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Register a new userOn gauge invariance of transverse momentum dependent distributions at small x
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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.
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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.
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.
We derive analytical results for unintegrated color dipole gluon distribution function at small transverse momentum. By Fourier transforming the $S$-matrix for large dipoles we derive the results in the form of a series of Bells polynomials. Interestingly, when resumming the series in leading log accuracy, the results showing up striking similarity with the Sudakov form factor with role play of coupling is being done by a constant that stems from the saddle point condition along the saturation line.
We compute the contribution of twist-2 and twist-3 parton distribution functions to the small-$b$ expansion for transverse momentum dependent (TMD) distributions at all powers of $b$. The computation is done by the twist-decomposition method based on the spinor formalism for all eight quark TMD distributions. The newly computed terms are accompanied by the prefactor $(M^2b^2)^n$ and represent the target-mass corrections to the resummed cross-section. For the first time, a non-trivial expression for the pretzelosity distribution is derived.
The world-line representation of quantum field theory is a powerful framework for the computation of perturbative multi-leg Feynman amplitudes. In particular, in gauge theories, it provides an efficient way, via point particle Grassmann functional integrals, to compute spinor and color traces in these amplitudes. Further, semi-classical approximations to quantum mechanical world-line trajectories provide useful intuition in a wide range of dynamical problems. We develop here the world-line approach to compute deeply inelastic structure functions in the small x Regge limit of QCD. In particular, in a shockwave approximation valid in this limit, we show how one recovers the well-known dipole model for unpolarized structure functions. In a follow-up work, we will discuss the world-line computation of polarized structure functions at small x.
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