def METHOD_NAME(s, tau, umin, umax, q1, q2, l, wc_eff):
    r"""Partial result for the cross section of $\bar q1 q2 \to \ell^-\nu$.
    Returns $\int_{umin}^{umax} \frac{d^2\sigma}{d\tau du}$, integrated analytically over $u=m_T^2/s$.
    Parameters:
    - `s`: Hadronic center of mass energy GeV$^2$
    - `tau`: $\tau$, ratio of partonic to hadronic center of mass energy, dimensionless
    - `umin`, `umax: integration boundaries for the variable $u=m_T^2/s$
    - `q1, q2`: initial state quarks (with q1 up-type)
    - `l`: lepton flavour, should be 'e', 'mu', or 'tau'
    - `wc_eff`: SM + SMEFT amplitude for the process as dictionary with entries corresponding to different Wilson coefficients
    """
    i1 = fermion_indices[q1]
    i2 = fermion_indices[q2]
    il = fermion_indices[l]
    if tau > umax:
        prefac1 = umax * sqrt(1-umax/tau) - umin * sqrt(1-umin/tau)
        prefac2 = tau * ( sqrt(1-umax/tau) - sqrt(1-umin/tau) )
    else:
        prefac1 = - umin * sqrt(1-umin/tau)
        prefac2 = - tau * sqrt(1-umin/tau)
    S = 0
    # sum over neutrino flavours
    for inu in range(3):
        S += s * (
            prefac1 * (
                + 16 * abs(wc_eff['CTRR_enuud'][il, inu, i1, i2])**2
                + abs(wc_eff['CVLL_enuud'][il, inu, i1, i2])**2
            )
            - prefac2 *(
                + 3 * abs(wc_eff['CSRL_enuud'][il, inu, i1, i2])**2
                + 3 * abs(wc_eff['CSRR_enuud'][il, inu, i1, i2])**2
                + 16 * abs(wc_eff['CTRR_enuud'][il, inu, i1, i2])**2
                + 4 * abs(wc_eff['CVLL_enuud'][il, inu, i1, i2])**2
            )
        )
    return S/(576*pi)