Related papers: An exact sum rule for transversely polarized DIS
We calculate the unpolarized and polarized two--loop massless off--shell operator matrix elements in QCD to $O(\varepsilon)$ in the dimensional parameter in an automated way. Here we use the method of arbitrary high Mellin moments and…
We calculate the twist-4 corrections to the integral of $g_1(x,Q^2)$ in the framework of QCD sum rules using an interpolating nucleon field which contains explicitly a gluonic degree of freedom. This information can be used together with…
An exact series representation of the even frequency moments of the dynamic structure factor is derived. Truncations are proposed that allow to evaluate the explicitly unknown second, fourth and fifth frequency moments for the finite…
Hadron properties are modified when the hadron is embedded in a nuclear medium. Here we discuss the Gerasimov-Drell-Hearn, GDH, sum rule for polarised photoproduction from a polarised nucleon within a polarised nuclear target. Strong…
We construct explicit invariant measures for a family of infinite products of random, independent, identically-distributed elements of SL(2,C). The matrices in the product are such that one entry is gamma-distributed along a ray in the…
Infinite-dimensional Newton methods can be effectively used to derive numerical proofs of the existence of solutions to partial differential equations (PDEs). In computer-assisted proofs of PDEs, the original problem is transformed into the…
Generation of T-odd single spin asymmetries (SSA) by the various ingredients of QCD factorization is discussed. The possible use of SSA in studies of Generalized Parton Distribution (GPD) at HERA with the polarized lepton beam is suggested.…
A comprehensive study is made for the magnetic moments of octet baryons in the method of QCD sum rules. A complete set of QCD sum rules is derived using the external field method and generalized interpolating fields. For each member, three…
A new derivation is given for the representation, under certain conditions, of the integral dispersion relations of scattering theory through local forms. The resulting expressions have been obtained through an independent procedure to…
Efficiency of intrinsic operator techniques (using only products and ranks of tensor operators) is first evidenced by condensed proofs of already known $\bigtriangledown$-triangle sum rules of su(2)/su$_q$(2). {\em A new compact}…
We construct and analyze approximation rates of deep operator networks (ONets) between infinite-dimensional spaces that emulate with an exponential rate of convergence the coefficient-to-solution map of elliptic second-order partial…
We introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of…
We describe an elementary method to get non-asymptotic estimates for the moments of Hermitian random matrices whose elements are Gaussian independent random variables. As the basic example, we consider the GUE matrices. Immediate…
The generalized Baldin sum rule for virtual photon scattering, the unpolarized analogy of the generalized Gerasimov-Drell-Hearn integral, provides an important way to investigate the transition between perturbative QCD and hadronic…
We calculate the hadronic matrix elements to $O(p^4)$ in the chiral expansion for the ($\Delta S =1$) $K^0 \to 2 \pi$ decays and the ($\Delta S=2$) $\bar K^0$-$K^0$ oscillation. This is done within the framework of the chiral quark model.…
We propose an operator product expansion for planar form factors of local operators in $\mathcal{N}=4$ SYM theory. This expansion is based on the dual conformal symmetry of these objects or, equivalently, the conformal symmetry of their…
We use a quantum loop expansion to derive sum rule constraints on polarized photoabsorption cross sections in the Standard Model, generalizing earlier results obtained by Altarelli, Cabibbo, and Maiani. We show that the logarithmic integral…
Let $u_1,\ldots,u_n$ be unitary operators on a Hilbert space $H$. We study the norm $$\left\|\sum^{i=n}_{i=1} u_i \otimes \bar u_i\right\|\leqno (1)$$ of the operator $\sum u_i \otimes \bar u_i$ acting on the Hilbertian tensor product…
In this paper, we prove convergence rates for time discretisation schemes for semi-linear stochastic evolution equations with additive or multiplicative Gaussian noise, where the leading operator $A$ is the generator of a strongly…
The newy developed approach to model nucleon generalized parton distributions (GPDs) H and E$ is based on two types of their representation in terms of double distributions. Within this approach, we re-consider the derivation of GPD sum…