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This article explores the calculation of non-perturbative parameters presentin the matrix element of semileptonic inclusive $B$ decay. These are importantfor inclusive determination of the Cabbibo-Kobayashi-Maskawa (CKM) parametersin the standard model. We focus on calculating the rate for radiative inclusivedecay, $B\to X_u\ell \nu_{\ell}\gamma$, where $\gamma$ is hard. By comparingboth the radiative and non-radiative ($B\to X_u \ell \nu_{\ell}$) modes arefound to require the same non-perturbative parameters. We propose formingratios, $R_1$ and $R_2$, from $B\to X_u \ell \nu_{\ell}\gamma$ and $B\to X_u\ell \nu_{\ell}$ widths in different lepton energy ranges respectively. Ourresults provide an efficient way to unambiguously calculate thenon-perturbative parameters, especially when combined with total widthcalculations of $B\to X_u \ell \nu_{\ell}$. This is in heavy quark expansionshown explicitly by working to $\mathcal{O}(\frac{1}{m_b})$ and determining$\lambda_1$ and $\lambda_2$.

$B\to X_u\ell\nu_{\ell}\gamma$ and determination of non-perturbative parameters