##  Appendix D NSV resummation constants $\bar{g}^{c}_{i}(\omega)$

The resummation constants $\bar{g}^{c}_{i}(\omega)$ given in Eq.(4) are
presented below. Here $\bar{L}_{\omega}=\log(1-\omega)$,
$L_{qr}=\log(\frac{Q^{2}}{\mu_{R}^{2}})$,
$L_{fr}=\log(\frac{\mu_{F}^{2}}{\mu_{R}^{2}})$ and
$\omega=\beta_{0}a_{s}(\mu_{R}^{2})\log(N)$. Also, $\textbf{B}_{DIS,i}^{c}$
are the threshold exponent given in Ravindran:2005vv .

$\displaystyle\autobreak\overline{g}^{c}_{2}(\omega)=\par\frac{A^{c}_{1}}{2\beta_{0}}\overline{L}_{\omega}\,,\par$
$\displaystyle\autobreak\overline{g}^{c}_{3}(\omega)=\frac{1}{(1-\omega)}\bigg{[}-\frac{A^{c}_{2}\omega}{2\beta_{0}}\par+\frac{\beta_{1}A^{c}_{1}}{2\beta_{0}^{2}}\bigg{\\{}\omega+\overline{L}_{\omega}\bigg{\\}}\par-\frac{A^{c}_{1}}{2}\bigg{\\{}1+\gamma_{E}-L_{qr}+L_{fr}-L_{fr}\omega\bigg{\\}}\par+\frac{\mathbb{B}_{DIS,1}^{c}}{2}\bigg{]}\,,\par\par$
$\displaystyle\autobreak\par\overline{g}^{c}_{4}(\omega)=\frac{1}{(1-\omega)^{2}}\bigg{[}\par-\frac{\beta_{1}}{2\beta_{0}}\mathbb{B}_{DIS,1}^{c}\overline{L}_{\omega}\par\par+\frac{\beta_{0}}{2}\mathbb{B}_{DIS,1}^{c}\bigg{\\{}1+\gamma_{E}-L_{qr}\bigg{\\}}\par-\frac{A^{c}_{3}}{4\beta_{0}}\bigg{\\{}2\omega-\omega^{2}\bigg{\\}}\par+\frac{\beta_{1}A^{c}_{2}}{4\beta_{0}^{2}}\bigg{\\{}2\omega-\omega^{2}+2\overline{L}_{\omega}\bigg{\\}}\par-\frac{A^{c}_{2}}{2}\bigg{\\{}1+\gamma_{E}-L_{qr}+L_{fr}-2L_{fr}\omega+L_{fr}\omega^{2}\bigg{\\}}\par+\frac{\beta_{1}^{2}A^{c}_{1}}{4\beta_{0}^{3}}\bigg{\\{}\omega^{2}-\overline{L}_{\omega}^{2}\bigg{\\}}\par-\frac{\beta_{2}A^{c}_{1}}{4\beta_{0}^{2}}\bigg{\\{}\omega^{2}\bigg{\\}}\par+\frac{\beta_{1}A^{c}_{1}}{2\beta_{0}}\bigg{\\{}\overline{L}_{\omega}+\overline{L}_{\omega}\gamma_{E}-L_{qr}\overline{L}_{\omega}\bigg{\\}}\par-\frac{\beta_{0}A^{c}_{1}}{4}\bigg{\\{}2\gamma_{E}+\gamma_{E}^{2}+\zeta_{2}-2L_{qr}-2L_{qr}\gamma_{E}+L_{qr}^{2}-L_{fr}^{2}+2L_{fr}^{2}\omega-
L_{fr}^{2}\omega^{2}\bigg{\\}}\par+\frac{\mathbb{B}_{DIS,2}^{c}}{2}\par\bigg{]}\,,\par$
$\displaystyle\autobreak\par\overline{g}^{c}_{5}(\omega)=\frac{1}{(1-\omega)^{3}}\bigg{[}\par-\frac{\beta_{1}^{2}\mathbb{B}_{DIS,1}^{c}}{2\beta_{0}^{2}}\bigg{\\{}\omega+\overline{L}_{\omega}-\overline{L}_{\omega}^{2}\bigg{\\}}\par+\frac{\beta_{2}}{2\beta_{0}}\omega\mathbb{B}_{DIS,1}^{c}\par\par-\frac{\beta_{1}}{\beta_{0}}\overline{L}_{\omega}\mathbb{B}_{DIS,2}^{c}\par\par+\frac{\beta_{1}\mathbb{B}_{DIS,1}^{c}}{2}\bigg{\\{}1+\gamma_{E}-2\overline{L}_{\omega}-2\overline{L}_{\omega}\gamma_{E}-L_{qr}+2L_{qr}\overline{L}_{\omega}\bigg{\\}}\par+\beta_{0}\mathbb{B}_{DIS,2}^{c}\bigg{\\{}1+\gamma_{E}-L_{qr}\bigg{\\}}\par+\frac{\beta_{0}^{2}\mathbb{B}_{DIS,1}^{c}}{2}\bigg{\\