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We present a compact form of the massive $1\to 3$ tree-level QCD splitting functions and discuss a decomposition of the results in terms of lower-order expressions, scalar dipole antenna functions and pure higher-order remainders. The…
We study the Wigner functions of the nucleon which provide multidimensional images of the quark distributions in phase space and combine in a single picture all the information contained in the generalized parton distributions (GPDs) and…
Transition generalized parton distributions have emerged as a novel tool for studying the quantum chromodynamics (QCD) structure of resonances. They provide an integrated picture of the transition form factors and the transition parton…
We report on recent progress on the splitting functions for the evolution of parton distributions and related quantities, the (lightlike) cusp anomalous dimensions, in perturbative QCD. New results are presented for the four-loop…
We summarize recent results on the evolution of unpolarized parton densities and deep-inelastic structure functions in massless perturbative QCD. Due to last year's extension of the integer-moment calculations of the three-loop splitting…
It is well-known that direct analytic continuation of DGLAP evolution kernel (splitting functions) from space-like to time-like kinematics breaks down at three loops. We identify the origin of this breakdown as splitting functions are not…
We study the planar-flow distributions of narrow, highly boosted, massive QCD jets. Using the factorization properties of QCD in the collinear limit, we compute the planar-flow jet function from the one-to-three splitting function at…
Parton distribution functions give the probability to find partons (quarks and gluons) in a hadron as a function of the fraction x of the proton's momentum carried by the parton. They are conventionally defined in terms of matrix elements…
Quasi-parton distribution functions have received a lot of attentions in both perturbative QCD and lattice QCD communities in recent years because they not only carry good information on the parton distribution functions, but also could be…
Quark distribution and spectator functions are estimated in a diquark spectator model. The representation of the functions in terms of non-local operators together with the rather simple model allow estimates for the yet experimentally…
We review the status of the calculation of the time-like splitting functions for the evolution of fragmentation functions to the next-to-next-to-leading order in perturbative QCD. By employing relations between space-like and time-like…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…
We report on the status of a direct computation of the time-like splitting functions at next-to-next-to-leading order in QCD. Time-like splitting functions govern the collinear kinematics of inclusive hadron production and the evolution of…
Typically, when we are given the section (or projection) function of a convex body, it means that in each direction we know the size of the central section (or projection) perpendicular to this direction. Suppose now that we can only get…
Azimuthal asymmetries in high-energy processes, most pronounced showing up in combination with single or double (transverse) spin asymmetries, can be understood with the help of transverse momentum dependent (TMD) parton distribution and…
I review the factorisation properties of tree level amplitudes when three particles $i$, $j$, $k$ are collinear. The triple collinear splitting functions contain both iterated single unresolved contributions, and genuine double unresolved…
The representation of quark distribution and fragmentation functions in terms of non-local operators is combined with a simple spectator model. This allows us to estimate these functions for the nucleon and the pion ensuring correct…
We summarize recent higher-order QCD results based, directly or indirectly, on the Mellin-space computation of the next-to-next-to-leading-order splitting functions governing the evolution of hadronic parton distributions. Specifically, we…
Spectral functions at finite temperature and two-loop order are investigated, for a medium consisting of massless particles. We consider them in the timelike and spacelike domains, allowing the propagating particles to be any valid…
We construct the quasi-parton distributions of mesons for two-dimensional QCD with either scalar or spinor quarks using the $1/N_c$ expansion. We show that in the infinite momentum limit, the parton distribution function is recovered in…