X87000107
  * [18] F. Murgia and M. Melis, Phys. Rev. D 51 (1995) 3487 doi:10.1103/PhysRevD.51.3487 [hep-ph/9412205].
  * [19] N. Kivel, Eur. Phys. J. A 56 (2020) no.2, 64 [erratum: Eur. Phys. J. A 57 (2021) no.9, 271] doi:10.1140/epja/s10050-021-00575-9 [arXiv:1910.02850 [hep-ph]].
  * [20] N. Kivel, [arXiv:2109.05847 [hep-ph]].
  * [21] V. Braun, R. J. Fries, N. Mahnke and E. Stein, Nucl. Phys. B 589 (2000) 381 Erratum: [Nucl. Phys. B 607 (2001) 433] doi:10.1016/S0550-3213(00)00516-2, 10.1016/S0550-3213(01)00254-1 [hep-ph/0007279].
  * [22] V. M. Braun, S. E. Derkachov, G. P. Korchemsky and A. N. Manashov, Nucl. Phys. B 553 (1999), 355-426 doi:10.1016/S0550-3213(99)00265-5 [arXiv:hep-ph/9902375 [hep-ph]].
  * [23] V. M. Braun, A. N. Manashov and J. Rohrwild, Nucl. Phys. B 807 (2009) 89 doi:10.1016/j.nuclphysb.2008.08.012 [arXiv:0806.2531 [hep-ph]].
  * [24] S. Krankl and A. Manashov, Phys. Lett. B 703 (2011), 519-523 doi:10.1016/j.physletb.2011.08.028 [arXiv:1107.3718 [hep-ph]].
  * [25] I. V. Anikin, V. M. Braun and N. Offen, Phys. Rev. D 88 (2013) 114021 doi:10.1103/PhysRevD.88.114021 [arXiv:1310.1375 [hep-ph]].
  * [26] P. Wein and A. Schäfer, JHEP 05 (2015), 073 doi:10.1007/JHEP05(2015)073 [arXiv:1501.07218 [hep-ph]].
  * [27] I. V. Anikin and A. N. Manashov, Phys. Rev. D 93 (2016) no.3, 034024 doi:10.1103/PhysRevD.93.034024 [arXiv:1512.07141 [hep-ph]].
  * [28] G. S. Bali et al. [RQCD Collaboration], Eur. Phys. J. A 55 (2019) no.7, 116 doi:10.1140/epja/i2019-12803-6 [arXiv:1903.12590 [hep-lat]].
  * [29] B. Aubert et al. [BaBar], Phys. Rev. D 76 (2007), 092006 doi:10.1103/PhysRevD.76.092006 [arXiv:0709.1988 [hep-ex]].
  * [30] M. Ablikim et al. [BESIII], Phys. Rev. D 97 (2018) no.3, 032013 doi:10.1103/PhysRevD.97.032013 [arXiv:1709.10236 [hep-ex]].
  * [31] M. Ablikim et al. [BESIII], Phys. Rev. Lett. 124 (2020) no.4, 042001 doi:10.1103/PhysRevLett.124.042001 [arXiv:1905.09001 [hep-ex]].
  * [32] M. Ablikim et al. [BESIII], Phys. Rev. D 103 (2021) no.1, 012005 doi:10.1103/PhysRevD.103.012005 [arXiv:2010.08320 [hep-ex]].
  * [33] M. Ablikim et al. [BESIII], Phys. Lett. B 814 (2021), 136110 doi:10.1016/j.physletb.2021.136110 [arXiv:2009.01404 [hep-ex]].
  * [34] M. Ablikim et al. [BESIII], [arXiv:2103.12486 [hep-ex]].
  * [35] M. Ablikim et al. [BESIII], Phys. Lett. B 820 (2021), 136557 doi:10.1016/j.physletb.2021.136557 [arXiv:2105.14657 [hep-ex]].
  * [36] M. Ablikim et al. [BESIII], [arXiv:2110.04510 [hep-ex]].
  * [37] J. Kublbeck, H. Eck and R. Mertig, Nucl. Phys. B Proc. Suppl. 29 (1992), 204-208
  * [38] V. Shtabovenko, R. Mertig and F. Orellana, Comput. Phys. Commun. 256 (2020), 107478 doi:10.1016/j.cpc.2020.107478 [arXiv:2001.04407 [hep-ph]].
  * [39] P.A. Zyla et al. [Particle Data Group], PTEP 2020 (2020) no.8, 083C01 doi:10.1093/ptep/ptaa104
  * [40] E. J. Eichten and C. Quigg, Phys. Rev. D 52 (1995) 1726 [hep-ph/9503356].
  * [41] P. Ball and V. M. Braun, Nucl. Phys. B 543 (1999), 201-238 doi:10.1016/S0550-3213(99)00014-0 [arXiv:hep-ph/9810475 [hep-ph]].
  * [42] P. Ball, V. M. Braun, Y. Koike and K. Tanaka, Nucl. Phys. B 529 (1998), 323-382 doi:10.1016/S0550-3213(98)00356-3 [arXiv:hep-ph/9802299 [hep-ph]].
  * [43] M. Beneke, A. P. Chapovsky, M. Diehl and T. Feldmann, Nucl. Phys. B 643 (2002), 431-476 doi:10.1016/S0550-3213(02)00687-9 [arXiv:hep-ph/0206152 [hep-ph]].