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Register a new userCombining TMD factorization and collinear factorization
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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.)
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In this section, we discuss some basic features of transverse momentum dependent, or unintegrated, parton distribution functions. In particular, when these correlation functions are combined in a factorization formulae with hard processes beyond the simplest cases, there are basic problems with universality and factorization. We discuss some of these problems as well as the opportunities that they offer.
We give an overview of the current status of perturbative QCD factorization theorems in processes that involve transverse momentum dependent (TMD) parton distribution functions (PDFs) and fragmentation functions (FF). We enumerate those cases where TMD-factorization is well-established, and mention cases where it is likely to fail. We discuss recent progress in the implementation of specific TMD-factorization calculations, including the implementation of evolution. We also give examples of hard part calculations. We end by discussing future strategies for the implementation of TMD-factorization in phenomenological applications.
In using transverse-momentum-dependent (TMD) parton densities and fragmentation functions, important non-perturbative information is at large transverse position $b_T$. This concerns both the TMD functions and their evolution. Fits to high energy data tend to predict too rapid evolution when extrapolated to low energies where larger values of $b_T$ dominate. I summarize a new analysis of the issues. It results in a proposal for much weaker $b_T$ dependence at large $b_T$ for the evolution kernel, while preserving the accuracy of the existing fits. The results are particularly important for using transverse-spin-dependent functions like the Sivers function.
We analyze two consequences of the relationship between collinear factorization and $k_t$-factorization. First, we show that the $k_t$-factorization gives a fundamental justification for the choice of the hard scale $Q^2$ done in the collinear factorization. Second, we show that in the collinear factorization there is an uncertainty on this choice which will not be reduced by higher orders. This uncertainty is absent within the $k_t$-factorization formalism.
In the original Collins-Soper-Sterman (CSS) presentation of the results of transverse-momentum-dependent (TMD) factorization for the Drell-Yan process, results for perturbative coefficients can be obtained from calculations for collinear factorization. Here we show how to use these results, plus known results for the quark form factor, to obtain coefficients for TMD factorization in more recent formulations, e.g., that due to Collins, and apply them to known results at order $alpha_s^2$ and $alpha_s^3$. We also show that the non-perturbative functions as obtained from fits to data are equal in the two schemes. We compile the higher-order perturbative inputs needed for the updated CSS scheme by appealing to results obtained in a variety of different formalisms. In addition, we derive the connection between bo
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