arXiv subjects
Publications and source records attributed to I. O. Cherednikov.
We discuss different operator definitions of the transverse-momentum dependent (TMD) parton densities from the point of view of their renormalization-group (RG) properties and UV evolution. We also consider the structure of the gauge links (Wilson lines) in these operator definitions and examine the role of the soft factor in the factorization formula within the TMD approach to semi-inclusive processes.
The current status of the theoretical understanding of the transverse-momentum dependent parton densities (TMDs) is discussed. Special attention is payed to the difference between the operator definitions of TMDs proposed so far, the treatment of specific divergences, the geometry of the gauge links, and the role of the soft factors.
We propose a consistent treatment of divergences emerging in the computation of transverse-momentum-dependent parton densities in leading $α_s$-order of QCD perturbation theory.
We summarize the renormalization-group properties of transverse-momentum dependent (TMD) parton distribution functions (PDF)s arguing that in the light-cone gauge the overlapping ultraviolet and rapidity divergences cannot be solely controlled by (dimensional) regularization, but necessitate their renormalization. In doing so, we show that at the one-loop order this additional divergence entails an anomalous dimension which can be attributed to a cusp in the gauge contour at light-cone infinity. Then, we present a recent analysis of TMD PDFs which incorporates in the gauge links the Pauli term $\sim F^{μν}[γ_μ,γ_ν]$. This generalized treatment of gauge invariance is shown to be justified, in the sense that it does not modify the behavior of the leading-twist contribution, though it contributes to the anomalous dimension of that of twist-three. An important consequence of the inclusion of the spin-dependent Pauli term is the appearance of a constant phase---the same for the leading twist-two and subleading distribution functions---that ensues from the interaction of the Pauli term in the transverse gauge link with the gauge field accompanying the fermion. Remarkably, this phase has opposite sign for the Drell-Yan process as compared to the semi-inclusive DIS.
We propose a new framework for transverse-momentum dependent parton distribution functions, based on a generalized conception of gauge invariance which includes into the Wilson lines the Pauli term $\sim F^{μν}[γ_μ, γ_ν]$. We discuss the relevance of this nonminimal term for unintegrated parton distribution functions, pertaining to spinning particles, and analyze its influence on their renormalization-group properties. It is shown that while the Pauli term preserves the probabilistic interpretation of twist-two distributions---unpolarized and polarized---it gives rise to additional pole contributions to those of twist-three. The anomalous dimension induced this way is a matrix, calling for a careful analysis of evolution effects. Moreover, it turns out that the crosstalk between the Pauli term and the longitudinal and the transverse parts of the gauge fields, accompanying the fermions, induces a constant, but process-dependent, phase which is the same for leading and subleading distribution functions. We include Feynman rules for the calculation with gauge links containing the Pauli term and comment on the phenomenological implications of our approach.
We discuss the state-of-the-art of the theory of transverse-momentum dependent parton densities (TMD)s, paying special attention to their renormalization properties, the structure of the gauge links in the operator definition, and the role of the soft factor in the factorization formula within the TMD approach to the semi-inclusive processes. We argue that the use of the lightcone axial gauge offers certain advantages for a consistent definition of TMDs as compared to the off-the-light-cone gauges, or covariant gauges with off-the-lightcone gauge links.
Different approaches to define transverse-momentum dependent parton distribution functions are considered from the point of view of their renormalization-group properties. The associated one-loop anomalous dimensions of these quantities are presented and compared to each other. We give arguments in favor of the "pure light-like" definition, and the use of the light-cone gauge.
The ultraviolet and rapidity divergences of transverse-momentum dependent parton distribution functions with lightlike and transverse gauge links is studied, also incorporating a soft eikonal factor. We find that in the light-cone gauge with $q^-$-independent pole prescriptions extra divergences appear which amount, at one-loop, to a cusp-like anomalous dimension. We show that such contributions are absent when the Mandelstam-Leibbrandt prescription is used. In the first case, the soft factor cancels the anomalous-dimension defect, while in the second case its ultraviolet-divergent part reduces to unity.
The renormalization-group properties of transverse-momentum dependent parton distribution functions in the light-cone gauge with the Mandelstam-Leibbrandt prescription for the gluon propagator are addressed. An expression for the transverse component of the gauge field at light-cone infinity, which plays a crucial role in the description of the final-/initial-state interactions in the light-cone axial gauge, is obtained. The leading-order anomalous dimension is calculated in this gauge and the relation to the results obtained in other gauges is worked out. It is shown that, using the Mandelstam-Leibbrandt prescription, the ensuing anomalous dimension does not receive contributions from extra rapidity divergences related to a cusped junction point of the Wilson lines.
We discuss duality in ``two-photon''-like processes in the scalar $φ^3_E$ model and also in the process $γ^*γ\toππ$ in QCD. Duality implies the equivalence between two distinct nonperturbative mechanisms. These two mechanisms, one involving a twist-3 Generalized Distribution Amplitude, the other employing a leading-twist Transition Distribution Amplitude, are associated with different regimes of factorization. In the kinematical region, where the two mechanisms overlap, duality is observed for the scalar $φ^3_E$ model, while in the QCD case the appearance of duality turns out to be sensitive to the particular nonperturbative model applied and can, therefore, be used as a tool for selecting the most appropriate one.
