the deuteron reduces to ${\hat{\boldsymbol{D}}}_{\rm PC}=(\tau_z(1)-\tau_z(2))\bmr$ therefore $d^2_{\rm PC}$ in Eq. (\[eq:da\]) receives contribution only from the component $^3P_1$ which has $T=1$. This component is generated by the TRV potential components proportional to $({\boldsymbol{\sigma}_1}+{\boldsymbol{\sigma}_2})$, namely those proportional to $g_1$, $\Delta_3$, $C_3$ and $C_4$.

  $\Lambda$(MeV)          $450$               $500$               $550$
  ---------------- ------------------- ------------------- -------------------
  $a_n(a_p)$        $\m0.934\pm0.001$   $\m0.939\pm0.001$   $\m0.938\pm0.001$
  $a_1$             $\m0.192\pm0.006$   $\m0.197\pm0.004$   $\m0.194\pm0.003$
  $a_\Delta$        $ -0.306\pm0.174$   $ -0.341\pm0.153$   $ -0.349\pm0.137$
  $A_3$             $\m0.013\pm0.004$   $\m0.013\pm0.004$   $\m0.013\pm0.004$
  $A_4$             $ -0.013\pm0.004$   $ -0.013\pm0.004$   $ -0.013\pm0.004$

  :  \[tab:2hdpc\] Values of the deuteron coefficients $a_n$ and $a_p$ in units of $d_p$ and $d_n$ and of $a_1$, $a_\Delta$, $A_3$, $A_4$ in units of $e$ fm for the three different choices of cutoff parameters $\Lambda$.

The coefficient $a_\Delta$ can be written as, $$a_\Delta=a_\Delta(0)+\big(c_1a_\Delta(1)+c_2a_\Delta(2)+c_3a_\Delta(3)\big)+
  a_\Delta(RC)\ ,\label{eq:adelta}$$ where the first term comes from $V_{TRV}^{(3\pi,0)}$, the term in parenthesis from $V_{TRV}^{(3\pi,1)}$, where the LECs $c_1$, $c_2$ and $c_3$ appear, and the last term from $V_{TRV}^{(3\pi,{\rm RC})}$. In Table \[tab:2had\] we report the values of the coefficients $a_\Delta(i)$ evaluated using the N4LO PC potential for the various cut-off.

  $\Lambda$(MeV)      $450$       $500$       $550$
  ---------------- ----------- ----------- -----------
  $a_\Delta(0) $    $ -0.872$   $ -0.894$   $ -0.894$
  $a_\Delta(1) $    $\m0.117$   $\m0.120$   $\m0.120$
  $a_\Delta(2) $    $ -0.119$   $ -0.119$   $ 