Related papers: Integrability of three-particle evolution equation…
We consider the anomalous dimension $\gamma_{gg}^{(3)}(N)$ of the twist-two gluon operator of arbitrary Lorentz spin $N$ in the quark flavor singlet sector of a general gauge theory at four loops and construct its contribution proportional…
We investigate dispersive estimates for the massless three dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies a $\langle t\rangle^{-1}$ decay rate as an operator from $L^1$ to $L^\infty$…
We compute the three loop MSbar anomalous dimension for the 3-quark operator corresponding to the proton. This requires the treatment of gamma^5 within dimensional regularization as well as evanescent operators generated through the…
This paper addresses the exponential stability of the trivial solution of some types of evolution equations driven by H\"older continuous functions with H\"older index greater than $1/2$. The results can be applied to the case of equations…
We demonstrate that the large-spin expansion of the energy of Gubser-Klebanov-Polyakov (GKP) strings that rotate in RxS2 and AdS3 can be expressed in terms of Lambert's W-function. We compute the leading, subleading and next-to-subleading…
The analytic structure of the $qqq$ wave function, obtained recently in the high momentum regime of QCD, is employed for the formulation of baryonic transition amplitudes via quark loops. A new aspect of this study is the role of a direct…
Motivated by physical and topological applications, we study representations of the group $\mathcal{LB}_3$ of motions of $3$ unlinked oriented circles in $\mathbb{R}^3$. Our point of view is to regard the three strand braid group…
We analyse the twist-three amplitudes that can give rise to single-spin asymmetries in hadron-hadron scattering; in so doing we bring to light a novel factorisation property. As already known, the requirement of an imaginary part leads to…
We compute the twist-2 matching of the transverse-momentum-dependent (TMD) linearly polarized gluon parton distribution and fragmentation functions at next-to-next-to-next-to-leading order (N$^3$LO) in QCD, supplemented by…
We discuss a generalised version of Sklyanin's Boundary Quantum Inverse Scattering Method applied to the spin-1/2, trigonometric sl(2) case, for which both the twisted-periodic and boundary constructions are obtained as limiting cases. We…
We construct universal parton evolution equation that produces space- and time-like anomalous dimensions for the maximally super-symmetric N=4 Yang--Mills field theory model, and find that its kernel satisfies the Gribov--Lipatov…
We consider here the class of fully-nonlinear symmetry-integrable third-order evolution equations in 1+1 dimensions that were proposed recently in the journal Open Communications in Nonlinear Mathematical Physics, vol. 2, 216--228 (2022).…
We study the exact solution of quantum integrable system associated with the $A^{(2)}_3$ twist Lie algebra, where the boundary reflection matrices have non-diagonal elements thus the $U(1)$ symmetry is broken. With the help of the fusion…
We present the threshold N$^3$LO perturbative QCD corrections to the rapidity distributions of dileptons in the Drell-Yan process and Higgs boson in gluon fusion. Sudakov resummation of QCD amplitudes, renormalization group invariance, and…
In the QCD energy-momentum tensor $T^{\mu\nu}$, the terms that contribute to physical matrix elements are expressed as the sum of the gauge-invariant quark part and gluon part. Each part undergoes the renormalization due to the interactions…
Using the methods of the recently proposed Quantum Spectral Curve (QSC) originating from integrability of ${\cal N}=4$ Super--Yang-Mills theory we analytically continue the scaling dimensions of twist-2 operators and reproduce the so-called…
We indicate that the random aperiodic oscillation of the gluon distributions in a modified Balisky--Fadin--Kuraev--Lipatov (BFKL) equation has positive Lyapunov exponents. This first example of chaos in QCD evolution equations, raises the…
We derive the analogues of the Dirac and Pauli equations from a spatially fourth-order Klein--Gordon equation with a universal length scale. Starting from a singularly perturbed variant of Maxwell's equations, we deduce a 32-dimensional…
We explore the possibility to construct higher-twist parton distributions in a nucleon at some low reference scale from convolution integrals of the light-cone wave functions (WFs). To this end we introduce simple models for the…
We derive a new twist-3 partonic sum rule for the transverse spin of the proton, which involves the well-know quark spin structure function $g_T(x)=g_1(x)+g_2(x)$, the less-studied but known transverse gluon polarization density $\Delta…