Abstract
We calculate power corrections to TMD factorization for particle production by gluon-gluon fusion in hadron-hadron collisions.
Highlights
To find TMD factorization at the tree level we need to calculate the functional integral (2.4) in the background fields of the strength given by eqs. (3.10) and (3.12)
We have formulated the approach to TMD factorization based on the factorization in rapidity and found the leading higher-twist contribution to the production of a scalar particle (e.g. Higgs) by gluon-gluon fusion in the hadron-hadron scattering
Up to now our results are obtained in the tree-level approximation when the question of exact matching of cutoffs in rapidity does not arise
Summary
We consider production of an (imaginary) scalar particle Φ in proton-proton scattering. X denotes the sum over full set of “out” states It can be represented by double functional integral. It should be emphasized that the boundary conditions (2.9) mean the summation over all intermediate states in corresponding projectile and target matrix elements in the functional integrals over projectile and target fields. It is known that in the tree approximation the double functional integral (2.13) is given by a set of retarded Green functions in the background fields [21,22,23] (see appendix A for the proof). Since the double functional integral (2.13) is given by a set of retarded Green functions (in the background field A + B), the calculation of tree-level contributions to, say, F 2(x) in the r.h.s. of eq (2.13) is equivalent to solving YM. As we will demonstrate below, the relevant operators are quark and gluon fields with Wilson-line type gauge links collinear to either p2 for A fields or p1 for B fields
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