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Register a new userOn the QCD Evolution of Transverse Momentum Dependent Distributions
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Federico Alberto Ceccopieri
Publication date
2014
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English
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We reconsider the evolution equations for transverse momentum dependent distributions recently proposed by us and recast them in a form which allows the comparison with results recently appeared in the literature. We show under which conditions the obtained results might be consistent with each other.
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Transverse-momentum-dependent (TMD) gluon distributions have different operator definitions, depending on the process under consideration. We study that aspect of TMD factorization in the small-x limit, for the various unpolarized TMD gluon distributions encountered in the literature. To do this, we consider di-jet production in hadronic collisions, since this process allows to be exhaustive with respect to the possible operator definitions, and is suitable to be investigated at small x. Indeed, for forward and nearly back-to-back jets, one can apply both the TMD factorization and Color Glass Condensate (CGC) approaches to compute the di-jet cross-section, and compare the results. Doing so, we show that both descriptions coincide, and we show how to express the various TMD gluon distributions in terms of CGC correlators of Wilson lines, while keeping Nc finite. We then proceed to evaluate them by solving the JIMWLK equation numerically. We obtain that at large transverse momentum, the process dependence essentially disappears, while at small transverse momentum, non-linear saturation effects impact the various TMD gluon distributions in very different ways. We notice the presence of a geometric scaling regime for all the TMD gluon distributions studied: the dipole one, the Weizsacker-Williams one, and the six others involved in forward di-jet production.
The properties and behaviour of the solutions of the recently obtained $k_t$-dependent evolution equations are investigated. When used to reproduce transverse momentum spectra of hadrons in Semi-Inclusive DIS, an encouraging agreement with data is found. The present analysis also supports at the phenomenological level the factorization properties of the Semi-Inclusive DIS cross-sections in terms of $k_t$-dependent distributions. Further improvements and possible developments of the proposed evolution equations are envisaged.
We investigate the predictive power of transverse-momentum-dependent (TMD) distributions as a function of the light-cone momentum fraction $x$ and the hard scale $Q$ defined by the process. We apply the saddle point approximation to the unpolarized quark and gluon transverse momentum distributions and evaluate the position of the saddle point as a function of the kinematics. We determine quantitatively that the predictive power for an unpolarized transverse momentum distribution is maximal in the large-$Q$ and small-$x$ region. For cross sections the predictive power of the TMD factorization formalism is generally enhanced by considering the convolution of two distributions, and we explicitly consider the case of $Z$ and $H^0$ boson production. In the kinematic regions where the predictive power is not maximal, the distributions are sensitive to the non-perturbative hadron structure. Thus, these regions are critical for investigating hadron tomography in a three-dimensional momentum space.
The interplay between the small x limit of QCD amplitudes and QCD factorization at moderate x has been studied extensively in recent years. It was finally shown that semiclassical formulations of small x physics can have the form of an infinite twist framework involving Transverse Momentum Dependent (TMD) distributions in the eikonal limit. In this work, we demonstrate that small x distributions can be formulated in terms of transverse gauge links. This allows in particular for direct and efficient decompositions of observables into subamplitudes involving gauge invariant sub-operators which span parton distributions.
Transverse momentum dependent (TMD) distributions at small x exhibit a rich infinite twist structure that encompasses the leading twist (partonic) distributions as well as the physics of gluon saturation. Progress to further the connection between the standard TMD framework at moderate x and small x has been recently made. In this context, we show that light cone Wilson line operators at small-x can be formulated in terms of transverse gauge links. This new formulation of small x operators allows a direct matching with the standard leading twist gluon TMD distributions and provides an efficient and general prescription for computing TMD distributions at small x beyond leading twist.
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