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Register a new userSoft-collinear factorization in B decays
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M. Beneke
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The combination of collinear factorization with effective field theory originally developed for soft interactions of heavy quarks provides the foundations of the theory of exclusive and semi-inclusive B decays. In this article I summarize some of the later conceptual developments of the so-called QCD factorization approach that make use of soft-collinear effective theory. Then I discuss the status and results of the calculation of the hard-scattering functions at the next order, and review very briefly some of the phenomenology, covering aspects of charmless, electroweak penguin and radiative (semi-leptonic) decays.
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Universality in QCD factorization of parton densities, fragmentation functions, and soft factors is endangered by the process dependence of the directions of Wilson lines in their definitions. We find a choice of directions that is consistent with factorization and that gives universality between e^+e^- annihilation, semi-inclusive deep-inelastic scattering, and the Drell-Yan process. Universality is only modified by a time-reversal transformation of the soft function and parton densities between Drell-Yan and the other processes, whose only effect is the known reversal of sign for T-odd parton densities like the Sivers function. The modifications of the definitions needed to remove rapidity divergences with light-like Wilson lines do not affect the results.
In QCD the amplitude for B0 -> D(*)+pi- factorizes in the large Nc limit or in the large energy limit Q >> Lambda_QCD where Q = {m_b, m_c, m_b-m_c}. Data also suggests factorization in exclusive processes B-> D* pi+ pi- pi- pi0 and B-> D* omega pi-, however by themselves neither large Nc nor large Q can account for this. Noting that the condition for large energy release in B0-> D+ pi- is enforced by the SV limit, m_b, m_c >> m_b-m_c >> Lambda, we propose that the combined large Nc and SV limits justify factorization in B -> D(*) X. This combined limit is tested with the inclusive decay spectrum measured by CLEO. We also give exact large Nc relations among isospin amplitudes for B -> D(*)X and B -> D(*) D-bar(*)X, which can be used to test factorization through exclusive or inclusive measurements. Predictions for the modes B-> D(*) pi pi, B-> D(*)K K-bar and B-> D(*) D-bar(*) K are discussed using available data.
We examine some of the complications involved when combining (matching) TMD factorization with collinear factorization to allow accurate predictions over the whole range of measured transverse momentum in a process like Drell-Yan. Then we propose some improved methods for combining the two types of factorization. (This talk is based on work reported in arXiv:1605.00671.)
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 $O(Lambda_{rm QCD}left/m_Qright.)$. 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 $Bto gamma e u_e$ is $5.21times 10^{-6}$, 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 $Dto gamma e u_e$, the result of the branching ratio is $1.92times 10^{-5}$.
Glauber gluons in Drell-Yan processes are soft gluons with the transverse momenta much larger than their momentum components along the directions of initial hadrons. Their existence has been a serious challenge in proving the factorization of Drell-Yan processes. The recently proposed soft collinear effect theory of QCD can provide a transparent way to show factorizations for a class of processes, but it does not address the effect of glauber gluons. In this letter we first confirm the existence of glauber gluons through an example. We then add glauber gluons into the effective theory and study their interaction with other particles. In the framework of the effective theory with glauber gluons we are able to show that the effects of glauber gluons in Drell-Yan processes are canceled and the factorization holds in the existence of glauber gluons. Our work completes the proof or argument of factorization of Drell-Yan process in the framework of the soft collinear effective theory.
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