On the equivalence of regularization schemes

We illustrated via the sunset diagram that dimensional regularization 'deforms' the nonlocal contents of multi-loop diagrams with its equivalence to cut-off regularization scheme recovered only after sub-divergence were subtracted. Then we employed a differential equation approach for calculating loop diagrams to verify that dimensional regularization deformed the 'low energy' contents before subtraction. The virtues of the differential equation approach were argued especially in non-perturbative perspective.Comment: 9 pages, LaTex, no figure, revised version, new style,to appear in Comm.Theor.Phy

Factorization of Radiative Leptonic Decays of B−B^- and D−D^- Mesons Including the Soft Photon Region

In this work, we study the radiative leptonic decays of $B^-$ and $D^-$ mesons using factorization approach. Factorization is proved to be valid explicitly at 1-loop level at any order of $O(\Lambda_{\rm QCD}\left/m_Q\right.)$. We consider the contribution in the soft photon region that $E_{\gamma} \sim \left. \Lambda^2_{\rm QCD} /\right. m_Q$. The numerical results shows that, the soft photon region is very important for both the $B$ and $D$ mesons. The branching ratios of $B\to \gamma e\nu_e$ is $5.21\times 10^{-6}$, which is about $3$ times of the result obtained by only considering the hard photon region $E_{\gamma}\sim m_Q$. And for the case of $D\to \gamma e\nu_e$, the result of the branching ratio is $1.92\times 10^{-5}$.Comment: arXiv admin note: text overlap with arXiv:1409.035

Factorization of Radiative Leptonic Decays of B−B^- and D−D^- Mesons

In this work, we study the factorization of the radiative leptonic decays of $B^-$ and $D^-$ mesons, the contributions of the order $O(\Lambda _{\rm QCD}\left/m_Q\right.)$ are taken into account. The factorization is proved to be valid explicitly at the order $O(\alpha _s\Lambda _{\rm QCD}\left/m_Q\right.)$. The hard kernel is obtained. The numerical results are calculated using the wave-function obtained in relativistic potential model. The $O(\Lambda _{\rm QCD}\left/m_Q\right.)$ contribution is found to be very important, the correction to the decay amplitudes of $B^-\to \gamma e\bar{\nu}$ is about $20\% - 30\%$. For $D$ mesons, the $O(\Lambda _{\rm QCD}\left/m_Q\right.)$ contributions are more important.Comment: 26 pages, 8 figures. Version to appear in Nucl. Phys.