相关论文: Dipole operators in Fierz identities
We consider the renormalisation of composite quark-antiquark operators with one and two lattice covariant derivatives related to the lowest moments of generalised parton distributions (GPDs) and meson distribution amplitudes (DAs). Their…
We define several differential graded operads, some of them being related to families of polytopes : simplices and permutohedra. We also obtain a presentation by generators and relations of the operad K on associahedra introduced in a…
We study one dimensional dipole cascade models in the high-energy limit of QCD. Motivated by data on hadron multiplicities in the LHCb kinematical range, we generalize existing cascade models for splitting and recombination to account also…
We present examples of on-shell recurrence relations for determining rational functions appearing in one-loop QCD amplitudes. In particular, we give relations for one-loop QCD amplitudes with all legs of positive helicity, or with one leg…
The order $\alpha_s$ corrections to the Wilson coefficients of the dipole operators ($O_7,O_8$) at the matching scale $\mu =m_W$ are a crucial ingredient for a complete next- to-leading logarithmic calculation of the branching ratio for $b…
Recent applications of single-scale four-loop tadpoles are briefly reviewed. An algorithm for the evaluation of current correlators based on differential equations is described and applied to obtain high moments of the vacuum polarization…
Using simultaneously two operator identities, we consider the inversion of the convolution operators on a rectangular. The structure of the inverse operators and of some corresponding forms, which are important in signal processing, is…
We revisit the proof of the perturbative QCD factorization for the exclusive processes $\rho \gamma^{\star} \to \pi(\rho)$ at the two-parton twist-3 level. It is pointed out that the residual collinear divergences observed in the…
Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fr\'echet space of all Dirichlet series that are uniformly convergent in all half-planes $\{s \in \mathbb{C}…
We use the classical Fourier analysis to introduce analytic families of weighted differential operators on the unit sphere. These operators are polynomial functions of the usual Beltrami-Laplace operator. New inversion formulas are obtained…
We find shift operators for the Dotsenko-Fateev equation, which is a differential equation of order 3, and for the three Fuchsian differential equations of order 4, 5 and 6, respectively, which are connected with the Dotsenko-Fateev…
The approximate representation of operators by finite matrices is analysed in terms of accuracy and convergence. The identity operator, for example, can be reconstructed using a basis of harmonic oscillator states leading to a narrow peak…
In this paper, we study harmonic analysis on the affine Poincar\'e group $\mathcal{P}_{aff}$, which is a non-unimodular group, and obtain pseudo-differential operators with operator valued symbols. More precisely, we study the boundedness…
We consider the flavour-changing operators associated with the strong axial and trace anomalies. Their short-distance generation through penguin-like diagrams is obtained within the QCD external field formalism. Standard-model operator…
Fractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets…
We present an operator learning approach for a class of evolution operators using a composition of a learned lift into the space of diffeomorphisms of the domain and the group action on the field space. In turn, this transforms the…
In this paper, we study scalar the forth order linear differential operators over an oriented 2-dimensional manifold. We investigate differential invariants of these operators and show their application to the equivalence problem.
The flavor-changing electromagnetic dipole operator O_7 gives the dominant contribution to the B -> Xs gamma decay rate. We calculate two-loop QCD corrections to its matrix element together with the corresponding bremsstrahlung…
Dipole-dipole interactions lead to frequency shifts that are expected to limit the performance of next-generation atomic clocks. In this work, we compute dipolar frequency shifts accounting for the intrinsic atomic multilevel structure in…
I present one-loop perturbative calculations of matching coefficients between matrix elements in continuum regulated QCD and lattice QCD with overlap fermions, with emphasis a recently-proposed variant discretization of the overlap. These…