Renormalization of twist-four operators in light-cone gauge

We compute one-loop renormalization group equations for non-singlet twist-four operators in QCD. The calculation heavily relies on the light-cone gauge formalism in the momentum fraction space that essentially rephrases the analysis of all two-to two and two-to-three transition kernels to purely algebraic manipulations both for non- and quasipartonic operators. This is the first brute force calculation of this sector available in the literature. Fourier transforming our findings to the coordinate space, we checked them against available results obtained within a conformal symmetry-based formalism that bypasses explicit diagrammatic calculations and confirmed agreement with the latter.Comment: 58 pages, 16 figures; dedicated to the memory of Eduard A. Kurae

Counting Form Factors of Twist-Two Operators

We present a simple method to count the number of hadronic form factors based on the partial wave formalism and crossing symmetry. In particular, we show that the number of independent nucleon form factors of spin-n, twist-2 operators (the vector current and energy-momentum tensor being special examples) is n+1. These generalized form factors define the generalized (off-forward) parton distributions that have been studied extensively in the recent literature. In proving this result, we also show how the J^{PC} rules for onium states arise in the helicity formalism.Comment: 7 pages, LaTeX (revtex

Disentangling positivity constraints for generalized parton distributions

Positivity constraints are derived for the generalized parton distributions (GPDs) of spin-1/2 hadrons. The analysis covers the full set of eight twist-2 GPDs. Several new inequalities are obtained which constrain GPDs by various combinations of usual (forward) unpolarized and polarized parton distributions including the transversity distribution.Comment: 9 pages (REVTEX), typos correcte

The fundamental group of reductive Borel-Serre and Satake compactifications

Let $G$ be an almost simple, simply connected algebraic group defined over a number field $k$, and let $S$ be a finite set of places of $k$ including all infinite places. Let $X$ be the product over $v\in S$ of the symmetric spaces associated to $G(k_v)$, when $v$ is an infinite place, and the Bruhat-Tits buildings associated to $G(k_v)$, when $v$ is a finite place. The main result of this paper is an explicit computation of the fundamental group of the reductive Borel-Serre compactification of $\Gamma\backslash X$, where $\Gamma$ is an $S$-arithmetic subgroup of $G$. In the case that $\Gamma$ is neat, we show that this fundamental group is isomorphic to $\Gamma/E\Gamma$, where $E\Gamma$ is the subgroup generated by the elements of $\Gamma$ belonging to unipotent radicals of $k$-parabolic subgroups. Analogous computations of the fundamental group of the Satake compactifications are made. It is noteworthy that calculations of the congruence subgroup kernel $C(S,G)$ yield similar results.Comment: 21 pages, 1 figure, uses Xy-pic 3.8.6; in version 2, title changed to more accurately reflect main result, expository material on congruence subgroup problem removed, many small corrections and improvements in expositio

Real and Virtual Nucleon Compton Scattering in the Perturbative Limit

We present the results of calculations analyzing nucleon Compton scattering to lowest order using perturbative QCD (pQCD) methods. Two scenarios are considered: (1) the incoming photon is real; and (2) the incoming photon is virtual. The case of a real photon has been previously analyzed at least 5 times using pQCD, but no two results are in agreement. Here it is shown that our result agrees with that of Brooks and Dixon published in 2000. The case of a virtual photon has been previously analyzed only once using pQCD. However, doubt has been cast on the validity of that result. The results presented here for virtual photon are believed to be more reliable. Some consideration is given of how to compare these results with experiment. Following the lead of Brooks and Dixon, for the proton, this involves normalizing the cross section using the Dirac proton form factor, which we also calculate. Finally, there is a comparison of our results with recent experiments.Comment: 36 pages, 11 figure

Sensitivity and Linearity of Superconducting Radio-Frequency Single-Electron Transistors: Effects of Quantum Charge Fluctuations

We have investigated the effects of quantum fluctuations of quasiparticles on the operation of superconducting radio-frequency single-electron transistors (RF-SETs) for large values of the quasiparticle cotunneling parameter $\alpha=8E_{J}/E_{c}$, where $E_{J}$ and $E_{c}$ are the Josephson and charging energies. We find that for $\alpha>1$, subgap RF-SET operation is still feasible despite quantum fluctuations that renormalize the SET charging energy and wash out quasiparticle tunneling thresholds. Surprisingly, such RF-SETs show linearity and signal-to-noise ratio superior to those obtained when quantum fluctuations are weak, while still demonstrating excellent charge sensitivity.Comment: Submitted to Phys. Rev. Let

Solution of the off-forward leading logarithmic evolution equation based on the Gegenbauer moments inversion

Using the conformal invariance the leading-log evolution of the off-forward structure function is reduced to the forward evolution described by the conventional DGLAP equation. The method relies on the fact that the anomalous dimensions of the Gegenbauer moments of the off-forward distribution are independent on the asymmetry, or skewedness, parameter and equal to the DGLAP ones. The integral kernels relating the forward and off-forward functions with the same Mellin and Gegenbauer moments are presented for arbitrary asymmetry value.Comment: 11 pages, LaTeX, no figures, revised version, references adde