{}2\gamma_{E}+\gamma_{E}^{2}+\zeta_{2}-2L_{qr}-2L_{qr}\gamma_{E}+L_{qr}^{2}\bigg{\\}}\par-\frac{A^{c}_{4}}{6\beta_{0}}\bigg{\\{}3\omega-3\omega^{2}+\omega^{3}\bigg{\\}}\par+\frac{\beta_{1}A^{c}_{3}}{6\beta_{0}^{2}}\bigg{\\{}3\omega-3\omega^{2}+\omega^{3}+3\overline{L}_{\omega}\bigg{\\}}\par-\frac{A^{c}_{3}}{2}\bigg{\\{}1+\gamma_{E}-L_{qr}+L_{fr}-3L_{fr}\omega+3L_{fr}\omega^{2}-L_{fr}\omega^{3}\bigg{\\}}\par+\frac{\beta_{1}^{2}A^{c}_{2}}{6\beta_{0}^{3}}\bigg{\\{}3\omega^{2}-\omega^{3}-3\overline{L}_{\omega}^{2}\bigg{\\}}\par-\frac{\beta_{2}A^{c}_{2}}{6\beta_{0}^{2}}\bigg{\\{}3\omega^{2}-\omega^{3}\bigg{\\}}\par+\frac{\beta_{1}A^{c}_{2}\overline{L}_{\omega}}{\beta_{0}}\bigg{\\{}1+\gamma_{E}-L_{qr}\bigg{\\}}\par-\frac{A^{c}_{2}\beta_{0}}{2}\bigg{\\{}2\gamma_{E}+\gamma_{E}^{2}+\zeta_{2}-2L_{qr}-2L_{qr}\gamma_{E}+L_{qr}^{2}-L_{fr}^{2}+3L_{fr}^{2}\omega-3L_{fr}^{2}\omega^{2}+L_{fr}^{2}\omega^{3}\bigg{\\}}\par-\frac{\beta_{1}^{3}A^{c}_{1}}{12\beta_{0}^{4}}\bigg{\\{}3\omega^{2}-2\omega^{3}+6\overline{L}_{\omega}\omega+3\overline{L}_{\omega}^{2}-2\overline{L}_{\omega}^{3}\bigg{\\}}\par+\frac{\beta_{1}\beta_{2}A^{c}_{1}}{6\beta_{0}^{3}}\bigg{\\{}3\omega^{2}-2\omega^{3}+3\overline{L}_{\omega}\omega\bigg{\\}}\par-\frac{\beta_{3}A^{c}_{1}}{12\beta_{0}^{2}}\bigg{\\{}3\omega^{2}-2\omega^{3}\bigg{\\}}\par+\frac{\beta_{1}^{2}A^{c}_{1}}{2\beta_{0}^{2}}\bigg{\\{}\omega+\omega\gamma_{E}+\overline{L}_{\omega}+\overline{L}_{\omega}\gamma_{E}-\overline{L}_{\omega}^{2}-\overline{L}_{\omega}^{2}\gamma_{E}-L_{qr}\omega-
L_{qr}\overline{L}_{\omega}+L_{qr}\overline{L}_{\omega}^{2}\bigg{\\}}\par-\frac{\beta_{2}A^{c}_{1}}{2\beta_{0}}\bigg{\\{}\omega+\omega\gamma_{E}-L_{qr}\omega\bigg{\\}}\par-\frac{A^{c}_{1}\beta_{1}}{4}\bigg{\\{}2\gamma_{E}+\gamma_{E}^{2}+\zeta_{2}-4\overline{L}_{\omega}\gamma_{E}-2\overline{L}_{\omega}\gamma_{E}^{2}-2\overline{L}_{\omega}\zeta_{2}-2L_{qr}-2L_{qr}\gamma_{E}+4L_{qr}\overline{L}_{\omega}+4L_{qr}\overline{L}_{\omega}\gamma_{E}+L_{qr}^{2}-2L_{qr}^{2}\overline{L}_{\omega}-L_{fr}^{2}+3L_{fr}^{2}\omega-3L_{fr}^{2}\omega^{2}+L_{fr}^{2}\omega^{3}\bigg{\\}}\par-\frac{A^{c}_{1}\beta_{0}^{2}}{6}\bigg{\\{}3\gamma_{E}^{2}+\gamma_{E}^{3}+2\zeta_{3}+3\zeta_{2}+3\zeta_{2}\gamma_{E}-6L_{qr}\gamma_{E}-3L_{qr}\gamma_{E}^{2}-3L_{qr}\zeta_{2}+3L_{qr}^{2}+3L_{qr}^{2}\gamma_{E}-L_{qr}^{3}+L_{fr}^{3}-3L_{fr}^{3}\omega+3L_{fr}^{3}\omega^{2}-L_{fr}^{3}\omega^{3}\bigg{\\}}\par+\frac{\mathbb{B}_{DIS,3}^{c}}{2}\par\bigg{]}\,.\par\par\par$
(80)

As before here also we provide the above results along with
$\bar{g}^{c}_{6}(\omega)$ in the ancillary files with the arXiv submission.

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