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Register a new userGauge-invariant TMD factorization for Drell-Yan hadronic tensor at small x
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Ian Balitsky
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The Drell-Yan hadronic tensor for electromagnetic (EM) current is calculated in the Sudakov region $sgg Q^2gg q_perp^2$ with ${1over Q^2}$ accuracy, first at the tree level and then with the double-log accuracy. It is demonstrated that in the leading order in $N_c$ 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: $f_1$ responsible for total DY cross section, and Boer-Mulders function $h_1^perp$. The order-of-magnitude estimates of angular distributions for DY process seem to agree with LHC results at corresponding kinematics.
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The Drell-Yan process is studied in the framework of TMD factorization in the Sudakov region $sgg Q^2gg q_perp^2$ corresponding to recent LHC experiments with $Q^2$ of order of mass of Z-boson and transverse momentum of DY pair $sim$ few tens GeV. The DY hadronic tensors are expressed in terms of quark and quark-gluon TMDs with ${1over Q^2}$ and ${1over N_c^2}$ accuracy. It is demonstrated that in the leading order in $N_c$ the higher-twist quark-quark-gluon TMDs reduce to leading-twist TMDs due to QCD equation of motion. The resulting hadronic tensors depend on two leading-twist TMDs: $f_1$ responsible for total DY cross section, and Boer-Mulders function $h_1^perp$. The corresponding qualitative and semi-quantitative predictions seem to agree with LHC data on five angular coefficients $A_0-A_4$ of DY pair production. The remaining three coefficients $A_5-A_7$ are determined by quark-quark-gluon TMDs multiplied by extra ${1over N_c}$ so they appear to be relatively small in accordance with LHC results.
We extract the pion transverse momentum dependent (TMD) parton distribution by fitting the pion-induced Drell-Yan process within the framework of TMD factorization. The analysis is done at the next-to-next-to-leading order (NNLO) with proton TMD distribution and non-perturbative TMD evolution extracted earlier in the global fit. We observe the significant difference in the normalization of transverse momentum differential cross-section measured by E615 experiment and the theory prediction.
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 consider the azimuthal distribution of the final observed hadron in semi-inclusive deep-inelastic scattering and the lepton pair in the Drell-Yan process. In particular, we focus on the $cos phi$ modulation of the unpolarized cross section and on its dependence upon transverse momentum. At low transverse momentum, for these observables we propose a factorized expression based on tree-level approach and conjecture that the same formula is valid in transverse-momentum dependent (TMD) factorization when written in terms of subtracted TMD parton distributions. Our formula correctly matches with the collinear factorization results at high transverse momentum, solves a long-standing problem and is a necessary step towards the extension of the TMD factorization theorems up to the subleading twist.
The transverse-momentum ($Q_T$) distribution of low-mass Drell-Yan pairs is calculated in QCD perturbation theory with all-order resummation of $alpha_s (alpha_s ln(Q^2_T/Q^2))^n$ type terms. We demonstrate that the rapidity distribution of low-mass Drell-Yan pairs at large-enough transverse momentum is an advantageous source of constraints on the gluon distribution and its nuclear dependence. We argue that low-mass Drell-Yan pairs in the forward region provide a good and clean probe of small-$x$ gluons at collider energies.
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