55,150 research outputs found

### No Generalized TMD-Factorization in the Hadro-Production of High Transverse Momentum Hadrons

It has by now been established that standard QCD factorization using
transverse momentum dependent parton distribution functions fails in
hadro-production of nearly back-to-back hadrons with high transverse momentum.
The essential problem is that gauge invariant transverse momentum dependent
parton distribution functions cannot be defined with process-independent Wilson
line operators, thus implying a breakdown of universality. This has led
naturally to proposals that a correct approach is to instead use a type of
"generalized" transverse momentum dependent factorization in which the basic
factorized structure is assumed to remain valid, but with transverse momentum
dependent parton distribution functions that contain non-standard, process
dependent Wilson line structures. In other words, to recover a factorization
formula, it has become common to assume that it is sufficient to simply modify
the Wilson lines in the parton correlation functions for each separate hadron.
In this paper, we will illustrate by direct counter-example that this is not
possible in a non-Abelian gauge theory. Since a proof of generalized transverse
momentum dependent factorization should apply generally to any hard
hadro-production process, a single counter-example suffices to show that a
general proof does not exist. Therefore, to make the counter-argument clear and
explicit, we illustrate with a specific calculation for a double spin asymmetry
in a spectator model with a non-Abelian gauge field. The observed breakdown of
generalized transverse momentum dependent factorization challenges the notion
that the role of parton transverse momentum in such processes can be described
using separate correlation functions for each external hadron.Comment: 19 pages, 11 figures, typos fixed and minor explanations added,
version to appear in Physical Review

### QCD Factorization for Semi-Inclusive Deep-Inelastic Scattering at Low Transverse Momentum

We demonstrate a factorization formula for semi-inclusive deep-inelastic
scattering with hadrons in the current fragmentation region detected at low
transverse momentum. To facilitate the factorization, we introduce the
transverse-momentum dependent parton distributions and fragmentation functions
with gauge links slightly off the light-cone, and with soft-gluon radiations
subtracted. We verify the factorization to one-loop order in perturbative
quantum chromodynamics and argue that it is valid to all orders in perturbation
theory.Comment: 28 pages, figures include

### Universality of soft and collinear factors in hard-scattering factorization

Universality in QCD factorization of parton densities, fragmentation
functions, and soft factors is endangered by the process dependence of the
directions of Wilson lines in their definitions. We find a choice of directions
that is consistent with factorization and that gives universality between
e^+e^- annihilation, semi-inclusive deep-inelastic scattering, and the
Drell-Yan process. Universality is only modified by a time-reversal
transformation of the soft function and parton densities between Drell-Yan and
the other processes, whose only effect is the known reversal of sign for T-odd
parton densities like the Sivers function. The modifications of the definitions
needed to remove rapidity divergences with light-like Wilson lines do not
affect the results.Comment: 4 pages. Extra references. Text and references as in published
versio

### Demonstration of the Equivalence of Soft and Zero-Bin Subtractions

Calculations of collinear correlation functions in perturbative QCD and
Soft-Collinear Effective Theory (SCET) require a prescription for subtracting
soft or zero-bin contributions in order to avoid double counting the
contributions from soft modes. At leading order in $\lambda$, where $\lambda$
is the SCET expansion parameter, the zero-bin subtractions have been argued to
be equivalent to convolution with soft Wilson lines. We give a proof of the
factorization of naive collinear Wilson lines that is crucial for the
derivation of the equivalence. We then check the equivalence by computing the
non-Abelian two-loop mixed collinear-soft contribution to the jet function in
the quark form factor. These results provide strong support for the
equivalence, which can be used to give a nonperturbative definition of the
zero-bin subtraction at lowest order in $\lambda$.Comment: 14 pages, 3 figure

### k_T factorization is violated in production of high-transverse-momentum particles in hadron-hadron collisions

We show that hard-scattering factorization is violated in the production of
high-p_T hadrons in hadron-hadron collisions, in the case that the hadrons are
back-to-back, so that k_T factorization is to be used. The explicit
counterexample that we construct is for the single-spin asymmetry with one beam
transversely polarized. The Sivers function needed here has particular
sensitivity to the Wilson lines in the parton densities. We use a greatly
simplified model theory to make the breakdown of factorization easy to check
explicitly. But the counterexample implies that standard arguments for
factorization fail not just for the single-spin asymmetry but for the
unpolarized cross section for back-to-back hadron production in QCD in
hadron-hadron collisions. This is unlike corresponding cases in e^+e^-
annihilation, Drell-Yan, and deeply inelastic scattering. Moreover, the result
endangers factorization for more general hadroproduction processes.Comment: 10 pages. V. 2: Title change, misprints and minor corrections, as in
journal versio

### Calculation of TMD Evolution for Transverse Single Spin Asymmetry Measurements

The Sivers transverse single spin asymmetry (TSSA) is calculated and compared
at different scales using the TMD evolution equations applied to previously
existing extractions. We apply the Collins-Soper-Sterman (CSS) formalism, using
the version recently developed by Collins. Our calculations rely on the
universality properties of TMD-functions that follow from the TMD-factorization
theorem. Accordingly, the non-perturbative input is fixed by earlier
experimental measurements, including both polarized semi-inclusive deep
inelastic scattering (SIDIS) and unpolarized Drell-Yan (DY) scattering. It is
shown that recent COMPASS measurements are consistent with the suppression
prescribed by TMD evolution.Comment: 4 pages, 2 figures. Version published in Physical Review Letter

### Collins-Soper Equation for the Energy Evolution of Transverse-Momentum and Spin Dependent Parton Distributions

The hadron-energy evolution (Collins and Soper) equation for all the
leading-twist transverse-momentum and spin dependent parton distributions is
derived in the impact parameter space. Based on the result, we present
resummation formulas for the spin structure functions in the semi-inclusive
deep inelastic scattering.Comment: 16 pages, 4 figures included, revised versio

### Structure of divergences in Drell-Yan process with small transverse momentum

We consider the structure of divergences in Drell-Yan process with small
transverse momentum. The factorization proof is not trivial because various
kinds of divergences are intertwined in the collinear and soft parts at high
orders. We prescribe a method to disentangle the divergences in the framework
of the soft-collinear effective theory. The rapidity divergence is handled by
introducing the $\delta$ regulator in the collinear Wilson lines. The collinear
part, which consists of the transverse-momentum-dependent parton distribution
function (TMDPDF), is free of the rapidity divergence after the soft zero-bin
subtraction. There still remains the problem of mixing between the ultraviolet
and infrared divergences, which forbids the renormalization group description.
We show that the mixing is cancelled by the soft function. This suggests that
the collinear and soft parts should be treated as a whole in constructing a
consistent factorization theorem. The renormalization group behavior of the
combined collinear and soft parts is presented explicitly at one loop. We also
show that the integrated PDF can be obtained by integrating the TMDPDF over the
transverse momentum.Comment: 26 pages, 2 figures. Version published in PR

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