Gauge-invariant TMD factorization for Drell-Yan hadronic tensor at small x

Abstract

The Drell-Yan hadronic tensor for electromagnetic (EM) current is calculated in the Sudakov region $$ s\gg {Q}^2\gg {q}_{\perp}^2 $$ s ≫ Q 2 ≫ q ⊥ 2 with $$ \frac{1}{Q^2} $$ 1 Q 2 accuracy, first at the tree level and then with the double-log accuracy. It is demonstrated that in the leading order in Nc the higher-twist quark-quark-gluon TMDs reduce to leading-twist TMDs due to QCD equation of motion. The resulting tensor for unpolarized hadrons is EM gauge-invariant and depends on two leading-twist TMDs: f1 responsible for total DY cross section, and Boer-Mulders function $$ {h}_1^{\perp } $$ h 1 ⊥ . The order-of-magnitude estimates of angular distributions for DY process seem to agree with LHC results at corresponding kinematics.

Drell-Yan angular lepton distributions at small x from TMD factorization.

“…For example, the correction ∼ 5 As demonstrated in ref. [16], the relevant terms contributions to hadronic tensors (2.6) with this accuracy are…”

“…Beyond the tree level, the integration over C fields produces logarithms of the cutoffs σ p and σ t which match the corresponding logs in TMDs of the projectile and the target, see the discussion in ref. [16] As discussed in ref. [16], central fields at the tree level are given by a set of Feynman diagrams with retarded propagators in background field A + B and ψ A + ψ B , see figure 3.…”

“…[16] As discussed in ref. [16], central fields at the tree level are given by a set of Feynman diagrams with retarded propagators in background field A + B and ψ A + ψ B , see figure 3. 3 The set of such "retarded" diagrams represent the solution of QCD equations of motion 2 Although the kinematics is best suited for LHC collider, I call A hadron "projectile" and B hadron "target" for convenience.…”

“…In the first paper [14], A. Tarasov and the author calculated power corrections to the total cross section of Z-boson production using the method developed in earlier paper [15]. The second paper [16] was devoted to calculation of angular coefficients for DY process mediated by virtual photon. Unfortunately, it is hard to compare these results with experiment due to the fact that the LHC measurements of angular distributions are performed at the invariant mass ∼ 100 GeV where the contribution of Z-boson is dominant.…”

“…Unfortunately, it is hard to compare these results with experiment due to the fact that the LHC measurements of angular distributions are performed at the invariant mass ∼ 100 GeV where the contribution of Z-boson is dominant. The present paper is devoted to generalization of the approach of papers [14] and [16] to angular distributions of DY pair production by unpolarized protons at LHC kinematics.…”