Transverse momentum dependent operator expansion at next-to-leading power

Abstract

We develop a method of transverse momentum dependent (TMD) operator expansion that yields the TMD factorization theorem on the operator level. The TMD operators are systematically ordered with respect to TMD-twist, which allows a certain separation of kinematic and genuine power corrections. The process dependence enters via the boundary conditions for the background fields. As a proof of principle, we derive the effective operator for hadronic tensor in TMD factorization up to the next-to-leading power (∼ qT/Q) at the next-to-leading order for any process with two detected states.

Factorization connecting continuum and lattice TMDs

“…However, the perturbative quasito-Collins matching coefficient C q is only known at one-loop, except for certain logarithmic terms constrained by its RGE, see section 3.2.2. Recently there has been renewed interest in TMDs at subleading power, with for example a derivation of the necessary form of the factorization formula for polarized SIDIS at subleading power [81,82]. Finding continuumto-lattice factorization formulas for subleading power TMDs would be interesting.…”

Factorization for Azimuthal Asymmetries in SIDIS at Next-to-Leading Power

“…21 20 Correlators with a distinct dependence on both momenta were found independently in the recent work of ref. [96]. 21 In appendix D.3, we provide more details on how to relate our Bρ B and Ĝρ B to their Φρ A and ∆ρ A , respectively.…”

“…The focus of ref. [96] was to to develop a generic formalism to obtain the power expansion of TMDs in Drell-Yan, SIDIS and semi-inclusive annhilation (SIA), and hence did not yet provide explicit results for structure functions. In the following, we briefly compare their approach to determining the operators required at subleading power to ours.…”

“…The method of ref. [96], dubbed TMD operator expansion, is based on expressing the hadronic tensor in eq. (4.3) in terms of a functional integral, which in the absence of time ordering involves a causal and an anti-causal field [128].…”

“…SCET has already been used to study subleading-power factorization in other processes, allowing us to leverage various results in the literature [42,43,, see also [82][83][84][85][86][87][88][89][90][91][92]. Recently, there have been first attempts to study TMD factorization at subleading power, including analysis at small-x [93,94] and investigations of the factorization structure with SCET and similar techniques [95,96].…”