We study the phenomenon of duality in hard exclusive reactions to which QCD factorization applies. Considering "two-photon"-like processes in the scalar $ϕ^3_E$ model and also hadron-pair production from the collisions of a real (transversely polarized) and a highly virtual, longitudinally polarized, photon in QCD, we identify two regimes of factorization each of them associated with a distinct nonperturbative mechanism. One mechanism involves twist-3 Generalized Distribution Amplitudes, whereas the other one employs leading-twist Transition Distribution Amplitudes. In the case of the scalar $ϕ^3_E$ model, we find duality in that kinematical region where the two mechanisms overlap. In the QCD case, the appearance of duality is sensitive to the particular nonperturbative model applied and can, therefore, be used as an additional adjudicator.
We find that in "two-photon"-like processes in the scalar $φ^3_E$ model and also in hadron-pair production arising from the collisions of a real (transversely polarized) and a highly virtual, longitudinally polarized, photon in QCD, there is duality between two distinct nonperturbative mechanisms. These two mechanisms, one involving a twist-3 Generalized Distribution Amplitude, the other employing a leading-twist Transition Distribution Amplitude, are associated with different regimes of factorization. In the kinematical region, where the two mechanisms overlap, duality is observed for the scalar $φ^3_E$ model, while in the QCD case the appearance of duality turns out to be sensitive to the particular nonperturbative model applied and can, therefore, be used as a tool for selecting the most appropriate one.
We present some recently obtained results on transverse-momentum dependent parton distribution functions (TMD PDFs), the latter being important ingredients for the description of semi-inclusive hadronic processes. Special attention is payed to the renormalization group (RG) properties of these objects. In particular, their leading-order anomalous dimension is calculated in the light-cone gauge. It is shown that the RG properties can be used to reveal, in the most economic way, the general structure of the gauge links entering the operator definition of TMD PDFs.
The UV divergences associated with transverse-momentum dependent (TMD) parton distribution functions (PDF) are calculated together with the ensuing one-loop anomalous dimensions in the light-cone gauge. Time-reversal-odd effects in the anomalous dimensions are observed and the role of Glauber gluons is discussed. A generalized renormalization procedure of TMD PDFs is proposed, relying upon the renormalization of contour-dependent operators with obstructions.
The renormalization properties of unintegrated (transverse-momentum dependent) parton distribution functions (TMD PDF's) are used for analyzing their completely gauge-invariant definition. To this end, the UV anomalous dimension is calculated at the one-loop order in the light-cone gauge and a consistent treatment of the extra singularities, which produce undesirable contributions in the anomalous dimensions, is given. The generalized definition of a TMD PDF, based on the renormalization procedure for the Wilson exponentials with obstructions, is proposed. The reduction of the re-defined TMD PDF to the integrated PDF's, as well as their probabilistic interpretation, are discussed.
We discuss the renormalization of gauge-invariant transverse-momentum dependent (TMD), i.e., unintegrated, parton distribution functions (PDFs) and carry out the calculation of their anomalous dimension at one loop. We show that in the light-cone gauge, TMD PDFs contain UV divergences that may be attributed to the renormalization effect on a cusp-like junction point of the gauge contours at infinity. In order to eliminate the anomalous dimension ensuing from this cusp, we propose to use in the definition of the TMD PDFs, a soft counter term in terms of a path-ordered phase factor along a particular cusped contour extending to transverse light-cone infinity and comprising light-like and transverse segments. We argue that this additional factor is analogous to the "intrinsic" Coulomb phase factor found before in QED.
We discuss recent developments in the understanding of gauge-invariant transverse-momentum dependent (TMD) parton-distribution functions (PDF). We compute the leading-order $\overline{\text{MS}\vphantom{^1}}$-scheme anomalous dimension of such a quantity in the light-cone gauge and show that it receives a contribution that can be associated with a cusp obstruction at transverse light-cone infinity. This anomalous dimension is intimately related to expectation values composed of fields and eikonal factors along a cusped contour and is absent in covariant gauges. The implications of these findings are addressed and a modified definition of TMD PDFs is proposed.
The renormalization-group properties of gauge-invariant transverse-momentum dependent (TMD) parton distribution functions (PDF) in QCD are addressed. We perform an analysis of their leading-order anomalous dimensions, which are local quantities, making use of the renormalization properties of contour-dependent composite operators in QCD. We argue that attaching individual gauge links with transverse segments to quark fields in the light-cone gauge, the associated gauge contours are joined at light-cone infinity through a cusp-like junction point. We find that the renormalization effect on the junction point creates an anomalous dimension which has to be compensated in order to recover the results in a covariant gauge. To this end, we include in the definition of the TMD PDF an additional soft counter term (gauge link) along that cusped contour. We show that the eikonal factors entering this counter term are peculiar to the Mandelstam field formalism and are absent when one uses a direct gauge contour.