相关论文: Limitations on using the operator product expansio…
This paper deals with quantitative spectral stability for compact operators acting on $L^2(X,m)$, where $(X,m)$ is a measure space. Under fairly general assumptions, we provide a characterization of the dominant term of the asymptotic…
The conventional and linearly polarized Weizs\"acker-Williams gluon distributions at small x are defined from the two-point function of the gluon field in light-cone gauge. They appear in the cross section for dijet production in deep…
We explain how Regge theory and perturbative evolution may be made compatible at small x. The result not only gives striking support to the two-pomeron description of small-x behaviour, but gives a rather clean test of perturbative QCD…
In logarithmic conformal field theory, primary fields come together with logarithmic partner fields on which the stress-energy tensor acts non-diagonally. Exploiting this fact and global conformal invariance of two- and three-point…
We discuss the quantitative consequences of the resummation of the small-x contributions to the anomalous dimensions beyond next-to-leading order in alpha_s and up to next order in ln(1/x) (NLx) in a framework based on the renormalization…
We provide the last missing ingredient necessary to approximate one-loop amplitudes in QCD with massive quarks in the limit of vanishing energy of a single gluon up to terms suppressed by this energy. Our main result is a soft operator…
We obtain the operator product expansion of the self-energy in the O(N) non-linear $\sigma$-model to all orders in the coupling and the large momentum, and to next-to-leading order in 1/N. In the light of this result we discuss recent…
We consider BMO spaces of operator-valued functions, among them the space of operator-valued functions $B$ which define a bounded paraproduct on $L^2(H)$. We obtain several equivalent formulations of $\|\pi_B\|$ in terms of the norm of the…
Reynolds' lubrication approximation is used extensively to study flows between moving machine parts, in narrow channels, and in thin films. The solution of Reynolds' equation may be thought of as the zeroth order term in an expansion of the…
It is shown that in the leading twist approximation of the Wilson operator product expansion with "frozen" and analytic strong coupling constants, Bessel-inspired behavior of the structure functions F2 and F2cc and also the derivative d(ln…
A dedicated test of the perturbative QCD NLO parton evolution in the very small-$x$ region is performed. We find a good agreement with recent precision HERA-data for $F_2^p(x,Q^2)$, as well as with the present determination of the curvature…
The longitudinal structure function in deep inelastic scattering is one of the observables from which the gluon distribution can be unfolded. Consequently, this observable can be used to constrain the QCD dynamics at small $x$. In this work…
We consider Schr\"odinger operators of the form $H_R = - d^2/ d x^2 + q + i \gamma \chi_{[0,R]}$ for large $R>0$, where $q \in L^1(0,\infty)$ and $\gamma > 0$. Bounds for the maximum magnitude of an eigenvalue and for the number of…
We study nonperturbative corrections up to O(1/m_b^3) in the inclusive rare B decay B -> X_s l^+ l^- by performing an operator product expansion. The values of the matrix elements entering at this order are unknown and introduce…
We compute the two and three-point correlation functions of chiral primary operators in the large N limit of the (0,2), d=6 superconformal theory. We also consider the operator product expansion of Wilson surfaces in the (0,2) theory and…
In the leading twist approximation of the Wilson operator product expansion with "frozen" and analytic strong coupling constants we show that Bessel-inspired behavior of the structure function F2 at small x, obtained for a flat initial…
We show that the twist decomposition of non-local scalar off-cone QCD-operators, which in $x-$space is infinite, after Fourier transformation with the singular functions $1/(x^2 - {\text{i}} \epsilon)^\lambda$ for $\lambda = 1$ and 2…
We point out that the analysis in arXiv:1003.0482 actually verifies the universality of transverse momentum dependent quark distributions at small $x$, which supports the observation in our earlier work arXiv:0904.4150. Once the gluon…
We apply the operator product expansion to resum the leading nonperturbative corrections to the endpoint region of the lepton spectrum in inclusive semileptonic $B\to X_q\,\ell\,\bar\nu$ decays, taking into account a finite quark mass $m_q$…
We consider the multiple products of relevant and marginal scalar composite operators at the Gaussian fixed-point in $D=4$ dimensions. This amounts to perturbative construction of the $\phi^4$ theory where the parameters of the theory are…