docs: def get_gpbar(ebar, gbar, v, C, scale_high):
      r"""Function to numerically determine the hypercharge gauge coupling
      in terms of $\bar e$, $\bar g$, v, and the Wilson coefficients."""
      if C['phiWB'] == 0:  # this is the trivial case
          gpbar = ebar * gbar / sqrt(gbar**2 - ebar**2)
      else:  # if epsilon != 0, need to iterate
          def f0(x):  # we want the root of this function
              gpb = x
              gb = gbar
              eps = C['phiWB'] * (v**2 / scale_high**2)
              ebar_calc = (gb * gpb / sqrt(gb**2 + gpb**2) *
                          (1 - eps * gb * gpb / (gb**2 + gpb**2)))
              return (ebar_calc - ebar).real
          gpbar = scipy.optimize.brentq(f0, 0, 3)
      return gpbar * (1 - C['phiB'] * (v**2 / scale_high**2))