Search

Abstract.: We computed the twist-4 part of the photon spin-flip amplitude in deeply virtual Compton scattering on a nucleon in the Wandzura–Wilczek approximation. We found a factorizable contribution, which arises from photon scattering on quarks with non-zero angular momentum along the collision axis. As the genuine twist-2 amplitude arises at the NLO, for moderate virtualities of the hard photon, GeV, a kinematical twist-4 correction can give a numerically important contribution to the photon helicity-flip amplitude.

Abstract.: We applied QCD light-cone sum rules to estimate power corrections to the helicity-conserving amplitude in the process . We found that above GeV power corrections are numerically small and the twist-2 part dominates.The amplitude can be reliably calculated in this region using models of distribution amplitudes as input. We found that the magnitude of the NLO corrections depends rather strongly on the normalization of the gluonic distribution amplitude.

It is known [1] that ind=2+ε dimensional regularization any four-fermion interaction generates an infinite number of counterterms of the form

We present a three-loop calculation for the contribution of the anomalous dimension γψ in the RG function for the full UN-symmetric model using dimensional regularization with d=2+ε. This model contains an infinite number of independent four-fermion interactions and couplings gn. In the MS scheme, the three-loop contribution in γψ depends on all of the charges. In the symmetric subtraction scheme for ε=0, only the dependence on the three lower charges g0,1.2l remains. The results of a three-loop calculation of γψ for the Thirring model and for the Gross-Neveu model are discussed; they seem to contradict the equivalence of all four-fermion interactions for d=2, N=1. It is shown that this equivalence appears only for the symmetric subtraction scheme. The precise meaning of (2+ε)-expansions of the critical dimensions is discussed for when the multiplication renormalizability is absent in the Gross-Neveu model.

We discuss the problem of equivalence between the standard (integer-dimensional d=2) and the d=2+ε dimensional renormalization schemes for the complete UN-symmetrical four-fermion interaction model. To ensure the multiplicative renormalizability of the theory, we need three charges in the first case; in the second, we need an infinite series of independent charges g ≡ {gn, n=0, 1, ...}. After the usual MS-renormalization. there exists a UV-finite renormalization of fields. Charges g→g'(g) exist such that the renormalized Green's functions in the limit ε→0 depend only on the three lower charges g'n(g) with n=0, 1, 2. rather than on the whole set. This ensures the possibility of establishing the equivalence of the two renormalization schemes. The results of calculations in the MS scheme up to two loops for the β-functions, and up to three loops for the anomalous field dimension γφ are presented. These are presented together with the derivation of the “projection technique” relations, which allows one to express the higher renormalized composite operators of the 4F-interaction via the lower ones in the limit ε→0.

Using the conformal invariance of the Green's functions for the fields in the Gross-Neveu model in the critical regime that was proved earlier, we now use the conformal-bootstrap method for arbitrary space dimensiond to calculate the critical dimension of the master field (index ?) in order 1/n3 and of the auxiliary field in order 1/n2, i.e., to an order higher by one than the previously known results.

A self-consistent method for calculating the chiral anomaly in dimensional regularization without the four-dimensional symbols γ5 and ɛμνλρ is proposed. The method is applied to the calculation and analysis of chiral symmetry in massless quantum electrodynamics.

We present a discussion of radiative decays χcJ→γρ(ω,ϕ). The decay amplitudes are computed within the QCD factorization framework. NRQCD has been used in the heavy meson sector as well as a collinear expansion in order to describe the overlap with light mesons in the final state. The color-singlet contributions to all helicity amplitudes have been computed using the light-cone distribution amplitudes of twist-2 and twist-3. All obtained expressions are well defined at least in the leading-order approximation. The color-octet contributions have also been studied in the Coulomb limit in order to exhibit their scaling behavior. In order to understand the relevance of the different contributions we perform numerical estimates using the color-singlet contributions. For the χc1→γV⊥ decays, to vector mesons with transverse polarization, we find that the color-singlet contribution potentially allows for a reliable description. On the other hand, for the χc1→γV∥ decays, to vector mesons with longitudinal polarization, our findings indicate that the color-octet mechanism may be important for a good description. We expect that more accurate measurements of the decay χc2→γV⊥,∥ can help to better understand the mechanism of radiative decays. [ABSTRACT FROM AUTHOR]